quantum hypothesis means

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. However, we may not be able to detect them easily in larger objects. This may give the wrong impression that quantum phenomena are bizarre or otherworldly. In fact, quantum science closes gaps in our knowledge of physics to give us a more complete picture of our everyday lives.

Quantum discoveries have been incorporated into our foundational understanding of materials, chemistry, biology, and astronomy. These discoveries are a valuable resource for innovation, giving rise to devices such as lasers and transistors, and enabling real progress on technologies once considered purely speculative, such as quantum computers . Physicists are exploring the potential of quantum science to transform our view of gravity and its connection to space and time. Quantum science may even reveal how everything in the universe (or in multiple universes) is connected to everything else through higher dimensions that our senses cannot comprehend.

The Origins of Quantum Physics

The field of quantum physics arose in the late 1800s and early 1900s from a series of experimental observations of atoms that didn't make intuitive sense in the context of classical physics. Among the basic discoveries was the realization that matter and energy can be thought of as discrete packets, or quanta, that have a minimum value associated with them. For example, light of a fixed frequency will deliver energy in quanta called "photons." Each photon at this frequency will have the same amount of energy, and this energy can't be broken down into smaller units. In fact, the word "quantum" has Latin roots and means "how much."

Knowledge of quantum principles transformed our conceptualization of the atom, which consists of a nucleus surrounded by electrons. Early models depicted electrons as particles that orbited the nucleus, much like the way satellites orbit Earth. Modern quantum physics instead understands electrons as being distributed within orbitals, mathematical descriptions that represent the probability of the electrons' existence in more than one location within a given range at any given time. Electrons can jump from one orbital to another as they gain or lose energy, but they cannot be found between orbitals.

Other central concepts helped to establish the foundations of quantum physics:

• Wave-particle duality: This principle dates back to the earliest days of quantum science. It describes the outcomes of experiments that showed that light and matter had the properties of particles or waves, depending on how they were measured. Today, we understand that these different forms of energy are actually neither particle nor wave. They are distinct quantum objects that we cannot easily conceptualize.
• Superposition : This is a term used to describe an object as a combination of multiple possible states at the same time. A superposed object is analogous to a ripple on the surface of a pond that is a combination of two waves overlapping. In a mathematical sense, an object in superposition can be represented by an equation that has more than one solution or outcome.
• Uncertainty principle : This is a mathematical concept that represents a trade-off between complementary points of view. In physics, this means that two properties of an object, such as its position and velocity, cannot both be precisely known at the same time. If we precisely measure the position of an electron, for example, we will be limited in how precisely we can know its speed.
• Entanglement : This is a phenomenon that occurs when two or more objects are connected in such a way that they can be thought of as a single system, even if they are very far apart. The state of one object in that system can't be fully described without information on the state of the other object. Likewise, learning information about one object automatically tells you something about the other and vice versa.

Mathematics and the Probabilistic Nature of Quantum Objects

Because many of the concepts of quantum physics are difficult if not impossible for us to visualize, mathematics is essential to the field. Equations are used to describe or help predict quantum objects and phenomena in ways that are more exact than what our imaginations can conjure.

Mathematics is also necessary to represent the probabilistic nature of quantum phenomena. For example, the position of an electron may not be known exactly. Instead, it may be described as being in a range of possible locations (such as within an orbital), with each location associated with a probability of finding the electron there.

Given their probabilistic nature, quantum objects are often described using mathematical "wave functions," which are solutions to what is known as the Schrödinger equation . Waves in water can be characterized by the changing height of the water as the wave moves past a set point. Similarly, sound waves can be characterized by the changing compression or expansion of air molecules as they move past a point. Wave functions don't track with a physical property in this way. The solutions to the wave functions provide the likelihoods of where an observer might find a particular object over a range of potential options. However, just as a ripple in a pond or a note played on a trumpet are spread out and not confined to one location, quantum objects can also be in multiple places—and take on different states, as in the case of superposition—at once.

Observation of Quantum Objects

The act of observation is a topic of considerable discussion in quantum physics. Early in the field, scientists were baffled to find that simply observing an experiment influenced the outcome. For example, an electron acted like a wave when not observed, but the act of observing it caused the wave to collapse (or, more accurately, "decohere") and the electron to behave instead like a particle. Scientists now appreciate that the term "observation" is misleading in this context, suggesting that consciousness is involved. Instead, "measurement" better describes the effect, in which a change in outcome may be caused by the interaction between the quantum phenomenon and the external environment, including the device used to measure the phenomenon. Even this connection has caveats, though, and a full understanding of the relationship between measurement and outcome is still needed.

The Double-Slit Experiment

Perhaps the most definitive experiment in the field of quantum physics is the double-slit experiment . This experiment, which involves shooting particles such as photons or electrons through a barrier with two slits, was originally used in 1801 to show that light is made up of waves. Since then, numerous incarnations of the experiment have been used to demonstrate that matter can also behave like a wave and to demonstrate the principles of superposition, entanglement, and the observer effect.

The field of quantum science may seem mysterious or illogical, but it describes everything around us, whether we realize it or not. Harnessing the power of quantum physics gives rise to new technologies, both for applications we use today and for those that may be available in the future .

Dive Deeper

Quantum mechanics: Definitions, axioms, and key concepts of quantum physics

Quantum mechanics, or quantum physics, is the body of scientific laws that describe the wacky behavior of photons, electrons and the other subatomic particles that make up the universe.

• How is it different?
• Who developed it?
• Wave-particle duality
• Describing atoms
• Schrödinger's cat
• Quantum entanglement
• Quantum computing
• Quantum mechanics and general relativity

Bibliography

At the smallest scales, the universe behaves very differently than the everyday world we observe around us. Quantum mechanics is the subfield of physics that describes this bizarre behavior of microscopic particles — atoms , electrons, photons and almost everything else in the molecular and submolecular realm.  

Developed during the first half of the 20th century, the results of quantum mechanics are often extremely strange and counterintuitive. However, studying them has allowed physicists to reach a greater understanding about the nature of the universe, and could one day change the way we as humans process information.

How is quantum mechanics different from classical physics?

At the scale of atoms and electrons, many of the equations of classical mechanics , which describe the movement and interactions of things at everyday sizes and speeds, cease to be useful. 

In classical mechanics, objects exist in a specific place at a specific time . In quantum mechanics, objects instead exist in a haze of probability; they have a certain chance of being at point A, another chance of being at point B and so on.

Who developed quantum mechanics?

Unlike Albert Einstein 's famous theory of relativity , which was developed at roughly the same time, the origins of quantum mechanics cannot be attributed to a single scientist. Rather, multiple scientists contributed to a foundation that gradually gained acceptance and experimental verification between the late 1800s and 1930, according to the University of St. Andrews in Scotland . 

In 1900, German physicist Max Planck was trying to explain why objects at specific temperatures, like the 1,470-degree-Fahrenheit (800 degrees Celsius) filament of a light bulb, glowed a specific color — in this case, red, according to the Perimeter Institute . Planck realized that equations used by physicist Ludwig Boltzmann to describe the behavior of gases could be translated into an explanation for this relationship between temperature and color. The problem was that Boltzmann's work relied on the fact that any given gas was made from tiny particles, meaning that light, too, was made from discrete bits. 

This idea flew in the face of ideas about light at the time, when most physicists believed that light was a continuous wave and not a tiny packet. Planck himself didn't believe in either atoms or discrete bits of light, but his concept was given a boost in 1905, when Einstein published a paper, " Concerning an Heuristic Point of View Toward the Emission and Transformation of Light. " 

Einstein envisioned light traveling not as a wave, but as some manner of "energy quanta." This packet of energy, Einstein suggested in his paper, could "be absorbed or generated only as a whole," specifically when an atom "jumps" between quantized vibration rates. This is where the "quantum" part of quantum mechanics comes from.

With this new way to conceive of light, Einstein offered insights into the behavior of nine phenomena in his paper, including the specific colors that Planck described being emitted from a light bulb filament. It also explained how certain colors of light could eject electrons off metal surfaces — a phenomenon known as the photoelectric effect .

What is wave-particle duality?

In quantum mechanics, particles can sometimes exist as waves and sometimes exist as particles. This can be most famously seen in the double-slit experiment, where particles such as electrons are shot at a board with two slits cut into it, behind which sits a screen that lights up when an electron hits it. If the electrons were particles, they would create two bright lines where they had impacted the screen after passing through one or the other of the slits, according to a popular article in Nature .

