explain quantum hypothesis

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Science Simplified: What Is Quantum Mechanics?

By Argonne National Laboratory March 23, 2024

Quantum mechanics, a field of physics exploring the fundamental nature of matter and energy, reveals phenomena like objects existing in multiple states or places, essential for advancing modern technologies and secure communications. Credit: SciTechDaily.com

What Is Quantum Mechanics?

Imagine a world where objects can seem to exist in two places at once or affect each other from across the universe.

Although we don’t see these types of things in our everyday lives, similar curiosities appear to exist all around us in the fundamental behavior of our universe and its smallest building blocks. These peculiar characteristics of nature are described by a branch of physics called quantum mechanics.

In the early 1900s, scientists began to develop quantum mechanics in order to explain the results of a number of experiments that defied any other interpretation. Today, scientists use this theory to create powerful technologies — unhackable communication of messages, faster drug discovery and higher-quality images on your phone and TV screens.

So, what is quantum? In a more general sense, the word “quantum” can refer to the smallest possible amount of something. The field of quantum mechanics deals with the most fundamental bits of matter, energy and light and the ways they interact with each other to make up the world.

Unlike the way in which we usually think about the world, where we imagine things to have particle- or wave-like properties separately (baseballs and ocean waves, for example), such notions don’t work in quantum mechanics. Depending on the situation, scientists may observe the same quantum object as being particle-like or wave-like. For example, light cannot be thought of as only a photon (a light particle) or only a light wave, because we might observe both sorts of behaviors in different experiments.

Day to day, we see things in one “state” at a time: here or there, moving or still, right-side up or upside down. The state of an object in quantum mechanics isn’t always so straightforward. For example, before we look to determine the locations of a set of quantum objects, they can exist in what’s called a superposition — or a special type of combination — of one or more locations. The different possible states combine and interfere with each other like waves in a pond, and the objects only have a definite position after we’ve looked. Superposition is one of the main features that make quantum computers possible because it enables us to represent information in new and useful ways.

Another interesting quantum behavior is tunneling, where a quantum object, like an electron, can sometimes pass through barriers it otherwise wouldn’t be able to get through. This happens because superposition allows for a small chance of the electron being on the other side of the barrier. Quantum tunneling has applications such as in flash memory devices, powerful microscopes and quantum computers.

When quantum objects interact, they are linked to each other through a connection called entanglement. This connection holds even if the objects are separated by large distances. Einstein called it “spooky action at a distance.” Scientists are making use of it for ultra-secure communication, and it is an essential feature in quantum computing .

At the U.S. Department of Energy’s (DOE) Argonne National Laboratory, scientists take advantage of world-class expertise and research facilities to develop quantum technologies to store, transport and protect information, and to investigate our universe, from the intricate dynamics deep within an atom to events as grand as the birth of the universe itself. Argonne also leads Q-NEXT, a DOE national quantum information science research center working to develop quantum materials and devices and capture the power of quantum technology for communication.

Credit: Argonne National Laboratory

What Is Quantum Information Science?

Leveraging counter-intuitive behavior on the atomic scale to create powerful changes in information science on a practical scale.

Scientists are racing to develop quantum-based systems that can store, transport, manipulate, and protect information.

Qubits—quantum bits—are the fundamental components of quantum computing and other quantum information systems. They are analogous to the bit in classical computers, either 0 or 1. What makes qubits truly strange is that they can simultaneously be both 0 and 1. This overlapping state gives quantum computers tremendously increased horsepower. The qubit itself can come in many different forms—electrons, particles of light, even tiny defects in otherwise highly structured materials.

Scientists are seeking to design qubits that maintain information in their quantum states for seconds (“coherence”) and can link with other qubits (“entanglement”).

Quantum technologies could transform national and financial security, drug discovery, and the design and manufacturing of new materials, while deepening our understanding of the universe.

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6 comments on "science simplified: what is quantum mechanics".

Quantum mechanics, a field of physics exploring the fundamental nature of matter and energy, reveals phenomena like objects existing in multiple states or places. Is this your science simplified that what is quantum mechanics?

What are the multiple states or places in quantum mechanics? According to topological vortex gravitational field theory, the simplest multiple states are the left and right rotation of the vortex, and the simplest multiple places are the front and back of the vortex. The physical essence of quantum mechanics is to describe the spin and interaction of 2D topological vortices, rather than a cat that is both dead and alive in high-dimensional spacetime. Quantum gravity comes from the spin of topological vortices.

The universe does not do algebra, formula or fraction. The universe is geometrythe, and is the superposition, deflection, and twisting of geometric shapes.

Today, we have already entered the era of the internet. With the help of artificial intelligence and big data, discussions on scientific knowledge have become open and transparent. However, a group of editors of so-called academic journals (such as Physical Review Letters, Nature, Science, etc.) are self-righteous and mystifying themselves. They only care about their own so-called sufficiently high priority rating, general significance, discipline, novelty, etc., and do not care about what science and pseudoscience are.

Science and pseudoscience are not determined by a publication, an organization or a person, nor by you or me, but by mathematics the final say. Physical models must be based on mathematics or mathematical models in order to be scientific, convincing, and in accordance with natural laws.

The origin of geometry lies in the concerns of everyday life. The branch of geometry (mathematics) known as topology has become a cornerstone of modern physics. Topological vortex and antivortex are two bidirectional coupled continuous chaotic systems. They exhibit parity conservation, charge conjugation, and time reversal symmetry. The synchronization effect is extremely important in their interactions. The synchronization effect of the superposition, deflection, and twisting of multiple or countless topological vortices will make spacetime motion more complex. To understand this complex world, physics should respect the authenticity of topological vortex in low dimensional spacetime, rather than simply relying on a few formulas, numbers, or imagined particles.

Spin is a natural property of topological vortices. Spin is synchronized with energy, spin is synchronized with gravitation, spin is synchronized with time, spin is synchronized with evolution. The perpetually swirling topological vortices defy traditional physics’ expectations. One physical properties of topological vortices is them to spontaneously begin to change periodically in time, even though the system does not experience corresponding periodic interference. Therefore, in the interaction of topological vortices, time is both absolute and relative，and physics often requires treating space and time at the same level.

Low-dimensional spacetime matter is the foundation of high-dimensional spacetime matter. Low-dimensional spacetime matter (such as topological vortex) can form new material structures and derive more complex physical properties via interactions and self-organization. It is extremely wrong and irresponsible to imagine low dimensional spacetime matter using high-dimensional spacetime matter，such as a cat in quantum mechanics.

Science must follow mathematical rules. For example, the Standard Model (SM) is considered to be one of the most significant achievements of physics in the 20th century. However, the magnetic moment of μ particle is larger than expected, revealed by a g-2 experiment at Fermilab, suggests that the established theory (such as SM) of fundamental particles is incomplete. Furthermore, the SM omitting gravitation, it not involved the time problem and when the particle movement starts. Mathematics is the foundation of science. Physics must respect the scientific nature of mathematics and mathematical models. The SM must be based on mathematical models in order to be scientific, convincing, and in line with natural laws.

I hope researchers are not fooled by the pseudoscientific theories of the Physical Review Letters (PRL), and hope more people dare to stand up and fight against rampant pseudoscience. The so-called academic journals (such as Physical Review Letters, Nature, Science, etc.) firmly believe that two high-dimensional spacetime objects (such as two sets of cobalt-60) rotating in opposite directions can be transformed into two objects that mirror each other, is a typical case of pseudoscience rampant. If researchers are really interested in Science and Physics, you can browse https://zhuanlan.zhihu.com/p/643404671 and https://zhuanlan.zhihu.com/p/595280873 .

I am well aware that my relentless repetition can make some people unhappy, but in the fight against rampant pseudoscience, that’s all I can do.

Please think carefully, 1. What are the qubits? 2. Why can qubits simultaneously be both 0 and 1? 3. What is the physical reality of qubits? and so on.

The Physical Review Letters (PRL) is the most evil, ugly, and dirty publication in the history of science. Nature and Science have been influenced by Physical Review Letters (PRL) and are even more notorious. The behavior of these pseudo-academic publications has seriously hindered the progress and development of human society in science and technology.

… At the end it looks like The God really plays dices… and to be more precise it looks like it liked particular game of, hugh that is French… craps

Very good! To be precise, what God plays is two spinning coin. However, until you see the coin, you will not be able to determine whether you are seeing a Left-handed or right-handed spin coin. Best wishes to you.

Therefore, at the moment of Creation, the geometric shapes of matter and antimatter are consistent. It is only the synchronous effect of countless “spinning coin” that makes spacetime motion more complex.

If there really is God, symmetry is God. Symmetry creates the world, symmetry creates all things. The world we see and observe is asymmetric because we can never see or observe the entirety of the world.

Physics library

Course: physics library > unit 17, the quantum mechanical model of the atom.

Heisenberg uncertainty principle
Quantum numbers
Quantum numbers for the first four shells
Louis de Broglie proposed that all particles could be treated as matter waves with a wavelength λ ‍ , given by the following equation:
Erwin Schrödinger proposed the quantum mechanical model of the atom, which treats electrons as matter waves.
Schrödinger's equation, H ^ ψ = E ψ ‍ , can be solved to yield a series of wave function ψ ‍ , each of which is associated with an electron binding energy, E ‍ .
The square of the wave function, ψ 2 ‍ , represents the probability of finding an electron in a given region within the atom.
An atomic orbital is defined as the region within an atom that encloses where the electron is likely to be 90% of the time.
The Heisenberg uncertainty principle states that we can't know both the energy and position of an electron. Therefore, as we learn more about the electron's position, we know less about its energy, and vice versa.
Electrons have an intrinsic property called spin, and an electron can have one of two possible spin values: spin-up or spin-down.
Any two electrons occupying the same orbital must have opposite spins.

Introduction to the quantum mechanical model

"We must be clear that when it comes to atoms, language can only be used as in poetry." —Niels Bohr

Review of Bohr's model of hydrogen

Wave-particle duality and the de broglie wavelength.

λ = h mv ‍

λ = h mv = 6.626 × 10 − 34 kg ⋅ m 2 s ( 0.145 kg ) ( 46.7 m s ) = 9.78 × 10 − 35 m ‍

Example 1: Calculating the de Broglie wavelength of an electron

λ = h mv = 6.626 × 10 − 34 kg ⋅ m 2 s ( 9.1 × 10 − 31 kg ) ( 2.2 × 10 6 m s ) = 3.3 × 10 − 10 m ‍

Standing waves

Schrödinger's equation.

H ^ ψ = E ψ ‍

Orbitals and probability density

n ‍ , the principal quantum number, is the major factor in determining the energy of an orbital. Orbitals with the same n ‍ value are said to share the same electron shell .
l ‍ , the angular quantum number, defines the shape of the orbital. Orbitals with the same n ‍ value but different values of l ‍ are called subshells.
m l ‍ , the magnetic quantum number, is related to the orbital's orientation in space.
m s ‍ , the spin quantum number, indicates the spin of an electron. Electrons can be spin-up ( m s = + 1 2 ) ‍ or spin-down ( m s = − 1 2 ) ‍ .

Shapes of atomic orbitals

Electron spin: the stern-gerlach experiment.

Louis de Broglie proposed that all particles could be treated as matter waves with a wavelength λ ‍ given by the following equation:

λ = h m v ‍

Attributions

“ Quantum Mechanics and Atomic Orbitals ” from UC Davis ChemWiki, CC BY-NC-SA 3.0
" Representations of Orbitals " from UC Davis ChemWiki, CC BY-NC-SA 3.0
" Electronic Orbitals " from UC Davis ChemWiki, CC BY-NC-SA 3.0

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21.1 Planck and Quantum Nature of Light

Section learning objectives.

By the end of this section, you will be able to do the following:

Describe blackbody radiation
Define quantum states and their relationship to modern physics
Calculate the quantum energy of lights
Explain how photon energies vary across divisions of the electromagnetic spectrum

Teacher Support

The learning objectives in this section will help your students master the following standards:

(D) : explain the impacts of the scientific contributions of a variety of historical and contemporary scientists on scientific thought and society.
(B) : compare and explain the emission spectra produced by various atoms; and
(D) : give examples of applications of atomic and nuclear phenomena such as radiation therapy, diagnostic imaging, and nuclear power, and examples of quantum phenomena such as digital cameras.

Section Key Terms

Blackbodies.

Prior to beginning this section, it would be a good idea to review wave concepts including frequency, wavelength, and amplitude. Have students write down a list of equations or statements that relate to the three concepts.
[BL] [OL] Discuss what could be meant by the term blackbody . Why do some objects appear black? Furthermore, why do we see objects that are red as red? It is said that black is the absence of color , but what does that mean in terms of the light reflected into our eyes?
[AL] Discuss what can happen to energy when it strikes a surface. Discuss how it can be reflected or transmitted. If a blackbody is perfectly black, what must be happening to all of the energy incident upon it?
[EL]Reinforce that the term blackbody is nothing more than its name suggests—that is, a body that is perfectly black. Discuss what perfectly black means. Is a black piece of paper perfectly black ?

Our first story of curious significance begins with a T-shirt. You are likely aware that wearing a tight black T-shirt outside on a hot day provides a significantly less comfortable experience than wearing a white shirt. Black shirts, as well as all other black objects, will absorb and re-emit a significantly greater amount of radiation from the sun. This shirt is a good approximation of what is called a blackbody .

Occasionally, texts refer to blackbody and perfect blackbody as two different concepts. It is likely best to refer to anything that is not a perfect blackbody as an approximation of a blackbody in order to avoid confusion.

A perfect blackbody is one that absorbs and re-emits all radiated energy that is incident upon it. Imagine wearing a tight shirt that did this! This phenomenon is often modeled with quite a different scenario. Imagine carving a small hole in an oven that can be heated to very high temperatures. As the temperature of this container gets hotter and hotter, the radiation out of this dark hole would increase as well, re-emitting all energy provided it by the increased temperature. The hole may even begin to glow in different colors as the temperature is increased. Like a burner on your stove, the hole would glow red, then orange, then blue, as the temperature is increased. In time, the hole would continue to glow but the light would be invisible to our eyes. This container is a good model of a perfect blackbody.

It is the analysis of blackbodies that led to one of the most consequential discoveries of the twentieth century. Take a moment to carefully examine Figure 21.2 . What relationships exist? What trends can you see? The more time you spend interpreting this figure, the closer you will be to understanding quantum physics!

It is important for students to make sense of Figure 21.2 before progressing further. Have students independently create a list of observations from the graph. When presenting their observations, press the students on the specifics of their observations.

[BL] Discuss what variables are being graphed. Have them complete the statement: ________ is dependent upon ________. Discuss what is meant by intensity. What is the difference between being mad and intensely mad ?

[OL] Discuss what the peak of each graph refers to. Ask if the radiation intensity depends upon the wavelength of the radiation. How do they know this? What do the peaks on each graph mean?

[AL] Discuss why there are three lines on the graph. Does it make sense that an increase in temperature would cause the line of the graph to be raised? Why does this make sense? A good challenging exercise would be to have the students re-graph the information in order to represent EM radiation intensity against frequency.

Tips For Success

When encountering a new graph, it is best to try to interpret the graph before you read about it. Doing this will make the following text more meaningful and will help to remind yourself of some of the key concepts within the section.

Understanding Blackbody Graphs

Figure 21.2 is a plot of radiation intensity against radiated wavelength. In other words, it shows how the intensity of radiated light changes when a blackbody is heated to a particular temperature.

It may help to just follow the bottom-most red line labeled 3,000 K, red hot. The graph shows that when a blackbody acquires a temperature of 3,000 K, it radiates energy across the electromagnetic spectrum. However, the energy is most intensely emitted at a wavelength of approximately 1000 nm. This is in the infrared portion of the electromagnetic spectrum. While a body at this temperature would appear red-hot to our eyes, it would truly appear ‘infrared-hot’ if we were able to see the entire spectrum.

A few other important notes regarding Figure 21.2 :

As temperature increases, the total amount of energy radiated increases. This is shown by examining the area underneath each line.
Regardless of temperature, all red lines on the graph undergo a consistent pattern. While electromagnetic radiation is emitted throughout the spectrum, the intensity of this radiation peaks at one particular wavelength.
As the temperature changes, the wavelength of greatest radiation intensity changes. At 4,000 K, the radiation is most intense in the yellow-green portion of the spectrum. At 6,000 K, the blackbody would radiate white hot, due to intense radiation throughout the visible portion of the electromagnetic spectrum. Remember that white light is the emission of all visible colors simultaneously.
As the temperature increases, the frequency of light providing the greatest intensity increases as well. Recall the equation v = f λ . v = f λ . Because the speed of light is constant, frequency and wavelength are inversely related. This is verified by the leftward movement of the three red lines as temperature is increased.

Discuss the bullet points above. Why does an increase in temperature result in an increase in the total amount of energy radiated? Do you have personal experience with the relationship described in bullet point #3? Students may not have answers as to the causal factors for some of the observations in the above bullet points. Remind them that this is okay as these why questions were the big questions being asked by physicists at the turn of the twentieth century!

[BL] [OL] Do you have personal evidence to show that as temperature increases the energy radiated increases as well?

[AL] Remind students that temperature is just a measure of the average kinetic energy of particles in a gas. Does this definition support bullet point #1?

While in science it is important to categorize observations, theorizing as to why the observations exist is crucial to scientific advancement. Why doesn’t a blackbody emit radiation evenly across all wavelengths? Why does the temperature of the body change the peak wavelength that is radiated? Why does an increase in temperature cause the peak wavelength emitted to decrease? It is questions like these that drove significant research at the turn of the twentieth century. And within the context of these questions, Max Planck discovered something of tremendous importance.

Planck’s Revolution

Planck’s revolution is very much the story of the scientific method—reconciling disconnects between theory and experimental results. Encourage the students to think of other events—either historical or within their own lives—in which a predominant theory was shown to be incorrect when confronted with overwhelming evidence to the contrary. Possible examples include the geocentric model, the ether, or the four elements.

The prevailing theory at the time of Max Planck’s discovery was that intensity and frequency were related by the equation I = 2 k T λ 2 . I = 2 k T λ 2 . This equation, derived from classical physics and using wave phenomena, infers that as wavelength increases, the intensity of energy provided will decrease with an inverse-squared relationship. This relationship is graphed in Figure 21.3 and shows a troubling trend. For starters, it should be apparent that the graph from this equation does not match the blackbody graphs found experimentally. Additionally, it shows that for an object of any temperature, there should be an infinite amount of energy quickly emitted in the shortest wavelengths. When theory and experimental results clash, it is important to re-evaluate both models. The disconnect between theory and reality was termed the ultraviolet catastrophe .

Due to concerns over the ultraviolet catastrophe, Max Planck began to question whether another factor impacted the relationship between intensity and wavelength. This factor, he posited, should affect the probability that short wavelength light would be emitted. Should this factor reduce the probability of short wavelength light, it would cause the radiance curve to not progress infinitely as in the classical theory, but would instead cause the curve to precipitate back downward as is shown in the 5,000 K, 4,000 K, and 3,000 K temperature lines of the graph in Figure 21.3 . Planck noted that this factor, whatever it may be, must also be dependent on temperature, as the intensity decreases at lower and lower wavelengths as the temperature increases.

The determination of this probability factor was a groundbreaking discovery in physics, yielding insight not just into light but also into energy and matter itself. It would be the basis for Planck’s 1918 Nobel Prize in Physics and would result in the transition of physics from classical to modern understanding. In an attempt to determine the cause of the probability factor, Max Planck constructed a new theory. This theory, which created the branch of physics called quantum mechanics , speculated that the energy radiated by the blackbody could exist only in specific numerical, or quantum , states. This theory is described by the equation E = n h f , E = n h f , where n is any nonnegative integer (0, 1, 2, 3, …) and h is Planck’s constant , given by h = 6.626 × 10 −34 J ⋅ s , h = 6.626 × 10 −34 J ⋅ s , and f is frequency.

Through this equation, Planck’s probability factor can be more clearly understood. Each frequency of light provides a specific quantized amount of energy. Low frequency light, associated with longer wavelengths would provide a smaller amount of energy, while high frequency light, associated with shorter wavelengths, would provide a larger amount of energy. For specified temperatures with specific total energies, it makes sense that more low frequency light would be radiated than high frequency light. To a degree, the relationship is like pouring coins through a funnel. More of the smaller pennies would be able to pass through the funnel than the larger quarters. In other words, because the value of the coin is somewhat related to the size of the coin, the probability of a quarter passing through the funnel is reduced!

Furthermore, an increase in temperature would signify the presence of higher energy. As a result, the greater amount of total blackbody energy would allow for more of the high frequency, short wavelength, energies to be radiated. This permits the peak of the blackbody curve to drift leftward as the temperature increases, as it does from the 3,000 K to 4,000 K to 5,000 K values. Furthering our coin analogy, consider a wider funnel. This funnel would permit more quarters to pass through and allow for a reduction in concern about the probability factor .

In summary, it is the interplay between the predicted classical model and the quantum probability that creates the curve depicted in Figure 21.3 . Just as quarters have a higher currency denomination than pennies, higher frequencies come with larger amounts of energy. However, just as the probability of a quarter passing through a fixed diameter funnel is reduced, so is the probability of a high frequency light existing in a fixed temperature object. As is often the case in physics, it is the balancing of multiple incredible ideas that finally allows for better understanding.

Quantization

[EL]Quantum is related to the word quantity, a measure of the amount of something. Discuss why the term quantum would be useful in this context.

