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What Is Quantum Physics?

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

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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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.

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• Published: 28 April 2023

Fresh perspectives on the foundations of quantum physics

• Eric G. Cavalcanti 1 ,
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• Flaminia Giacomini 3 &
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As we are at the beginning of the second century of quantum physics, we asked four researchers to share their views on new research directions trying to answer old, yet still open, questions in the foundations of quantum theory.

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Acknowledgements

E.G.C. acknowledges L. del Rio, N. Tischler, H. Wiseman, W. Zeng and participants of the Towards Experimental Wigner’s Friends workshop in San Francisco for useful discussions on the LF experimental programme, as well as support from grant no. FQXi-RFP-CPW-2019 from the Foundational Questions Institute and Fetzer Franklin Fund. R.C. acknowledges support from the Serrapilheira Institute (grant no. Serra – 1708-15763) and the Simons Foundation (grant no. 1023171, RC). F.G. would like to thank R. Renner for helpful comments on a first draft of her contribution, and acknowledges support from the Swiss National Science Foundation via the Ambizione Grant PZ00P2-208885. Y.-C.L. is grateful to N. Gisin for the many inspiring discussions on quantum foundations and for introducing to him the exciting topic of entangled measurements, and acknowledges support from the National Science and Technology Council and the National Center for Theoretical Sciences, Taiwan.

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Eric G. Cavalcanti

International Institute of Physics, IIP-UFRN, Natal, Brazil

Rafael Chaves

Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland

Flaminia Giacomini

Department of Physics and Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan, Taiwan

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Eric Cavalcanti is an Associate Professor at Griffith University in Queensland, Australia. He has also worked at the University of Sydney and University of Oxford, after a PhD in Physics from the University of Queensland. His research focus is on quantum foundations and quantum information theory, and he has also made contributions to a wide range of fields including philosophy of science, quantum atom-optics and experimental atomic collisions.

Rafael Chaves is a research leader at the International Institute of Physics in Natal, Brazil. Previously, he worked in ICFO and the Universities of Freiburg and Cologne as a postdoctoral researcher. His contributions include quantum computation, communication and machine learning. The focus of his research is on the interface between quantum information and causal inference, developing new tools and concepts to investigate the emergence of non-classical features in quantum networks.

Flaminia Giacomini is an SNSF Ambizione Fellow at ETH Zurich. She received her PhD from the University of Vienna and then held a postdoctoral fellowship at Perimeter Institute for Theoretical Physics. Her research uses quantum information tools to answer fundamental questions at the interface between quantum theory and general relativity. Her research interests span from conceptual consequences of the lack of a classical spacetime, such as quantum time, quantum reference frames and indefinite causality, to the study of the observational implications of the quantum nature of gravity in table-top experiments.

Yeong-Cherng Liang is a professor of physics and a research group leader based at the National Cheng Kung University (NCKU), Taiwan. He received his PhD from the University of Queensland, Australia, in 2008. He then did postdoctoral research at the University of Sydney, the University of Geneva and ETH Zürich, before taking up a faculty position at NCKU in 2015. His expertise is in quantum foundations, especially quantum nonlocality, quantum entanglement and their applications in quantum information.

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Cavalcanti, E.G., Chaves, R., Giacomini, F. et al. Fresh perspectives on the foundations of quantum physics. Nat Rev Phys 5 , 323–325 (2023). https://doi.org/10.1038/s42254-023-00586-z

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Essay: Where Can Quantum Geometry Lead Us?

Päivi Törmä

Phys. Rev. Lett. 131 , 240001 – Published 11 December 2023

• Citing Articles (9)
• The concept of quantum geometry.—
• Relevance of quantum geometry to…
• Experiments: Present and future.—
• Updating computational methods.—
• The annoying necessity of nitpicking.—
• Widening quantum geometry.—
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• ACKNOWLEDGMENTS

Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry, including the amplitude distance characterized by the quantum metric, has started to receive attention in the last few years. Various quantum transport and interaction phenomena have been found to be critically influenced by quantum geometry. For example, quantum geometry allows counterintuitive flow of supercurrent in a flat band where single electrons are immobile. In this Essay, I will discuss my view of the important open problems and future applications of this research topic and will try to inspire the reader to come up with further ideas. At its best, quantum geometry can open a new chapter in band theory and lead to breakthroughs as transformative as room-temperature superconductivity. However, first, more experiments directly showing the effect of quantum geometry are needed. We also have to integrate quantum geometry analysis in our most advanced numerical methods. Further, the ramifications of quantum geometry should be studied in a wider range, including electric and electromagnetic responses and interaction phenomena in free- and correlated-electron materials, bosonic systems, optics, and other fields.

Part of a series of Essays which concisely present author visions for the future of their field .

• Received 17 November 2023

DOI: https://doi.org/10.1103/PhysRevLett.131.240001

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• Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland
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(a) Atoms in materials may form a lattice that the electrons “feel.” Each unit cell of the lattice can have several orbitals, labeled α and β in our example, which only has two. The orbital states | α ⟩ and | β ⟩ are orthogonal and can be illustrated by the Bloch sphere, (b), middle. The states of the electrons in a band may involve one orbital only, indicated by a single color in (b), left. The distance between two states when the change in the lattice momentum Δ k is infinitesimally small then vanishes because the orbital state remains the same. The quantum geometry is trivial in this case and the quantum metric g = 0 . In the nontrivial case (b), right, the electron state in a band can be a superposition of two orbitals (“mixed” color). Then, upon a change in k that changes this superposition, the new state will have a finite quantum distance from the original one due to the orthogonality of the orbital states; the quantum metric is nonzero. For a simple model example, see [ 12 ].

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Philosophical Issues in Quantum Theory

This article is an overview of the philosophical issues raised by quantum theory, intended as a pointer to the more in-depth treatments of other entries in the Stanford Encyclopedia of Philosophy.

1. Introduction

2.1 quantum states and classical states, 2.2 quantum mechanics and quantum field theory, 2.3 quantum state evolution, 3. entanglement, nonlocality, and nonseparability, 4.1 the measurement problem formulated, 4.2 approaches to the measurement problem, 4.3 extended wigner’s friend scenarios as a source of no-go theorems, 4.4 the role of decoherence, 4.5 comparison of approaches to the measurement problem, 5.1 the question of quantum state realism., 5.2 ontological category of quantum states, 6. quantum computing and quantum information theory, 7. reconstructions of quantum mechanics and beyond, other internet resources, related entries.