Instead, when the experiment is conducted, an interference pattern forms on the screen. This pattern of dark and bright bands makes sense only if the electrons are waves, with crests (high points) and troughs (low points), that can interfere with one another. Even when a single electron is shot through the slits at a time, the interference pattern shows up — an effect akin to a single electron interfering with itself. 

In 1924, French physicist Louis de Broglie used the equations of Einstein's theory of special relativity to show that particles can exhibit wave-like characteristics and that waves can exhibit particle-like characteristics — a finding for which he won the Nobel Prize a few years later .

How does quantum mechanics describe atoms?

In the 1910s, Danish physicist Niels Bohr tried to describe the internal structure of atoms using quantum mechanics. By this point, it was known that an atom was made of a heavy, dense, positively charged nucleus surrounded by a swarm of tiny, light, negatively charged electrons. Bohr put the electrons into orbits around the nucleus, like planets in a subatomic solar system , except they could only have certain predefined orbital distances. By jumping from one orbit to another, the atom could receive or emit radiation at specific energies, reflecting their quantum nature.

Shortly afterward, two scientists, working independently and using separate lines of mathematical thinking, created a more complete quantum picture of the atom, according to the American Physical Society . In Germany, physicist Werner Heisenberg accomplished this by developing "matrix mechanics." Austrian-Irish physicist Erwin Schrödinger developed a similar theory called "wave mechanics." Schrödinger showed in 1926 that these two approaches were equivalent.

The Heisenberg-Schrödinger model of the atom, in which each electron acts as a wave around the nucleus of an atom, replaced the earlier Bohr model. In the Heisenberg-Schrödinger model of the atom, electrons obey a "wave function" and occupy "orbitals" rather than orbits. Unlike the circular orbits of the Bohr model, atomic orbitals have a variety of shapes, ranging from spheres to dumbbells to daisies, according to an explanatory website from chemist Jim Clark .

What is the Schrödinger's cat paradox?

Schrödinger's cat is an often-misunderstood thought experiment describing the qualms that some of the early developers of quantum mechanics had with its results. While Bohr and many of his students believed that quantum mechanics suggested that particles don't have well-defined properties until they are observed, Schrödinger and Einstein were unable to believe such a possibility because it would lead to ridiculous conclusions about the nature of reality. 

In 1935, Schrödinger proposed an experiment in which the life or death of a cat would depend on the random flip of a quantum particle, whose state would remain unseen until a box was opened. Schrödinger hoped to show the absurdity of Bohr's ideas with a real-world example that depended on the probabilistic nature of a quantum particle but yielded a nonsensical result.

According to Bohr's interpretation of quantum mechanics, until the box was opened, the cat existed in the impossible dual position of being both alive and dead at the same time. (No actual cat has ever been subjected to this experiment.) Both Schrödinger and Einstein believed that this helped show that quantum mechanics was an incomplete theory and would eventually be superseded by one that accorded with ordinary experience. 

Even today, physicists struggle to explain why subatomic particles can seemingly exist in a superposition of different states, but large structures — like the universe itself — seemingly do not. Proposed tweaks to Schrödinger's equations could help resolve this tension, but so far none have been widely accepted by the scientific community.

What is quantum entanglement?

Schrödinger and Einstein helped highlight another strange result of quantum mechanics that neither could fully fathom. In 1935, Einstein, along with physicists Boris Podolsky and Nathan Rosen, showed that two quantum particles can be set up so that their quantum states would always be correlated with one another, according to the Stanford Encyclopedia of Philosophy . The particles essentially always "knew" about each other's properties. That means that measuring the state of one particle would instantaneously tell you the state of its twin, no matter how far apart they were, a result that Einstein called "spooky action at a distance," but which Schrödinger soon dubbed " entanglement ."

Entanglement has been shown to be one of the most essential aspects of quantum mechanics and occurs in the real world all the time . Researchers frequently conduct experiments using quantum entanglement and the phenomenon is part of the basis for the emerging field of quantum computing .

What is quantum computing?

Unlike classical computers that process data using binary bits, which can be in one of two states — 0 or 1 — quantum computers use particles such as electrons or photons. These quantum bits, or qubits, represent a superposition of both 0 and 1 — meaning they can exist in multiple states at once. 

This superposition enables quantum computers to perform calculations in parallel by processing all states of a qubit at the same time. Furthermore, quantum entanglement allows multiple qubits to share information and interact simultaneously, regardless of the distance between particles.

While quantum superposition and entanglement make the processing potential of quantum computers  much higher than classical computers, the field has a long way to go. Currently, quantum computers are too small, too difficult to maintain and too error-prone to compete with the best classical computers. However, many experts expect this will one day change as the field advances.

Are quantum mechanics and general relativity incompatible?

At the moment, physicists lack a full explanation for all observed particles and forces in the universe, which is often called a theory of everything. Einstein's relativity describes large and massive things, while quantum mechanics describes small and insubstantial things. The two theories are not exactly incompatible, but nobody knows how to make them fit together.

Many researchers have sought a theory of quantum gravity, which would introduce gravity into quantum mechanics and explain everything from the subatomic to the supergalactic realms. There are a great deal of proposals for how to do this, such as inventing a hypothetical quantum particle for gravity called the graviton, but so far, no single theory has been able to fit all observations of objects in our universe. Another popular proposal, string theory, which posits that the most fundamental entities are tiny strings vibrating in many dimensions, has started to become less widely accepted by physicists since little evidence in its favor has been discovered. Other researchers have also worked on theories involving loop quantum gravity , in which both time and space come in discrete, tiny chunks, but so far no one idea has managed to gain a major hold among the physics community.

This article was originally written by Live Science contributor Robert Coolman and was updated by Adam Mann on March 2, 2022. It was updated again by Brandon Specktor on April 29, 2024.

Bow, E. (2019, June 19). A quick quantum history of the light bulb. Inside the Perimeter https://insidetheperimeter.ca/quick-quantum-history-of-the-light-bulb/  

Clark, J. (2021, May). Atomic orbitals . https://www.chemguide.co.uk/atoms/properties/atomorbs.html  

Coolman, R. (2014, September 11). What is classical mechanics? Live Science. https://www.livescience.com/47814-classical-mechanics.html

O'Connor, J. J., & Robertson, E. F. (1996, May). A history of quantum mechanics. https://mathshistory.st-andrews.ac.uk/HistTopics/The_Quantum_age_begins/

Einstein, A. (1905). On a heuristic point of view concerning the production and transformation of light . Annals of Physics. https://einsteinpapers.press.princeton.edu/vol2-trans/100

Mann, A. (2020, February 28) Schrodinger’s cat: The favorite misunderstood pet of quantum mechanics . Live Science. https://www.livescience.com/schrodingers-cat.html

Mann, A. (2019, August 29) What is the theory of everything ? Space.com. https://www.space.com/theory-of-everything-definition.html  

Moskowitz, C. (2012, March 25). Largest molecules yet behave like waves in quantum double-slit experiment . Live Science. https://www.livescience.com/19268-quantum-double-slit-experiment-largest-molecules.html  

Schirber, M. (2019, July 9). What is relativity? Live Science. https://www.livescience.com/32216-what-is-relativity.html

The Nobel Prize (n.d.). Louis de Broglie facts. https://www.nobelprize.org/prizes/physics/1929/broglie/facts/  

Tretkoff, E. (2008, February). This month in physics history: February 1927 Heisenberg’s uncertainty principle . American Physical Society. https://www.aps.org/publications/apsnews/200802/physicshistory.cfm  

Wood, C. (2019, August 27). What is quantum gravity? Space.com. https://www.space.com/quantum-gravity.html  

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Adam Mann is a freelance journalist with over a decade of experience, specializing in astronomy and physics stories. He has a bachelor's degree in astrophysics from UC Berkeley. His work has appeared in the New Yorker, New York Times, National Geographic, Wall Street Journal, Wired, Nature, Science, and many other places. He lives in Oakland, California, where he enjoys riding his bike. 

• Robert Coolman Live Science Contributor

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• Introduction

Basic considerations

Planck’s radiation law.