[ BL , OL , AL ]Quantum vs. continuous states is well described when considering clocks. A digital clock represents quantum states—it reads 11:14 a.m., then 11:15 a.m. An analog clock with a continually gliding second hand is a good representation of continuous states—it does not appear to pause at any one instant. What would you consider an analog clock that ticks each second? What would you consider a grandfather clock?

It may be helpful at this point to further consider the idea of quantum states. Atoms, molecules, and fundamental electron and proton charges are all examples of physical entities that are quantized —that is, they appear only in certain discrete values and do not have every conceivable value. On the macroscopic scale, this is not a revolutionary concept. A standing wave on a string allows only particular harmonics described by integers. Going up and down a hill using discrete stair steps causes your potential energy to take on discrete values as you move from step to step. Furthermore, we cannot have a fraction of an atom, or part of an electron’s charge, or 14.33 cents. Rather, everything is built of integral multiples of these substructures.

That said, to discover quantum states within a phenomenon that science had always considered continuous would certainly be surprising. When Max Planck was able to use quantization to correctly describe the experimentally known shape of the blackbody spectrum, it was the first indication that energy was quantized on a small scale as well. This discovery earned Planck the Nobel Prize in Physics in 1918 and was such a revolutionary departure from classical physics that Planck himself was reluctant to accept his own idea. The general acceptance of Planck’s energy quantization was greatly enhanced by Einstein’s explanation of the photoelectric effect (discussed in the next section), which took energy quantization a step further.

Worked Example

How many photons per second does a typical light bulb produce.

Assuming that 10 percent of a 100-W light bulb’s energy output is in the visible range (typical for incandescent bulbs) with an average wavelength of 580 nm, calculate the number of visible photons emitted per second.

The number of visible photons per second is directly related to the amount of energy emitted each second, also known as the bulb’s power. By determining the bulb’s power, the energy emitted each second can be found. Since the power is given in watts, which is joules per second, the energy will be in joules. By comparing this to the amount of energy associated with each photon, the number of photons emitted each second can be determined.

The power in visible light production is 10.0 percent of 100 W, or 10.0 J/s. The energy of the average visible photon is found by substituting the given average wavelength into the formula

E = n h f = n h c λ . E = n h f = n h c λ .

By rearranging the above formula to determine energy per photon, this produces

The number of visible photons per second is thus

p h o t o n s sec = 10.0 J / s 3.43 × 10 − 19 J / p h o t o n = 2.92 × 10 19 p h o t o n s / s. p h o t o n s sec = 10.0 J / s 3.43 × 10 − 19 J / p h o t o n = 2.92 × 10 19 p h o t o n s / s.

This incredible number of photons per second is verification that individual photons are insignificant in ordinary human experience. However, it is also a verification of our everyday experience—on the macroscopic scale, photons are so small that quantization becomes essentially continuous.

How does Photon Energy Change with Various Portions of the EM Spectrum?

Refer to the Graphs of Blackbody Radiation shown in the first figure in this section. Compare the energy necessary to radiate one photon of infrared light and one photon of visible light.

To determine the energy radiated, it is necessary to use the equation E = n h f . E = n h f . It is also necessary to find a representative frequency for infrared light and visible light.

According to the first figure in this section, one representative wavelength for infrared light is 2000 nm (2.000 × 10 -6 m). The associated frequency of an infrared light is

Using the equation E = n h f E = n h f , the energy associated with one photon of representative infrared light is

The same process above can be used to determine the energy associated with one photon of representative visible light. According to the first figure in this section, one representative wavelength for visible light is 500 nm.

This example verifies that as the wavelength of light decreases, the quantum energy increases. This explains why a fire burning with a blue flame is considered more dangerous than a fire with a red flame. Each photon of short-wavelength blue light emitted carries a greater amount of energy than a long-wavelength red light. This example also helps explain the differences in the 3,000 K, 4,000 K, and 6,000 K lines shown in the first figure in this section. As the temperature is increased, more energy is available for a greater number of short-wavelength photons to be emitted.

Practice Problems

An AM radio station broadcasts at a frequency of 1,530 kHz . What is the energy in Joules of a photon emitted from this station?

10.1 × 10 -26 J
1.01 × 10 -28 J
1.01 × 10 -29 J
1.01 × 10 -27 J

A photon travels with energy of 1.0 eV. What type of EM radiation is this photon?

visible radiation
microwave radiation
infrared radiation
ultraviolet radiation

Check Your Understanding

Do reflective or absorptive surfaces more closely model a perfect blackbody?

reflective surfaces
absorptive surfaces
The T-shirt reflects some light.
The T-shirt absorbs all incident light.
The T-shirt re-emits all the incident light.
The T-shirt does not reflect light.

Why do we not notice quantization of photons in everyday experience?

because the size of each photon is very large
because the mass of each photon is so small
because the energy provided by photons is very large
because the energy provided by photons is very small
The red flame is hotter because red light has lower frequency.
The red flame is hotter because red light has higher frequency.
The blue flame is hotter because blue light has lower frequency.
The blue flame is hotter because blue light has higher frequency.
Increase, because more high-energy UV photons can enter the eye.
Increase, because less high-energy UV photons can enter the eye.
Decrease, because more high-energy UV photons can enter the eye.
Decrease, because less high-energy UV photons can enter the eye.
The wavelength of the most intense radiation will vary randomly.
The wavelength of the most intense radiation will increase.
The wavelength of the most intense radiation will remain unchanged.
The wavelength of the most intense radiation will decrease.

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Book title: Physics
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2: The Postulates of Quantum Mechanics

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University of Sheffield

The entire structure of quantum mechanics (including its relativistic extension) can be formulated in terms of states and operations in Hilbert space. We need rules that map the physical quantities such as states, observables, and measurements to the mathematical structure of vector spaces, vectors and operators. There are several ways in which this can be done, and here we summarize these rules in terms of five postulates.

Postulate 1

A physical system is described by a Hilbert space $\mathscr{H}$, and the state of the system is represented by a ray with norm 1 in $\mathscr{H}$.

There are a number of important aspects to this postulate. First, the fact that states are rays, rather than vectors means that an overall phase $e^{i \varphi}$ of the state does not have any physically observable consequences, and $e^{i \varphi}|\psi\rangle$ represents the same state as $|\psi\rangle$. Second, the state contains all information about the system. In particular, there are no hidden variables in this standard formulation of quantum mechanics. Finally, the dimension of $\mathscr{H}$ may be infinite, which is the case, for example, when $\mathscr{H}$ is the space of square-integrable functions.

As an example of this postulate, consider a two-level quantum system (a qubit). This system can be described by two orthonormal states $|0\rangle$ and $|1\rangle$. Due to linearity of Hilbert space, the superposition $\alpha|0\rangle+\beta|1\rangle$ is again a state of the system if it has norm 1, or

\[(\alpha ^ { * } \langle0|+\beta^{*}\langle 1|)(\alpha|0\rangle+\beta|1\rangle)=1 \quad \text { or } \quad|\alpha|^{2}+|\beta|^{2}=1\tag{2.1}\]

This is called the superposition principle: any normalised superposition of valid quantum states is again a valid quantum state. It is a direct consequence of the linearity of the vector space, and as we shall see later, this principle has some bizarre consequences that have been corroborated in many experiments.

Postulate 2

Every physical observable $A$ corresponds to a self-adjoint (Hermitian 1 ) operator $\hat{A}$ whose eigenvectors form a complete basis.

We use a hat to distinguish between the observable and the operator, but usually this distinction is not necessary. In these notes, we will use hats only when there is a danger of confusion.

As an example, take the operator $X$:

\[X|0\rangle=|1\rangle \quad \text { and } \quad X|1\rangle=|0\rangle.\tag{2.2}\]

This operator can be interpreted as a bit flip of a qubit. In matrix notation the state vectors can be written as

\[|0\rangle=\left(\begin{array}{l}1 \\ 0 \end{array}\right) \quad \text { and } \quad|1\rangle=\left(\begin{array}{l} 0 \\ 1 \end{array}\right),\tag{2.3}\]

which means that $X$ is written as

\[X=\left(\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right)\tag{2.4}\]

with eigenvalues ±1. The eigenstates of $X$ are

\[|\pm\rangle=\frac{|0\rangle \pm|1\rangle}{\sqrt{2}}.\tag{2.5}\]

These states form an orthonormal basis.

Postulate 3

The eigenvalues of $A$ are the possible measurement outcomes, and the probability of finding the outcome $a_{j}$ in a measurement is given by the Born rule:

\[p\left(a_{j}\right)=\left|\left\langle a_{j} \mid \psi\right\rangle\right|^{2},\tag{2.6}\]

where $|\psi\rangle$ is the state of the system, and $\left|a_{j}\right\rangle$ is the eigenvector associated with the eigenvalue $a_{j}$ via $A\left|a_{j}\right\rangle=a_{j}\left|a_{j}\right\rangle$. If $a_{j}$ is $m$-fold degenerate, then

\[p(a_{j})=\sum_{l=1}^{m}|\langle a_{j}^{(l)} \mid \psi\rangle|^{2},\tag{2.7}\]

where the $\left|a_{j}^{(l)}\right\rangle$ span the $m$-fold degenerate subspace

The expectation value of $A$ with respect to the state of the system $|\psi\rangle$ is denoted by $\langle A\rangle$, and evaluated as

\[\langle A\rangle=\langle\psi|A| \psi\rangle=\langle\psi|(\sum_{j} a_{j}|a_{j}\rangle\langle a_{j}|)| \psi\rangle=\sum_{j} p(a_{j}) a_{j}\tag{2.8}\]

This is the weighted average of the measurement outcomes. The spread of the measurement outcomes (or the uncertainty) is given by the variance

\[(\Delta A)^{2}=\left\langle(A-\langle A\rangle)^{2}\right\rangle=\left\langle A^{2}\right\rangle-\langle A\rangle^{2}\tag{2.9}\]

So far we mainly dealt with discrete systems on finite-dimensional Hilbert spaces. But what about continuous systems, such as a particle in a box, or a harmonic oscillator? We can still write the spectral decomposition of an operator A but the sum must be replace by an integral:

\[A=\int d a f_{A}(a)|a\rangle\langle a|\tag{2.10}\]

where $|a\rangle$ is an eigenstate of $A$. Typically, there are problems with the normalization of $|a\rangle$, which is related to the impossibility of preparing a system in exactly the state $|a\rangle$. We will not explore these subtleties further in this course, but you should be aware that they exist. The expectation value of $A$ is

\[\langle A\rangle=\langle\psi|A| \psi\rangle=\int d a f_{A}(a)\langle\psi \mid a\rangle\langle a \mid \psi\rangle \equiv \int d a f_{A}(a)|\psi(a)|^{2},\tag{2.11}\]

where we defined the wave function $\psi(a)=\langle a \mid \psi\rangle$, and $|\psi(a)|^{2}$ is properly interpreted as the probability density that you remember from second-year quantum mechanics.

The probability of finding the eigenvalue of an operator $A$ in the interval $a$ and $a+d a$ given the state $|\psi\rangle$ is

\[\langle\psi|(|a\rangle\langle a| d a)| \psi\rangle \equiv d p(a),\tag{2.12}\]

since both sides must be infinitesimal. We therefore find that

\[\frac{d p(a)}{d a}=|\psi(a)|^{2}\tag{2.13}\]

Postulate 4

The dynamics of quantum systems is governed by unitary transformations

We can write the state of a system at time $t$ as $|\psi(t)\rangle$, and at some time $t_{0}<t$ as $\left|\psi\left(t_{0}\right)\right\rangle$. The fourth postulate tells us that there is a unitary operator $U\left(t, t_{0}\right)$ that transforms the state at time $t_{0}$ to the state at time $t$:

\[|\psi(t)\rangle=U\left(t, t_{0}\right)\left|\psi\left(t_{0}\right)\right\rangle\tag{2.14}\]

Since the evolution from time $t$ to $t$ is denoted by $U(t, t)$ and must be equal to the identity, we deduce that $U$ depends only on time differences: $U\left(t, t_{0}\right)=U\left(t-t_{0}\right)$, and $U(0)=\mathbb{I}$.

As an example, let $U(t)$ be generated by a Hermitian operator $A$ according to

$U(t)=\exp \left(-\frac{i}{\hbar} A t\right)\tag{2.15}$

The argument of the exponential must be dimensionless, so $A$ must be proportional to $\hbar$ times an angular frequency (in other words, an energy). Suppose that $|\psi(t)\rangle$ is the state of a qubit, and that $A=\hbar \omega X$. If $|\psi(0)\rangle=|0\rangle$ we want to calculate the state of the system at time $t$. We can write

\[|\psi(t)\rangle=U(t)|\psi(0)\rangle=\exp (-i \omega t X)|0\rangle=\sum_{n=0}^{\infty} \frac{(-i \omega t)^{n}}{n !} X^{n}\tag{2.16}\]

Observe that $X^{2}=\mathbb{I}$, so we can separate the power series into even and odd values of n:

\[|\psi(t)\rangle=\sum_{n=0}^{\infty} \frac{(-i \omega t)^{2 n}}{(2 n) !}|0\rangle+\sum_{n=0}^{\infty} \frac{(-i \omega t)^{2 n+1}}{(2 n+1) !} X|0\rangle=\cos (\omega t)|0\rangle-i \sin (\omega t)|1\rangle\tag{2.17}\]

In other words, the state oscillates between $|0\rangle$ and $|1\rangle$.

The fourth postulate also leads to the Schrödinger equation. Let’s take the infinitesimal form of Eq. (2.14):

\[|\psi(t+d t)\rangle=U(d t)|\psi(t)\rangle\tag{2.18}\]

We require that $U(d t)$ is generated by some Hermitian operator $H$:

\[U(d t)=\exp \left(-\frac{i}{\hbar} H d t\right)\tag{2.19}\]

$H$ must have the dimensions of energy, so we identify it with the energy operator, or the Hamiltonian. We can now take a Taylor expansion of $|\psi(t+d t)\rangle$ to first order in dt:

\[|\psi(t+d t)\rangle=|\psi(t)\rangle+d t \frac{d}{d t}|\psi(t)\rangle+\ldots,\tag{2.20}\]

and we expand the unitary operator to first order in dt as well:

\[U(d t)=1-\frac{i}{\hbar} H d t+\ldots\tag{2.21}\]

We combine this into

\[|\psi(t)\rangle+d t \frac{d}{d t}|\psi(t)\rangle=\left(1-\frac{i}{\hbar} H d t\right)|\psi(t)\rangle,\tag{2.22}\]

which can be recast into the Schrödinger equation:

\[i \hbar \frac{d}{d t}|\psi(t)\rangle=H|\psi(t)\rangle\tag{2.23}\]Therefore, the Schrödinger equation follows directly from the postulates!

Postulate 5

If a measurement of an observable $A$ yields an eigenvalue $a_{j}$, then immediately after the measurement, the system is in the eigenstate $\left|a_{j}\right\rangle$ corresponding to the eigenvalue

This is the infamous projection postulate, so named because a measurement “projects” the system to the eigenstate corresponding to the measured value. This postulate has as observable consequence that a second measurement immediately after the first will also find the outcome $a_{j}$. Each measurement outcome $a_{j}$ corresponds to a projection operator $P_{j}$ on the subspace spanned by the eigenvector(s) belonging to $a_{j}$. A (perfect) measurement can be described by applying a projector to the state, and renormalize:

\[|\psi\rangle \rightarrow \frac{P_{j}|\psi\rangle}{\| P_{j}|\psi\rangle \|}\tag{2.24}\]

This also works for degenerate eigenvalues.

We have established earlier that the expectation value of $A$ can be written as a trace:

\[\langle A\rangle=\operatorname{Tr}(|\psi\rangle\langle\psi| A)\tag{2.25}\]

Now instead of the full operator $A$, we calculate the trace of $P_{j}=\left|a_{j}\right\rangle\left\langle a_{j}\right|$:

\[\left\langle P_{j}\right\rangle=\operatorname{Tr}\left(|\psi\rangle\langle\psi| P_{j}\right)=\operatorname{Tr}\left(|\psi\rangle\left\langle\psi \mid a_{j}\right\rangle\left\langle a_{j}\right|\right)=\left|\left\langle a_{j} \mid \psi\right\rangle\right|^{2}=p\left(a_{j}\right)\tag{2.26}\]

So we can calculate the probability of a measurement outcome by taking the expectation value of the projection operator that corresponds to the eigenstate of the measurement outcome. This is one of the basic calculations in quantum mechanics that you should be able to do.

The Measurement Problem

The projection postulate is somewhat problematic for the interpretation of quantum mechanics, because it leads to the so-called measurement problem : Why does a measurement induce a non-unitary evolution of the system? After all, the measurement apparatus can also be described quantum mechanically 2 and then the system plus the measurement apparatus evolves unitarily. But then we must invoke a new device that measures the combined system and measurement apparatus. However, this in turn can be described quantum mechanically, and so on.

On the other hand, we do see definite measurement outcomes when we do experiments, so at some level the projection postulate is necessary, and somewhere there must be a “collapse of the wave function”. Schrödinger already struggled with this question, and came up with his famous thought experiment about a cat in a box with a poison-filled vial attached to a Geiger counter monitoring a radioactive atom (Figure 1). When the atom decays, it will trigger the Geiger counter, which in turn causes the release of the poison killing the cat. When we do not look inside the box (more precisely: when no information about the atom-counter-vial-cat system escapes from the box), the entire system is in a quantum superposition. However, when we open the box, we do find the cat either dead or alive. One solution of the problem seems to be that the quantum state represents our knowledge of the system, and that looking inside the box merely updates our information about the atom, counter, vial and the cat. So nothing “collapses” except our own state of mind.

Screen Shot 2021-11-22 at 5.00.08 PM.png

However, this cannot be the entire story, because quantum mechanics clearly is not just about our opinions of cats and decaying atoms. In particular, if we prepare an electron in a spin “up” state $|\uparrow\rangle$, then whenever we measure the spin along the $z$-direction we will find the measurement outcome “up”, no matter what we think about electrons and quantum mechanics. So there seems to be some physical property associated with the electron that determines the measurement outcome and is described by the quantum state.

Various interpretations of quantum mechanics attempt to address these (and other) issues. The original interpretation of quantum mechanics was mainly put forward by Niels Bohr, and is called the Copenhagen interpretation . Broadly speaking, it says that the quantum state is a convenient fiction, used to calculate the results of measurement outcomes, and that the system cannot be considered separate from the measurement apparatus. Alternatively, there are interpretations of quantum mechanics, such as the Ghirardi-Rimini-Weber interpretation , that do ascribe some kind of reality to the state of the system, in which case a physical mechanism for the collapse of the wave function must be given. Many of these interpretations can be classified as hidden variable theories, which postulate that there is a deeper physical reality described by some “hidden variables” that we must average over. This in turn explains the probabilistic nature of quantum mechanics. The problem with such theories is that these hidden variables must be quite weird: they can change instantly depending on events light-years away3 , thus violating Einstein’s theory of special relativity. Many physicists do not like this aspect of hidden variable theories.

Alternatively, quantum mechanics can be interpreted in terms of “many worlds”: the Many Worlds interpretation states that there is one state vector for the entire universe, and that each measurement splits the universe into different branches corresponding to the different measurement outcomes. It is attractive since it seems to be a philosophically consistent interpretation, and while it has been acquiring a growing number of supporters over recent years 4 , a lot of physicists have a deep aversion to the idea of parallel universes.

Finally, there is the epistemic interpretation , which is very similar to the Copenhagen interpretation in that it treats the quantum state to a large extent as a measure of our knowledge of the quantum system (and the measurement apparatus). At the same time, it denies a deeper underlying reality (i.e., no hidden variables). The attractive feature of this interpretation is that it requires a minimal amount of fuss, and fits naturally with current research in quantum information theory. The downside is that you have to abandon simple scientific realism that allows you to talk about the properties of electrons and photons, and many physicists are not prepared to do that.

As you can see, quantum mechanics forces us to abandon some deeply held (classical) convictions about Nature. Depending on your preference, you may be drawn to one or other interpretation. It is currently not know which interpretation is the correct one.

Calculate the eigenvalues and the eigenstates of the bit flip operator $X$, and show that the eigenstates form an orthonormal basis. Calculate the expectation value of $X$ for $|\psi\rangle=1 / \sqrt{3}|0\rangle+i \sqrt{2 / 3}|1\rangle$.
Show that the variance of $A$ vanishes when $|\psi\rangle$ is an eigenstate of $A$.
Prove that an operator is Hermitian if and only if it has real eigenvalues.
Show that a qubit in an unknown state $|\psi\rangle$ cannot be copied. This is the no-cloning theorem. Hint: start with a state $|\psi\rangle|i\rangle$ for some initial state $|i\rangle$, and require that for $|\psi\rangle=|0\rangle$ and $|\psi\rangle=|1\rangle$ the cloning procedure is a unitary transformation $|0\rangle|i\rangle \rightarrow|0\rangle|0\rangle$ and $|1\rangle|i\rangle \rightarrow|1\rangle|1\rangle$.

\[(\Delta A)^{2}(\Delta B)^{2} \geq \frac{1}{4}|\langle[A, B]\rangle|^{2}\tag{2.27}\]

Hint: define $|f\rangle=(A-\langle A\rangle)|\psi\rangle$ and $|g\rangle=i(B-\langle B\rangle)|\psi\rangle$, and use that $|\langle f \mid g\rangle| \geq \frac{1}{2} \mid\langle f \mid g\rangle+\langle g|f\rangle|$.