Despite its status as a core part of contemporary physics, there is no consensus among physicists or philosophers of physics on the question of what, if anything, the empirical success of quantum theory is telling us about the physical world. This gives rise to the collection of philosophical issues known as “the interpretation of quantum mechanics”. One should not be misled by this terminology into thinking that what we have is an uninterpreted mathematical formalism with no connection to the physical world. Rather, there is a common operational core that consists of recipes for calculating probabilities of outcomes of experiments performed on systems subjected to certain state preparation procedures. What are often referred to as different “interpretations” of quantum mechanics differ on what, if anything, is added to the common core. Two of the major approaches, hidden-variables theories and collapse theories, involve formulation of physical theories distinct from standard quantum mechanics; this renders the terminology of “interpretation” even more inappropriate.

Much of the philosophical literature connected with quantum theory centers on the problem of whether we should construe the theory, or a suitable extension or revision of it, in realist terms, and, if so, how this should be done. Various approaches to what is called the “Measurement Problem” propose differing answers to these questions. There are, however, other questions of philosophical interest. These include the bearing of quantum nonlocality on our understanding of spacetime structure and causality, the question of the ontological character of quantum states, the implications of quantum mechanics for information theory, and the task of situating quantum theory with respect to other theories, both actual and hypothetical. In what follows, we will touch on each of these topics, with the main goal being to provide an entry into the relevant literature, including the Stanford Encyclopedia entries on these topics. Contemporary perspectives on many of the issues touched on in this entry can be found in The Routledge Companion to Philosophy of Physics (Knox and Wilson, eds., 2021); The Oxford Handbook of the History of Quantum Interpretations (Freire, et al. eds., 2022) contains essays on the history of discussions of these issues.

2. Quantum Theory

In this section we present a brief introduction to quantum theory; see the entry on quantum mechanics for a more detailed introduction.

In classical physics, with any physical system is associated a state space, which represents the totality of possible ways of assigning values to the dynamical variables that characterize the state of the system. For systems of a great many degrees of freedom, a complete specification of the state of the system may be unavailable or unwieldy; classical statistical mechanics deals with such a situation by invoking a probability distribution over the state space of the system. A probability distribution that assigns any probability other than one or zero to some physical quantities is regarded as an incomplete specification of the state of the system. In quantum mechanics, things are different. There are no quantum states that assign definite values to all physical quantities, and probabilities are built into the standard formulation of the theory.

In formulating a quantum theory of some system, one usually begins with the Hamiltonian or Lagrangian formulation of the classical mechanical theory of that system. In the Hamiltonian formulation of classical mechanics, the configuration of a system is represented by a set of coordinates. These could be, for example, the positions of each of a set of point particles, but one can also consider more general cases, such as angular coordinates that specify the orientation of a rigid body. For every coordinate there is an associated conjugate momentum . If the coordinate indicates the position of some object, the momentum conjugate to that coordinate may be what we usually call “momentum,” that is, the velocity of the body multiplied by its mass. If the coordinate is an angle, the momentum conjugate to it is an angular momentum.

Construction of a quantum theory of a physical system proceeds by first associating the dynamical degrees of freedom with operators . These are mathematical objects on which operations of multiplication and addition are defined, as well as multiplication by real and complex numbers. Another way of saying this is that the set of operators forms an algebra . Typically, it is said that an operator represents an observable , and the result of an experiment on a system is said to yield a value for some observable. Two or more observables are said to be compatible if there is some possible experiment that simultaneously yields values for all of them. Others require mutually exclusive experiments; these are said to be incompatible .

Of course, in a classical theory, the dynamical quantities that define a state also form an algebra also, as they can be multiplied and added, and multiplied by real or complex numbers. Quantum mechanics differs from classical mechanics in that the order of multiplication of operators can make a difference. That is, for some operators \(A\),\(B\), the product \(AB\) is not equal to the product \(BA.\) If \(AB = BA,\) the operators are said to commute .

The recipe for constructing a quantum theory of a given physical systems prescribes algebraic relations between the operators representing the dynamical variables of the system. Compatible observables are associated with operators that commute with each other. Operators representing conjugate variables are required to satisfy what are called the canonical commutation relations . If \(q\) is some coordinate, and \(p\) its conjugate momentum, the operators \(Q\) and \(P\) representing them are required to not commute. Instead, the difference between \(PQ\) and \(QP\) is required to be a multiple of the identity operator (that is, the operator \(I\) that satisfies, for all operators \(A\), \(IA = AI).\)

A quantum state is a specification, for every experiment that can be performed on the system, of probabilities for the possible outcomes of that experiment. These can be summed up as an assignment of an expectation value to each observable. These states are required to be linear . This means that, if an operator \(C\), corresponding to some observable, is the sum of operators \(A\) and \(B\), corresponding to other observables, then the expectation value that a quantum state assigns to \(C\) must be the sum of the expectation values assigned to \(A\) and \(B\). This is a nontrivial constraint, as it is required to hold whether or not the observables represented are compatible. A quantum state, therefore, relates expectation values for quantities yielded by incompatible experiments.

Incompatible observables, represented by noncommuting operators, give rise to uncertainty relations; see the entry on the uncertainty principle . These relations entail that there are no quantum states that assign definite values to the observables that satisfy them, and place bounds on how close they can come to be simultaneously well-defined in any quantum state.

For any two distinct quantum states, \(\rho\), \(\omega\), and any real number between 0 and 1, there is a corresponding mixed state . The probability assigned to any experimental outcome by this mixed state is \(p\) times the probability it is assigned by \(\rho\) plus \(1-p\) times the probability assigned to it by \(\omega\). One way to physically realize the preparation of a mixed state is to employ a randomizing device, for example, a coin with probability \(p\) of landing heads and probability \(1-p\) of landing tails, and to use it to choose between preparing state \(\rho\) and preparing state \(\omega\). We will see another way to prepare a mixed state after we have discussed entanglement, in section 3. A state that is not a mixture of any two distinct states is called a pure state .

It is both useful and customary, though not strictly necessary, to employ a Hilbert space representation of a quantum theory. In such a representation, the operators corresponding to observables are represented as acting on elements of an appropriately constructed Hilbert space (see the entry on quantum mechanics for details). Usually, the Hilbert space representation is constructed in such a way that vectors in the space represent pure states; such a representation is called an irreducible representation . Irreducible representations, in which mixed states are also represented by vectors, are also possible.