• Einstein and the photoelectric effect
• Bohr’s theory of the atom
• Scattering of X-rays
• De Broglie’s wave hypothesis
• Schrödinger’s wave mechanics
• Electron spin and antiparticles
• Identical particles and multielectron atoms
• Time-dependent Schrödinger equation
• Axiomatic approach
• Incompatible observables
• Heisenberg uncertainty principle
• Quantum electrodynamics
• The electron: wave or particle?
• Hidden variables
• Paradox of Einstein, Podolsky, and Rosen
• Measurement in quantum mechanics
• Decay of the kaon
• Cesium clock
• A quantum voltage standard

• What is Richard Feynman famous for?
• What did Werner Heisenberg do during World War II?
• What is Werner Heisenberg best known for?
• How did Werner Heisenberg contribute to atomic theory?

quantum mechanics

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• Boston University - The Quantum Mechanical View of the Atom
• Space.com - 10 mind-boggling things you should know about quantum physics
• Energy.gov - Quantum Mechanics
• Chemistry LibreTexts - The Basics of Quantum Mechanics
• Open Library Publishing Platform - Quantum Mechanics
• Internet Encyclopedia of Philosophy - Interpretations of Quantum Mechanics
• Stanford Encyclopedia of Philosophy - Quantum Mechanics
• quantum mechanics - Student Encyclopedia (Ages 11 and up)
• Table Of Contents

quantum mechanics , science dealing with the behaviour of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituents— electrons , protons, neutrons, and other more esoteric particles such as quarks and gluons. These properties include the interactions of the particles with one another and with electromagnetic radiation (i.e., light, X-rays, and gamma rays).

The behaviour of matter and radiation on the atomic scale often seems peculiar, and the consequences of quantum theory are accordingly difficult to understand and to believe. Its concepts frequently conflict with common-sense notions derived from observations of the everyday world. There is no reason, however, why the behaviour of the atomic world should conform to that of the familiar, large-scale world. It is important to realize that quantum mechanics is a branch of physics and that the business of physics is to describe and account for the way the world—on both the large and the small scale—actually is and not how one imagines it or would like it to be.

The study of quantum mechanics is rewarding for several reasons. First, it illustrates the essential methodology of physics. Second, it has been enormously successful in giving correct results in practically every situation to which it has been applied. There is, however, an intriguing paradox . In spite of the overwhelming practical success of quantum mechanics, the foundations of the subject contain unresolved problems—in particular, problems concerning the nature of measurement. An essential feature of quantum mechanics is that it is generally impossible, even in principle, to measure a system without disturbing it; the detailed nature of this disturbance and the exact point at which it occurs are obscure and controversial. Thus, quantum mechanics attracted some of the ablest scientists of the 20th century, and they erected what is perhaps the finest intellectual edifice of the period.

Historical basis of quantum theory

At a fundamental level, both radiation and matter have characteristics of particles and waves . The gradual recognition by scientists that radiation has particle-like properties and that matter has wavelike properties provided the impetus for the development of quantum mechanics. Influenced by Newton, most physicists of the 18th century believed that light consisted of particles, which they called corpuscles. From about 1800, evidence began to accumulate for a wave theory of light. At about this time Thomas Young showed that, if monochromatic light passes through a pair of slits, the two emerging beams interfere, so that a fringe pattern of alternately bright and dark bands appears on a screen. The bands are readily explained by a wave theory of light. According to the theory, a bright band is produced when the crests (and troughs) of the waves from the two slits arrive together at the screen; a dark band is produced when the crest of one wave arrives at the same time as the trough of the other, and the effects of the two light beams cancel. Beginning in 1815, a series of experiments by Augustin-Jean Fresnel of France and others showed that, when a parallel beam of light passes through a single slit, the emerging beam is no longer parallel but starts to diverge; this phenomenon is known as diffraction. Given the wavelength of the light and the geometry of the apparatus (i.e., the separation and widths of the slits and the distance from the slits to the screen), one can use the wave theory to calculate the expected pattern in each case; the theory agrees precisely with the experimental data.

Early developments

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, a body emits radiation at all wavelengths. The energy radiated at different wavelengths is a maximum at a wavelength that depends on the temperature of the body; the hotter the body, the shorter the wavelength for maximum radiation. Attempts to calculate the energy distribution for the radiation from a blackbody using classical ideas were unsuccessful. (A blackbody is a hypothetical ideal body or surface that absorbs and reemits all radiant energy falling on it.) One formula, proposed by Wilhelm Wien of Germany, did not agree with observations at long wavelengths, and another, proposed by Lord Rayleigh (John William Strutt) of England, disagreed with those at short wavelengths.

In 1900 the German theoretical physicist Max Planck made a bold suggestion. He assumed that the radiation energy is emitted, not continuously, but rather in discrete packets called quanta . The energy E of the quantum is related to the frequency ν by E = h ν. The quantity h , now known as Planck’s constant , is a universal constant with the approximate value of 6.62607 × 10 −34 joule∙second. Planck showed that the calculated energy spectrum then agreed with observation over the entire wavelength range.

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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• Published: 22 December 2023

The tangled state of quantum hypothesis testing

• Mario Berta 1 , 2 ,
• Fernando G. S. L. Brandão 3 , 4 ,
• Gilad Gour 5 ,
• Ludovico Lami   ORCID: orcid.org/0000-0003-3290-3557 6 , 7 , 8 ,
• Martin B. Plenio   ORCID: orcid.org/0000-0003-4238-8843 9 ,
• Bartosz Regula   ORCID: orcid.org/0000-0001-7225-071X 10 &
• Marco Tomamichel   ORCID: orcid.org/0000-0001-5410-3329 11 , 12  

Nature Physics volume  20 ,  pages 172–175 ( 2024 ) Cite this article

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Quantum hypothesis testing—the task of distinguishing quantum states—enjoys surprisingly deep connections with the theory of entanglement. Recent findings have reopened the biggest questions in hypothesis testing and reversible entanglement manipulation.

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Department of Computing, Imperial College London, London, UK

Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

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AWS Center for Quantum Computing, Pasadena, CA, USA

Department of Mathematics and Statistics, Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta, Canada

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• Ludovico Lami

Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands

Institute for Theoretical Physics, University of Amsterdam, Amsterdam, The Netherlands

Institut für Theoretische Physik und IQST, Universität Ulm, Ulm, Germany

Martin B. Plenio

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Revision notes for IB Physics

Topic 12: quantum and nuclear physics (hl).

See the guide for this topic.

12.1 – The interaction of matter with radiation

• Einstein proposed that light consists of particles called photons.
• Quantum refers to the smallest discrete amount of something. A photon is a quantum of electromagnetic radiation (light).
• Photons exhibit wave properties under refraction or interference.
• Photons exhibit wave properties under its emission or absorption.
• A photon’s energy (E) is proportional to its frequency (f) and is given by

where h is Planck’s constant, c is the speed of light, and λ is its wavelength (electromagnetic wave).

The photoelectric effect

• Photoelectric effect refers to the emission of electrons from a metal surface as a result of the absorption of electromagnetic wave energy.

• An example of the photoelectric effect on a sample metal surface.

Incident electromagnetic waves with lower frequency have a smaller chance of inducing the photoelectric effect.

• Why does the intensity of light affect the number of ejected electrons?

The number of photons per unit time in the incident light is proportional to the light intensity.

An increase in the intensity of the incident light allows a higher number of photon-electron interactions. Therefore, more electrons are ejected.

• Why is there a minimum frequency below which no electrons are ejected?

There exists a minimum energy below which electrons would not be ejected from the metal. This minimum energy level depends on the metal in use and is called the work function (φ).

Since E=hf, φ=hf0 where f0 is called the threshold frequency.

• How does the frequency of the incident light affect the maximum kinetic energy of the ejected electrons?

The work function corresponds to the potential energy which binds the electron to the nucleus.

Since total energy = potential energy + kinetic energy,

which may be represented on graph by the following

Matter waves

• The De Broglie hypothesis suggests that all matter exhibits wave-like properties. In particular, the momentum of a particle is related to its wavelength where the De Broglie wavelength may be deduced by the following formula

where p is momentum, h is Planck’s constant, λ is wavelength, m is mass, and v is velocity.

• The term “wave-particle duality” refers to matter acting as both waves and particles.

Pair production and pair annihilation

All matters have their antimatter counterparts which resemble their corresponding matter in every way except for the sign of their charge and the direction of their spin.

Pair production

When a high energy photon collides with a nucleus, it makes a pair of electron and positron (electron antimatter) and gives kinetic energy to each particle.

Pair annihilation

When matter collides with its corresponding antimatter, they annihilate one another with the conservation of energy, momentum, and charge.

The positron (+e) collides with the electron (-e), annihilating each other into two photons with exactly opposite directions and the same amount of momentum.

Quantization of angular momentum in the Bohr model for hydrogen

• Bohr developed a model for hydrogen that was able to explain the emission and absorption spectra of hydrogen.
• His model assumed discrete orbital paths in which electrons orbit the nucleus through, the same way planets orbit stars.
• The orbits were quantized in terms of their allowable angular momentum (rotational momentum).