Show that this reduces to Heisenberg’s uncertainty relation when $A$ and $B$ are canonically conjugate observables, for example position and momentum.
Does this method work for deriving the uncertainty principle between energy and time?

\[H=E\left(\begin{array}{ccc} 0 & i & 0 \\ -i & 0 & 0 \\ 0 & 0 & -1 \end{array}\right) \quad \text { and } \quad|\psi\rangle=\frac{1}{\sqrt{5}}\left(\begin{array}{c} 1-i \\ 1-i \\ 1 \end{array}\right)\tag{2.28}\]

where $E$ is a constant with dimensions of energy. Calculate the energy eigenvalues and the expectation value of the Hamiltonian.

Show that the momentum and the total energy can be measured simultaneously only when the potential is constant everywhere. What does a constant potential mean in terms of the dynamics of a particle?

1 In Hilbert spaces of infinite dimensionality, there are subtle differences between self-adjoint and Hermitian operators. We ignore these subtleties here, because we will be mostly dealing with finite-dimensional spaces.

2 This is something most people require from a fundamental theory: quantum mechanics should not just break down for macroscopic objects. Indeed, experimental evidence of macroscopic superpositions has been found in the form of “cat states”.

3 . . . even though the averaging over the hidden variables means you can never signal faster than light.

4 There seems to be some evidence that the Many Worlds interpretation fits well with the latest cosmological models based on string theory

Quantum physics

By Richard Webb

What is quantum physics? Put simply, it’s the physics that explains how everything works: the best description we have of the nature of the particles that make up matter and the forces with which they interact.

Quantum physics underlies how atoms work, and so why chemistry and biology work as they do. You, me and the gatepost – at some level at least, we’re all dancing to the quantum tune. If you want to explain how electrons move through a computer chip, how photons of light get turned to electrical current in a solar panel or amplify themselves in a laser , or even just how the sun keeps burning, you’ll need to use quantum physics.

The difficulty – and, for physicists, the fun – starts here. To begin with, there’s no single quantum theory. There’s quantum mechanics , the basic mathematical framework that underpins it all, which was first developed in the 1920s by Niels Bohr, Werner Heisenberg , Erwin Schrödinger and others. It characterises simple things such as how the position or momentum of a single particle or group of few particles changes over time.

But to understand how things work in the real world, quantum mechanics must be combined with other elements of physics – principally, Albert Einstein’s special theory of relativity , which explains what happens when things move very fast – to create what are known as quantum field theories.

Three different quantum field theories deal with three of the four fundamental forces by which matter interacts: electromagnetism, which explains how atoms hold together; the strong nuclear force, which explains the stability of the nucleus at the heart of the atom; and the weak nuclear force, which explains why some atoms undergo radioactive decay.

Over the past five decades or so these three theories have been brought together in a ramshackle coalition known as the “ standard model ” of particle physics. For all the impression that this model is slightly held together with sticky tape, it is the most accurately tested picture of matter’s basic working that’s ever been devised. Its crowning glory came in 2012 with the discovery of the Higgs boson , the particle that gives all other fundamental particles their mass, whose existence was predicted on the basis of quantum field theories as far back as 1964.

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Conventional quantum field theories work well in describing the results of experiments at high-energy particle smashers such as CERN’s Large Hadron Collider , where the Higgs was discovered, which probe matter at its smallest scales. But if you want to understand how things work in many less esoteric situations – how electrons move or don’t move through a solid material and so make a material a metal, an insulator or a semiconductor, for example – things get even more complex.

The billions upon billions of interactions in these crowded environments require the development of “effective field theories” that gloss over some of the gory details. The difficulty in constructing such theories is why many important questions in solid-state physics remain unresolved – for instance why at low temperatures some materials are superconductors that allow current without electrical resistance, and why we can’t get this trick to work at room temperature.

But beneath all these practical problems lies a huge quantum mystery. At a basic level, quantum physics predicts very strange things about how matter works that are completely at odds with how things seem to work in the real world. Quantum particles can behave like particles, located in a single place; or they can act like waves, distributed all over space or in several places at once . How they appear seems to depend on how we choose to measure them, and before we measure they seem to have no definite properties at all – leading us to a fundamental conundrum about the nature of basic reality .

This fuzziness leads to apparent paradoxes such as Schrödinger’s cat , in which thanks to an uncertain quantum process a cat is left dead and alive at the same time . But that’s not all. Quantum particles also seem to be able to affect each other instantaneously even when they are far away from each other. This truly bamboozling phenomenon is known as entanglement , or, in a phrase coined by Einstein (a great critic of quantum theory), “ spooky action at a distance ”. Such quantum powers are completely foreign to us, yet are the basis of emerging technologies such as ultra-secure quantum cryptography and ultra-powerful quantum computing .

But as to what it all means, no one knows. Some people think we must just accept that quantum physics explains the material world in terms we find impossible to square with our experience in the larger, “classical” world. Others think there must be some better, more intuitive theory out there that we’ve yet to discover.

In all this, there are several elephants in the room. For a start, there’s a fourth fundamental force of nature that so far quantum theory has been unable to explain. Gravity remains the territory of Einstein’s general theory of relativity , a firmly non-quantum theory that doesn’t even involve particles. Intensive efforts over decades to bring gravity under the quantum umbrella and so explain all of fundamental physics within one “ theory of everything ” have come to nothing.

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Meanwhile cosmological measurements indicate that over 95 per cent of the universe consists of dark matter and dark energy , stuffs for which we currently have no explanation within the standard model , and conundrums such as the extent of the role of quantum physics in the messy workings of life remain unexplained. The world is at some level quantum – but whether quantum physics is the last word about the world remains an open question.

Take our expert-led quantum physics course and discover the principles that underpin modern physics

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Science News

A century of quantum mechanics questions the fundamental nature of reality.

The quantum revolution upended our understanding of nature, and a lot of uncertainty remains

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Quantum theory describes a reality ruled by probabilities. How to reconcile that reality with everyday experiences is still unclear.

Max Löffler

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It doesn’t, of course. Quantum theory represents the ultimate outcome of superior logical reasoning, arriving at truths that could never be discovered merely by observing the visible world.

It turns out that in the microworld — beyond the reach of the senses — phenomena play a game with fantastical rules. Matter’s basic particles are not tiny rocks, but more like ghostly waves that maintain multiple possible futures until forced to assume the subatomic equivalent of substance. As a result, quantum math does not describe a relentless cause-and-effect sequence of events as Newtonian science had insisted. Instead science morphs from dictator to oddsmaker; quantum math tells only probabilities for different possible outcomes. Some uncertainty always remains.

illustration of two arched doorways showing particles and waves

The quantum revolution

The discovery of quantum uncertainty was what first impressed the world with the depth of the quantum revolution. German physicist Werner Heisenberg, in 1927, astounded the scientific community with the revelation that deterministic cause-and-effect physics failed when applied to atoms. It was impossible, Heisenberg deduced, to measure both the location and velocity of a subatomic particle at the same time. If you measured one precisely, some uncertainty remained for the other.

“A particle may have an exact place or an exact speed, but it can not have both,” as Science News Letter , the predecessor of Science News , reported in 1929 . “Crudely stated, the new theory holds that chance rules the physical world.” Heisenberg’s uncertainty principle “is destined to revolutionize the ideas of the universe held by scientists and laymen to an even greater extent than Einstein’s relativity.”

black and white image of Werner Heisenberg standing in front of a chalkboard

Heisenberg’s breakthrough was the culmination of a series of quantum surprises. First came German physicist Max Planck’s discovery, in 1900, that light and other forms of radiation could be absorbed or emitted only in discrete packets, which Planck called quanta. A few years later Albert Einstein argued that light also traveled through space as packets, or particles, later called photons. Many physicists dismissed such early quantum clues as inconsequential. But in 1913, the Danish physicist Niels Bohr used quantum theory to explain the structure of the atom. Soon the world realized that reality needed reexamining.

By 1921, awareness of the quantum revolution had begun to expand beyond the confines of physics conferences. In that year, Science News Bulletin , the first iteration of Science News , distributed what was “believed to be the first popular explanation” of the quantum theory of radiation, provided by American physical chemist William D. Harkins. He proclaimed that the quantum theory “is of much more practical importance” than the theory of relativity.

“Since it concerns itself with the relations between matter and radiation,” Harkins wrote , quantum theory “is of fundamental significance in connection with almost all processes which we know.” Electricity, chemical reactions and how matter responds to heat all require quantum-theoretic explanations.

As for atoms, traditional physics asserts that atoms and their parts can move about “in a large number of different ways,” Harkins stated. But quantum theory maintains that “of all the states of motion (or ways of moving) prescribed by the older theory, only a certain number actually do occur.” Therefore, events previously believed “to occur as continuous processes, actually do occur in steps.”

Quantum theory “is of fundamental significance in connection with almost all processes which we know.” William Harkins

But in 1921 quantum physics remained embryonic. Some of its implications had been discerned, but its full form remained undeveloped in detail. It was Heisenberg, in 1925, who first transformed the puzzling jumble of clues into a coherent mathematical picture. His decisive advance was developing a way to represent the energies of electrons in atoms using matrix algebra. With aid from German physicists Max Born and Pascual Jordan, Heisenberg’s math became known as matrix mechanics. Shortly thereafter, Austrian physicist Erwin Schrödinger developed a competing equation for electron energies, viewing the supposed particles as waves described by a mathematical wave function. Schrödinger’s “wave mechanics” turned out to be mathematically equivalent to Heisenberg’s particle-based approach, and “quantum mechanics” became the general term for the math describing all subatomic systems.

Still, some confusion remained. It wasn’t clear how an approach picturing electrons as particles could be equivalent to one supposing electrons to be waves. Bohr, by then regarded as the foremost of the world’s atomic physicists, pondered the question deeply and by 1927 arrived at a novel viewpoint he called complementarity.

Bohr argued that the particle and wave views were complementary; both were necessary for a full description of subatomic phenomena. Whether a “particle” — say, an electron — exhibited its wave or particle nature depended on the experimental setup observing it. An apparatus designed to find a particle would find a particle; an apparatus geared to detect wave behavior would find a wave.

At about the same time, Heisenberg derived his uncertainty principle. Just as wave and particle could not be observed in the same experiment, position and velocity could not both be precisely measured at the same time. As physicist Wolfgang Pauli commented, “Now it becomes day in quantum theory.”

But the quantum adventure was really just beginning.

illustration of a head floating in a purple box with a red flash in the forehead

A great debate

Many physicists, Einstein among them, deplored the implications of Heisenberg’s uncertainty principle. Its introduction in 1927 eliminated the possibility of precisely predicting the outcomes of atomic observations. As Born had shown, you could merely predict the probabilities for the various possible outcomes, using calculations informed by the wave function that Schrödinger had introduced. Einstein famously retorted that he could not believe that God would play dice with the universe. Even worse, in Einstein’s view, the wave-particle duality described by Bohr implied that a physicist could affect reality by deciding what kind of measurement to make. Surely, Einstein believed, reality existed independently of human observations.

On that point, Bohr engaged Einstein in a series of discussions that came to be known as the Bohr-Einstein debate, a continuing dialog that came to a head in 1935. In that year, Einstein, with collaborators Nathan Rosen and Boris Podolsky, described a thought experiment supposedly showing that quantum mechanics could not be a complete theory of reality.

In a brief summary in Science News Letter in May 1935, Podolsky explained that a complete theory must include a mathematical “counterpart for every element of the physical world.” In other words, there should be a quantum wave function for the properties of every physical system. Yet if two physical systems, each described by a wave function, interact and then fly apart, “quantum mechanics … does not enable us to calculate the wave function of each physical system after the separation.” (In technical terms, the two systems become “entangled,” a term coined by Schrödinger.) So quantum math cannot describe all elements of reality and is therefore incomplete.

Bohr soon responded , as reported in Science News Letter in August 1935. He declared that Einstein and colleagues’ criterion for physical reality was ambiguous in quantum systems. Einstein, Podolsky and Rosen assumed that a system (say an electron) possessed definite values for certain properties (such as its momentum) before those values were measured. Quantum mechanics, Bohr explained, preserved different possible values for a particle’s properties until one of them was measured. You could not assume the existence of an “element of reality” without specifying an experiment to measure it.

black and white image of Neils Bohr and Albert Einstein seated

Einstein did not relent. He acknowledged that the uncertainty principle was correct with respect to what was observable in nature, but insisted that some invisible aspect of reality nevertheless determined the course of physical events. In the early 1950s physicist David Bohm developed such a theory of “hidden variables” that restored determinism to quantum physics, but made no predictions that differed from the standard quantum mechanics math. Einstein was not impressed with Bohm’s effort. “That way seems too cheap to me,” Einstein wrote to Born, a lifelong friend.

Einstein died in 1955, Bohr in 1962, neither conceding to the other. In any case it seemed like an irresolvable dispute, since experiments would give the same results either way. But in 1964, physicist John Stewart Bell deduced a clever theorem about entangled particles, enabling experiments to probe the possibility of hidden variables. Beginning in the 1970s, and continuing to today, experiment after experiment confirmed the standard quantum mechanical predictions. Einstein’s objection was overruled by the court of nature.

Still, many physicists expressed discomfort with Bohr’s view (commonly referred to as the Copenhagen interpretation of quantum mechanics). One particularly dramatic challenge came from the physicist Hugh Everett III in 1957. He insisted that an experiment did not create one reality from the many quantum possibilities, but rather identified only one branch of reality. All the other experimental possibilities existed on other branches, all equally real. Humans perceive only their own particular branch, unaware of the others just as they are unaware of the rotation of the Earth. This “many worlds interpretation” was widely ignored at first but became popular decades later, with many adherents today.

Since Everett’s work, numerous other interpretations of quantum theory have been offered. Some emphasize the “reality” of the wave function, the mathematical expression used for predicting the odds of different possibilities. Others emphasize the role of the math as describing the knowledge about reality accessible to experimenters.

Some interpretations attempt to reconcile the many worlds view with the fact that humans perceive only one reality. In the 1980s, physicists including H. Dieter Zeh and Wojciech Zurek identified the importance of a quantum system’s interaction with its external environment, a process called quantum decoherence. Some of a particle’s many possible realities rapidly evaporate as it encounters matter and radiation in its vicinity. Soon only one of the possible realities remains consistent with all the environmental interactions, explaining why on the human scale of time and size only one such reality is perceived.

This insight spawned the “consistent histories” interpretation, pioneered by Robert Griffiths and developed in more elaborate form by Murray Gell-Mann and James Hartle. It is widely known among physicists but has received little wider popularity and has not deterred the pursuit of other interpretations. Scientists continue to grapple with what quantum math means for the very nature of reality.

Illustration of rainbow in space ending in two flashes

It from quantum bit

In the 1990s, the quest for quantum clarity took a new turn with the rise of quantum information theory. Physicist John Archibald Wheeler, a disciple of Bohr, had long emphasized that specific realities emerged from the fog of quantum possibilities by irreversible amplifications — such as an electron definitely establishing its location by leaving a mark after hitting a detector. Wheeler suggested that reality as a whole could be built up from such processes, which he compared to yes or no questions — is the electron here? Answers corresponded to bits of information, the 1s and 0s used by computers. Wheeler coined the slogan “it from bit” to describe the link between existence and information.

Taking the analogy further, one of Wheeler’s former students, Benjamin Schumacher, devised the notion of a quantum version of the classical bit of information. He introduced the quantum bit, or qubit, at a conference in Dallas in 1992 .

Schumacher’s qubit provided a basis for building computers that could process quantum information. Such “quantum computers” had previously been envisioned, in different ways, by physicists Paul Benioff, Richard Feynman and David Deutsch. In 1994, mathematician Peter Shor showed how a quantum computer manipulating qubits could crack the toughest secret codes, launching a quest to design and build quantum computers capable of that and other clever computing feats. By the early 21st century, rudimentary quantum computers had been built; the latest versions can perform some computing tasks but are not powerful enough yet to make current cryptography methods obsolete. For certain types of problems, though, quantum computing may soon achieve superiority over standard computers .

A new unit of info

Benjamin Schumacher introduced the quantum bit, or qubit, in 1992, which offers a foundation for quantum computing. The qubit can exist as both a 0 and 1. When the qubit is represented on a sphere, the angles formed by the radius to the point on the sphere determine the odds of measuring a 0 or 1.

graphic showing the qubit as a sphere with angles showing the odds of measuring 0 or 1

Quantum computing’s realization has not resolved the debate over quantum interpretations. Deutsch believed that quantum computers would support the many worlds view. Hardly anyone else agrees, though. And decades of quantum experiments have not provided any support for novel interpretations — all the results comply with the traditional quantum mechanics expectations. Quantum systems preserve different values for certain properties until one is measured, just as Bohr insisted. But nobody is completely satisfied, perhaps because the 20th century’s other pillar of fundamental physics, Einstein’s theory of gravity (general relativity), does not fit in quantum theory’s framework.

For decades now, the quest for a quantum theory of gravity has fallen short of success, despite many promising ideas. Most recently a new approach suggests that the geometry of spacetime, the source of gravity in Einstein’s theory, may in some way be built from the entanglement of quantum entities . If so, the mysterious behavior of the quantum world defies understanding in terms of ordinary events in space and time because quantum reality creates spacetime, rather than occupying it. If so, human observers witness an artificial, emergent reality that gives the impression of events happening in space and time while the true, inaccessible reality doesn’t have to play by the spacetime rules.

In a crude way this view echoes that of Parmenides, the ancient Greek philosopher who taught that all change is an illusion. Our senses show us the “way of seeming,” Parmenides declared; only logic and reason can reveal “the way of truth.” Parmenides didn’t reach that insight by doing the math, of course (he said it was explained to him by a goddess). But he was a crucial figure in the history of science, initiating the use of rigorous deductive reasoning and relying on it even when it led to conclusions that defied sensory experience.

Yet as some of the other ancient Greeks realized, the world of the senses does offer clues about the reality we can’t see. “Phenomena are a sight of the unseen,” Anaxagoras said. As Carroll puts it, in modern terms, “the world as we experience it” is certainly related to “the world as it really is.”

“But the relationship is complicated,” he says, “and it’s real work to figure it out.”

In fact, it took two millennia of hard work for the Greek revolution in explaining nature to mature into Newtonian science’s mechanistic understanding of reality. Three centuries later quantum physics revolutionized science’s grasp of reality to a comparable extent. Yet the lack of agreement on what it all means suggests that perhaps science needs to dig a little deeper still.

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Clara Sousa-Silva seeks molecular signatures of life in alien atmospheres

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What Is Entanglement and Why Is It Important?

This article was reviewed by a member of Caltech's Faculty .

Entanglement is at the heart of quantum physics and future quantum technologies. Like other aspects of quantum science, the phenomenon of entanglement reveals itself at very tiny, subatomic scales. When two particles, such as a pair of photons or electrons, become entangled, they remain connected even when separated by vast distances. In the same way that a ballet or tango emerges from individual dancers, entanglement arises from the connection between particles. It is what scientists call an emergent property.

How do scientists explain quantum entanglement?

In the video below, Caltech faculty members take a stab at explaining entanglement. Featured: Rana Adhikari, professor of physics; Xie Chen, professor of theoretical physics; Manuel Endres, professor of physics and Rosenberg Scholar; and John Preskill, Richard P. Feynman Professor of Theoretical Physics, Allen V. C. Davis and Lenabelle Davis Leadership Chair, and director of the Institute for Quantum Information and Matter.

Unbreakable Correlation

When researchers study entanglement , they often use a special kind of crystal to generate two entangled particles from one. The entangled particles are then sent off to different locations. For this example, let's say the researchers want to measure the direction the particles are spinning, which can be either up or down along a given axis. Before the particles are measured, each will be in a state of superposition , or both "spin up" and "spin down" at the same time.

If the researcher measures the direction of one particle's spin and then repeats the measurement on its distant, entangled partner, that researcher will always find that the pair are correlated: if one particle's spin is up, the other's will be down (the spins may instead both be up or both be down, depending on how the experiment is designed, but there will always be a correlation). Returning to our dancer metaphor, this would be like observing one dancer and finding them in a pirouette, and then automatically knowing the other dancer must also be performing a pirouette. The beauty of entanglement is that just knowing the state of one particle automatically tells you something about its companion, even when they are far apart.

Are particles really connected across space?

But are the particles really somehow tethered to each other across space, or is something else going on? Some scientists, including Albert Einstein in the 1930s, pointed out that the entangled particles might have always been spin up or spin down, but that this information was hidden from us until the measurements were made. Such "local hidden variable theories" argued against the mind-boggling aspect of entanglement, instead proposing that something more mundane, yet unseen, is going on.

Thanks to theoretical work by John Stewart Bell in the 1960s, and experimental work done by Caltech alumnus John Clauser (BS '64) and others beginning in the 1970s, scientists have ruled out these local hidden-variable theories. A key to the researchers' success involved observing entangled particles from different angles. In the experiment mentioned above, this means that a researcher would measure their first particle as spin up, but then use a different viewing angle (or a different spin axis direction) to measure the second particle. Rather than the two particles matching up as before, the second particle would have gone back into a state of superposition and, once observed, could be either spin up or down. The choice of the viewing angle changed the outcome of the experiment, which means that there cannot be any hidden information buried inside a particle that determines its spin before it is observed. The dance of entanglement materializes not from any one particle but from the connections between them.