A Hilbert space is a vector space. This means that, for any two vectors \(|\psi\rangle\), \(|\phi\rangle\) , in the space, representing pure states, and any complex numbers \(a\), \(b\), there is another vector, \(a |\psi\rangle + b |\phi\rangle\), that also represents a pure state. This is called a superposition of the states represented by \(|\psi\rangle\) and \(|\phi\rangle\) . Any vector in a Hilbert space can be written as a superposition of other vectors in infinitely many ways. Sometimes, in discussing the foundations of quantum mechanics, authors fall into talking as if some state are superpositions and others are not. This is simply an error. Usually what is meant is that some states yield definite values for macroscopic observables, and others cannot be written in any way that is not a superposition of macroscopically distinct states.

The noncontroversial operational core of quantum theory consists of rules for identifying, for any given system, appropriate operators representing its dynamical quantities. In addition, there are prescriptions for evolving the state of system when it is acted upon by specified external fields or subjected to various manipulations (see section 1.3 ). Application of quantum theory typically involves a distinction between the system under study, which is treated quantum mechanically, and experimental apparatus, which is not. This division is sometimes known as the Heisenberg cut .

Whether or not we can expect to be able to go beyond the noncontroversial operational core of quantum theory, and take it to be more than a means for calculating probabilities of outcomes of experiments, remains a topic of contemporary philosophical discussion.

Quantum mechanics is usually taken to refer to the quantized version of a theory of classical mechanics, involving systems with a fixed, finite number of degrees of freedom. Classically, a field, such as, for example, an electromagnetic field, is a system endowed with infinitely many degrees of freedom. Quantization of a field theory gives rise to a quantum field theory . The chief philosophical issues raised by quantum mechanics remain when the transition is made to a quantum field theory; in addition, new interpretational issues arise. There are interesting differences, both technical and interpretational, between quantum mechanical theories and quantum field theories; for an overview, see the entries on quantum field theory and quantum theory: von Neumann vs. Dirac .

The standard model of quantum field theory, successful as it is, does not yet incorporate gravitation. The attempt to develop a theory that does justice both the quantum phenomena and to gravitational phenomena gives rise to serious conceptual issues (see the entry on quantum gravity ).

2.3.1 Schrödinger and Heisenberg pictures

When constructing a Hilbert space representation of a quantum theory of a system that evolves over time, there are some choices to be made. One needs to have, for each time t , a Hilbert space representation of the system, which involves assigning operators to observables pertaining to time t . An element of convention comes in when deciding how the operators representing observables at different times are to be related.

For concreteness, suppose that have a system whose observables include a position, \(x\), and momentum, \(p\), with respect to some frame of reference. There is a sense in which, for two distinct times, \(t\) and \(t'\), position at time \(t\) and position at time \(t'\) are distinct observables, and also a sense in which they are values, at different times, of the same observable. Once we have settled on operators \(\hat{X}\) and \(\hat{P}\) to represent position and momentum at time \(t\), we still have a choice of which operators represent the corresponding quantities at time \(t.\) On the Schrödinger picture , the same operators \(\hat{X}\) and \(\hat{P}\) are used to represent position and momentum, whatever time is considered. As the probabilities for results of experiments involving these quantities may be changing with time, different vectors must be used to represent the state at different times.

The equation of motion obeyed by a quantum state vector is the Schrödinger equation. It is constructed by first forming the operator \(\hat{H}\)corresponding to the Hamiltonian of the system, which represents the total energy of the system. The rate of change of a state vector is proportional to the result of operating on the vector with the Hamiltonian operator \(\hat{H}\).

There is an operator that takes a state at time 0 into a state at time \(t\); it is given by

This operator is a linear operator that implements a one-one mapping of the Hilbert space to itself that preserves the inner product of any two vectors; operators with these properties are called unitary operators , and, for this reason, evolution according to the Schrödinger equation is called unitary evolution.

For our purposes, the most important features of this equation is that it is deterministic and linear . The state vector at any time, together with the equation, uniquely determines the state vector at any other time. Linearity means that, if two vectors \(\ket{\psi_1(0)}\) and \(\ket{\psi_2(0)}\) evolve into vectors \(\ket{\psi_1(t) }\) and \(\ket{\psi_2(t)}\), respectively, then, if the state at time 0 is a linear combination of these two, the state at any time \(t\) will be the corresponding linear combination of \(\ket{\psi_1(t)}\) and \(\ket{\psi_2(t)}\).

\[ a\ket{\psi_{1}(0)} + b\ket{\psi_{2}(0)} \rightarrow a\ket{\psi_{1}(t)} + b\ket{\psi_{2}(t)} . \]

The Heisenberg picture, on the other hand, employs different operators \(\hat{X}(t)\), \(\hat{X}(t')\) for position, depending on the time considered (and similarly for momentum and other observables). If \(\hat{A}(t)\)is a family of Heisenberg picture operators representing some observable at different times, the members of the family satisfy the Heisenberg equation of motion,

One sometimes hears it said that, on the Heisenberg picture, the state of the system is unchanging. This is incorrect. It is true that there are not different state vectors corresponding to different times, but that is because a single state vector serves for computing probabilities for all observables pertaining to all times. These probabilities do change with time.

2.3.2. The collapse postulate

As mentioned, standard applications of quantum theory involve a division of the world into a system that is treated within quantum theory, and the remainder, typically including the experimental apparatus, that is not treated within the theory. Associated with this division is a postulate about how to assign a state vector after an experiment that yields a value for an observable, according to which, after an experiment, one replaces the quantum state with an eigenstate corresponding to the value obtained. Unlike the unitary evolution applied otherwise, this is a discontinuous change of the quantum state, sometimes referred to as collapse of the state vector , or state vector reduction . There are two interpretations of the postulate about collapse, corresponding to two different conceptions of quantum states. If a quantum state represents nothing more than knowledge about the system, then the collapse of the state to one corresponding to an observed result can be thought of as mere updating of knowledge. If, however, quantum states represent physical reality, in such a way that distinct pure states always represent distinct physical states of affairs, then the collapse postulate entails an abrupt, perhaps discontinuous, change of the physical state of the system. Considerable confusion can arise if the two interpretations are conflated.

The collapse postulate occurs already in the general discussion at the fifth Solvay Conference in 1927 (see Bacciagaluppi and Valentini, 2009, 437–450). It is also found in Heisenberg’s The Physical Principles of the Quantum Theory , based on lectures presented in 1929 (Heisenberg, 1930a, 27; 1930b, 36). Von Neumann, in his reformulation of quantum theory a few years later, distinguished between two types of processes: Process 1:, which occurs upon performance of an experiment, and Process 2:, the unitary evolution that takes place as long as no measurement is made (von Neumann, 1932; 1955, §V.I). He does not take this distinction to be a difference between two physically distinct processes. Rather, the invocation of one process or the other depends on a somewhat arbitrary division of the world into an observing part and an observed part (see von Neumann,1932, 224; 1955, 420).