• Therefore, the orbital radii and energies are also quantized.
• The energy of the orbit is the energy required to ionize (remove) an electron and can be given through the following equation in relation to the order of orbit (n)

• When the electrons are excited, they jump to higher energy orbits and eventually drop back down to a more stable orbit by releasing excess energy by the form of light. The energy of the light released is therefore equal to the difference in energy of the two orbits.

The wave function

By quantum physics, all particles do not have a defined position until they are observed. Instead, all particles are described as “a wave function”.

TL;DR : The wave function gives the probability of finding a particle at a given point which is given by the square of the amplitude of the wave function at that location.

The uncertainty principle for energy and time and position and momentum

The Heisenberg uncertainty principle states that

• If the energy state only lasts for a brief period of time, its energy is uncertain.
• Position and momentum cannot be measured simultaneously with precision. The more precisely the position is determined, the less precisely the momentum is known, and vice versa.

Tunnelling, potential barrier and factors affecting tunnelling probability

• Imagine throwing a ball at a wall and having it disappear the instant before making contact and appearing on the other side. The wall remains intact and the ball did not break through it. Believe it or not, there is a finite (if extremely small) probability that this even would occur. This phenomenon is called quantum tunnelling.

• The position of a particle is described as a wave function (see previous section).
• From the graph above, the observable particle is most likely to be at the position where its wave function has the largest amplitude. However, although the amplitude of the wave function will decay exponentially, since the wave function does not reach an amplitude of zero, the wave function can exit the barrier. Once the wave function exits the barrier, its amplitude no longer decays. This means that a particle has a certain probability of bouncing off a barrier and a certain probability of passing through the other side.

• This explains how tunnelling is frequent in nanoscale but negligible at the macroscopic level.

12.2 – Nuclear physics

Rutherford scattering and nuclear radius.

Rutherford’s undergraduate students, Geiger and Marsden, bombarded a sheet of gold foil by alpha particles.

The alpha particles passed through the gold foil in most cases, a small percentage of alpha particles were deflected by small angles of deflection, and an even smaller percentage of alpha particles were deflected by large angles of deflection.

Rutherford thus deduced that the atom consists of a small compact positive nucleus (where alpha particles deflect by large angles) with a majority of volume existing as empty space (where alpha particles pass right through).

Nuclear energy levels

• In the same way electrons can move between discrete energy levels, the nucleus of an atom can too.
• Atoms that decay through gamma decay emit distinct frequencies of gamma rays which correspond to distinct energy levels.

The neutrino

• A neutrino is a type of lepton. Since they have no electrical charge or strong charge, most neutrinos do not react with other particles and pass right through earth with no interaction.
• Neutrinos are produced in many particle decays, such as in beta decay. When a neutron at rest (zero momentum) decays by releasing a proton and an electron, because of the law of conservation of momentum, the resultant products of decay must have a total momentum of zero, which the observed proton and electron clearly does not portray. Therefore, we suggest the presence of another particle to balance the momentum – by the release of an antineutrino (neutrino antimatter). This was confirmed by experimentation.

• Neutrinos were produced in great abundance in the early universe and rarely interact with matter. This may suggest that neutrinos contribute to the total mass of the universe and affects its expansion.

The law of radioactive decay and the decay constant

Apart from half-lives (see topic 7), the activity of radioactive decay can also be shown exponentially by the law of radioactive decay.

• The decay constant (λ) represents the probability of decay of a nucleus per unit time and is dependent on the type of element.

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Quantum Theory

Quantum physics is the field that deals with the research of energy and matter at the most fundamental level. It studies the properties and behaviours of the very building blocks of the Universe. While quantum physics examines subatomic particles, such as electrons, photons, neutrinos, etc., quantum processes are all around us, influencing every scale.

What Is Quantum Theory?

Quantum theory is the foundational theory for explaining subatomic phenomena. The theory basically explains the nature and behaviour of matter and energy on the atomic level. 

Generally, classical physics is often used to explain physical phenomena at a macroscopic level. However, quantum theory takes things further and explains the phenomena that occur at the subatomic level. Quantum theory, along with general relativity , are broad and important fields of physics which offer a new way of looking at the world. 

Development of Quantum Theory

In the early 1900s, a German physicist named Max Planck stated his quantum hypothesis, where he explained that radiation from a sparkling body changed its shades from red to orange to blue when the temperature was increased. This phenomenon was also known as black body radiation.

During his experiments, he found out that energy existed in singular units, just like matter, instead of consistent electromagnetic waves. With this assumption, it was made clear that energy was quantifiable. The discovery of these units was the primary supposition of the quantum hypothesis.

• Later, Planck composed a numerical condition, including a figure to express the individual units of energy. He termed it quanta. With this, he was further able to solidify his assumption about the findings. Planck won the Nobel Prize in Physics for his hypothesis in 1918. However, advancements by different researchers over a thirty-year time span all added to the cutting-edge comprehension of the quantum hypothesis.
• In 1905, Albert Einstein took the theory further by stating that radiation, apart from energy, is quantised in a similar way. He also used the hypothesis to explain the photoelectric effect .
• Louis de Broglie, a French physicist in the year 1924, also suggested that there is no major contrast in the behaviour of matter and energy. At the subatomic level, both can act either as waves or particles. This hypothesis is known as the principle of wave-particle duality .
• Similarly, in the year 1926, an Austrian physicist named Erwin Schrödinger also came up with the partial differential equation for the wave functions of particles. His equation also describes the time evolution of a quantum state.
• Further, as the years progressed, in 1927, Werner Heisenberg suggested that exact, concurrent estimation of two corresponding qualities, for example, the position and force of a subatomic molecule – is unthinkable. This led to the development of the Heisenberg uncertainty principle .

Quantum Theory’s Influence and Applications

After the establishment of the theory in the previous century, many researchers have worked and developed a new iteration of the quantum hypothesis. Some of the popular ones include Niel Bohr’s Copenhagen interpretation and the many-worlds or multi-verse theory. Over a span of thirty years or more, there have been different interpretations of the theory as well.

In any case, today, the principles of quantum theory are being applied in many fields. Quantum mechanics, as such, is used to explain the different features of the universe as well as reveal the individual behaviours of subatomic particles such as protons, electrons, neutrons, photons and others. 

Apart from Physics, quantum mechanics is also used in chemistry, and its application is known as quantum chemistry. Quantum mechanics offers quantitative insight into chemical bonding processes, and most of the calculations performed in modern computational chemistry are based on quantum mechanics.

More significantly, most of the modern technology is based on the quantum theory, where quantum effects are significant.

Some of the other applications of the quantum theory are found in

• Quantum optics
• Quantum computing
• Light-emitting diodes
• Superconducting magnets
• Optical amplifiers and lasers
• Transistors
• Semiconductors
• Magnetic resonance imaging
• Electron microscopy

Frequently Asked Questions on Quantum Theory

Define quantum theory..

Quantum theory is a theory in physics based on the division of radiant energy into finite quanta and is used in a variety of processes requiring energy transfer or transformation on an atomic or molecular scale.

Who developed quantum theory?

The founding father of quantum theory is Max Planck. He received the Nobel Prize in Physics for his work on quanta. Albert Einstein is also regarded as one of the pioneers of quantum theory, as he described light (photons) as packets of energy (quanta) in his theory of the photoelectric effect, for which he won the Nobel Prize in 1921.

Explain Heisenberg’s uncertainty principle.

Heisenberg’s uncertainty principle states it is impossible to know both the position and speed of a particle, such as a photon or an electron, with perfect accuracy; the more we nail down the particle’s position, the less we know about its speed, and vice versa. The principle was proposed by German physicist Werner Heisenberg in 1927.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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4 The Quantum Hypothesis

• Published: September 2017
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Although 1900 ended with the classical physics of Newton and Maxwell reigning supreme, that reign did not last long, and Chapter 4 shows why. The first crack in this edifice was the failure to detect the presence of the ether, the medium that supposedly carried electromagnetic waves. Next was Thomson’s discovery of the electron, proving that atoms, believed to have been indestructible, were not: they had a structure. Yet another new development, the discovery of radioactivity, also could not be explained by classical physics. Nor could it explain the experimental data from blackbody radiation measurements, yet Planck’s peculiar formula involving his quantum hypothesis, did so perfectly. It introduced a new fundamental constant, named for him. And while his quantum hypothesis did not gain any traction for five years, in 1905 Einstein used it to explain the photoelectric effect, which classical electrodynamics had been unable to do.