Relativity Remains Intact

A common misconception about entanglement is that the particles are communicating with each other faster than the speed of light, which would go against Einstein's special theory of relativity. Experiments have shown that this is not true, nor can quantum physics be used to send faster-than-light communications. Though scientists still debate how the seemingly bizarre phenomenon of entanglement arises, they know it is a real principle that passes test after test. In fact, while Einstein famously described entanglement as "spooky action at a distance," today's quantum scientists say there is nothing spooky about it.

"It may be tempting to think that the particles are somehow communicating with each other across these great distances, but that is not the case," says Thomas Vidick , a professor of computing and mathematical sciences at Caltech. "There can be correlation without communication," and the particles "can be thought of as one object."

Let's say you have two entangled balls, each in its own box. Each ball is in a state of superposition, or both yellow and red at the same time...

Networks of Entanglement

Entanglement can also occur among hundreds, millions, and even more particles. The phenomenon is thought to take place throughout nature, among the atoms and molecules in living species and within metals and other materials. When hundreds of particles become entangled, they still act as one unified object. Like a flock of birds, the particles become a whole entity unto itself without being in direct contact with one another. Caltech scientists focus on the study of these so-called many-body entangled systems, both to understand the fundamental physics and to create and develop new quantum technologies. As John Preskill, Caltech's Richard P. Feynman Professor of Theoretical Physics, Allen V. C. Davis and Lenabelle Davis Leadership Chair, and director of the Institute for Quantum Information and Matter, says, "We are making investments in and betting on entanglement being one of the most important themes of 21st-century science."

Dive Deeper

The Many-Worlds Theory, Explained

Quantum physics is strange. At least, it is strange to us, because the rules of the quantum world, which govern the way the world works at the level of atoms and subatomic particles (the behavior of light and matter, as the renowned physicist Richard Feynman put it), are not the rules that we are familiar with — the rules of what we call “common sense.”

The quantum rules, which were mostly established by the end of the 1920s, seem to be telling us that a cat can be both alive and dead at the same time, while a particle can be in two places at once. But to the great distress of many physicists, let alone ordinary mortals, nobody (then or since) has been able to come up with a common-sense explanation of what is going on. More thoughtful physicists have sought solace in other ways, to be sure, namely coming up with a variety of more or less desperate remedies to “explain” what is going on in the quantum world.

These remedies, the quanta of solace, are called “interpretations.” At the level of the equations, none of these interpretations is better than any other, although the interpreters and their followers will each tell you that their own favored interpretation is the one true faith, and all those who follow other faiths are heretics. On the other hand, none of the interpretations is worse than any of the others, mathematically speaking. Most probably, this means that we are missing something. One day, a glorious new description of the world may be discovered that makes all the same predictions as present-day quantum theory, but also makes sense. Well, at least we can hope.

Meanwhile, I thought I might provide an agnostic overview of one of the more colorful of the hypotheses, the many-worlds, or multiple universes, theory. For overviews of the other five leading interpretations, I point you to my book, “ Six Impossible Things .” I think you’ll find that all of them are crazy, compared with common sense, and some are more crazy than others. But in this world, crazy does not necessarily mean wrong, and being more crazy does not necessarily mean more wrong.

If you have heard of the Many Worlds Interpretation (MWI), the chances are you think that it was invented by the American Hugh Everett in the mid-1950s. In a way that’s true. He did come up with the idea all by himself. But he was unaware that essentially the same idea had occurred to Erwin Schrödinger half a decade earlier. Everett’s version is more mathematical, Schrödinger’s more philosophical, but the essential point is that both of them were motivated by a wish to get rid of the idea of the “collapse of the wave function,” and both of them succeeded.

As Schrödinger used to point out to anyone who would listen, there is nothing in the equations (including his famous wave equation) about collapse. That was something that Bohr bolted on to the theory to “explain” why we only see one outcome of an experiment — a dead cat or a live cat — not a mixture, a superposition of states. But because we only detect one outcome — one solution to the wave function — that need not mean that the alternative solutions do not exist. In a paper he published in 1952, Schrödinger pointed out the ridiculousness of expecting a quantum superposition to collapse just because we look at it. It was, he wrote, “patently absurd” that the wave function should “be controlled in two entirely different ways, at times by the wave equation, but occasionally by direct interference of the observer, not controlled by the wave equation.”

Although Schrödinger himself did not apply his idea to the famous cat, it neatly resolves that puzzle. Updating his terminology, there are two parallel universes, or worlds, in one of which the cat lives, and in one of which it dies. When the box is opened in one universe, a dead cat is revealed. In the other universe, there is a live cat. But there always were two worlds that had been identical to one another until the moment when the diabolical device determined the fate of the cat(s). There is no collapse of the wave function. Schrödinger anticipated the reaction of his colleagues in a talk he gave in Dublin, where he was then based, in 1952. After stressing that when his eponymous equation seems to describe different possibilities (they are “not alternatives but all really happen simultaneously”), he said:

Nearly every result [the quantum theorist] pronounces is about the probability of this or that or that … happening — with usually a great many alternatives. The idea that they may not be alternatives but all really happen simultaneously seems lunatic to him, just impossible. He thinks that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish. It is strange that he should believe this. For I understand he grants that unobserved nature does behave this way—namely according to the wave equation. The aforesaid alternatives come into play only when we make an observation — which need, of course, not be a scientific observation. Still it would seem that, according to the quantum theorist, nature is prevented from rapid jellification only by our perceiving or observing it … it is a strange decision.

In fact, nobody responded to Schrödinger’s idea. It was ignored and forgotten, regarded as impossible. So Everett developed his own version of the MWI entirely independently, only for it to be almost as completely ignored. But it was Everett who introduced the idea of the Universe “splitting” into different versions of itself when faced with quantum choices, muddying the waters for decades.

It was Hugh Everett who introduced the idea of the Universe “splitting” into different versions of itself when faced with quantum choices, muddying the waters for decades.

Everett came up with the idea in 1955, when he was a PhD student at Princeton. In the original version of his idea, developed in a draft of his thesis, which was not published at the time, he compared the situation with an amoeba that splits into two daughter cells. If amoebas had brains, each daughter would remember an identical history up until the point of splitting, then have its own personal memories. In the familiar cat analogy, we have one universe, and one cat, before the diabolical device is triggered, then two universes, each with its own cat, and so on. Everett’s PhD supervisor, John Wheeler, encouraged him to develop a mathematical description of his idea for his thesis, and for a paper published in the Reviews of Modern Physics in 1957, but along the way, the amoeba analogy was dropped and did not appear in print until later. But Everett did point out that since no observer would ever be aware of the existence of the other worlds, to claim that they cannot be there because we cannot see them is no more valid than claiming that the Earth cannot be orbiting around the Sun because we cannot feel the movement.

Everett himself never promoted the idea of the MWI. Even before he completed his PhD, he had accepted the offer of a job at the Pentagon working in the Weapons Systems Evaluation Group on the application of mathematical techniques (the innocently titled game theory) to secret Cold War problems (some of his work was so secret that it is still classified) and essentially disappeared from the academic radar. It wasn’t until the late 1960s that the idea gained some momentum when it was taken up and enthusiastically promoted by Bryce DeWitt, of the University of North Carolina, who wrote: “every quantum transition taking place in every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriad copies of itself.” This became too much for Wheeler, who backtracked from his original endorsement of the MWI, and in the 1970s, said: “I have reluctantly had to give up my support of that point of view in the end — because I am afraid it carries too great a load of metaphysical baggage.” Ironically, just at that moment, the idea was being revived and transformed through applications in cosmology and quantum computing.

“Every quantum transition taking place in every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriad copies of itself.”

The power of the interpretation began to be appreciated even by people reluctant to endorse it fully. John Bell noted that “persons of course multiply with the world, and those in any particular branch would experience only what happens in that branch,” and grudgingly admitted that there might be something in it:

The “many worlds interpretation” seems to me an extravagant, and above all an extravagantly vague, hypothesis. I could almost dismiss it as silly. And yet … It may have something distinctive to say in connection with the “Einstein Podolsky Rosen puzzle,” and it would be worthwhile, I think, to formulate some precise version of it to see if this is really so. And the existence of all possible worlds may make us more comfortable about the existence of our own world … which seems to be in some ways a highly improbable one.

The precise version of the MWI came from David Deutsch, in Oxford, and in effect put Schrödinger’s version of the idea on a secure footing, although when he formulated his interpretation, Deutsch was unaware of Schrödinger’s version. Deutsch worked with DeWitt in the 1970s, and in 1977, he met Everett at a conference organized by DeWitt — the only time Everett ever presented his ideas to a large audience. Convinced that the MWI was the right way to understand the quantum world, Deutsch became a pioneer in the field of quantum computing, not through any interest in computers as such, but because of his belief that the existence of a working quantum computer would prove the reality of the MWI.

This is where we get back to a version of Schrödinger’s idea. In the Everett version of the cat puzzle, there is a single cat up to the point where the device is triggered. Then the entire Universe splits in two. Similarly, as DeWitt pointed out, an electron in a distant galaxy confronted with a choice of two (or more) quantum paths causes the entire Universe, including ourselves, to split. In the Deutsch–Schrödinger version, there is an infinite variety of universes (a Multiverse) corresponding to all possible solutions to the quantum wave function. As far as the cat experiment is concerned, there are many identical universes in which identical experimenters construct identical diabolical devices. These universes are identical up to the point where the device is triggered. Then, in some universes the cat dies, in some it lives, and the subsequent histories are correspondingly different. But the parallel worlds can never communicate with one another. Or can they?

Deutsch argues that when two or more previously identical universes are forced by quantum processes to become distinct, as in the experiment with two holes, there is a temporary interference between the universes, which becomes suppressed as they evolve. It is this interaction that causes the observed results of those experiments. His dream is to see the construction of an intelligent quantum machine — a computer — that would monitor some quantum phenomenon involving interference going on within its “brain.” Using a rather subtle argument, Deutsch claims that an intelligent quantum computer would be able to remember the experience of temporarily existing in parallel realities. This is far from being a practical experiment. But Deutsch also has a much simpler “proof” of the existence of the Multiverse.

What makes a quantum computer qualitatively different from a conventional computer is that the “switches” inside it exist in a superposition of states. A conventional computer is built up from a collection of switches (units in electrical circuits) that can be either on or off, corresponding to the digits 1 or 0. This makes it possible to carry out calculations by manipulating strings of numbers in binary code. Each switch is known as a bit, and the more bits there are, the more powerful the computer is. Eight bits make a byte, and computer memory today is measured in terms of billions of bytes — gigabytes, or Gb. Strictly speaking, since we are dealing in binary, a gigabyte is 2 30 bytes, but that is usually taken as read. Each switch in a quantum computer, however, is an entity that can be in a superposition of states. These are usually atoms, but you can think of them as being electrons that are either spin up or spin down. The difference is that in the superposition, they are both spin up and spin down at the same time — 0 and 1. Each switch is called a qbit, pronounced “cubit.”

Using a rather subtle argument, Deutsch claims that an intelligent quantum computer would be able to remember the experience of temporarily existing in parallel realities.

Because of this quantum property, each qbit is equivalent to two bits. This doesn’t look impressive at first sight, but it is. If you have three qbits, for example, they can be arranged in eight ways: 000, 001, 010, 011, 100, 101, 110, 111. The superposition embraces all these possibilities. So three qbits are not equivalent to six bits (2 x 3), but to eight bits (2 raised to the power of 3). The equivalent number of bits is always 2 raised to the power of the number of qbits. Just 10 qbits would be equivalent to 2 10 bits, actually 1,024, but usually referred to as a kilobit. Exponentials like this rapidly run away with themselves. A computer with just 300 qbits would be equivalent to a conventional computer with more bits than there are atoms in the observable Universe. How could such a computer carry out calculations? The question is more pressing since simple quantum computers, incorporating a few qbits, have already been constructed and shown to work as expected. They really are more powerful than conventional computers with the same number of bits.

Deutsch’s answer is that the calculation is carried out simultaneously on identical computers in each of the parallel universes corresponding to the superpositions. For a three-qbit computer, that means eight superpositions of computer scientists working on the same problem using identical computers to get an answer. It is no surprise that they should “collaborate” in this way, since the experimenters are identical, with identical reasons for tackling the same problem. That isn’t too difficult to visualize. But when we build a 300-qbit machine—which will surely happen—we will, if Deutsch is right, be involving a “collaboration” between more universes than there are atoms in our visible Universe. It is a matter of choice whether you think that is too great a load of metaphysical baggage. But if you do, you will need some other way to explain why quantum computers work.

Most quantum computer scientists prefer not to think about these implications. But there is one group of scientists who are used to thinking of even more than six impossible things before breakfast — the cosmologists. Some of them have espoused the Many Worlds Interpretation as the best way to explain the existence of the Universe itself.

Their jumping-off point is the fact, noted by Schrödinger, that there is nothing in the equations referring to a collapse of the wave function. And they do mean the wave function; just one, which describes the entire world as a superposition of states — a Multiverse made up of a superposition of universes.

Some cosmologists have espoused the Many Worlds Interpretation as the best way to explain the existence of the Universe itself.

The first version of Everett’s PhD thesis (later modified and shortened on the advice of Wheeler) was actually titled “The Theory of the Universal Wave Function.” And by “universal” he meant literally that, saying:

Since the universal validity of the state function description is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the whole universe. In this sense this theory can be called the theory of the “universal wave function,” since all of physics is presumed to follow from this function alone.

… where for the present purpose “state function” is another name for “wave function.” “All of physics” means everything, including us — the “observers” in physics jargon. Cosmologists are excited by this, not because they are included in the wave function, but because this idea of a single, uncollapsed wave function is the only way in which the entire Universe can be described in quantum mechanical terms while still being compatible with the general theory of relativity. In the short version of his thesis published in 1957, Everett concluded that his formulation of quantum mechanics “may therefore prove a fruitful framework for the quantization of general relativity.” Although that dream has not yet been fulfilled, it has encouraged a great deal of work by cosmologists since the mid-1980s, when they latched on to the idea. But it does bring with it a lot of baggage.

The universal wave function describes the position of every particle in the Universe at a particular moment in time. But it also describes every possible location of those particles at that instant. And it also describes every possible location of every particle at any other instant of time, although the number of possibilities is restricted by the quantum graininess of space and time. Out of this myriad of possible universes, there will be many versions in which stable stars and planets, and people to live on those planets, cannot exist. But there will be at least some universes resembling our own, more or less accurately, in the way often portrayed in science fiction stories. Or, indeed, in other fiction. Deutsch has pointed out that according to the MWI, any world described in a work of fiction, provided it obeys the laws of physics, really does exist somewhere in the Multiverse. There really is, for example, a “Wuthering Heights” world (but not a “Harry Potter” world).

That isn’t the end of it. The single wave function describes all possible universes at all possible times. But it doesn’t say anything about changing from one state to another. Time does not flow. Sticking close to home, Everett’s parameter, called a state vector, includes a description of a world in which we exist, and all the records of that world’s history, from our memories, to fossils, to light reaching us from distant galaxies, exist. There will also be another universe exactly the same except that the “time step” has been advanced by, say, one second (or one hour, or one year). But there is no suggestion that any universe moves along from one time step to another. There will be a “me” in this second universe, described by the universal wave function, who has all the memories I have at the first instant, plus those corresponding to a further second (or hour, or year, or whatever). But it is impossible to say that these versions of “me” are the same person. Different time states can be ordered in terms of the events they describe, defining the difference between past and future, but they do not change from one state to another. All the states just exist. Time, in the way we are used to thinking of it, does not “flow” in Everett’s MWI.

John Gribbin, described by the Spectator as “one of the finest and most prolific writers of popular science around,” is the author of, among other books, “ In Search of Schrödinger’s Cat ,” “ The Universe: A Biography ,” and “ Six Impossible Things ,” from which this article is excerpted. He is a Visiting Fellow in Astronomy at the University of Sussex, UK.

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Many-Worlds Interpretation of Quantum Mechanics

The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics. The MWI provides a solution to the measurement problem of quantum mechanics.

1. Introduction

2.1 what is “a world”, 2.2 who am i, 3.1 the quantum state of a macroscopic object, 3.2 the quantum state of a world, 3.3 the quantum state of the universe, 3.5 preferred basis, 3.6 the measure of existence, 4.1 probability from uncertainty, 4.2 illusion of probability from post-measurement uncertainty, 4.3 probability postulate from symmetry arguments, 5. tests of the mwi, 6.1 ockham’s razor, 6.2 the problem of preferred basis, 6.3 the wave function is not enough, 6.4 derivation of the probability postulate, 6.5 social behavior of a believer in the mwi, 7. why the mwi, other internet resources, related entries.

The fundamental idea of the MWI, going back to Everett 1957, is that there are myriads of worlds in the Universe in addition to the world we are aware of. In particular, every time a quantum experiment with different possible outcomes is performed, all outcomes are obtained, each in a different newly created world, even if we are only aware of the world with the outcome we have seen. The reader can split the world right now using this interactive quantum world splitter . The creation of worlds takes place everywhere, not just in physics laboratories, for example, the explosion of a star during a supernova.

There are numerous variations and reinterpretations of the original Everett proposal, most of which are briefly discussed in the entry on Everett’s relative state formulation of quantum mechanics . Here, a particular approach to the MWI (which differs from the popular “actual splitting worlds” approach in De Witt 1970) will be presented in detail, followed by a discussion relevant for many variants of the MWI.

The MWI consists of two parts:

A theory which yields the time evolution of the quantum state of the (single) Universe.
A prescription which sets up a correspondence between the quantum state of the Universe and our experiences.

Part (i) states that the ontology of the universe is a quantum state, which evolves according to the Schrödinger equation or its relativistic generalization. It is a rigorous mathematical theory and is not problematic philosophically. Part (ii) involves “our experiences” which do not have a rigorous definition. An additional difficulty in setting up (ii) follows from the fact that human languages were developed at a time when people did not suspect the existence of parallel worlds.

The mathematical part of the MWI, (i), yields less than mathematical parts of some other theories such as Bohmian mechanics. The Schrödinger equation itself does not explain why we experience definite results in quantum measurements. In contrast, in Bohmian mechanics the mathematical part yields almost everything, and the analog of (ii) is very simple: it is the postulate according to which only the “Bohmian positions” (and not the quantum wave) correspond to our experience. The Bohmian positions of all particles yield the familiar picture of the (single) world we are aware of. The simplicity of part (ii) of Bohmian mechanics comes at the price of adding problematic physical features to part (i), e.g., the nonlocal dynamics of Bohmian trajectories.

2. Definitions

A world is the totality of macroscopic objects: stars, cities, people, grains of sand, etc. in a definite classically described state.

The concept of a “world” in the MWI belongs to part (ii) of the theory, i.e., it is not a rigorously defined mathematical entity, but a term defined by us (sentient beings) to describe our experience. When we refer to the “definite classically described state” of, say, a cat, it means that the position and the state (alive, dead, smiling, etc.) of the cat is specified according to our ability to distinguish between the alternatives, and that this specification corresponds to a classical picture, e.g., no superpositions of dead and alive cats are allowed in a single world.

Another concept, which is closer to Everett’s original proposal, see Saunders 1995, is that of a relative, or perspectival world defined for every physical system and every one of its states: following Lewis 1986 we call it a centered world . This concept is useful when a world is centered on a perceptual state of a sentient being. In this world, all objects which the sentient being perceives have definite states, but objects that are not under observation might be in a superposition of different (classical) states. The advantage of a centered world is that a quantum phenomenon in a distant galaxy does not split it, while the advantage of the definition presented here is that we can consider a world without specifying a center; our usual language is just as useful for describing worlds that existed at times when there were no sentient beings.

The concept of a world in the MWI is based on the layman’s conception of a world; however, several features are different. Obviously, the definition of the world as everything that exists does not hold in the MWI. “Everything that exists” is the Universe, and there is only one Universe. The Universe incorporates many worlds similar to the one the layman is familiar with. A layman believes that our present world has a unique past and future. According to the MWI, a world defined at some moment of time corresponds to a unique world at a time in the past, but to a multitude of worlds at a time in the future.

I am an object, such as the Earth, a cat, etc. “I” is defined at a particular time by a complete (classical) description of the state of my body and of my brain. “I” and “Lev” do not refer to the same things (even though my name is Lev). At the present moment there are many different “Lev”s in different worlds (not more than one in each world), but it is meaningless to say that now there is another “I”. I have a particular, well defined past: I correspond to a particular “Lev” in 2020, but not to a particular “Lev” in the future: I correspond to a multitude of “Lev”s in 2030. This correspondence is seen in my memory of a unique past: a “Lev” in 2021 shares memories with one particular “Lev” in 2020 but with multiple “Lev”s in 2030. In the framework of the MWI it is meaningless to ask: Which “Lev” in 2030 will I be? I will correspond to them all. Every time I perform a quantum experiment (with several outcomes) it only seems to me that a single definite result is obtained. Indeed, the “Lev” who obtains this particular result thinks this way. However, this “Lev” cannot be identified as the only “Lev” after the experiment. The “Lev” before the experiment corresponds to multiple “Lev”s who obtain all possible results.

Although this approach to the concept of personal identity seems somewhat unusual, it is plausible in the light of the critique of personal identity by Parfit 1986. Parfit considers some artificial situations in which a person splits into several copies, and argues that there is no good answer to the question: “Which copy is me?” He concludes that personal identity is not what matters when the observer divides. Saunders and Wallace 2008a argue that based on the semantics of Lewis 1986 one can find a meaning for this question. However, in their reply (Saunders and Wallace 2008b) to Tappenden 2008 they emphasise that their work is not about the nature of “I”, but about “serviceability”. Indeed, as it will be explained below, I should behave as if “Which copy is me?” is a legitimate question.