The collapse postulate does not appear in the first edition (1930) of Dirac’s Principles of Quantum Mechanics ; it is introduced in the second edition (1935). Dirac formulates it as follows.

When we measure a real dynamical variable \(\xi\), the disturbance involved in the act of measurement causes a jump in the state of the dynamical system. From physical continuity, if we make a second measurement of the same dynamical variable \(\xi\) immediately after the first, the result of the second measurement must be the same as that of the first. Thus after the first measurement has been made, there is no indeterminacy in the result of the second. Hence, after the first measurement has been made, the system is in an eigenstate of the dynamical variable \(\xi\), the eigenvalue it belongs to being equal to the result of the first measurement. This conclusion must still hold if the second measurement is not actually made. In this way we see that a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured, the eigenvalue this eigenstate belongs to being equal to the result of the measurement (Dirac 1935: 36).

Unlike von Neumann and Heisenberg, Dirac is treating the “jump” as a physical process.

Neither von Neumann nor Dirac take awareness of the result by a conscious observer to be a necessary condition for collapse. For von Neumann, the location of the cut between the “observed” system and the “observer”is somewhat arbitrary. It may be placed between the system under study and the experimental apparatus. On the other hand, we could include the experimental apparatus in the quantum description, and place the cut at the moment when light indicating the result hits the observer’s retina. We could also go even further, and include the retina and relevant parts of the observer’s nervous system in the quantum system. That the cut may be pushed arbitrarily far into the perceptual apparatus of the observer is required, according to von Neumann, by the principle of psycho-physical parallelism .

A formulation of a version of the collapse postulate according to which a measurement is not completed until the result is observed is found in London and Bauer (1939). For them, as for Heisenberg, this is a matter of an increase of knowledge on the part of the observer.

Wigner (1961) combined elements of the two interpretations. Like those who take the collapse to be a matter of updating of belief in light of information newly acquired by an observer, he takes collapse to take place when a conscious observer becomes aware of an experimental result. However, like Dirac, he takes it to be a real physical process. His conclusion is that consciousness has an influence on the physical world not captured by the laws of quantum mechanics. This involves a rejection of von Neumann’s principle of psycho-physical parallelism, according to which it must be possible to treat the process of subjective perception as if it were a physical process like any other.

There is a persistent misconception that, for von Neumann, collapse is to be invoked only when a conscious observer becomes aware of the result. As noted, this is the opposite of his view, as the cut may be placed between the observed system and the experimental apparatus, and it is for him an important point that the location of the cut be somewhat arbitrary. In spite of this, von Neumann’s position is sometimes conflated with Wigner’s speculative proposal, and Wigner’s proposal is sometimes erroneously referred to as the von Neumann-Wigner interpretation .

None of the standard formulations are precise about when the collapse postulate is to be applied; there is some lee-way as to what is to count as an experiment, or (for versions that require reference to an observer) what is to count as an observer. Some, including von Neumann and Heisenberg, have taken it to be a matter of principle that there be some arbitrariness in where to apply the postulate. It is common wisdom that, in practice, this arbitrariness is innocuous. The rule of thumb that seems to be applied, in practice, in setting the split between the parts of the world treated quantum-mechanically and things treated as classical objects has been formulated by J. S. Bell as, “[w]hen in doubt enlarge the quantum system,” to the point at which including more in the quantum system makes negligible difference to practical predictions (Bell 1986, 362; Bell 2004, 189). If anything is to be counted as “standard” quantum mechanics, it is the operational core we have discussed, supplemented by a heuristic rule of application of this sort. Standard quantum mechanics works very well. If, however, one seeks a theory that is capable of describing all systems, including macroscopic ones, and can yield an account of the process by which macroscopic events, including experimental outcomes, come about, this gives rise to the so-called “measurement problem”, which we will discuss after we have introduced the notion of entanglement (see section 3 ).

2.3.3. Wave functions

Among the Hilbert-space representations of a quantum theory are wave-function representations.

Associated with any observable is its spectrum , the range of possible values that the observable can take on. Given any physical system and any observable for that system, one can always form a Hilbert-space representation for the quantum theory of that system by considering complex-valued functions on the spectrum of that observable. The set of such functions form a vector space. Given a measure on the spectrum of the observable, we can form a Hilbert space out of the set of complex-valued square-integrable functions on the spectrum by treating functions that differ only on a set of zero measure as equivalent (that is, the elements of our Hilbert space are really equivalence classes of functions), and by using the measure to define an inner product (see entry on Quantum Mechanics if this terminology is unfamiliar).

If the spectrum of the chosen observable is a continuum (as it is, for example, for position or momentum), a Hilbert-space representation of this sort is called a wave function representation, and the functions that represent quantum states, wave functions (also “wave-functions,” or “wavefunctions”). The most familiar representations of this form are position-space wave functions, which are functions on the set of possible configurations of the system, and momentum-space wave functions, which are functions of the momenta of the systems involved.

Given two disjoint physical systems, \(A\) and \(B\), with which we associate Hilbert spaces \(H_{A}\) and \(H_{B}\), the Hilbert space associated with the composite system is the tensor product space, denoted \(H_{A} \otimes H_{B}\).

When the two systems are independently prepared in pure states \(\ket{\psi}\) and \(\ket{\phi}\), the state of the composite system is the product state \(\ket{\psi} \otimes \ket{\phi}\) (sometimes written with the cross, \(\otimes\), omitted).

In addition to the product states, the tensor product space contains linear combinations of product states, that is, state vectors of the form

The tensor product space can be defined as the smallest Hilbert space containing all of the product states. Any pure state represented by a state vector that is not a product vector is an entangled state .

The state of the composite system assigns probabilities to outcomes of all experiments that can be performed on the composite system. We can also consider a restriction to experiments performed on system \(A\), or a restriction to experiments performed to \(B\). Such restrictions yields states of \(A\) and \(B\), respectively, called the reduced states of the systems. When the state of the composite system \(AB\) is an entangled state, then the reduced states of \(A\) and \(B\) are mixed states. To see this, suppose that in the above state the vectors \(\ket{\phi_{1}}\) and \(\ket{\phi_{2}}\) represent distinguishable states. If one confines one’s attention to experiments performed on \(A\), it makes no difference whether an experiment is also performed on \(B\). An experiment performed on \(B\) that distinguishes \(\ket{\phi_{1}}\) and \(\ket{\phi_{2}}\) projects the state of \(A\) into either \(\ket{\psi_{1}}\) or \(\ket{\psi_{2}}\), with probabilities \(\abs{a}^{2}\) and \(\abs{b}^{2}\), respectively, and probabilities for outcomes of experiments performed on \(A\) are the corresponding averages of probabilities for states \(\ket{\psi_{1}}\) and \(\ket{\psi_{2}}\). These probabilities, as mentioned, are the same as those for the situation in which no experiment is performed on \(B\). Thus, even if no experiment is performed on \(B\), the probabilities of outcomes of experiments on \(A\) are exactly as if system \(A\) is either in the state represented by \(\ket{\psi_{1}}\) or the state represented by \(\ket{\psi_{2}}\), with probabilities \(\abs{a}^{2}\) and \(\abs{b}^{2}\), respectively.