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Planck’s Hypothesis

Assumptions used:

1. The particles/oscillators near the surface of the blackbody which emits the blackbody radiation can only have discrete values of energy, E n : E n =nhf, where n is a positive interger, f is the frequency of the oscillating particle, h is the Planck’s constant.

• Particles can only have discrete values of energy. Each energy value corresponds to a quantum state of the particle, represented by the corresponding quantum number.

2. In order for a particle to transit from one quantum state to another, the particle has to absorb or emit energy. The difference in the energy between the initial and the final state in the transition must be absorbed or emitted as a SINGLE quantum of energy. Smallest amount of energy involved is when the transition occurs between two adjacent states: E = hf.

• Energy is quantized in steps of hf
• One quanta of energy or radiation is known as a photon

Planck’s Law Of Blackbody Radiation:

$$I \left( v, T \right) dv = \left( \frac{2hv^{3}}{c^{2}} \right) \frac{1}{e^{\frac{hv}{kt}} – 1} dv$$

, where I(ν,T) dν is the amount of energy per unit surface area per unit time per unit solid angle emitted in the frequency range between ν and ν + dν by a black body at temperature T; h is the Planck constant; c is the speed of light in a vacuum; k is the Boltzmann constant; ν is frequency of electromagnetic radiation; and T is the temperature in kelvins. Deriving the momentum of a photon: Using E = pc and E = hf,

$$\begin{eqnarray*} E &=& hf \\ E &=& h \left( \frac{c}{\lambda} \right), \, \text{since} \, f = \frac{c}{\lambda} \end{eqnarray*}$$

Substituting E = pc into $E = h \left(\frac{c}{λ} \right)$:

$$\begin{eqnarray*} h \left( \frac{v}{\lambda} \right) &=& pv \\ p &=& \left( \frac{h}{\lambda} \right) \end{eqnarray*}$$

Back To Quantum Theory Of Light

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Can Thermodynamics Go Quantum?

September 12, 2024

Peter Greenwood for Quanta Magazine

Introduction

The principles of thermodynamics are cornerstones of our understanding of physics. But they were discovered in the era of steam-driven technology, long before anyone dreamed of quantum mechanics. In this episode, the theoretical physicist Nicole Yunger Halpern talks to host Steven Strogatz about how physicists today are reinterpreting concepts such as work, energy and information for a quantum world.

Listen on  Apple Podcasts ,  Spotify ,  TuneIn  or your favorite podcasting app, or you can stream it from  Quanta .

[Theme plays]

STEVEN STROGATZ: In the mid-1800s, engineers were grappling with questions at the forefront of the Industrial Revolution: how to convert steam into mechanical work, translate rushing streams into electrical energy or pump water out of mines. Their inquiries and observations built the groundwork of a new science: thermodynamics.

By the early 1900s, we had not one, but three laws of thermodynamics. These laws have since become ubiquitous and proven fundamental to our understanding of physics in everyday life. But as our knowledge of the physical world continues to grow, the limits of these old mechanical notions become more apparent — especially as we approach the quantum scale.

I’m Steve Strogatz, and this is “The Joy of Why,” a podcast from Quanta Magazine where I take turns at the mic with my cohost, Janna Levin , exploring the biggest unanswered questions in math and science today.

In this episode, we’re going to ask, what do concepts like work and heat mean on an atomic or even subatomic level? And can our laws of thermodynamics be reinterpreted in quantum terms?

[Theme fades out]

We’re joined by Nicole Yunger Halpern. She is a theoretical physicist at the National Institute of Standards and Technology and an adjunct assistant professor at the University of Maryland. Her research lies at the intersection of quantum physics, information processing and thermodynamics. She’s also the author of an award-winning book, Quantum Steampunk: The Physics of Yesterday’s Tomorrow .

Nicole, it’s a great pleasure to have you with us on “The Joy of Why.”

NICOLE YUNGER HALPERN: It’s a delight to be here. Thanks for having me.

STROGATZ: Well, thank you for joining us. I really am excited about this. I was just asking my wife on the drive over to the studio about the word “steampunk.” I have to admit that I’m not familiar with this. She mentioned to me that even jewelry can be done in steampunk style.

YUNGER HALPERN: Steampunk comes up in costumes and conventions and jewelry and film, in books and short stories all over the place. It’s combines the aesthetic of the 1800s. So the Victorian-era people in waistcoats and petticoats and top hats, and also the American wild, wild west and Beijing, Japan, as well as futuristic technologies.

STROGATZ: Huh, excellent. Well, it’s a very intriguing title, Quantum Steampunk . I hope our listeners will check out the book.

So let’s start talking about the Victorian era and the thermodynamics ideas that grew out of that. We now think of it as classical thermodynamics, and I mentioned the laws of thermodynamics. There are so many things to unpack — the three laws, ideas like work, heat, energy, entropy, efficiency. Take us through some of those ideas, at least, to start with.

YUNGER HALPERN: Thermodynamics is something that we all have a sense of, but maybe we kind of take it for granted. And maybe that’s because thermodynamics is so general. It’s the study of energy, period. The forms that energy can be in and the transformations amongst those forms.

Energy can be transmitted in the form of heat and in the form of work. Work is coordinated, directed energy that can be directly harnessed to do something useful, like power a factory or charge a battery.

Heat is random, uncoordinated energy. It’s the energy of particles jiggling about randomly. Heat engines turn this random heat into coordinated, useful work.

And heat and work feature in the laws of thermodynamics. The number has been growing a bit, depending on whom you ask. There might be three, there might be four, there might be five.

The zeroth law of thermodynamics was actually developed after the first three, but people thought it was so important that it should be given precedence. And so it tells us that there are thermometers. Suppose that you have a cup of tea and I have a cup of tea. We want to be able to compare their temperatures. How can we do that? We can do it using a thermometer.

The first law tells us that the total amount of energy in the world remains constant. The second law tells us that the entropy of a closed, isolated system remains constant or increases only, at least on average. And the third law tells us that you can’t actually cool any system down to the lowest conceivable temperature, absolute zero — zero Kelvin — in any finite number of steps. So that is a very brief history of thermodynamics.

STROGATZ: Excellent. Great. That is a good summary. The second law always feels to me like the really deep one.

YUNGER HALPERN: Yes.

STROGATZ: Right? I mean, the concept of entropy, it’s often phrased as some measure of disorder in a system. Do you want to talk to us about entropy just for a minute?

YUNGER HALPERN: Sure, I think of entropy as a measure of uncertainty . And all sorts of things can have entropies associated with them. For instance, the weather on any given day in the Boston area is extremely random. It could be sunny or rainy or cloudy or snowy. And suppose that we learn on some given day what the weather is. So we’ve learned some amount of information and the amount of information we learn can be seen as an entropic quantity. And then suppose that we average this amount of information that we learn over all of the days. That’s another entropic quantity, a pretty common one.

And we can translate the story into thermodynamics by saying we have physicists’ favorite thermodynamic system — a classical gas in a box. And suppose that we know only large-scale properties of a gas, like the total number of particles and the volume. There are lots of different microstates or configurations associated that are consistent with this large-scale macro state. By a microstate, I mean a list of all of the particles’ positions, all of their momentum, and maybe some other properties, depending on what sorts of particles we have.

So, if we know just these large-scale properties, how ignorant are we about the microstates? And that’s essentially the thermodynamic entropy.

STROGATZ: It’s amazing, this idea of the gas in a box. Because it’s true, that is the universal example. And I’m actually, at this very moment, sitting in a box called a studio. The door is closed. There is gas in here. It’s the air around me.

YUNGER HALPERN: I’m very glad.

STROGATZ: I mean, as far as I can tell. Now, I suppose it’s conceivable that all the air molecules could spontaneously go into the corner, and you might hear me gasping. But that would be a very rare event.

Would that be a state, if all the molecules were in the corner? That would be, what? Very low entropy, I suppose?

YUNGER HALPERN: Right, so there’s a lot of debate, especially in the philosophical community, about how to define thermodynamic entropy. But the way that we’re often taught to reason in statistical physics classes, we would say tend to say, yes, the state in which the particles are all clumped together in the corner of the box is indeed a low-entropy state.

STROGATZ: There’s a concept that comes up a lot: equilibrium. Can you remind us, what does that mean? Like when we speak of a system being at thermodynamic equilibrium, what is that? Why does it matter?

YUNGER HALPERN: Equilibrium is a rather quiet state of a system. It’s a state in which large-scale properties like the total temperature and total volume remain approximately constant over time, and there’s no net flow of anything like heat or particles into or out of the system.