3. Correspondence Between the Formalism and Our Experience

We should not expect to have a detailed and complete explanation of our experience in terms of the wave function of $10^{33}$ particles that we and our immediate environment are made of. We just have to be able to draw a basic picture which is free of paradoxes. There are many attempts to provide an explanation of what we see based on the MWI or its variants in Lockwood 1989, Gell-Mann and Hartle 1990, Albert 1992, Saunders 1993, Penrose 1994, Chalmers 1996, Deutsch 1996, Joos et al. 2003, Schlosshauer 2007, Wallace 2012, Cunningham 2014, Vaidman 2016a, Zurek 2018, Vaidman 2019, and Tappenden 2019a. A sketch of the connection between the wave function of the Universe and our experience follows.

The basis for the correspondence between the quantum state (the wave function) of the Universe and our experience is the description that physicists give in the framework of standard quantum theory for objects composed of elementary particles. Elementary particles of the same kind are identical (see the elaborate discussion in the entry on identity and individuality in quantum theory ). The essence of an object is the (massively entangled) quantum state of its particles and not the particles themselves. One quantum state of a set of elementary particles might be a cat and another state of the same particles might be a small table. An object is a spatial pattern of such a quantum state. Clearly, we cannot now write down an exact wave function of a cat. We know, to a reasonable approximation, the wave function of the elementary particles that constitute a nucleon. The wave function of the electrons and the nucleons that together make up an atom is known with even better precision. The wave functions of molecules (i.e. the wave functions of the ions and electrons out of which molecules are built) are well studied. A lot is known about biological cells, and physicists are making progress in the quantum representation of biological systems Cao et. al 2020. Out of cells we construct various tissues and then the whole body of a cat or a table. So, let us denote the quantum state of a macroscopic object constructed in this way $\ket{\Psi}_\object.$

In our construction $\ket{\Psi}_\object$ represents an object in a definite state and position. According to the definition of a world we have adopted, in each world the cat is in a definite state: either alive or dead. Schrödinger’s experiment with the cat leads to a splitting of worlds even before opening the box. Note that in the centered world approach, the superposed Schrödinger’s cat is a member of the single world of the observer before she opens the sealed box with the cat. The observer directly perceives the facts related to the experiment and deduces that the cat is in a superposition.

Formally, the quantum state of an object which consists of $N$ particles is defined in $3N$ dimensional configuration space, see Albert 1996, 2015. However, in order to understand our experience, it is crucial to make a connection to $3$ dimensional space, see Stoica 2019. We only experience objects defined in $3D$-space. The causes of our experience are interactions, and in nature there are only local interactions in three spatial dimensions. These interactions can be expressed as couplings to some macroscopic variables of the object described by quantum waves well localized in $3D$-space, which are in a product with the relative variables state of the object (like entangled electrons in atoms) and other parts of the object, see Vaidman 2019 (Sec. 5.6). Another way to bridge between the wave function of the object and our experience of that object is the three-dimensional picture of the density of the wave function of molecules of the macroscopic object which has the familiar geometrical form of the object. Note that in some other interpretations of quantum mechanics, similar densities are given additional ontological significance (Allori et al. 2014.)

The wave function of all particles in the Universe corresponding to any particular world will be a product of the states of the sets of particles corresponding to all objects in the world multiplied by the quantum state $\ket{\Phi}$ of all the particles that do not constitute “objects”. Within a world, “objects” have definite macroscopic states by fiat:

The product state is only for variables which are relevant for the macroscopic description of the objects. There might be some entanglement between weakly coupled variables like nuclear spins belonging to different objects. In order to keep the form of the quantum state of the world (1), the quantum state of such variables should belong to $\ket{\Phi}.$

Consider a text-book description of quantum measurements based on the von Neumann 1955 approach according to which each quantum measurement ends up with the collapse of the wave function to the eigenstate of the measured variable. The quantum measurement device must be a macroscopic object with macroscopically different states corresponding to different outcomes. In this case, the MWI all-particles wave function corresponding to a world with a particular outcome is the same as in the von Neumann theory provided there is a collapse to the wave function with this outcome. The von Neumann 1955 analysis helps in understanding the correspondence between the wave function and our perception of the world. However, as Becker 2004 explains, the status of the wave function for von Neumann is not ontological as in the MWI described here, but epistemic: it summarises information about the results of measurements.

In most situations, only macroscopic objects are relevant to our experience. However, today’s technology has reached a point in which interference experiments are performed with single particles. In such situations a description of a world with states of only macroscopic objects, such as sources and detectors, is possible but cumbersome. Hence it is fruitful to add a description of some microscopic objects. Vaidman 2010 argues that the proper way to describe the relevant microscopic particles is by the two-state vector which consists of the usual, forward evolving state specified by the measurement in the past and a backward evolving state specified by the measurement in the future. Such a description provides a simple explanation of the weak trace the particles leave, Vaidman 2013.

The quantum state of the Universe (i.e. the Universal wave function) can be decomposed into a superposition of terms corresponding to different worlds:

Different worlds correspond to different classically described states of at least one object. Different classically described states correspond to orthogonal quantum states. Therefore, different worlds correspond to orthogonal states: all states $\ket{\Psi_{\world\ i}}$ are mutually orthogonal and consequently, $\sum \lvert\alpha_i\rvert^2 = 1$ (here we include as a “world” a situation in which there are no macroscopic objects).

The construction of the quantum state of the Universe in terms of the quantum states of objects presented above is only approximate; it is good only for all practical purposes (FAPP). Indeed, the concept of an object itself has no rigorous definition: should a mouse that a cat just swallowed be considered as a part of the cat? The concept of a “definite position” is also only approximately defined: how far should a cat be displaced for it to be considered to exist in a different position? If the displacement is much smaller than the quantum uncertainty, it must be considered to exist in the same place, because in this case the quantum state of the cat is almost the same and the displacement is undetectable in principle. But this is only an absolute bound, because our ability to distinguish various locations of the cat is far from this quantum limit. Furthermore, the state of an object (e.g. alive or dead) is meaningful only if the object is considered for a period of time. In our construction, however, the quantum state of an object is defined at a particular time. In fact, we have to ensure that the quantum state will have the shape of the object not only at that time, but for some period of time. Splitting of the world during this period of time is another source of ambiguity because there is no precise definition of when the splitting occurs. The time of splitting corresponds to the time of the collapse in the approach given by von Neumann 1955. He provided a very extensive discussion showing that it does not matter when exactly the collapse occurs, and this analysis shows also that it does not matter when the splitting in the MWI occurs.

The reason that it is possible to propose only an approximate prescription for the correspondence between the quantum state of the Universe and our experience is essentially the same reason for the claim of Bell 1990 that “ordinary quantum mechanics is just fine FAPP”. The concepts we use: “object”, “measurement”, etc. are not rigorously defined. Bell and many others were looking (until now in vain) for a “precise quantum mechanics”. Since it is not enough for a physical theory to be just fine FAPP, a quantum mechanics needs rigorous foundations. The MWI has rigorous foundations for (i), the “physics part” of the theory; only part (ii), corresponding to our experience, is approximate (just fine FAPP). But “just fine FAPP” means that the theory explains our experience for any possible experiment, and this is the goal of (ii). See Wallace 2002, 2010a, 2012 for more arguments why a FAPP definition of a world is enough.

The mathematical structure of the theory (i) allows infinitely many ways to decompose the quantum state of the Universe into a superposition of orthogonal states. The basis for the decomposition into world states follows from the definition of a world composed of objects in definite positions and states (“definite” on the scale of our ability to distinguish them). In the alternative approach, the basis of a centered world is defined directly by an observer. Therefore, given the nature of the observer and her concepts for describing the world, the particular choice of the decomposition (2) follows (up to a precision which is good FAPP, as required). If we do not ask why we are what we are, and why the world we perceive is what it is, but only how we can explain relations between the events we observe in our world, then the problem of the preferred basis does not arise: we and the concepts of our world define the preferred basis.

But if we do ask why we are what we are, we can explain more. Looking at the details of the physical world, the structure of the Hamiltonian, the value of the Planck constant, etc., one can understand why the sentient beings we know are of a particular type and why they have their particular concepts for describing their worlds. The main argument is that the locality of interactions yields the stability of worlds in which objects are well localized. The small value of the Planck constant allows macroscopic objects to be well localized for a long period of time. Worlds corresponding to localized quantum states $\ket{\Psi_{\world\ i}}$ do not split for a long enough time such that sentient beings can perceive the locations of macroscopic objects. By contrast, a “world” obtained in another decomposition, e.g., the “world +” which is characterized by the relative phase of a superposition of states of macroscopic objects being in macroscopically distinguishable states $A$ and $B$, $1/\sqrt{2}\,(\ket{\Psi_A} + \ket{\Psi_B})\ket{\Phi},$ splits immediately, during a period of time which is much smaller than the perception time of any feasible sentient being, into two worlds: the new “world+” and the “world$-$”: $1/\sqrt{2}\,(\ket{\Psi_A}-\ket{\Psi_B})\ket{\Phi'}.$ This is the phenomenon of decoherence which has attracted enormous attention in recent years, e.g., Joos et al. 2003, Zurek 2003, Schlosshauer 2007, Wallace 2012, Riedel 2017, Schlosshauer 2019, Boge 2019, Saunders forthcoming-a also in the “decoherent histories” framework of Gell-Mann and Hartle 1990, see Saunders 1995 and Riedel et al. 2016.

There are many worlds existing in parallel in the Universe. Although all worlds are of the same physical size (this might not be true if we take into account the quantum aspects of early cosmology), and in every world sentient beings feel as “real” as in any other world, there is a sense in which some worlds are larger than others. Vaidman 1998 describes this property as the measure of existence of a world.

There are two aspects of the measure of existence of a world. First, it quantifies the ability of the world to interfere with other worlds in a gedanken experiment, as expounded at the end of this section. Second, the measure of existence is the basis for introducing an illusion of probability in the MWI as described in the next chapter. The measure of existence is the parallel of the probability measure discussed in Everett 1957 and pictorially described in Lockwood 1989 (p. 230).

Given the decomposition (2), the measure of existence of the world $i$ is $\mu_i = \lvert \alpha_i\rvert^2.$ It can also be expressed as the expectation value of $\mathbf{P}_i$, the projection operator on the space of quantum states corresponding to the actual values of all physical variables describing the world $i$:

Note, that although the measure of existence of a world is expressed using the quantum state of the Universe (2), the concept of measure of existence, as the concept of a world belongs to part (ii) of the MWI, the bridge to our experience.

“I” also have a measure of existence. It is the sum of the measures of existence of all different worlds in which I exist. Note that I do not directly experience the measure of my existence. I feel the same weight, see the same brightness, etc. irrespectively of how tiny my measure of existence might be.

My current measure of existence is relevant only for gedanken situations like Wigner’s friend Wigner 1961 (recently revived by Frauchiger and Renner 2018) which demonstrates the meaning of the measure of existence of a world as a measure of its ability to interfere with other worlds. If I am a friend of Wigner, a gedanken superpower who can perform interference experiments with macroscopic objects like people, and I perform an experiment with two outcomes A and B such that two worlds will be created with different measures of existence, say $2\mu_{A}= \mu_{B}$, then there is a difference between Lev A and Lev B in how Wigner can affect their future through the interference of worlds. Both Lev A and Lev B consider performing a new experiment with the same device. Wigner can interfere the worlds in such a way that Lev A (the one with a smaller measure of existence) will not have the future with result A of the second experiment. However, Wigner cannot prevent the future result A from Lev B, see Vaidman 1998 (p. 256).

4. Probability in the MWI

The probability in the MWI cannot be introduced in a simple way as in quantum theory with collapse. However, even if there is no probability in the MWI, it is possible to explain our illusion of apparent probabilistic events. Due to the identity of the mathematical counterparts of worlds, we should not expect any difference between our experience in a particular world of the MWI and the experience in a single-world universe with collapse at every quantum measurement.

The difficulty with the concept of probability in a deterministic theory, such as the MWI, is that the only possible meaning for probability is an ignorance probability , but there is no relevant information that an observer who is going to perform a quantum experiment is ignorant about. The quantum state of the Universe at one time specifies the quantum state at all times. If I am going to perform a quantum experiment with two possible outcomes such that standard quantum mechanics predicts probability 1/3 for outcome A and 2/3 for outcome B, then, according to the MWI, both the world with outcome A and the world with outcome B will exist. It is senseless to ask: “What is the probability that I will get A instead of B?” because I will correspond to both “Lev”s: the one who observes A and the other one who observes B.

To solve this difficulty, Albert and Loewer 1988 proposed the Many Minds interpretation (in which the different worlds are only in the minds of sentient beings). In addition to the quantum wave of the Universe, Albert and Loewer postulate that every sentient being has a continuum of minds. Whenever the quantum wave of the Universe develops into a superposition containing states of a sentient being corresponding to different perceptions, the minds of this sentient being evolve randomly and independently to mental states corresponding to these different states of perception (with probabilities equal to the quantum probabilities for these states). In particular, whenever a measurement is performed by an observer, the observer’s minds develop mental states that correspond to perceptions of the different outcomes, i.e. corresponding to the worlds A or B in our example. Since there is a continuum of minds, there will always be an infinity of minds in any sentient being and the procedure can continue indefinitely. This resolves the difficulty: each “I” corresponds to one mind and it ends up in a state corresponding to a world with a particular outcome. However, this solution comes at the price of introducing additional structure into the theory, including a genuinely random process.

Saunders 2010 claims to solve the problem without introducing additional structure into the theory. Working in the Heisenberg picture, he uses appropriate semantics and mereology according to which distinct worlds have no parts in common, not even at early times when the worlds are qualitatively identical. In the terminology of Lewis 1986 (p. 206) we have the divergence of worlds rather than overlap. Wilson 2013, 2020 develops this idea by introducing a framework called “indexicalism”, which involves a set of distinct diverging “parallel” worlds in which each observer is located in only one world and all propositions are construed as self-locating (indexical). In Wilson’s words, “indexicalism” allows us to vindicate treating the weights as a candidate objective probability measure. However, it is not clear how this program can succeed, see Marchildon 2015, Harding 2020, Tappenden 2019a. It is hard to identify diverging worlds in our experience and there is nothing in the mathematical formalism of standard quantum mechanics which can be a counterpart of diverging worlds, see also Kent 2010 (p. 345). In the next section, the measure of existence of worlds is related to subjective ignorance probability.

There are more proposals to deal with the issue of probability in the MWI. Barrett 2017 argues that for a derivation of the Probability Postulate it is necessary to add some assumptions to unitary evolution. For example, Weissman 1999 has proposed a modification of quantum theory with additional non-linear decoherence (and hence with even more worlds than in the standard MWI) which can lead asymptotically to worlds of equal mean measure for different outcomes. Hanson 2003, 2006 proposed decoherence dynamics in which observers of different worlds “mangle” each other such that an approximate Born rule is obtained. Van Wesep 2006 used an algebraic method for deriving the probability rule, whereas Buniy et al. 2006 used the decoherent histories approach of Gell-Mann and Hartle 1990. Waegell and McQueen 2020 considered probability based on the ontology of `local worlds’ introduced by Waegell 2018, which is a concept inspired by the approach of Deutsch and Hayden 2000.

Vaidman 1998 introduced the ignorance probability of an agent in the framework of the MWI in a situation of post-measurement uncertainty, see also Tappenden 2011, Vaidman 2012, Tipler 2014, 2019b, Schwarz 2015. It seems senseless to ask: “What is the probability that Lev in the world $A$ will observe $A$?” This probability is trivially equal to 1. The task is to define the probability in such a way that we could reconstruct the prediction of the standard approach, where the probability for $A$ is 1/3. It is indeed senseless to ask you what is the probability that Lev in the world $A$ will observe $A$, but this might be a meaningful question when addressed to Lev in the world of the outcome $A$. Under normal circumstances, the world $A$ is created (i.e. measuring devices and objects which interact with measuring devices become localized according to the outcome $A)$ before Lev is aware of the result $A$. Then, it is sensible to ask this Lev about his probability of being in world $A$. There is a definite outcome which this Lev will see, but he is ignorant of this outcome at the time of the question. In order to make this point vivid, Vaidman 1998 proposed an experiment in which the experimenter is given a sleeping pill before the experiment. Then, while asleep, he is moved to room $A$ or to room $B$ depending on the results of the experiment. When the experimenter has woken up (in one of the rooms), but before he has opened his eyes, he is asked “In which room are you?” Certainly, there is a matter of fact about which room he is in (he can learn about it by opening his eyes), but he is ignorant about this fact at the time of the question.

This construction provides the ignorance interpretation of probability, but the value of the probability has to be postulated:

Probability Postulate An observer should set his subjective probability of the outcome of a quantum experiment in proportion to the total measure of existence of all worlds with that outcome.

This postulate (named the Born-Vaidman rule by Tappenden 2011) is a counterpart of the collapse postulate of the standard quantum mechanics according to which, after a measurement, the quantum state collapses to a particular branch with probability proportional to its squared amplitude. (See the section on the measurement problem in the entry on philosophical issues in quantum theory .) However, it differs in two aspects. First, it parallels only the second part of the collapse postulate, the Born Rule, and second, it is related only to part (ii) of the MWI, the connection to our experience, and not to the mathematical part of the theory (i).

The question of the probability of obtaining A makes sense for Lev in world A before he becomes aware of the outcome and for Lev in world B before he becomes aware of the outcome. Both “Lev”s have the same information on the basis of which they should give their answer. According to the probability postulate they will give the same answer: 1/3 (the relative measure of existence of the world $A)$. Since Lev before the measurement is associated with two “Lev”s after the measurement who have identical ignorance probability concepts for the outcome of the experiment, one can define the probability of the outcome of the experiment to be performed as the ignorance probability of the successors of Lev for being in a world with a particular outcome.

The “sleeping pill” argument does not reduce the probability of an outcome of a quantum experiment to a familiar concept of probability in the classical context. The quantum situation is genuinely different. Since all outcomes of a quantum experiment are realized, there is no probability in the usual sense. Nevertheless, this construction explains the illusion of probability. It leads believers in the MWI to behave according to the following principle:

Behavior Principle We care about all our successive worlds in proportion to their measures of existence.

With this principle our behavior should be similar to the behavior of a believer in the collapse theory who cares about possible future worlds in proportion to the probability of their occurrence.

The important part of the Probability Postulate is the supervenience of subjective probability on the measure of existence. Given this supervenience, the proportionality follows naturally from the following argument. By the assumption, if after a quantum measurement all the worlds have equal measures of existence, the probability of a particular outcome is simply proportional to the number of worlds with this outcome. The measures of existence of worlds are, in general, not equal, but the experimenters in all the worlds can perform additional specially tailored auxiliary measurements of some variables such that all the new worlds will have equal measures of existence. The experimenters should be completely indifferent to the results of these auxiliary measurements: their only purpose is to split the worlds into “equal-weight” worlds. Then, the additivity of the measure of existence yields the Probability Postulate.

There are many other arguments (apart from the empirical evidence) supporting the Probability Postulate. Gleason’s 1957 theorem about the uniqueness of the probability measure uses a natural principle that the probability of an outcome is independent of splitting into parallel worlds. Tappenden 2000, 2017 adopts a different semantics according to which “I” live in all branches and have “distinct experiences” in different “superslices”. He uses “weight of a superslice” instead of “measure of existence” and argues that it is intelligible to associate probabilities according to the Probability Postulate. Exploiting a variety of ideas in decoherence theory such as the relational theory of tense and theories of identity over time, Saunders 1998 argues for the “identification of probability with the Hilbert Space norm” (which equals the measure of existence). Page 2003 promotes an approach named Mindless Sensationalism . The basic concept in this approach is a conscious experience. He assigns weights to different experiences depending on the quantum state of the universe, as the expectation values of presently-unknown positive operators corresponding to the experiences (similar to the measures of existence of the corresponding worlds). Page writes “… experiences with greater weights exist in some sense more …” (2003, 479). In all of these approaches, the postulate is introduced through an analogy with treatments of time, e.g., the measure of existence of a world is analogous to the duration of a time interval. Note also Greaves 2004 who advocates the “Behavior Principle” on the basis of the decision-theoretic reflection principle related to the next section.

In an ambitious work Deutsch 1999 claimed to derive the Probability Postulate from the quantum formalism and classical decision theory. In Deutsch’s argument the notion of probability is operationalised by being reduced to an agent’s betting preferences. So an agent who is indifferent between receiving $20 on those branches where spin “up” is observed and receiving $10 on all branches by definition is deemed to give probability 1/2 to the spin-up branches. Deutsch then attempts, using some symmetry arguments, to prove that the only rationally coherent strategy for an agent is to assign these operationalised “probabilities” to equal the quantum-mechanical branch weights. Wallace 2003, 2007, 2010b, 2012 developed this approach by making explicit the tacit assumptions in Deutsch’s argument. In the most recent version of these proofs, the central assumptions are (i) the symmetry structure of unitary quantum mechanics; (ii) that an agent’s preferences are consistent across time; (iii) that an agent is indifferent to the fine-grained branching structure of the world per se. Early criticisms of the Deutsch-Wallace approach focussed on circularity concerns (Barnum et al. 2000, Baker 2007, Hemmo and Pitowsky 2007). As the program led to more explicit proofs, criticism turned to the decision-theoretic assumptions being made Lewis 2010, Albert 2010, Kent 2010, Price 2010). The analysis of the Deutsch-Wallace program continues in a flurry of (mostly critical) papers Adlam 2014, Dawid and Thébault 2014, Dawid and Thébault 2015, Dizadji-Bahmani 2015, Jansson 2016, Read 2018, Mandolesi 2018, Mandolesi 2019, Araujo 2019, Brown and Ben Porath 2020, Saunders forthcoming-b.