In general, any state, pure or mixed, that is neither a product state nor a mixture of product states, is called an entangled state.

The existence of pure entangled states means that, if we consider a composite system consisting of spatially separated parts, then, even when the state of the system is a pure state, the state is not determined by the reduced states of its component parts. Thus, quantum states exhibit a form of nonseparability . See the entry on holism and nonseparability in physics for more information.

Quantum entanglement results in a form of nonlocality that is alien to classical physics. Even if we assume that the reduced states of \(A\) and \(B\) do not completely characterize their physical states, but must be supplemented by some further variables, there are quantum correlations that cannot be reduced to correlations between states of \(A\) and \(B\); see the entries on Bell’s Theorem and action at a distance in quantum mechanics .

4. The measurement problem

If quantum theory is meant to be (in principle) a universal theory, it should be applicable, in principle, to all physical systems, including systems as large and complicated as our experimental apparatus. It is easy to show that linear evolution of quantum states, when applied to macroscopic objects, will routinely lead to superpositions of macroscopically distinct states. Among the circumstances in which this will happen are experimental set-ups, and much of the early discussions focussed on how to construe the process of measurement in quantum-mechanical terms. For this reason, the interpretational issues have come to be referred to as the measurement problem . In the first decades of discussion of the foundations of quantum mechanics, it was commonly referred to as the problem of observation .

Consider a schematized experiment. Suppose we have a quantum system that can be prepared in at least two distinguishable states, \(\ket{0} _{S}\) and \(\ket{1} _{S}\). Let \(\ket{R} _{A}\) be a ready state of the apparatus, that is, a state in which the apparatus is ready to make a measurement.

If the apparatus is working properly, and if the measurement is a minimally disturbing one, the coupling of the system \(S\) with the apparatus \(A\) should result in an evolution that predictably yields results of the form

where \(\ket{“0” } _{A}\) and \(\ket{“1”} _{A}\) are apparatus states indicating results 0 and 1, respectively.

Now suppose that the system \(S\) is prepared in a superposition of the states \(\ket{0} _{S}\) and \(\ket{1}_{S}\).

where \(a\) and \(b\) are both nonzero. If the evolution that leads from the pre-experimental state to the post-experimental state is linear Schrödinger evolution, then we will have

This is not an eigenstate of the instrument reading variable, but is, rather, a state in which the reading variable and the system variable are entangled with each other. The eigenstate-eigenvalue link, applied to a state like this, does not yield a definite result for the instrument reading. The problem of what to make of this is called the “measurement problem” which is discussed in more detail below.

If quantum state evolution proceeds via the Schrödinger equation or some other linear equation, then, as we have seen in the previous section, typical experiments will lead to quantum states that are superpositions of terms corresponding to distinct experimental outcomes. It is sometimes said that this conflicts with our experience, according to which experimental outcome variables, such as pointer readings, always have definite values. This is a misleading way of putting the issue, as it is not immediately clear how to interpret states of this sort as physical states of a system that includes experimental apparatus, and, if we can’t say what it would be like to observe the apparatus to be in such a state, it makes no sense to say that we never observe it to be in a state like that.

Nonetheless, we are faced with an interpretational problem. If we take the quantum state to be a complete description of the system, then the state is, contrary to what would antecedently expect, not a state corresponding to a unique, definite outcome. This is what led J.S. Bell to remark, “Either the wavefunction, as given by the Schrödinger equation, is not everything, or it is not right” (Bell 1987: 41, 2004: 201). This gives us a ( prima facie ) tidy way of classifying approaches to the measurement problem:

• There are approaches that involve a denial that a quantum wave function (or any other way of representing a quantum state) yields a complete description of a physical system.
• There are approaches that involve modification of the dynamics to produce a collapse of the quantum state in appropriate circumstances.
• There are approaches that reject both horns of Bell’s dilemma, and hold that quantum states undergo unitary evolution at all times and that a quantum state-description is, in principle, complete.

We include in the first category approaches that deny that a quantum state should be thought of as representing anything in reality at all. These include variants of the Copenhagen interpretation, as well as pragmatic and other anti-realist approaches. Also in the first category are approaches that seek a completion of the quantum state description. These include hidden-variables approaches and modal interpretations. The second category of interpretation motivates a research programme of finding suitable indeterministic modifications of the quantum dynamics. Approaches that reject both horns of Bell’s dilemma are typified by Everettian, or “many-worlds” interpretations.

4.2.1 The “Copenhagen interpretation”

Since the mid-1950’s, the term “Copenhagen interpretation” has been commonly used for whatever it is that the person employing the term takes to be the ‘orthodox’ viewpoint regarding the philosophical issues raised by quantum mechanics. According to Howard (2004), the phrase was first used by Heisenberg (1955, 1958), and is intended to suggest a commonality of views among Bohr and his associates, included Born and Heisenberg himself. Recent historiography has emphasized diversity of viewpoints among the figures associated with the Copenhagen interpretation; see the entry on Copenhagen interpretation of quantum mechanics , and references therein. Readers should be aware that the term is not univocal, and that different authors might mean different things when speaking of the“Copenhagen interpretation.”

4.2.2 Non-realist and pragmatist approaches to quantum mechanics

From the early days of quantum mechanics, there has been a strain of thought that holds that the proper attitude to take towards quantum mechanics is an instrumentalist or pragmatic one. On such a view, quantum mechanics is a tool for coordinating our experience and for forming expectations about the outcomes of experiments. Variants of this view include some versions of the Copenhagen interpretation. More recently, views of this sort have been advocated by physicists, including QBists, who hold that quantum states represent subjective or epistemic probabilities (see Fuchs et al. , 2014). The philosopher Richard Healey defends a related view on which quantum states, though objective, are not to be taken as representational (see Healey 2012, 2017a, 2020). For more on these approaches, see entry on Quantum-Bayesian and pragmatist views of quantum theory .