So suppose that we have had a hot cup of tea. We have let it sit on the counter for a long time. It has come to have the same temperature as the rest of the room, and a little bit of the water has evaporated away. At this point, the tea is at thermal equilibrium with its environment.

STROGATZ: And so it always seems kind of like an artificial thing that happens in a chemistry lab or in this famous tea cooling off on the kitchen counter. Whereas in real life, you know, I’m eating food all day long, it seems — just had a cookie before coming to the studio. I can’t relate to thermodynamic equilibrium very well. Is that fair to say? In our everyday life, what things are at equilibrium and what things are not?

YUNGER HALPERN: A great deal in our lives, including life itself, as you point out, is far out of equilibrium.

Organisms keep themselves far out of equilibrium by doing just what you said, by eating so that they consume energy in a well-organized form and expel it in a very highly entropic form. So you radiate lots of heat. This helps keep us far out of equilibrium.

If you have run a bath and let it sit around too long, you might have experienced equilibrium unpleasantly. Or made a cup of coffee and gotten distracted by your work, so that you end up having to drink cold coffee, you might have experienced equilibrium.

STROGATZ: I see. So it does seem like a sort of final state. It’s like after everything settles down. There’s no drive for anything to change anymore, it sounds like.

YUNGER HALPERN: Exactly, there is no drive.

STROGATZ: So when you mentioned the different laws of thermodynamics, what kinds of systems do the laws apply to? What other caveats do we need to make about those systems in order for the laws to apply?

YUNGER HALPERN: Well, the laws of thermodynamics were originally formulated by people who had in mind large classical systems. They didn’t necessarily think of these systems as consisting of many, many particles. The theory of atomism was not entirely accepted by the Victorian era. But they were thinking of systems that, at least now we will all acknowledge, consist of lots and lots of particles.

Around the turn of the 20th century, people discovered Brownian motion, which is random jiggling of particles that’s observable with a microscope, and it led people to accept very broadly that, in fact, materials do consist of very small particles. They jiggle around randomly, and occasional jiggling in the wrong direction led to some minor changes in at least the second law of thermodynamics.

But what’s really surprising to me is that the laws of thermodynamics seem to be going strong, even though we’ve learned a great deal since even the turn of the 20th century about small systems, biological systems, chemical systems and even quantum systems.

STROGATZ: Well, so we’ve been talking so far from the point of view of these particles that you keep mentioning — the atoms or molecules — systems made up of enormous numbers.

But now we’re going to start to get into the quantum aspects of thermodynamics with you. Is the main novelty conceptually the idea that we have just very few particles now? Or is it that we’re using quantum ideas instead of classical ideas?

YUNGER HALPERN: I see quantum thermodynamics as involving the extension of conventional thermodynamics to small systems, quantum systems and far-from-equilibrium systems.

Although not all these categories have been addressed only by quantum thermodynamicists. For instance, there was a lot of really amazing work done in far-from-equilibrium statistical mechanics during the 20th century in the field of non-equilibrium statistical mechanics, which is kind of adjacent to and admired by and friends with quantum thermodynamics.

STROGATZ: Interesting. So if I heard you right, you said there are going to be three kinds of things to think about: far-from-equilibrium, quantum and small numbers. All three of those we could think of as at the edge of what was traditional thermodynamics. By traditional, I mean like the subject that [Josiah Willard] Gibbs and [James Clerk] Maxwell and people like that helped develop in the late 1800s. They didn’t have the math or the physical concepts to really handle small systems, far-from-equilibrium systems, or they wouldn’t have even known about quantum systems at that point.

YUNGER HALPERN: That’s a good way of putting it.

STROGATZ: I’m surprised by your answer. It’s interesting. I thought you would just say quantum, but you’ll deal with large numbers. But so you can allow for small systems, too.

YUNGER HALPERN: One of the reasons is, suppose that we want to address quantum thermodynamics. That is complicated to do, so it can be simpler to make a model that is amenable to small systems, solve some problems using this model, and after you’ve solved those problems, you know, add in some more quantum features — like coherences, which sometimes I describe as the wavelike nature of quantum particles.

And this is, in fact, what happened a number of years ago in the intersection of quantum thermodynamics and quantum information theory. Some colleagues of mine created a model for certain systems. They wanted for this model to describe quantum thermodynamic systems. But just solving the classical version of the small-scale problem was complicated enough. After that problem was solved, then people could make progress on the really quantum features. So the classical small-scale system problem was in service of the quantum thermodynamics.

STROGATZ: Hmm, alright, so we have a lot to discuss here. [laughing] I’m a bit daunted because it’s conceptually very rich and feels to me very new.

YUNGER HALPERN: The recent wave of quantum thermodynamics that has become widely accepted as a subfield is very new. There’s been this trend over the past 10 to 15 years in which quantum thermodynamics has grown a great deal.

Quantum thermodynamics first started being thought about during the 1930s. A quantum engine was proposed in the 1950s and ’60s. There was work in the ’80s. But these pieces of work were not always accepted by the wider community, and quantum thermodynamics itself was sometimes called an oxymoron, because thermodynamics was developed for large classical systems, so people just couldn’t understand what it could possibly have to say about quantum systems.

But in the early 2010s or so, as I was starting my graduate work, quantum thermodynamics started to grow a great deal, I think for two reasons. First, the field of quantum information science had matured in the early 2000s, and we could use it as a mathematical, conceptual and experimental toolkit for understanding quantum systems through how they store and process information. We could use those tools in quantum thermodynamics.

And second, some people managed to secure a very large grant for quantum thermodynamics. And so over the past 10 to 15 years, quantum thermodynamics has really boomed, and I think that’s why it feels so new.

STROGATZ: Well, let’s unpack some of the words that you’ve been using here. We keep saying “quantum,” but maybe we should just offer a quick reminder of what are some of the key features that distinguish quantum phenomena or quantum systems we keep speaking of from classical systems. Like, what’s the hallmark of something being fundamentally quantum mechanical?

YUNGER HALPERN: Some features are, quantum systems tend to be small. They can have wavelike and particle-like natures. They can be disturbed a great deal by measurement in a way that classical systems aren’t. They can entangle with each other, [and] so form very strong relationships, which lead to really strong correlations. A quantum particle can have only certain amounts of energy, not absolutely any possible amount of energy from zero on upward.

STROGATZ: Yeah, that’s really where the word came from, isn’t it?

YUNGER HALPERN: Right, “quantum” literally means a small packet of something. And so an atom, say, can receive quanta of energy, and so jump between kind of rungs on their energy ladder to go from one discrete amount of energy to another discrete amount of energy.

STROGATZ: Yeah, it’s all very deep and mysterious. Is it fair to say that we discovered quantum ideas in the context of physics originally, in the quanta of quantized energy levels in atoms, but really, quantum ideas are more general than physics. For instance, could quantum theory be a kind of generalization of probability theory and information theory, divorced from applications to atoms?

YUNGER HALPERN: Quantum information science indeed has spread into computer science and mathematics and engineering, and it’s also inherently in chemistry.

I think of quantum information science in two ways. On the one hand, I think of quantum information science as, as I mentioned, a mathematical, conceptual and experimental toolkit for understanding quantum systems through how they store and process information, such as these strong correlations that I mentioned earlier — entanglement. And on the other hand, I think of quantum information science as the study of how we can use quantum phenomena, like disturbance by measurement, to process information — so solve computational problems, secure information, communicate information and so on — in ways that are impossible if we have just classical technologies.

STROGATZ: One of the ideas that I ran across while preparing to talk to you struck me as pretty mind-blowing, and I’m hoping you can help enlighten me and our listeners about it, was the relationship between information and work. That work can sometimes be done by changing the amount of information in a system? Am I getting that right? That, like, erasing information is tantamount to doing work, or something like that?

YUNGER HALPERN: So, work is a resource in thermodynamics because if we have work, then we can push a rock up a hill, or charge a battery, or power a car. Just as there are thermodynamic tasks, like charging batteries, there are information-processing tasks like storing information and solving computational problems.

And in information theory, information is a resource. What I find really interesting is that information can also serve as a resource in thermodynamics. If we have information and heat, we can kind of combine those to obtain work, which we could use to, say, power a car. And also the reverse is true. Work can be a resource in information processing.

You mentioned erasure. So suppose that you did a calculation and you’ve filled up a whole piece of scrap paper and now I need to do a calculation. I need scrap paper. And suppose you hand your calculation to me. I don’t know what your handwriting looks like, so it might be beautiful, so no offense — suppose it’s just really bad handwriting, so I can’t read anything.