Zurek 2005 offers a new twist to the Born rule derivation based on the permutation symmetry of states corresponding to worlds with equal measures of existence. He considered entangled systems and relies on “envariance” symmetry: a unitary evolution of a system which can be undone by the unitary evolution of the system it is entangled with. Zurek assumes that a manipulation of the second system does not change the probability of the measurement on the first system. The swap of the states of the system swaps the probabilities of the outcomes, because the outcomes are correlated with the other systems, where nothing has been changed. Since the swaps of the two systems lead to the original state, the probabilities should be unchanged, but they have swapped, so they must be equal.

Sebens and Carroll 2018 provided a proof of the Probability Postulate based on symmetry considerations in the framework of the self-location uncertainty of Vaidman 1998. However Kent 2015 and McQueen and Vaidman 2019 argued that their proof fails because it starts with a meaningless question. The proof considers a situation as in a sleeping pill experiment presented above: I was asleep during a quantum measurement, but unlike the original proposal, there was not any change in my state. I was not moved to different rooms according to the results of the experiment. Still, the question is asked: What is the probability for me to be in a world with a particular outcome? Whether that question can be meaningfully asked depends on whether I have branched. The critics argue that, although there are separate worlds, I have not yet branched and thus the question is not meaningful (at this stage, I am in both worlds). The Sebens and Carroll proof might get off the ground if the program of diverging worlds Saunders 2010, forthcoming-b succeeds. Note also that Dawid and Friederich 2020 criticise Sebens and Carroll 2018 on other grounds.

Vaidman 2012 uses symmetry to derive the Probability Postulate in another way. He starts from a situation which is symmetric in all relevant respects, so all outcomes must have equal probability. To derive the postulate, he assumes relativistic causality which tells us that the probability of an outcome of a measurement in one location cannot be affected by spatially remote manipulations, see McQueen and Vaidman 2019. Vaidman 2020 stresses, however, that relativistic causality of the evolution of the wave function of the Universe is not enough. In addition, we have to postulate the relativistic causality of the subjective experience of an observer within his world.

It has frequently been claimed, e.g. by De Witt 1970, that the MWI is in principle indistinguishable from the ideal collapse theory. This is not so. The collapse leads to effects that do not exist if the MWI is the correct theory. To observe the collapse we would need a super technology which allows for the “undoing” of a quantum experiment, including a reversal of the detection process by macroscopic devices. See Lockwood 1989 (p. 223), Vaidman 1998 (p. 257), and other proposals in Deutsch 1986. These proposals are all for gedanken experiments that cannot be performed with current or any foreseeable future technology. Indeed, in these experiments an interference of different worlds has to be observed. Worlds are different when at least one macroscopic object is in macroscopically distinguishable states. Thus, what is needed is an interference experiment with a macroscopic body. Today there are interference experiments with larger and larger objects (e.g., molecules with 2000 atoms, see Fein et al. 2019), but these objects are still not large enough to be considered “macroscopic”. Such experiments can only refine the constraints on the boundary where the collapse might take place. A decisive experiment should involve the interference of states which differ in a macroscopic number of degrees of freedom: an impossible task for today’s technology. It can be argued, see for example Parrochia 2020, that the burden of an experimental proof lies with the opponents of the MWI, because it is they who claim that there is a new physics beyond the well-tested Schrödinger equation. As the analysis of Schlosshauer 2006 shows, we have no such evidence.

The MWI is wrong if there is a physical process of collapse of the wave function of the Universe to a single-world quantum state. Some ingenious proposals for such a process have been made (see Pearle 1986 and the entry on collapse theories ). These proposals (and Weissman’s 1999 non-linear decoherence idea) have additional observable effects, such as a tiny energy non-conservation, that were tested in several experiments, e.g. Collett et al. 1995, Diosi 2015. The effects were not found and some (but not all!) of these models have been ruled out, see Vinante et al. 2020.

Much of the experimental evidence for quantum mechanics is statistical in nature. Greaves and Myrvold 2010 argued that our experimental data from quantum experiments supports the Probability Postulate of the MWI no less than it supports the Born rule in other approaches to quantum mechanics (see, however, Kent 2010, Albert 2010, and Price 2010 for some criticisms). Barrett and Huttegger 2020 argue that “even an ideal observer under ideal epistemic conditions may never have any empirical evidence whatsoever for believing that the results of one’s quantum-mechanical experiments are randomly determined”. Thus, statistical analysis of quantum experiments should not help us testing the MWI, but we might mention speculative cosmological arguments in support of the MWI by Page 1999, Kragh 2009, Aguirre and Tegmark 2011, and Tipler 2012.

6. Objections to the MWI

Some of the objections to the MWI follow from misinterpretations due to the multitude of various MWIs. The terminology of the MWI can be confusing: “world” is “universe” in Deutsch 1996, while “universe” is “multiverse”. There are two very different approaches with the same name “The Many-Minds Interpretation (MMI)”. The MMI of Albert and Loewer 1988 mentioned above should not be confused with the MMI of Lockwood et al. 1996 (which resembles the approach of Zeh 1981). Further, the MWI in the Heisenberg representation, Deutsch 2002, differs significantly from the MWI presented in the Schrödinger representation (used here). The MWI presented here is very close to Everett’s original proposal, but in the entry on Everett’s relative state formulation of quantum mechanics , as well as in his book, Barrett 1999, uses the name “MWI” for the splitting worlds view publicized by De Witt 1970. This approach has been justly criticized: it has both some kind of collapse (an irreversible splitting of worlds in a preferred basis) and the multitude of worlds. Now we consider some objections in detail.

It seems that the preponderance of opposition to the MWI comes from the introduction of a very large number of worlds that we do not see: this looks like an extreme violation of Ockham’s principle: “Entities are not to be multiplied beyond necessity”. However, in judging physical theories one could reasonably argue that one should not multiply physical laws beyond necessity either (such a version of Ockham’s Razor has been applied in the past), and in this respect the MWI is the most economical theory. Indeed, it has all the laws of the standard quantum theory, but without the collapse postulate, which is the most problematic of the physical laws. The MWI is also more economical than Bohmian mechanics, which has in addition the ontology of the particle trajectories and the laws which give their evolution. Tipler 1986a (p. 208) has presented an effective analogy with the criticism of Copernican theory on the grounds of Ockham’s razor.

One might also consider a possible philosophical advantage of the plurality of worlds in the MWI, similar to that claimed by realists about possible worlds, such as Lewis 1986 (see the discussion of the analogy between the MWI and Lewis’s theory by Skyrms 1976 and Wilson 2020). However, the analogy is not complete: Lewis’ theory considers all logically possible worlds, far more than all the worlds that are incorporated in the quantum state of the Universe.

A common criticism of the MWI stems from the fact that the formalism of quantum theory allows infinitely many ways to decompose the quantum state of the Universe into a superposition of orthogonal states. The question arises: “Why choose the particular decomposition (2) and not any other?” Since other decompositions might lead to a very different picture, the whole construction seems to lack predictive power.

The locality of physical interactions defines the preferred basis. As described in Section 3.5, only localized states of macroscopic objects are stable. And indeed, due to the extensive research on decoherence, the problem of preferred basis is not considered as a serious objection anymore, see Wallace 2010a. Singling out position as a preferred variable for solving the preferred basis problem might be considered as a weakness, but on the other hand, it is implausible that out of a mathematical theory of vectors in Hilbert space one can derive what our world should be. We have to add some ingredients to our theory and adding locality, the property of all known physical interactions, seems to be very natural (in fact, it plays a crucial role in all interpretations). Hemmo and Shenker 2020 also argued that something has to be added to the Hilbert space structure, but viewed the addition of a locality of interaction postulate as the reason that Ockham’s razor does not cut in favour of the MWI. Note, that taking position as a preferred variable is not an ontological claim here, in contrast to the options discussed in the next section.

As mentioned above, the gap between the mathematical formalism of the MWI, namely the wave function of the Universe, and our experience is larger than in other interpretations. This is the reason why many thought that the ontology of the wave function is not enough. Bell 1987 (p.201) felt that either the wave function is not everything, or it is not right. He was looking for a theory with local “beables”. Many followed Bell in search of a “primitive ontology” in 3+1 space-time, see Allori et al. 2014.

A particular reason why the wave function of the Universe cannot be the whole ontology lies in the argument, led by Maudlin 2010, that this is the wrong type of object. The wave function of the Universe (considered to have N particles) is defined in 3N dimensional configuration space, while we need an entity in 3+1 space-time (like the primitive ontology), see discussion by Albert 1996, Lewis 2004, Monton 2006, Ney 2021. Addition of “primitive ontology” to the wave function of the Universe helps us understand our experience, but complicates the mathematical part of the theory. In the framework of the MWI, it is not necessary. The expectation values of the density of each particle in space-time, which is the concept derived from the wave functions corresponding to different worlds, can play the role of “primitive ontology”. Since interactions between particles are local in space, this is what is needed for finding causal connections ending at our experience. The density of particles is gauge independent and also properly transforms between different Lorentz observers such that they all agree upon their experiences. In particular, the explanation of our experience is unaffected by the “narratability failure” problem of Albert 2013: the wave function description might be different for different Lorentz frames, but the description in terms of densities of particles is the same. Note also an alternative approach based on 3+1 space-time by Wallace and Timpson 2010 who, being dissatisfied with the wave function ontology, introduced the formulation of Spacetime State Realism . Recently more works appeared on this subject: Ney and Albert 2013, Myrvold 2015, Gao 2017, Lombardi et al. 2019, Maudlin 2019, Chen 2019, Carroll and Singh 2019. These works show significant difficulties in obtaining our world as emergent from the Universal wave function. This explains the skeptical tone of Everett’s relative-state formulation of quantum mechanics . But, as discussed in Sec.3, the success of the “emergence” program is not crucial: it is enough to find the counterpart of the world we experience in the Universal wave function.

A popular criticism of the MWI in the past, see Belinfante 1975, which was repeated by Putnam 2005, is based on the naive derivation of the probability of an outcome of a quantum experiment as being proportional to the number of worlds with this outcome. Such a derivation leads to the wrong predictions, but accepting the idea of probability being proportional to the measure of existence of a world resolves this problem. Although this involves adding a postulate, we do not complicate the mathematical part (i) of the theory since we do not change the ontology, namely, the wave function. It is a postulate belonging to part (ii), the connection to our experience, and it is a very natural postulate: differences in the mathematical descriptions of worlds are manifest in our experience, see Saunders 1998.

Another criticism related to probability follows from the claim, apparently made by Everett himself and later by many other proponents of the MWI, see De Witt 1970, that the Probability Postulate can be derived just from the formalism of the MWI. Unfortunately, the criticism of this derivation (which might well be correct) is considered to be a criticism of the MWI, see Kent 1990. The recent revival of this claim involving decision theory, Deutsch 1999, 2012, and some other symmetry arguments Zurek 2005, Sebens and Carroll 2018 also encountered strong criticisms (see Section 4.3) which might be perceived as criticisms of the MWI itself. Whereas the MWI may have no advantage over other interpretations insofar as the derivation of the Born rule is concerned, Papineau 2010 argues that it also has no disadvantages.

The issue, named by Wallace 2003 as the “incoherence” probability problem, is arguably the most serious difficulty. How can one talk about probability when all possible outcomes happen? This led Saunders and Wallace 2008a to introduce uncertainty to the MWI, see recent analysis in Saunders forthcoming-b. However, Section 4.2 shows how one can explain the illusion of probability of an observer in a world, while the Universe incorporating all the worlds remains deterministic, see also Vaidman 2014. Albert 2010, 2015 argue that Vaidman’s probability appears too late. Vaidman 2012 and McQueen and Vaidman 2019 answer Albert by viewing the probability as the value of a rational bet on a particular result. The results of the betting of the experimenter are relevant for his successors emerging in different worlds after performing the experiment. Since the experimenter is related to all of his successors and they all have identical rational strategies for betting, then this should also be the strategy of the experimenter before the experiment.

There are claims that a believer in the MWI will behave in an irrational way. One claim is based on the naive argument described in the previous section: a believer who assigns equal probabilities to all different worlds will make equal bets for the outcomes of quantum experiments that have unequal probabilities.

Another claim, Lewis 2000, is related to the strategy of a believer in the MWI who is offered to play a quantum Russian roulette game. The argument is that I, who would not accept an offer to play a classical Russian roulette game, should agree to play the roulette any number of times if the triggering occurs according to the outcome of a quantum experiment. Indeed, at the end, there will be one world in which Lev is a multi-millionaire and in all other worlds there will be no Lev Vaidman alive. Thus, in the future, Lev will be a rich and presumably happy man.

However, adopting the Probability Postulate leads all believers in the MWI to behave according to the Behavior Principle and with this principle our behavior is similar to the behavior of a believer in the collapse theory who cares about possible future worlds according to the probability of their occurrence. I should not agree to play quantum Russian roulette because the measure of existence of worlds with Lev dead will be much larger than the measure of existence of the worlds with a rich and alive Lev. This approach also resolves the puzzle which Wilson 2017 raises concerning The Quantum Doomsday Argument .

Although in most situations the Behavior Principle makes the MWI believer act in the usual way, there are some situations in which a belief in the MWI might cause a change in behaviour. Assume that I am forced to play a game of Russian roulette and given a choice between classical or quantum roulette. If my subjective preference is to ensure the existence of Lev in the future, I should choose a quantum version. However, if I am terribly afraid of dying, I should choose classical roulette which gives me some chance not to die.

Albrecht and Phillips 2014 claim that even a toss of a regular coin splits the world, so there is no need for a quantum splitter, supporting a common view that the splitting of worlds happens very often. Surely, there are many splitting events: every Geiger counter or single-photon detector splits the world, but the frequency of splitting outside a physics laboratory is a complicated physics question. Not every situation leads to a multitude of worlds: this would contradict our ability to predict how our world will look in the near future.

For proponents of the MWI, the main reason for adopting it is that it avoids the collapse of the quantum wave. (Other no-collapse theories are not better than MWI for various reasons, e.g., the nonlocality of Bohmian mechanics, see Brown and Wallace 2005; and the disadvantage of all of them is that they have some additional structure, see Vaidman 2014). The collapse postulate is a physical law that differs from all known physics in two aspects: it is genuinely random and it involves some kind of action at a distance. Note that action at a distance due to collapse is a controversial issue, see the discussion in Vaidman 2016b and Myrvold 2016. According to the collapse postulate the outcome of a quantum experiment is not determined by the initial conditions of the Universe prior to the experiment: only the probabilities are governed by the initial state. There is no experimental evidence in favor of collapse and against the MWI. We need not assume that Nature plays dice: science has stronger explanatory power. The MWI is a deterministic theory for a physical Universe and it explains why a world appears to be indeterministic for human observers.

The MWI does not have action at a distance. The most celebrated example of nonlocality of quantum mechanics given by Bell’s theorem in the context of the Einstein-Podolsky-Rosen argument cannot get off the ground in the framework of the MWI because it requires a single outcome of a quantum experiment, see the discussion in Bacciagaluppi 2002, Brown and Timpson 2016. Although the MWI removes the most bothersome aspect of nonlocality, action at a distance, the other aspect of quantum nonlocality, the nonseparability of remote objects manifested in entanglement, is still there. A “world” is a nonlocal concept. This explains why we observe nonlocal correlations in a particular world.

Deutsch 2012 claims to provide an alternative vindication of quantum locality using a quantum information framework. This approach started with Deutsch and Hayden 2000 analyzing the flow of quantum information using the Heisenberg picture. After discussions by Rubin 2001 and Deutsch 2002, Hewitt-Horsman and Vedral 2007 analyzed the uniqueness of the physical picture of the information flow. Timpson 2005 and Wallace and Timpson 2007 questioned the locality demonstration in this approach and the meaning of the locality claim was clarified in Deutsch 2012. Rubin 2011 suggested that this approach might provide a simpler route toward generalization of the MWI of quantum mechanics to the MWI of field theory. Recent works Raymond-Robichaud 2020, Kuypers and Deutsch 2021, Bédard 2021a, clarified the meaning of the Deutsch and Hayden proposal as an alternative local MWI which not only lacks action at a distance, but provides a set of local descriptions which completely describes the whole physical Universe. However, there is a complexity price. Bédard 2021b argues that “the descriptor of a single qubit has larger dimensionality than the Schrödinger state of the whole network or of the Universe!”

The MWI resolves most, if not all, paradoxes of quantum mechanics (e.g., Schrödinger’s cat), see Vaidman 1994, McQueen and Vaidman 2020. A physical paradox is a phenomenon contradicting our intuition. The laws of physics govern the Universe incorporating all the worlds and this is why, when we limit ourselves to a single world, we may run into a paradox. An example is getting information about a region from where no particle ever came using the interaction-free measurement of Elitzur and Vaidman 1993. Indeed, on the scale of the Universe there is no paradox: in other worlds particles were in that region.

Vaidman 2001 finds it advantageous to think about all worlds together even in analysing a controversial issue of classical probability theory, the Sleeping Beauty problem . Accepting the Probability Postulate reduces the analysis of probability to a calculation of the measures of existence of various worlds. Note, however, that the Quantum Sleeping Beauty problem also became a topic of a hot controversy: Lewis 2007, Papineau and Durà-Vilà 2009, Groisman et al. 2013, Bradley 2011, Wilson 2014, Schwarz 2015.

Strong proponents of the MWI can be found among cosmologists, e.g., Tipler 1986b, Aguirre and Tegmark 2011. In quantum cosmology the MWI allows for discussion of the whole Universe, thereby avoiding the difficulty of the standard interpretation which requires an external observer, see Susskind 2016 for more analysis of the connections between the MWI and cosmology. Bousso and Susskind 2012 argued that even considerations in the framework of string theory lead to the MWI.

Another community where many favor the MWI is that of the researchers in quantum information. In quantum computing, the key issue is the parallel processing performed on the same computer; this is very similar to the basic picture of the MWI. Recently the usefulness of the MWI for explaining the speedup of quantum computation has been questioned: Steane 2003, Duwell 2007, Cuffaro 2012, forthcoming. It is not that the quantum computation cannot be understood without the framework of the MWI; rather, it is just easier to think about quantum algorithms as parallel computations performed in parallel worlds, Deutsch and Jozsa 1992. There is no way to use all the information obtained in all parallel computations — the quantum computer algorithm is a method in which the outcomes of all calculations interfere, yielding the desired result. The cluster-state quantum computer also performs parallel computations, although it is harder to see how we get the final result. The criticism follows from identifying the computational worlds with decoherent worlds. A quantum computing process has no decoherence and the preferred basis is chosen to be the computational basis.

Recent studies suggest that some of the fathers of quantum mechanics held views close to the MWI: Allori et al. 2011 say this about Schrödinger, and Becker 2004 about von Neumann. At the birth of the MWI Wheeler 1957 wrote: “No escape seems possible from this relative state formulation if one wants to have a complete mathematical model for the quantum mechanics …” Since then, the MWI struggled against the Copenhagen interpretation of quantum mechanics , see Byrne 2010, Barrett and Byrne 2012, gaining legitimacy in recent years Deutsch 1996, Bevers 2011, Barrett 2011, Tegmark 2014, Susskind 2016, Zurek 2018 and Brown 2020 in spite of the very diverse opinions in the talks of its 50th anniversary celebration: Oxford 2007, Perimeter 2007, Saunders et al. 2010.

Berenstain 2020 argues that the MWI is the latest example of successive scientific revolutions which forced humans to abandon the prejudice that they occupy a privileged position at the center of the Universe. The heliocentric model of the Solar System, Darwinian evolution and the Special Theory of Relativity follow this pattern. The MWI offers metaphysical neutrality between the perspectives of observers on different branches of the Universal wave function, as opposed to single-world theories which give a privileged perspective on reality to one observer.

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Acknowledgments

I thank Michael Ridley for his work on the new edition of this entry. I am grateful to everybody who has borne with me through endless discussions of the MWI via email, Zoom (and face-to-face in pandemic-free parallel worlds). I acknowledge partial support by grant 2064/19 of the Israel Science Foundation.

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Library of Congress Catalog Data: ISSN 1095-5054

September 1, 2022

12 min read

Black Hole Discovery Helps to Explain Quantum Nature of the Cosmos

New insights from black hole research may elucidate the cosmological event horizon

By Edgar Shaghoulian

Illustration of a black hole with galaxies inside it.

KennBrown/Mondolithic Studios

W here did the universe come from? Where is it headed? Answering these questions requires that we understand physics on two vastly different scales: the cosmological, referring to the realm of galaxy superclusters and the cosmos as a whole, and the quantum—the counterintuitive world of atoms and nuclei.

For much of what we would like to know about the universe, classical cosmology is enough. This field is governed by gravity as dictated by Einstein's general theory of relativity, which doesn't concern itself with atoms and nuclei. But there are special moments in the lifetime of our universe—such as its infancy, when the whole cosmos was the size of an atom—for which this disregard for small-scale physics fails us. To understand these eras, we need a quantum theory of gravity that can describe both the electron circling an atom and Earth moving around the sun. The goal of quantum cosmology is to devise and apply a quantum theory of gravity to the entire universe.