4.2.2 Hidden-variables and modal interpretations

Theories whose structure include the quantum state but include additional structure, with an aim of circumventing the measurement problem, have traditionally been called “hidden-variables theories”. That a quantum state description cannot be regarded as a complete description of physical reality was argued for in a famous paper by Einstein, Podolsky and Rosen (EPR) and by Einstein in subsequent publications (Einstein 1936, 1948, 1949). See the entry on the Einstein-Podolsky-Rosen argument in quantum theory .

There are a number of theorems that circumscribe the scope of possible hidden-variables theories. The most natural thought would be to seek a theory that assigns to all quantum observables definite values that are merely revealed upon measurement, in such a way that any experimental procedure that, in conventional quantum mechanics, would count as a “measurement” of an observable yields the definite value assigned to the observable. Theories of this sort are called noncontextual hidden-variables theory. It was shown by Bell (1966) and Kochen and Specker (1967) that there are no such theories for any system whose Hilbert space dimension is greater than three (see the entry on the Kochen-Specker theorem ).

The Bell-Kochen-Specker Theorem does not rule out hidden-variables theories tout court . The simplest way to circumvent it is to pick as always-definite some observable or compatible set of observables that suffices to guarantee determinate outcomes of experiments; other observables are not assigned definite values and experiments thought of as “measurements” of these observables do not reveal pre-existing values.

The most thoroughly worked-out theory of this type is the pilot wave theory developed by de Broglie and presented by him at the Fifth Solvay Conference held in Brussels in 1927, revived by David Bohm in 1952, and currently an active area of research by a small group of physicists and philosophers. According to this theory, there are particles with definite trajectories, that are guided by the quantum wave function. For the history of the de Broglie theory, see the introductory chapters of Bacciagaluppi and Valentini (2009). For an overview of the de Broglie-Bohm theory and philosophical issues associated with it see the entry on Bohmian mechanics .

There have been other proposals for supplementing the quantum state with additional structure; these have come to be called modal interpretations ; see the entry on modal interpretations of quantum mechanics .

4.2.3 Dynamical Collapse Theories

As already mentioned, Dirac wrote as if the collapse of the quantum state vector precipitated by an experimental intervention on the system is a genuine physical change, distinct from the usual unitary evolution. If collapse is to be taken as a genuine physical process, then something more needs to be said about the circumstances under which it occurs than merely that it happens when an experiment is performed. This gives rise to a research programme of formulating a precisely defined dynamics for the quantum state that approximates the linear, unitary Schrödinger evolution in situations for which this is well-confirmed, and produces collapse to an eigenstate of the outcome variable in typical experimental set-ups, or, failing that, a close approximation to an eigenstate. The only promising collapse theories are stochastic in nature; indeed, it can be shown that a deterministic collapse theory would permit superluminal signalling. See the entry on collapse theories for an overview, and Gao, ed. (2018) for a snapshot of contemporary discussions.

Prima facie , a dynamical collapse theory of this type can be a quantum state monist theory, one on which, in Bell’s words, “the wave function is everything”. In recent years, this has been disputed; it has been argued that collapse theories require “primitive ontology” in addition to the quantum state. See Allori et al. (2008), Allori (2013), and also the entry on collapse theories , and references therein. Reservations about this approach have been expressed by Egg (2017, 2021), Myrvold (2018), and Wallace (2020).

4.2.4 Everettian, or “many worlds” theories

In his doctoral dissertation of 1957 (reprinted in Everett 2012), Hugh Everett III proposed that quantum mechanics be taken as it is, without a collapse postulate and without any “hidden variables”. The resulting interpretation he called the relative state interpretation.

The basic idea is this. After an experiment, the quantum state of the system plus apparatus is typically a superposition of terms corresponding to distinct outcomes. As the apparatus interacts with its environment, which may include observers, these systems become entangled with the apparatus and quantum system, the net result of which is a quantum state involving, for each of the possible experimental outcomes, a term in which the apparatus reading corresponds to that outcome, there are records of that outcome in the environment, observers observe that outcome, etc. . Everett proposed that each of these terms be taken to be equally real. From a God’s-eye-view, there is no unique experimental outcome, but one can also focus on a particular determinate state of one subsystem, say, the experimental apparatus, and attribute to the other systems participating in the entangled state a relative state , relative to that state of the apparatus. That is, relative to the apparatus reading ‘+’ is a state of the environment recording that result and states of observers observing that result (see the entry on Everett’s relative-state formulation of quantum mechanics , for more detail on Everett’s views).

Everett’s work has inspired a family of views that go by the name of “Many Worlds” interpretations; the idea is that each of the terms of the superposition corresponds to a coherent world, and all of these worlds are equally real. As time goes on, there is a proliferation of these worlds, as situations arise that give rise to a further multiplicity of outcomes (see the entry many-worlds interpretation of quantum mechanics , and Saunders 2007, for overviews of recent discussions; Wallace 2012 is an extended defense of an Everettian interpretation of quantum mechanics).

There is a family of distinct, but related views, that go by the name of “Relational Quantum Mechanics”. These views agree with Everett in attributing to a system definite values of dynamical variables only relative to the states of other systems; they differ in that, unlike Everett, they do not take the quantum state as their basic ontology (see the entry on relational quantum mechanics for more detail).

As mentioned, quantum theory, as standardly formulated, employs a division of the world into a part that is treated with the theory, and a part that is not. Both von Neumann and Heisenberg emphasized an element of arbitrariness in the location of the division. In some formulations, the division was thought of as a distinction between observer and observed, and it became common to say that quantum mechanics requires reference to an observer for its formulation.

The founders of quantum mechanics tended to assume implicitly that, though the “cut” is somewhat moveable, in any given analysis a division would be settled on, and one would not attempt to combine distinct choices of the cut in one analysis of an experiment. If, however, one thinks of the cut as marking the distinction between observer and observed, one is led to ask about situations involving multiple observers. Is each observer permitted to treat the other as a quantum system?

The consideration of such scenarios was initiated by Wigner (1961). Wigner considered a hypothetical scenario in which a friend conducts an observation, and he himself treats the joint system, consisting of the friend and the system experimented upon, as a quantum system. For this reason, scenarios of this sort have come to be known as “Wigner’s friend” scenarios. Wigner was led by consideration of such scenarious to hypothesize that conscious observers cannot be in a superposition of states corresponding to distinct perceptions; the introduction of conscious observers initiates a physical collapse of the quantum state; this involves, according to Wigner, “a violation of physical laws where consciousness plays a role” (Wigner 1961, 294 ;167, 181).