[Both laugh]

YUNGER HALPERN: Then, I need to erase that information in order to have useful scrap paper for performing my computation. That erasure process is going to cost thermodynamic work. There’s a fundamental limit, a fundamental lower bound, on the amount of work required to erase information. So both information and work can serve as resources in both thermodynamics and information processing.

STROGATZ: Isn’t there some way of thinking about the relation between information and work by thinking about our old friend, the box filled with gas?

YUNGER HALPERN: At least two stories grow up out of the setting that you’ve described. One story goes by the name of Szilard’s engine. Leo Szilard was a great Hungarian-American physicist. He said, suppose that we have a gas in a box. Let’s just suppose for convenience and simplicity that the gas consists of one particle, to make things really easy. And suppose that we know which side of the box the gas is in: the right-hand side rather than the left-hand side. We can think of this whole system as storing a bit of information.

So a bit, the basic unit of information, is something that can have one of two possible values. You know, one or zero, right or left. So if we know that the gas particle is in the right-hand side of the box, we have one bit of information. We know it’s in the right-hand side rather than left-hand side.

And we can turn this bit of information into work. We can slide a partition into the box down the center, so we trap our gas in the right-hand side. And suppose that we let the gas interact with some fixed temperature environment through the walls of the box, so heat can flow into the box or out of the box. And we can hook up a little weight to the partition, and let the partition slide. The gas is going to hit the partition, and it’s going to keep punching the partition until the partition reaches the left-hand side of the box.

So now, the gas can be anywhere in the entire box. The gas has expanded, and as it has expanded and moved the partition, the partition has lifted the weight. So, we’ve lifted a weight, we’ve done useful thermodynamic work on the weight.

But we no longer know where in the box the particle is. We lost our bit of information. So we traded information for work, using heat that flowed into the gas from the environment. It’s that heat which we transformed into work with help from our bit of information.

STROGATZ: Huh, it’s really very vivid. I love that explanation that you just gave. Let me see if I really got it, I think I did. One molecule or one particle in a box. We think of it on the right. We’ve got this partition, a sort of sliding wall, potentially. The whole box is in a room at a certain temperature, and then somehow that’s enough to get this particle bouncing around randomly in its available space. And occasionally it will hit the partition. Is that the idea? That I’m only going to hit the partition from one side. So the partition moves unidirectionally, right to left, like a piston expanding.

In some jerky way, it’s going to be sliding, gradually expanding the available volume for this particle. So far so good, right?

STROGATZ: And so we’re losing information as that’s happening, in the sense that we’re increasing the volume, and so we have less information about where the particle is, until ultimately, when we’ve jammed the partition all the way over to the left wall, we now know nothing. The particle could be anywhere.

I guess we have zero bits of information at this point about where it is.

YUNGER HALPERN: Exactly.

STROGATZ: Yet we did useful work through this Rube Goldberg setup that you described. I’ve done work by losing information.

STROGATZ: Unbelievable, that’s crazy.

YUNGER HALPERN: One thing I really love about Szilard’s engine is, this was described in a paper by Leo Szilard that was based on his Ph.D. thesis, which was praised by Einstein. And we’re still talking about it about a hundred years later. So I present this story as a motivation to grad students for something they can aspire to.

STROGATZ: Aha. So for listeners who wouldn’t know this name Leo Szilard, he’s pretty famous in the history, not just of science, but the history of the world because he’s the person who wrote the letter that Einstein signed to tell President Roosevelt that the U.S. needed to build an atomic bomb before Germany did.

YUNGER HALPERN: And he was also heavily involved after the Manhattan Project in causes of peace.

STROGATZ: Yes, right.

We’ll be right back after this message.

[Break for ad insertion]

STROGATZ: Welcome back.

So, this is Szilard’s engine, explaining how information can be traded for work. But you said there was a second example, about a box and a partition? Is there another one that we should talk about?

YUNGER HALPERN: I believe you alluded to this earlier: Landauer erasure.

STROGATZ: OK. Yes. Please tell me about those two words. Landauer. That’s Rolf Landauer ?

YUNGER HALPERN: An information scientist at IBM.

STROGATZ: Uh huh.

YUNGER HALPERN: He basically reversed Szilard’s engine. Suppose that there is a gas in a box. Again, let’s think of it as being one particle. And suppose we don’t know where the gas particle is. Its position in the box is totally random, and we want to reset the particle’s position to a nice clean state: the right-hand side of the box.

This is like taking that sheet of scrap paper that has been scribbled on totally randomly and erasing it to a nice clean state. We can do that by sliding a partition into the box, now right next to the left-hand wall, and pushing the partition to the box’s center. The gas is going to be trapped in the right-hand side.

Now, in order to slide the partition, we have to compress the gas, and this compression process requires us to spend work. At the end of the day, we have a bit of information. We know the gas is in the right-hand side of the box, rather than the left-hand side. But we have spent work. So, in this case, we could trade work for information.

STROGATZ: Hmm. And why is this a conceptually important thought experiment? You’re saying this is another way of understanding that there is a tradeoff between work and information?

YUNGER HALPERN: In part, yes. As you said, there’s a tradeoff. Both work and information are useful, in information processing and thermodynamics. And you alluded to something deeper — I agree about that impulse. If we want to compute and keep computing and keep computing, we’re going to run out of scrap paper sometime. The universe doesn’t have an infinite supply. So we’re going to have to erase some.

Charlie Bennett , somebody else at IBM, has argued that just ordinary computations can be performed at zero-energy cost. It would be very, very difficult to do and very impractical, but in principle possible. However, when it comes to erasure, there is this unavoidable work cost. So, there’s some part of computation — namely, erasure — that has an intrinsic fundamental thermodynamic cost.

When I first learned this, I was… I was thrilled and so surprised because computation and thermodynamics seem like they don’t necessarily have to have anything to do with each other, but they’re very closely bound up.

STROGATZ: Hmm, it’s really quite an astonishing idea. It seems like at least some aspects of thermodynamics very much bear on the information science of the future. I mean, if we’re going to do quantum computers soon, it sounds like we have to know something about thermodynamics. Did you say “Landauer limit” or something?

YUNGER HALPERN: Yes, it’s sometimes called the Landauer bound or the Landauer limit on the amount of work required. And there is a movement, maybe one could say, called the thermodynamics of information. And quantum thermodynamicists and our friends in adjacent fields really love putting together thermodynamics and information.

STROGATZ: So since I mentioned quantum computers, and I’m sure listeners are wondering: You know, we’re doing all these thought experiments with gases in boxes and moving partitions and things. This is not so far from reality, like maybe these things could become real at some point. So, should we shift gears now to that question of applications? Is there any hope in the near future or the long-term future to make quantum machines based on these principles? Or what should we think of in terms of coming applications?

YUNGER HALPERN: We could approach this question in a number of ways.

One is, experimentalists have recently started being able to investigate this Landauer limit on the work required for erasure. A group, for instance, in Finland, they used these electrons to store a bit of information, and they checked how much work they needed to erase the information.

You mentioned equilibrium earlier in the conversation. If we keep a system close to equilibrium, we don’t disturb it a whole lot. We don’t waste energy on riling it up. And so if we perform a process very slowly, such as the system is always in equilibrium or close to equilibrium, we can get away with spending relatively small amounts of work. And so they ran their process more and more slowly and saw what is the value of work, that seems like just below the amount of work that they had to pay, that they were approaching. And they found that their observations were consistent with Landauer’s bound.

This Landauer bound, this minimal amount of work required to erase a bit of information, that is pretty far from the amount of work that is actually spent to erase information in today’s hardware. We operate quite far from this fundamental limitation.

Some people are interested in trying to reach toward this bound to waste less energy. Heating of small parts of computers is a significant problem in both the classical realm of computing and the quantum realm of computing. That’s one motivation that people have for studying such fundamental limits.

And it does seem that quantum systems also obey an ultimate limit on the work cost of erasure. But the operations that we can perform, say in computation, can be different. And also, we can ask, as you did earlier, what if we have a quantum gas in our box rather than a classical gas? Does anything change?

Quite a few features change, and sometimes we can use quantum phenomena like entanglement as resources to help us out.

One of my favorite examples was proved by colleagues including Lídia del Rio , a Portuguese physicist. And they said, suppose that our piece of information that we want to erase is a piece of quantum information stored in a quantum particle that’s entangled. It has this set of strong correlations, more or less, with another quantum system. And so there’s this kind of reference system and, you know, we can manipulate the entanglement. But what we want to do is erase the quantum information in this particle of interest while keeping the reference system in its same state. We don’t want to disturb it too much.