Quantum cosmology is not for the faint of heart. It is the Wild West of theoretical physics, with little more than a handful of observational facts and clues to guide us. Its scope and difficulty have called out to young and ambitious physicists like mythological sirens, only to leave them foundering. But there is a palpable feeling that this time is different and that recent breakthroughs from black hole physics—which also required understanding a regime where quantum mechanics and gravity are equally important—could help us extract some answers in quantum cosmology. The fresh optimism was clear at a recent virtual physics conference I attended, which had a dedicated discussion session about the crossover between the two fields. I expected this event to be sparsely attended, but instead many of the luminaries in physics were there, bursting with ideas and ready to get to work.

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Event Horizons

The first indication that there is any relation between black holes and our universe as a whole is that both manifest “event horizons”—points of no return beyond which two people seemingly fall out of contact forever. A black hole attracts so strongly that at some point even light—the fastest thing in the universe—cannot escape its pull. The boundary where light becomes trapped is thus a spherical event horizon around the center of the black hole.

Credit: Jen Christiansen

Our universe, too, has an event horizon—a fact confirmed by the stunning and unexpected discovery in 1998 that not only is space expanding, but its expansion is accelerating . Whatever is causing this speedup has been called dark energy. The acceleration traps light just as black holes do: as the cosmos expands, regions of space repel one another so strongly that at some point not even light can overcome the separation. This inside-out situation leads to a spherical cosmological event horizon that surrounds us, leaving everything beyond a certain distance in darkness. There is a crucial difference between cosmological and black hole event horizons, however. In a black hole, spacetime is collapsing toward a single point—the singularity. In the universe at large, all of space is uniformly growing, like the surface of a balloon that is being inflated. This means that creatures in faraway galaxies will have their own distinct spherical event horizons, which surround them instead of us. Our current cosmological event horizon is about 16 billion light-years away. As long as this acceleration continues, any light emitted today that is beyond that distance will never reach us. (Cosmologists also speak of a particle horizon, which confusingly is often called a cosmological horizon as well. This refers to the distance beyond which light emitted in the early universe has not yet had time to reach us here on Earth. In our tale, we will be concerned only with the cosmological event horizon, which we will often just call the cosmological horizon. These are unique to universes that accelerate, like ours.)

The similarities between black holes and our universe don't end there. In 1974 Stephen Hawking showed that black holes are not completely black: because of quantum mechanics, they have a temperature and therefore emit matter and radiation, just as all thermal bodies do. This emission, called Hawking radiation, is what causes black holes to eventually evaporate away. It turns out that cosmological horizons also have a temperature and emit matter and radiation because of a very similar effect. But because cosmological horizons surround us and the radiation falls inward, they reabsorb their own emissions and therefore do not evaporate away like black holes.

Hawking's revelation posed a serious problem: if black holes can disappear, so can the information contained within them—which is against the rules of quantum mechanics. This is known as the black hole information paradox, and it is a deep puzzle complicating the quest to combine quantum mechanics and gravity. But in 2019 scientists made dramatic progress. Through a confluence of conceptual and technical advances, physicists argued that the information inside a black hole can actually be accessed from the Hawking radiation that leaves the black hole. (For more on how scientists figured this out, see the article by my colleague Ahmed Almheiri .)

This discovery has reinvigorated those of us studying quantum cosmology. Because of the mathematical similarities between black holes and cosmological horizons, many of us have long believed that we couldn't understand the latter without understanding the former. Figuring out black holes became a warm-up problem—one of the hardest of all time. We haven't fully solved our warm-up problem yet, but now we have a new set of technical tools that provide beautiful insight into the interplay of gravity and quantum mechanics in the presence of black hole event horizons.

Entropy and the Holographic Principle

Part of the recent progress on the black hole information paradox grew out of an idea called the holographic principle, put forward in the 1990s by Gerard 't Hooft of Utrecht University in the Netherlands and Leonard Susskind of Stanford University. The holographic principle states that a theory of quantum gravity that can describe black holes should be formulated not in the ordinary three spatial dimensions that all other physical theories use but instead in two dimensions of space, like a flat piece of paper. The primary argument for this approach is quite simple: a black hole has an entropy—a measure of how much stuff you can stick inside it—that is proportional to the two-dimensional area of its event horizon.

Contrast this with the entropy of a more traditional system—say, a gas in a box. In this case, the entropy is proportional to the three-dimensional volume of the box, not the area. This is natural: you can stick something at every point in space inside the box, so if the volume grows, the entropy grows. But because of the curvature of space within black holes, you can actually increase the volume without affecting the area of the horizon, and this will not affect the entropy! Even though it naively seems you have three dimensions of space to stick stuff in, the black hole entropy formula tells you that you have only two dimensions of space, an area's worth. So the holographic principle says that because of the presence of black holes, quantum gravity should be formulated as a more prosaic nongravitational quantum system in fewer dimensions. At least then the entropies will match.

The idea that space might not be truly three-dimensional is rather compelling, philosophically. At least one dimension of it might be an emergent phenomenon that arises from its deeper nature rather than being explicitly hardwired into the fundamental laws. Physicists who study space now understand that it can emerge from a large collection of simple constituents, similar to other emergent phenomena such as consciousness, which seems to arise from basic neurons and other biological systems.

One of the most exciting aspects of the progress in the black hole information paradox is that it points toward a more general understanding of the holographic principle, which previously had been made precise only in situations very different from our real universe. In the calculations from 2019, however, the way the information inside the black hole is encoded in the Hawking radiation is mathematically analogous to how a gravitational system is encoded in a lower-dimensional nongravitational system according to the holographic principle. And these techniques can be used in situations more like our universe, giving a potential avenue for understanding the holographic principle in the real world. A remarkable fact about cosmological horizons is that they also have an entropy, given by the exact same formula as the one we use for black holes. The physical interpretation of this entropy is much less clear, and many of us hope that applying the new techniques to our universe will shed light on this mystery. If the entropy is measuring how much stuff you can stick beyond the horizon, as with black holes, then we will have a sharp bound on how much stuff there can be in our universe.

Outside Observers

The recent progress on the black hole information paradox suggests that if we collect all the radiation from a black hole as it evaporates, we can access the information that fell inside the black hole. One of the most important conceptual questions in cosmology is whether the same is possible with cosmological event horizons. We think they radiate like black holes, so can we access what is beyond our cosmological event horizon by collecting its radiation? Or is there some other way to reach across the horizon? If not, then most of our vast, rich universe will eventually be lost forever. This is a grim image of our future—we will be left in the dark.

Almost all attempts to get a handle on this question have required physicists to artificially extricate themselves from the accelerating universe and imagine viewing it from the outside. This is a crucial simplifying assumption, and it more closely mimics a black hole, where we can cleanly separate the observer from the system simply by placing the observer far away. But there seems to be no escaping our cosmological horizon; it surrounds us, and it moves if we move, making this problem much more difficult. Yet if we want to apply our new tools from the study of black holes to the problems of cosmology, we must find a way to look at the cosmic horizon from the outside.

There are different ways to construct an outsider view. One of the simplest is to consider a hypothetical auxiliary universe that is quantum-mechanically entangled with our own and investigate whether an observer in the auxiliary universe can access the information in our cosmos, which is beyond the observer's horizon. In work I did with Thomas Hartman and Yikun Jiang, both at Cornell University, we constructed examples of auxiliary universes and other scenarios and showed that the observer can access information beyond the cosmological horizon in the same way that we can access information beyond the black hole horizon. (A complementary paper by Yiming Chen of Princeton University, Victor Gorbenko of EPFL in Switzerland and Juan Maldacena of the Institute for Advanced Study [IAS] in Princeton, N.J., showed similar results.)

But these analyses all have one serious deficiency: when we investigated “our” universe, we used a model universe that is contracting instead of expanding. Such universes are much simpler to describe in the context of quantum cosmology. We don't completely understand why, but it's related to the fact that we can think of the interior of a black hole as a contracting universe where everything is getting squished together. In this way, our newfound understanding of black holes could easily help us study this type of universe.

Even in these simplified situations, we are puzzling our way through some confusing issues. One problem is that it's easy to construct multiple simultaneous outsider views so that each outsider can access the information in the contracting universe. But this means multiple people can reach the same piece of information and manipulate it independently. Quantum mechanics, however, is exacting: not only does it forbid information from being destroyed, it also forbids information from being replicated. This idea is known as the no-cloning theorem, and the multiple outsiders seem to violate it. In a black hole, this isn't a problem, because although there can still be many outsiders, it turns out that no two of them can independently access the same piece of information in the interior. This limit is related to the fact that there is only one black hole and therefore just one event horizon. But in an expanding spacetime, different observers have different horizons. Recent work that Adam Levine of the Massachusetts Institute of Technology and I did together, however, suggests that the same technical tools from the black hole context work to avoid this inconsistency as well.

Toward a Truer Theory

Although there has been exciting progress, so far we have not been able to directly apply what we learned about black hole horizons to the cosmological horizon in our universe because of the differences between these two types of horizons.

The ultimate goal? No outsider view, no contracting universe, no work-arounds: we want a complete quantum theory of our expanding universe, described from our vantage point within the belly of the beast. Many physicists believe our best bet is to come up with a holographic description, meaning one using fewer than the usual three dimensions of space. There are two ways we can do this. The first is to use tools from string theory, which treats the elementary particles of nature as vibrating strings. When we configure this theory in exactly the right way, we can provide a holographic description of certain black hole horizons. We hope to do the same for the cosmological horizon. Many physicists have put a lot of work into this approach, but it has not yet yielded a complete model for an expanding universe like ours.

The other way to divine a holographic description is by looking for clues from the properties that such a description should have. This approach is part of the standard practice of science—use data to construct a theory that reproduces the data and hope it makes novel predictions as well. In this case, however, the data themselves are also theoretical. They are things we can reliably calculate even without a complete understanding of the full theory, just as we can calculate the trajectory of a baseball without using quantum mechanics. The idea works as follows: we calculate various things in classical cosmology, maybe with a little bit of quantum mechanics sprinkled in, but we try to avoid situations where quantum mechanics and gravity are equally important. This forms our theoretical data. For example, Hawking radiation is a piece of theoretical data. And what must be true is that the full, exact theory of quantum cosmology should be able to reproduce this theoretical datum in an appropriate regime, just as quantum mechanics can reproduce the trajectory of a baseball (albeit in a much more complicated way than classical mechanics).

Leading the charge in extracting these theoretical data is a powerful physicist with a preternatural focus on the problems of quantum cosmology: Dionysios Anninos of King's College London has been working on the subject for more than a decade and has provided many clues toward a holographic description. Others around the world have also joined the effort, including Edward Witten of IAS, a figure who has towered over quantum gravity and string theory for decades but who tends to avoid the Wild West of quantum cosmology. With his collaborators Venkatesa Chandrasekaran of IAS, Roberto Longo of the University of Rome Tor Vergata and Geoffrey Penington of the University of California, Berkeley, he is investigating how the inextricable link between an observer and the cosmological horizon affects the mathematical description of quantum cosmology.

Sometimes we are ambitious and try to calculate theoretical data when quantum mechanics and gravity are equally important. Inevitably we have to impose some rule or guess about the behavior of the full, exact theory in such instances. Many of us believe that one of the most important pieces of theoretical data is the amount and pattern of entanglement between constituents of the theory of quantum cosmology. Susskind and I formulated distinct proposals for how to compute these data, and in hundreds of e-mails exchanged during the pandemic, we argued incessantly over which was more reasonable. Earlier work by Eva Silverstein of Stanford, another brilliant physicist with a long track record in quantum cosmology, and her collaborators provides yet another proposal for computing these theoretical data.

The nature of entanglement in quantum cosmology is a work in progress, but it seems clear that nailing it will be an important step toward a holographic description. Such a concrete, calculable theory is what the subject desperately needs, so that we can compare its outputs with the wealth of theoretical data that are accumulating from scientists. Without this theory, we will be stuck at a stage akin to filling out the periodic table of elements without the aid of quantum mechanics to explain its patterns.

There is a rich history of physicists quickly turning to cosmology after learning something novel about black holes. The story has often been the same: we've been defeated and humbled, but after licking our wounds, we've returned to learn more from what black holes have to teach us. In this instance, the depth of what we've realized about black holes and the breadth of interest in quantum cosmology from scientists around the world may tell a different tale.

Edgar Shaghoulian is an assistant professor of physics at the University of California, Santa Cruz. His work focuses on black holes and quantum cosmology.

Scientific American Magazine Vol 327 Issue 3

Structure of Atom
Planks Quantum Theory

Planck's Quantum Theory - Quantization Of Energy

Introduction.

Before learning about Planck’s quantum theory, we need to know a few things.

As progress in the science field was happening, Maxwell’s suggestion about the wave nature of electromagnetic radiation was helpful in explaining phenomena such as interference, diffraction, etc. However, he failed to explain various other observations such as the nature of emission of radiation from hot bodies, photoelectric effect, i.e. ejection of electrons from a metal compound when electromagnetic radiation strikes it, the dependence of heat capacity of solids upon temperature, line spectra of atoms (especially hydrogen).

Black body radiation, recommended videos.

Planck’s quantum theory
Frequently Asked Questions – FAQs

Solids, when heated, emit radiation varying over a wide range of wavelengths. For example: when we heat solid colour, changes continue with a further increase in temperature. This change in colour happens from a lower frequency region to a higher frequency region as the temperature increases. For example, in many cases, it changes from red to blue. An ideal body which can emit and absorb radiation of all frequencies is called a black body. The radiation emitted by such bodies is called black body radiation.

Thus, we can say that variation of frequency for black body radiation depends on the temperature. At a given temperature, the intensity of radiation is found to increase with an increase in the wavelength of radiation which increases to a maximum value and then decreases with an increase in the wavelength. This phenomenon couldn’t be explained with the help of Maxwell’s suggestions. Hence, Planck proposed Planck’s quantum theory to explain this phenomenon.

Black body Radiation

Planck’s Quantum Theory

According to Planck’s quantum theory,

Different atoms and molecules can emit or absorb energy in discrete quantities only. The smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as quantum.
The energy of the radiation absorbed or emitted is directly proportional to the frequency of the radiation.

Meanwhile, the energy of radiation is expressed in terms of frequency as,

E = Energy of the radiation

h = Planck’s constant (6.626×10 –34 J.s)

ν = Frequency of radiation

Interestingly, Planck has also concluded that these were only an aspect of the processes of absorption and emission of radiation. They had nothing to do with the physical reality of the radiation itself. Later in the year 1905, famous German physicist, Albert Einstein also reinterpreted Planck’s theory to further explain the photoelectric effect. He was of the opinion that if some source of light was focused on certain materials, they can eject electrons from the material. Basically, Planck’s work led Einstein in determining that light exists in discrete quanta of energy, or photons.

Frequently Asked Questions on Black Body Radiation

What is a planck curve.

A black body’s energy density between λ and λ + dλ is the energy of a mode E = hc / λ times the density of photon states, times the probability that the mode is filled. This is the famous formula from Planck for a black body’s energy density.

What is Stefan’s law of radiation?

The law of Stefan-Boltzmann states that the overall radiant heat power released from a surface is proportional to its fourth absolute temperature power. The rule only refers to black bodies, imaginary surfaces that collect heat radiation from all events.

How is blackbody radiation produced?

Electromagnetic radiation is produced from all objects according to their temperature. An idealised object that consumes the electromagnetic energy that it comes into contact with is a black body. In a continuous continuum, which then emits thermal radiation according to its temperature.

What is Planck’s constant in simple terms?

The Planck constant compares the sum of energy a photon bears with its electromagnetic wave frequency. It is named after Max Planck, the physicist. In quantum mechanics, it is an essential quantity.

What is Planck’s number?

Planck’s constant is currently calculated by scientists to be 6.62607015 x 10 -34 joule-seconds. In 1900, Planck identified his game-changing constant by describing how the smallest bits of matter release energy in discrete bundles called quanta, essentially placing the “quanta” in quantum mechanics.

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The many-body dynamics of cold atoms and cross-country running

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Newton's third law of motion states that for every action, there is an equal and opposite reaction. The basic physics of running involves someone applying a force to the ground in the opposite direction of their sprint.

For senior Olivia Rosenstein, her cross-country participation provides momentum to her studies as an experimental physicist working with 2D materials, optics, and computational cosmology.

An undergraduate researcher with Professor Richard Fletcher in his Emergent Quantum Matter Group , she is helping to build an erbium-lithium trap for studies of many-body physics and quantum simulation. The group’s focus during this past fall was increasing the trap’s number of erbium atoms and decreasing the atoms’ temperature while preparing the experiment’s next steps.

To this end, Rosenstein helped analyze the behavior of the apparatus’s magnetic fields, perform imaging of the atoms, and develop infrared (IR) optics for future stages of laser cooling, which the group is working on now.

As she wraps up her time at MIT, she also credits her participation on MIT’s Cross Country team as the key to keeping up with her academic and research workload.

“Running is an integral part of my life,” she says. “It brings me joy and peace, and I am far less functional without it. ”

First steps

Rosenstein’s parents — a special education professor and a university director of global education programs — encouraged her to explore a wide range of subjects that included math and science. Her early interest in STEM included the University of Illinois Urbana-Champaign’s Engineering Outreach Society, where engineering students visit local elementary schools.

At Urbana High School, she was a cross-country runner — three-year captain of varsity cross country and track, and a five-time Illinois All-State athlete — whose coach taught advanced placement biology. “He did a lot to introduce me to the physiological processes that drive aerobic adaptation and how runners train,” she recall s.

So, she was leaning toward studying biology and physiology when she was applying to colleges. At first, she wasn’t sure she was “smart enough” for MIT.

“I figured everyone at MIT was probably way too stressed, ultracompetitive, and drowning in psets [problem sets], proposals, and research projects,” she says. But once she had a chance to talk to MIT students, she changed her mind.

“MIT kids work hard not because we’re pressured to, but because we’re excited about solving that nagging pset problem, or we get so engrossed in the lab that we don’t notice an extra hour has passed. I learned that people put a lot of time into their living groups, dance teams, music ensembles, sports, activism, and every pursuit in between. As a prospective student, I got to talk to some future cross-country teammates too, and it was clear that people here truly enjoy spending time together.”

Drawn to physics

As a first year, she was intent on Course 20, but then she found herself especially engaged with class 8.022 (Physics II: Electricity and Magnetism), taught by Professor Daniel Harlow.

“I remember there was one time he guided us to a conclusion with completely logical steps, then proceeded to point out all of the inconsistencies in the theory, and told us that unfortunately we would need relativity and more advanced physics to explain it, so we would all need to take those courses and maybe a couple grad classes and then we could come back satisfied.

“I thought, ‘Well shoot, I guess I have to go to physics grad school now.’ It was mostly a joke at the time, but he successfully piqued my interest.”

She compared the course requirements for bioengineering with physics and found she was more drawn to the physics classes. Plus, her time with remote learning also pushed her toward more hands-on activities.

“I realized I’m happiest when at least some of my work involves having something in front of me.”

The summer of her rising sophomore year, she worked in Professor Brian DeMarco’s lab at the University of Illinois in her hometown of Urbana.

“The group was constructing a trapped ion quantum computing apparatus, and I got to see how physics concepts could be used in practice,” she recalls. “I liked that experimentalists got to combine time studying theory with time building in the lab.”

She followed up with stints in Fletcher’s group, a MISTI internship in France with researcher Rebeca Ribeiro-Palau’s condensed matter lab , and an Undergraduate Research Opportunity Program project working on computational cosmology projects with Professor Mark Vogelsberger's group at the Kavli Institute for Astrophysics and Space Research, reviewing the evolution of galaxies and dark matter halos in self-interacting dark-matter simulations.

By the spring of her junior year, she was especially drawn to doing atomic, molecular, and optical (AMO) experiments experiments in class 8.14 (Experimental Physics II), the second semester of Junior Lab.

“Experimental AMO is a lot of fun because you get to study very interesting physics — things like quantum superposition, using light to slow down atoms, and unexplored theoretical effects — while also building real-world, tangible systems,” she says. “Achieving a MOT [magneto-optical trap] is always an exciting phase in an experiment because you get to see quantum mechanics at work with your own eyes, and it’s the first step towards more complex manipulations of the atoms. Current AMO research will let us test concepts that have never been observed before, adding to what we know about how atoms interact at a fundamental level.”

For the exploratory project, Rosenstein and her lab partner, Nicolas Tanaka, chose to build a MOT for rubidium using JLab’s ColdQuanta MiniMOT kit and laser locking through modulation transfer spectroscopy. The two presented at the class’s poster session to the department and won the annual Edward C. Pickering Award for Outstanding Original Project.

“We wanted the experience working with optics and electronics, as well as to create an experimental setup for future student use,” she says. “We got a little obsessed — at least one of us was in the lab almost every hour it was open for the final two weeks of class. Seeing a cloud of rubidium finally appear on our IR TV screen filled us with excitement, pride, and relief. I got really invested in building the MOT, and felt I could see myself working on projects like this for a long time in the future.”

She added, “I enjoyed the big questions being asked in cosmology, but couldn’t get over how much fun I had in the lab, getting to use my hands. I know some people can’t stand assembling optics, but it’s kind of like Legos for me, and I’m happy to spend an afternoon working on getting the mirror alignment just right and ignoring the outside world.”

As a senior, Rosenstein’s goal is to collect experience in experimental optics and cold atoms in preparation for PhD work. “I’d like to combine my passion for big physics questions and AMO experiments, perhaps working on fundamental physics tests using precision measurement, or tests of many-body physics.”