Frauchiger and Renner (2018) initiated the discussion of scenarios of this sort involving more than two observers, which have come to be called “extended Wigner’s friend” scenarios. Further results along these lines include Brukner (2018), Bong et al. (2020), and Guérin et al. (2021). The strategy of these investigations is to present some set of plausible-seeming assumptions (a different set, for each of the works cited), and to show, via consideration of a hypothetical situation involving multiple observers, the inconsistency of that set of assumptions. The theorems are, therefore, no-go theorems for approaches to the measurement problem that would seek to satisfy all of the members of the set of assumptions that has been shown to be inconsistent.

An assumption common to all of these investigations is that it is always permissible for one observer to treat systems containing other observers within quantum mechanics and to employ unitary evolution for those systems. This means that collapse is not regarded as a physical process. It is also assumed that each observer always perceives a unique outcome for any experiment performed by that observer; this excludes Everettian interpretations. Where the works cited vary is in the other assumptions made.

It should be noted that each of the major avenues of approach to the measurement problem is capable of giving an account of goings-on in any physical scenario, including the ones considered in these works. Each of them, therefore, must violate some member of the set of assumptions shown to be inconsistent. These results do not pose problems for existing approaches to the measurement problem; rather, they are no-go theorems for approaches that might seek to satisfy all of the set of assumptions shown to be inconsistent. As the assumptions considered include both unitary evolution and unique outcomes of experiments, and the scenarios considered involved situations involving superpositions of distinct experimental outcomes, these results concern theories on which the quantum state, as given by the Schrödinger equation, is not a complete description of reality, as it fails to determine the unique outcomes perceived by the observers. These preceptions could be thought of as supervening on brain states, in which case there is physical structure not included in the quantum state, or as attributes of immaterial minds. On either interpretation, the sorts of theories ruled out fall under the first horn of Bell’s dilemma, mentioned in section 4.2, and these no-go results in part reproduce, and in part extend, no-go results for certain sorts of modal interpretations (see entry on modal interpretations of quantum mechanics ).

These results involving extended Wigner’s friend scenarios have engendered considerable philosophical discussion; see Sudbery (2017, 2019), Healey (2018, 2020), Dieks (2019), Losada et al. (2019), Dascal (2020), Evans (2020), Fortin and Lombardi (2020), Kastner (2020), Muciño & Okon (2020), Bub (2020, 2021), Cavalcanti (2021), Cavalcanti and Wiseman (2021), and Żukowski and Markiewicz (2021).

A quantum state that is a superposition of two distinct terms, such as

where \(\ket{\psi_{1}}\) and \(\ket{\psi_{2}}\) are distinguishable states, is not the same state as a mixture of \(\ket{\psi_{1}}\) and \(\ket{\psi_{2}}\), which would be appropriate for a situation in which the state prepared was either \(\ket{\psi_{1}}\) or \(\ket{\psi_{2}}\), but we don’t know which. The difference between a coherent superposition of two terms and a mixture has empirical consequences. To see this, consider the double-slit experiment, in which a beam of particles (such as electrons, neutrons, or photons) passes through two narrow slits and then impinges on a screen, where the particles are detected. Take \(\ket{\psi_{1}}\) to be a state in which a particle passes through the top slit, and \(\ket{\psi_{2}}\), a state in which it passes through the bottom slit. The fact that the state is a superposition of these two alternatives is exhibited in interference fringes at the screen, alternating bands of high and low rates of absorption.

This is often expressed in terms of a difference between classical and quantum probabilities. If the particles were classical particles, the probability of detection at some point \(p\) of the screen would simply be a weighted average of two conditional probabilities: the probability of detection at \(p\), given that the particle passed through the top slit, and the probability of detection at \(p\), given that the particle passed through the bottom slit. The appearance of interference is an index of nonclassicality.

Suppose, now, that the electrons interact with something else (call it the environment ) on the way to the screen, that could serve as a “which-way” detector; that is, the state of this auxiliary system becomes entangled with the state of the electron in such a way that its state is correlated with \(\ket{\psi_{1}}\) and \(\ket{\psi_{2}}\). Then the state of the quantum system, \(s\), and its environment, \(e\), is

If the environment states \(\ket{\phi_{1}} _{e}\) are \(\ket{\phi_{2}}_{e}\) are distinguishable states, then this completely destroys the interference fringes: the particles interact with the screen as if they determinately went through one slit or the other, and the pattern that emerges is the result of overlaying the two single-slit patterns. That is, we can treat the particles as if they followed (approximately) definite trajectories, and apply probabilities in a classical manner.

Now, macroscopic objects are typically in interaction with a large and complex environment—they are constantly being bombarded with air molecules, photons, and the like. As a result, the reduced state of such a system quickly becomes a mixture of quasi-classical states, a phenomenon known as decoherence .

A generalization of decoherence lies at the heart of an approach to the interpretation of quantum mechanics that goes by the name of decoherent histories approach (see the entry on the consistent histories approach to quantum mechanics for an overview).

Decoherence plays important roles in the other approaches to quantum mechanics, though the role it plays varies with approach; see the entry on the role of decoherence in quantum mechanics for information on this.

Most of the above approaches take it that the goal is to provide an account of events in the world that recovers, at least in some approximation, something like our familiar world of ordinary objects behaving classically. None of the mainstream approaches accord any special physical role to conscious observers. There have, however, been proposals in that direction (see the entry on quantum approaches to consciousness for discussion).

All of the above-mentioned approaches are consistent with observation. Mere consistency, however, is not enough; the rules for connecting quantum theory with experimental results typically involve nontrivial (that is, not equal to zero or one) probabilities assigned to experimental outcomes. These calculated probabilities are confronted with empirical evidence in the form of statistical data from repeated experiments. Extant hidden-variables theories reproduce the quantum probabilities, and collapse theories have the intriguing feature of reproducing very close approximations to quantum probabilities for all experiments that have been performed so far but departing from the quantum probabilities for other conceivable experiments. This permits, in principle, an empirical discrimination between such theories and no-collapse theories.

A criticism that has been raised against Everettian theories is that it is not clear whether they can even make sense of statistical testing of this kind, as it does not, in any straightforward way, make sense to talk of the probability of obtaining, say, a ‘+” outcome of a given experiment when it is certain that all possible outcomes will occur on some branch of the wavefunction. This has been called the “Everettian evidential problem”. It has been the subject of much recent work on Everettian theories; see Saunders (2007) for an introduction and overview.

If one accepts that Everettians have a solution to the evidential problem, then, among the major lines of approach, none is favored in a straightforward way by the empirical evidence. There will not be space here to give an in-depth overview of these ongoing discussions, but a few considerations can be mentioned, to give the reader a flavor of the discussions; see entries on particular approaches for more detail.