It turns out that we can erase the particle of interest while on the whole gaining work instead of spending work, which is counterintuitive because we’re supposed to spend work in order to erase information.

The trick is to kind of burn the correlations, the entanglement between the particle of interest and the reference in the presence of heat. So entanglement together with heat serves as this kind of thermodynamic quote-unquote “fuel” that we can use to erase while extracting work. This doesn’t violate Landauer’s principle because Landauer wasn’t actually thinking about a quantum particle that’s entangled. This entanglement is kind of an extra resource that we’re adding to the Landauer story after making it quantum.

So everything’s consistent, but it could be a little surprising that we can use entanglement as a resource in this decades-old erasure story.

STROGATZ: Ooh, it’s so interesting and weird what you just described. So there’s a particle in a box and it’s entangled, let’s say, with another particle outside the box, is that right?

YUNGER HALPERN: In this case, it might be useful to think of a different kind of platform or physical system. In classical information science, we think of bits. You know, a transistor in an ordinary computer encodes a bit. It can be in the zero state or the one state.

When it comes to quantum information science, the basic unit of information is the qubit — the quantum bit. And we can store a qubit, for example, in a property of an electron. The electron doesn’t have to be in a box, but if we bring two electrons together and perform some operation on them, as just one example, then we can have two qubits that are entangled with each other.

STROGATZ: Uh huh. So, hmm, remind me how that goes. Like what particles, what properties are entangled? Just to make it concrete.

YUNGER HALPERN: So one example is the spin of an electron.

STROGATZ: OK.

YUNGER HALPERN: It can store a qubit. There are also all sorts of other platforms that people are using to store qubits. For instance, superconducting qubits is a really tiny circuit printed on a chip and a current can flow in one direction in the circuit or flow in the other direction. These are kind of the two options that help define a qubit.

STROGATZ: Uh huh. So maybe now we have two entangled superconducting circuits in your setup. OK. And then — but going back to the thing that was blowing my mind, which is that you could somehow “burn entanglement” to provide —

YUNGER HALPERN: With scare quotes.

STROGATZ: Yeah, scare quotes. It is scary. I mean, entanglement is itself so spooky and amorphous in the way that an average person thinks about it, that the idea that you could burn it and use it as a resource, this is the first I’ve ever heard of this idea.

Entanglement gets destroyed sort of on its own very commonly, right? That’s the reason we’re not familiar with it in our ordinary macroscopic lives.

So it sounds in a way like what you’re describing, in a way, could be commonplace. Like if, if the destroying the entanglement is the key, then well, we do that all the time.

YUNGER HALPERN: Merely destroying the entanglement in absolutely any way probably won’t do the trick, but if you can control and manipulate the entanglement in the right way, then you can consume it in order to get out your work.

STROGATZ: I see. So, if you manipulate the entanglement in the right way, that in some sense destroys it, it could be destroyed in a productive way.

STROGATZ: And does this whole thought experiment that you’re describing now, are you saying we’re close to being able to do this? Or we can at least imagine we can do this?

YUNGER HALPERN: I wouldn’t be surprised if someone had tried it. I don’t think I’ve seen a paper but increasing numbers of quantum thermodynamics experiments are being performed, so I wouldn’t be too surprised if someone performed this experiment in the near future.

The original theory of thermodynamics went hand in hand with the Industrial Revolution, which was useful in a very different sense. And now people are starting to pivot to try to make quantum thermodynamics, maybe quantum thermal machines, actually useful for us, and not only really cool curiosities.

STROGATZ: [laughs] Yeah. I do think that’s a nice, honest answer that you’re giving, that so much of the pleasure of this subject seems to be the light it sheds on two very deep subjects, thermodynamics and quantum theory, which continues to be fascinating. And it seems that by combining those two, we’re getting even deeper understanding of both fields. It’s starting to become imaginable to actually make things using these ideas.

I know that you’ve been interested in something called autonomous quantum machines. Could you tell us a little about that? What is an autonomous quantum machine, in your mind or in reality?

YUNGER HALPERN: Sure. Quantum thermodynamicists have designed quantum engines, quantum refrigerators, quantum batteries, quantum ratchets, and some of them have been realized experimentally. I think the experiments are very impressive, they demonstrate that the experimentalists have excellent control. And just the idea of making a quantum engine is very fun.

On the other hand, you wouldn’t want to invest in a company that provides quantum engines because a quantum engine is so small, it outputs very little energy but cooling a system down so that it behaves in a quantum fashion and then manipulating the engine costs loads of energy. So the engine isn’t worth it — except for the fun factor.

Now there are, even in classical thermodynamics, engines and refrigerators, machines, that are autonomous. They can run on their own without the need for control that changes over time. You just give the machine access to some energy in its environment. The machine will extract the energy from its environment and do its own thing.

We can also make quantum versions of these autonomous thermodynamic machines. And since autonomous machines don’t require lots of control, they offer some hope for actually making useful quantum thermodynamic machines.

I recently collaborated with the lab of Simone Gasparinetti at Chalmers University in Sweden. Chalmers University is building a quantum computer from superconducting qubits. These superconducting qubits are in a large classical refrigerator called a dilution refrigerator, which cools the qubits down to, I think, tens of milliKelvin.

But suppose that this quantum computer has just finished a calculation. It’s used some qubits up as scrap paper, which we keep returning to in this conversation. And if we want to perform the next quantum computation, we need to clean off the scrap paper. And in experimental language, that means we need to cool down the qubits even more in order to reset them. Even more than this classical refrigerator can manage.

One can design a chip to stick inside the classical refrigerator, that consists of more superconducting qubits that act as an autonomous quantum refrigerator. You can kind of hand over your computational qubits to this quantum refrigerator and let it do its thing, and then take the qubits away and use them in your computation. In order to get the quantum refrigerator to behave in a quantum way, you have to make it cold. But you just stick it inside this classical refrigerator, which is already cold because you’re already performing quantum computations.

So, the experiment that was done in Simone’s lab was a proof-of-principle experiment, but it performed a lot better than I expected. So we’re hoping that it’s the beginning of making autonomous quantum machines useful.

STROGATZ: Hmm. Uh huh. It makes me wonder, what is it about what you do and what you get to think about that brings you joy?

YUNGER HALPERN: Good question. I have always loved dealing in abstract ideas. I have always loved reading because that’s always given me the opportunity to build universes in my head. In high school, I was very attracted to philosophy and mathematics, computer science, physics and so on. And quantum thermodynamics gives me joy because it enables me to play with these abstract ideas. I get to build universes in my head, you know, models of all sorts of different systems for a job. And I get to engage with all these different subjects and all their ideas, but there’s also a sense of balance because there are applications of quantum information theory and quantum thermodynamics to quantum technologies like quantum computers and cryptography and so on. So, I get to, you know, play in the realm of ideas and also feel like maybe I’m doing something useful.

STROGATZ: [laughs] Very impressive. Nice. We’ve been speaking with theoretical physicist Nicole Yunger Halpern about the ins and outs of quantum thermodynamics. It’s really been fun, Nicole. Thank you so much for joining us.

YUNGER HALPERN: Thank you. It’s been a lot of fun.

STROGATZ: Thanks for listening. If you’re enjoying “The Joy of Why” and you’re not already subscribed, hit the subscribe or follow button where you’re listening. You can also leave a review for the show — it helps people find this podcast.

[Theme continues]

“The Joy of Why” is a podcast from Quanta Magazine , an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests or other editorial decisions in this podcast or in Quanta Magazine .

“The Joy of Why” is produced by PRX Productions . The production team is Caitlin Faulds, Livia Brock, Genevieve Sponsler, and Merritt Jacob. The executive producer of PRX Productions is Jocelyn Gonzales. Morgan Church and Edwin Ochoa provided additional assistance. From Quanta Magazine , John Rennie and Thomas Lin provided editorial guidance, with support from Matt Carlstrom, Samuel Velasco, Arleen Santana and Meghan Willcoxon. Samir Patel is Quanta ’s editor in chief.

Our theme music is from APM Music. Julian Lin came up with the podcast name. The episode art is by Peter Greenwood and our logo is by Jaki King and Kristina Armitage. Special thanks to the Columbia Journalism School and Bert Odom-Reed at the Cornell Broadcast Studios.

I’m your host, Steve Strogatz. If you have any questions or comments for us, please email us at [email protected] . Thanks for listening.

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