Simultaneously, she’s wrapping up her cosmology research, finishing a project in partnership with Katelin Schutz at McGill University, where they are testing a model to interpret 21-centimeter radio wave signals from the earliest stages of the universe and inform future telescope measurements. Her goal is to see how well an effective field theory (EFT) model can predict 21cm fields with a limited amount of information.

“The EFT we’re using was originally applied to very large-scale simulations, and we had hoped it would still be effective for a set of smaller simulations, but we found that this is not the case. What we want to know now, then, is how much data the simulation would have to have for the model to work. The research requires a lot of data analysis, finding ways to extract and interpret meaningful trends,” Rosenstein says. “It’s even more exciting knowing that the effects we’re seeing are related to the story of our universe , and the tools we’re developing could be used by astronomers to learn even more.”

After graduation, she will spend her summer as a quantum computing company intern. She will then use her Fulbright award to spend a year at ENS Paris-Saclay before heading to Caltech for her PhD.

Running past a crisis

Rosenstein credits her participation in cross country for getting through the pandemic, which delayed setting foot on MIT’s campus until spring 2021.

“The team did provide my main form of social interaction,” she says. “We were sad we didn’t get to compete, but I ran a time trial that was my fastest mile up to that point, which was a small win.”

In her sophomore year, her 38th-place finish at nationals secured her a spot as a National Collegiate Athletic Association All-American in her first collegiate cross-country season. A stress fracture curtailed her running for a bit until placing 12th as an NCAA DIII All-American. (The women’s team placed seventh overall, and the men’s team won MIT’s first NCAA national title.) When another injury sidelined her, she mentored first-year students as team captain and stayed engaged however she could, while biking and swimming to maintain training. She hopes to keep running in her life.

“Both running and physics deal a lot with delayed gratification: You’re not going to run a personal record every day, and you’re not going to publish a groundbreaking discovery every day. Sometimes you might go months or even years without feeling like you’ve made a big jump in your progress. If you can’t take that, you won’t make it as a runner or as a physicist.

“Maybe that makes it sound like runners and physicists are just grinding away, enduring constant suffering in pursuit of some grand goal. But there’s a secret: It isn’t suffering. Running every day is a privilege and a chance to spend time with friends, getting away from other work. Aligning optics, debugging code, and thinking through complex problems isn’t a day in the life of a masochist, just a satisfying Wednesday afternoon.”

She adds, “Cross country and physics both require a combination of naive optimism and rigorous skepticism. On the one hand, you have to believe you’re fully capable of winning that race or getting those new results, otherwise, you might not try at all. On the other hand, you have to be brutally honest about what it’s going to take because those outcomes won’t happen if you aren’t diligent with your training or if you just assume your experimental setup will work exactly as planned. In all, running and physics both consist of minute daily progress that integrates to a big result, and every infinitesimal segment is worth appreciating.”

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Publisher Correction
Open access
Published: 22 April 2024

Publisher Correction: Reply to: Quantum mechanical rules for observed observers and the consistency of quantum theory

Lídia del Rio ORCID: orcid.org/0000-0002-2445-2701 1 &
Renato Renner ORCID: orcid.org/0000-0001-5044-6113 1

Nature Communications volume 15 , Article number: 3388 ( 2024 ) Cite this article

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Quantum mechanics
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The Original Article was published on 09 April 2024

Correction to: Nature Communications https://doi.org/10.1038/s41467-024-47172-0 , published online 09 April 2024

In this article, the reasoning rule ‘(R) Consistency among agents…” in Theorem 1 should have read: ‘(C) Consistency among agents…’. The original article has been corrected.

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Lídia del Rio & Renato Renner

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Astrophysics research advances understanding of how gamma-ray bursts produce light

by Russ Nelson, University of Alabama in Huntsville

UAH astrophysics research advances understanding of how the light of gamma-ray bursts is produced

Gamma-ray bursts (GRBs) are intense bursts of gamma radiation, typically generating more energy in a few seconds than the sun will produce over its ten-billion-year lifetime. These transient phenomena present one of the most challenging puzzles in astrophysics, dating back to their accidental discovery in 1967 by a nuclear surveillance satellite.

Dr. Jon Hakkila, a researcher from The University of Alabama in Huntsville (UAH), a part of the University of Alabama System, is lead author on a paper in The Astrophysical Journal that promises to shed light on the behavior of these mysterious cosmic powerhouses by focusing on the motion of the jets where these forces originate. The paper is co-authored by UAH alumnus Dr. Timothy Giblin, Dr. Robert Preece and Dr. Geoffrey Pendleton of deciBel Research, Inc.

"Despite being studied for over fifty years, the mechanisms by which GRBs produce light are still unknown, a great mystery of modern astrophysics," Hakkila explains. "Understanding GRBs helps us understand some of the most rapid and powerful light-producing mechanisms that Nature employs. GRBs are so bright, they can be seen over the breadth of the universe, and—because light travels at a finite velocity—they allow us to see back to the earliest times that stars existed."

One reason for the mystery is the inability of theoretical models to provide consistent explanations of GRB characteristics for their light-curve behaviors. In astronomy, a light curve is a graph of the light intensity of a celestial object as a function of time. Studying light curves can yield significant information about the physical processes that produce them, as well as help define the theories about them. No two GRB light curves are identical, and the duration of emission can vary from milliseconds to tens of minutes as a series of energetic pulses.

"Pulses are the basic units of GRB emission," Hakkila says. "They indicate times when a GRB brightens and subsequently fades away. During the time a GRB pulse emits, it undergoes brightness variations that can sometimes occur on very short timescales. The strange thing about these variations is that they are reversible in the same way words like 'rotator' or 'kayak' (palindromes) are reversible.

"It is very hard to understand how this can happen, since time moves in only one direction. The mechanism that produces light in a GRB pulse somehow produces a brightness pattern, then subsequently generates this same pattern in reverse order. That is pretty weird, and it makes GRBs unique."

GRB emission is generally assumed to occur within relativistic jets —powerful streams of radiation and particles—launched from newly-formed black holes.

"In these models, the core of a dying massive star collapses to form a black hole, and material falling into the black hole is torn apart and redirected outward along two opposing beams, or jets," Hakkila notes. "The jet material pointing in our direction is ejected outward at nearly the speed of light. Since the GRB is relatively short-lived, it has always been assumed that the jet remains pointing at us throughout the event. But the time-reversed pulse characteristics have been very hard to explain if they originate from within a nonmoving jet."

To help demystify these characteristics, the paper proposes adding motion to the jet.

"The idea of a laterally-moving jet provides a simple solution by which time-reversed GRB pulse structure can be explained," the researcher says. "As the jet crosses the line-of-sight, an observer will see light produced first by one side of the jet, then the jet center, and finally the other side of the jet. The jet will brighten and then get fainter as the jet center crosses the line-of-sight, and radially-symmetric structure around the jet's core will be seen in reverse order as the jet gets fainter."

The rapid expansion of gamma-ray burst jets, coupled with the motion of the jet's "nozzle" relative to an observer, works to help illuminate the structure of GRB jets.

"Jets must spray material similar to the way a fire hose sprays water," Hakkila says. "The jet behaves more like a fluid than a solid object, and an observer who could see the entire jet would see it as being curved rather than straight. The motion of the nozzle causes light from different parts of the jet to reach us at different times, and this can be used to better understand the mechanism by which the jet produces light, as well as a laboratory for studying the effects of special relativity."

Journal information: Astrophysical Journal

Provided by University of Alabama in Huntsville

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1.2: Quantum Hypothesis Used for Blackbody Radiation Law

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Learning Objectives

To understand how energy is quantized in blackbody radiation

By the late 19th century, many physicists thought their discipline was well on the way to explaining most natural phenomena. They could calculate the motions of material objects using Newton’s laws of classical mechanics, and they could describe the properties of radiant energy using mathematical relationships known as Maxwell’s equations , developed in 1873 by James Clerk Maxwell, a Scottish physicist. The universe appeared to be a simple and orderly place, containing matter, which consisted of particles that had mass and whose location and motion could be accurately described, and electromagnetic radiation, which was viewed as having no mass and whose exact position in space could not be fixed. Thus matter and energy were considered distinct and unrelated phenomena. Soon, however, scientists began to look more closely at a few inconvenient phenomena that could not be explained by the theories available at the time.

One experimental phenomenon that could not be adequately explained by classical physics was blackbody radiation (Figure 1.2.1 ). Attempts to explain or calculate this spectral distribution from classical theory were complete failures. A theory developed by Rayleigh and Jeans predicted that the intensity should go to infinity at short wavelengths. Since the intensity actually drops to zero at short wavelengths, the Rayleigh-Jeans result was called the ultraviolet catastrophe (Figure 1.2.1 dashed line). There was no agreement between theory and experiment in the ultraviolet region of the blackbody spectrum.

Quantizing Electrons in the Radiator

In 1900, the German physicist Max Planck (1858–1947) explained the ultraviolet catastrophe by proposing that the energy of electromagnetic waves is quantized rather than continuous. This means that for each temperature, there is a maximum intensity of radiation that is emitted in a blackbody object, corresponding to the peaks in Figure 1.2.1 , so the intensity does not follow a smooth curve as the temperature increases, as predicted by classical physics. Thus energy could be gained or lost only in integral multiples of some smallest unit of energy, a quantum (the smallest possible unit of energy). Energy can be gained or lost only in integral multiples of a quantum.

Quantization

Although quantization may seem to be an unfamiliar concept, we encounter it frequently in quantum mechanics (hence the name). For example, US money is integral multiples of pennies. Similarly, musical instruments like a piano or a trumpet can produce only certain musical notes, such as C or F sharp. Because these instruments cannot produce a continuous range of frequencies, their frequencies are quantized. It is also similar to going up and down a hill using discrete stair steps rather than being able to move up and down a continuous slope. Your potential energy takes on discrete values as you move from step to step. Even electrical charge is quantized: an ion may have a charge of −1 or −2, but not −1.33 electron charges.

Planck's quantization of energy is described by the his famous equation:

\[ E=h \nu \label{Eq1.2.1} \]

where the proportionality constant $h$ is called Planck’s constant , one of the most accurately known fundamental constants in science

\[h=6.626070040(81) \times 10^{−34}\, J\cdot s \nonumber \]

However, for our purposes, its value to four significant figures is sufficient:

\[h = 6.626 \times 10^{−34} \,J\cdot s \nonumber \]

As the frequency of electromagnetic radiation increases, the magnitude of the associated quantum of radiant energy increases. By assuming that energy can be emitted by an object only in integral multiples of $hν$, Planck devised an equation that fit the experimental data shown in Figure 1.2.1 . We can understand Planck’s explanation of the ultraviolet catastrophe qualitatively as follows: At low temperatures, radiation with only relatively low frequencies is emitted, corresponding to low-energy quanta. As the temperature of an object increases, there is an increased probability of emitting radiation with higher frequencies, corresponding to higher-energy quanta. At any temperature, however, it is simply more probable for an object to lose energy by emitting a large number of lower-energy quanta than a single very high-energy quantum that corresponds to ultraviolet radiation. The result is a maximum in the plot of intensity of emitted radiation versus wavelength, as shown in Figure 1.2.1 , and a shift in the position of the maximum to lower wavelength (higher frequency) with increasing temperature.

At the time he proposed his radical hypothesis, Planck could not explain why energies should be quantized. Initially, his hypothesis explained only one set of experimental data—blackbody radiation. If quantization were observed for a large number of different phenomena, then quantization would become a law. In time, a theory might be developed to explain that law. As things turned out, Planck’s hypothesis was the seed from which modern physics grew.

Max Planck explain the spectral distribution of blackbody radiation as result from oscillations of electrons. Similarly, oscillations of electrons in an antenna produce radio waves. Max Planck concentrated on modeling the oscillating charges that must exist in the oven walls, radiating heat inwards and—in thermodynamic equilibrium—themselves being driven by the radiation field. He found he could account for the observed curve if he required these oscillators not to radiate energy continuously, as the classical theory would demand, but they could only lose or gain energy in chunks, called quanta , of size $h\nu$, for an oscillator of frequency $\nu$ (Equation $\ref{Eq1.2.1} $).

With that assumption, Planck calculated the following formula for the radiation energy density inside the oven:

\[ \begin{align} d\rho(\nu,T) &= \rho_\nu (T) d\nu \\[4pt] &= \dfrac {2 h \nu^3}{c^2} \cdot \dfrac {1 }{\exp \left( \dfrac {h\nu}{k_B T}\right)-1} d\nu \label{Eq2a} \end{align} \]

$\pi = 3.14159$
$h$ = $6.626 \times 10^{-34} J\cdot s$
$c$ = $3.00 \times 10^{8}\, m/s$
$\nu$ = $1/s$
$k_B$ = $1.38 \times 10^{-23} J/K$
$T$ is absolute temperature (in Kelvin)

Planck's radiation energy density (Equation $\ref{Eq2a}$) can also be expressed in terms of wavelength $\lambda$.

\[\rho (\lambda, T) = \dfrac {2 hc^2}{\lambda ^5} \left(\dfrac {1}{ e^{\dfrac {hc}{\lambda k_B T}} - 1}\right) \label{Eq2b} \]

With a wavelength of maximum energy density at:

\[ \lambda_{max}=\frac{hc}{4.965kT} \nonumber \]

Planck's equation (Equation $\ref{Eq2b}$) gave an excellent agreement with the experimental observations for all temperatures (Figure 1.2.2 ).

Max Planck (1858–1947)

Planck made many substantial contributions to theoretical physics, but his fame as a physicist rests primarily on his role as the originator of quantum theory. In addition to being a physicist, Planck was a gifted pianist, who at one time considered music as a career. During the 1930s, Planck felt it was his duty to remain in Germany, despite his open opposition to the policies of the Nazi government.

One of his sons was executed in 1944 for his part in an unsuccessful attempt to assassinate Hitler and bombing during the last weeks of World War II destroyed Planck’s home. After WWII, the major German scientific research organization was renamed the Max Planck Society.

Exercise 1.2.1

Use Equation $\ref{Eq2b}$ to show that the units of $ρ(λ,T)\,dλ$ are $J/m^3$ as expected for an energy density.

The near perfect agreement of this formula with precise experiments (e.g., Figure 1.2.3 ), and the consequent necessity of energy quantization, was the most important advance in physics in the century. His blackbody curve was completely accepted as the correct one: more and more accurate experiments confirmed it time and again, yet the radical nature of the quantum assumption did not sink in. Planck was not too upset—he didn’t believe it either, he saw it as a technical fix that (he hoped) would eventually prove unnecessary.

Part of the problem was that Planck’s route to the formula was long, difficult and implausible—he even made contradictory assumptions at different stages, as Einstein pointed out later. However, the result was correct anyway!

The mathematics implied that the energy given off by a blackbody was not continuous, but given off at certain specific wavelengths, in regular increments. If Planck assumed that the energy of blackbody radiation was in the form

\[E = nh \nu \nonumber \]

where $n$ is an integer, then he could explain what the mathematics represented. This was indeed difficult for Planck to accept, because at the time, there was no reason to presume that the energy should only be radiated at specific frequencies. Nothing in Maxwell’s laws suggested such a thing. It was as if the vibrations of a mass on the end of a spring could only occur at specific energies. Imagine the mass slowly coming to rest due to friction, but not in a continuous manner. Instead, the mass jumps from one fixed quantity of energy to another without passing through the intermediate energies.

To use a different analogy, it is as if what we had always imagined as smooth inclined planes were, in fact, a series of closely spaced steps that only presented the illusion of continuity.

The agreement between Planck’s theory and the experimental observation provided strong evidence that the energy of electron motion in matter is quantized. In the next two sections, we will see that the energy carried by light also is quantized in units of $h \bar {\nu}$. These packets of energy are called “photons.”

Contributors and Attributions

Michael Fowler (Beams Professor, Department of Physics , University of Virginia)

David M. Hanson, Erica Harvey, Robert Sweeney, Theresa Julia Zielinski (" Quantum States of Atoms and Molecules ")

IMAGES

Deriving Planck's Law
PPT
PPT
PLANK"S QUANTUM THEORY
Albert Einstein's Light-Quantum Hypothesis
PPT

VIDEO

Concept of Hypothesis
The Quantum Tapestry Hypothesis Explained Cosmic Interconnectedness
What Is A Hypothesis?
Multiverse? (Many Worlds Interpretation of Quantum Mechanics)
Explain Quantum Theory or Planck's Theory
Simulation Hypothesis 2: How Real Am Eye?

COMMENTS

Physics: The Quantum Hypothesis
The quantum hypothesis, first suggested by Max Planck (1858-1947) in 1900, postulates that light energy can only be emitted and absorbed in discrete bundles called quanta. Planck came up with the idea when attempting to explain blackbody radiation, work that provided the foundation for his quantum theory.
Quantum mechanics
Quantum mechanics is a fundamental theory in physics that describes the behavior of nature at and below the scale of atoms.: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
What Is Quantum Physics?
Quantum physics is the study of matter and energy at the most fundamental level. It aims to uncover the properties and behaviors of the very building blocks of nature. While many quantum experiments examine very small objects, such as electrons and photons, quantum phenomena are all around us, acting on every scale.
Quantum mechanics
Early developments Planck's radiation law. By the end of the 19th century, physicists almost universally accepted the wave theory of light. However, though the ideas of classical physics explain interference and diffraction phenomena relating to the propagation of light, they do not account for the absorption and emission of light. All bodies radiate electromagnetic energy as heat; in fact ...
Introduction to quantum mechanics
The idea of quantum field theory began in the late 1920s with British physicist Paul Dirac, when he attempted to quantize the energy of the electromagnetic field; just like in quantum mechanics the energy of an electron in the hydrogen atom was quantized. Quantization is a procedure for constructing a quantum theory starting from a classical ...
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In 1899, this spark was identified as light-excited electrons (called photoelectrons) leaving the metal's surface by J.J. Thomson (Figure 1.3.1 ). Figure 1.3.1 : The photoelectric effect involves irradiating a metal surface with photons of sufficiently high energy to cause the electrons to be ejected from the metal.
Science Simplified: What Is Quantum Mechanics?
Quantum mechanics is a theory that deals with the most fundamental bits of matter, energy and light and the ways they interact with each other to make up the world. This landmark theory originated in the early 20th century and is finding many real-world applications in the 21st century. Applying quantum mechanics in the laboratory, Argonne ...
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Erwin Schrödinger proposed the quantum mechanical model of the atom, which treats electrons as matter waves. , represents the probability of finding an electron in a given region within the atom. An atomic orbital is defined as the region within an atom that encloses where the electron is likely to be 90% of the time.
21.1 Planck and Quantum Nature of Light
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Initially, his hypothesis explained only one set of experimental data—blackbody radiation. If quantization were observed for a large number of different phenomena, then quantization would become a law. In time, a theory might be developed to explain that law. As things turned out, Planck's hypothesis was the seed from which modern physics grew.
2: The Postulates of Quantum Mechanics
This in turn explains the probabilistic nature of quantum mechanics. The problem with such theories is that these hidden variables must be quite weird: they can change instantly depending on events light-years away3 , thus violating Einstein's theory of special relativity. Many physicists do not like this aspect of hidden variable theories.
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Quantum mechanics questions the fundamental nature of reality
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The Many-Worlds Theory, Explained
The Many-Worlds Theory, Explained. A mind-bending, jargon-free account of the popular interpretation of quantum mechanics. Quantum physics is strange. At least, it is strange to us, because the rules of the quantum world, which govern the way the world works at the level of atoms and subatomic particles (the behavior of light and matter, as the ...
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Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic level. The nature and behavior of matter and energy at that level is sometimes referred to as quantum physics and quantum mechanics.
Many-Worlds Interpretation of Quantum Mechanics
First published Sun Mar 24, 2002; substantive revision Thu Aug 5, 2021. The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory ...
1.2: Quantum Hypothesis Used for Blackbody Radiation Law
Initially, his hypothesis explained only one set of experimental data—blackbody radiation. If quantization were observed for a large number of different phenomena, then quantization would become a law. In time, a theory might be developed to explain that law. As things turned out, Planck's hypothesis was the seed from which modern physics grew.
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Cite this article. del Rio, L., Renner, R. Publisher Correction: Reply to: Quantum mechanical rules for observed observers and the consistency of quantum theory.
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Computer model helps support theory of asteroid Kamo'oalewa as ejecta from the moon. ... a unique analog quantum processor. ... wobbly jets explain blinking gamma ray bursts. Jun 29, 2022.
1.2: Quantum Hypothesis Used for Blackbody Radiation Law
Initially, his hypothesis explained only one set of experimental data—blackbody radiation. If quantization were observed for a large number of different phenomena, then quantization would become a law. In time, a theory might be developed to explain that law. As things turned out, Planck's hypothesis was the seed from which modern physics grew.

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Physics library

Introduction to the quantum mechanical model

Review of Bohr's model of hydrogen

Example 1: Calculating the de Broglie wavelength of an electron

Standing waves

Orbitals and probability density

Shapes of atomic orbitals

Attributions

Additional References

21.1 Planck and Quantum Nature of Light

Teacher Support

Section Key Terms

Tips For Success

Understanding Blackbody Graphs

Planck’s Revolution

Quantization

Worked Example

How does Photon Energy Change with Various Portions of the EM Spectrum?

Practice Problems

Check Your Understanding

2: The Postulates of Quantum Mechanics

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Postulate 5

The Measurement Problem

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1. Introduction

2. Definitions

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Acknowledgments

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