Everettians take, as a virtue of the approach, the fact that it does not involve an extension or modification of the quantum formalism. Bohmians claim, in favor of the Bohmian approach, that a theory on these lines provides the most straightforward picture of events; ontological issues are less clear-cut when it comes to Everettian theories or collapse theories.

Another consideration is compatibility with relativistic causal structure. See Myrvold (2021) for an overview of relavistic constraints on approaches to the measurement problem.The de Broglie-Bohm theory requires a distinguished relation of distant simultaneity for its formulation, and, it can be argued, this is an ineliminable feature of any hidden-variables theory of this sort, that selects some observable to always have definite values (see Berndl et al. 1996; Myrvold 2002, 2021). On the other hand, there are collapse models that are fully relativistic. On such models, collapses are localized events. Though probabilities of collapses at spacelike separation from each other are not independent, this probabilistic dependence does not require us to single one out as earlier and the other later. Thus, such theories do not require a distinguished relation of distant simultaneity. There remains, however, some discussion of how to equip such theories with beables (or “elements of reality”). See the entry on collapse theories and references therein; see also, for some recent contributions to the discussion, Fleming (2016), Maudlin (2016), and Myrvold (2016). In the case of Everettian theories, one must first think about how to formulate the question of relativistic locality. Several authors have approached this issue in somewhat different ways, with a common conclusion that Everettian quantum mechanics is, indeed, local. (See Vaidman 1994; Bacciagaluppi 2002; Chapter 8 of Wallace 2012; Tipler 2014; Vaidman 2016; and Brown and Timpson 2016.)

5. Ontological Issues

As mentioned, a central question of interpretation of quantum mechanics concerns whether quantum states should be regarded as representing anything in physical reality. If this is answered in the affirmative, this gives rise to new questions, namely, what sort of physical reality is represented by the quantum state, and whether a quantum state could in principle give an exhaustive account of physical reality.

Harrigan and Spekkens (2010) have introduced a framework for discussing these issues. In their terminology, a complete specification of the physical properties is given by the ontic state of a system. An ontological model posits a space of ontic states and associates, with any preparation procedure, a probability distribution over ontic states. A model is said to be \(\psi\)- ontic if the ontic state uniquely determines the quantum state; that is, if there is a function from ontic states to quantum states (this includes both cases in which the quantum state also completely determines the physical state, and cases, such as hidden-variables theories, in which the quantum state does not completely determine the physical state). In their terminology, models that are not \(\psi\)-ontic are called \(\psi\) -epistemic . If a model is not \(\psi\)-ontic, this means that it is possible for some ontic states to be the result of two or more preparations that lead to different assignments of pure quantum states; that is, the same ontic state may be compatible with distinct quantum states.

This gives a nice way of posing the question of quantum state realism: are there preparations corresponding to distinct pure quantum states that can give rise to the same ontic state, or, conversely, are there ontic states compatible with distinct quantum states? Pusey, Barrett, and Rudolph (2012) showed that, if one adopts a seemingly natural independence assumption about state preparations—namely, the assumption that it is possible to prepare a pair of systems in such a way that the probabilities for ontic states of the two systems are effectively independent—then the answer is negative; any ontological model that reproduces quantum predictions and satisfies this Preparation Independence assumption must be a \(\psi\)-ontic model.

The Pusey, Barrett and Rudolph (PBR) theorem does not close off all options for anti-realism about quantum states; an anti-realist about quantum states could reject the Preparation Independence assumption, or reject the framework within which the theorem is set; see discussion in Spekkens (2015): 92–93. See Leifer (2014) for a careful and thorough overview of theorems relevant to quantum state realism, and Myrvold (2020) for a presentation of a case for quantum state realism based on theorems of this sort.

The major realist approaches to the measurement problem are all, in some sense, realist about quantum states. Merely saying this is insufficient to give an account of the ontology of a given interpretation. Among the questions to be addressed are: if quantum states represent something physically real, what sort of thing is it? This is the question of the ontological construal of quantum states. Another question is the EPR question, whether a description in terms of quantum states can be taken as, in principle, complete, or whether it must be supplemented by different ontology.

De Broglie’s original conception of the “pilot wave” was that it would be a field, analogous to an electromagnetic field. The original conception was that each particle would have its own guiding wave. However, in quantum mechanics as it was developed at the hands of Schrödinger, for a system of two or more particles there are not individual wave functions for each particle, but, rather, a single wave function that is defined on \(n\)-tuples of points in space, where \(n\) is the number of particles. This was taken, by de Broglie, Schrödinger and others, to militate against the conception of quantum wave functions as fields. If quantum states represent something in physical reality, they are unlike anything familiar in classical physics.

One response that has been taken is to insist that quantum wave functions are fields nonetheless, albeit fields on a space of enormously high dimension, namely, \(3n\), where \(n\) is the number of elementary particles in the universe. On this view, this high-dimensional space is thought of as more fundamental than the familiar three-dimensional space (or four-dimensional spacetime) that is usually taken to be the arena of physical events. See Albert (1996, 2013), for the classic statement of the view; other proponents include Loewer (1996), Lewis (2004), Ney (2012, 2013a,b, 2021), and North (2013). Most of the discussion of this proposal has taken place within the context of nonrelativistic quantum mechanics, which is not a fundamental theory. It has been argued that considerations of how the wave functions of nonrelativistic quantum mechanics arise from a quantum field theory undermines the idea that wave functions are relevantly like fields on configuration space, and also the idea that configuration spaces can be thought of as more fundamental than ordinary spacetime (Myrvold 2015).

A view that takes a wave function as a field on a high-dimensional space must be distinguished from a view that takes it to be what Belot (2012) has called a multi-field , which assigns properties to \(n\)-tuples of points of ordinary three-dimensional space. These are distinct views; proponents of the \(3n\)-dimensional conception make much of the fact that it restores Separability: on this view, a complete specification of the way the world is, at some time, is given by specification of local states of affairs at each address in the fundamental (\(3n\)-dimensional) space. Taking a wave function to be a multi-field, on the other hand, involves accepting nonseparability. Another difference between taking wave-functions as multi-fields on ordinary space and taking them to be fields on a high-dimensional space is that, on the multi-field view, there is no question about the relation of ordinary three-dimensional space to some more fundamental space.­ Hubert and Romano (2018) argue that wave-functions are naturally and straightforwardly construed as multi-fields.

It has been argued that, on the de Broglie-Bohm pilot wave theory and related pilot wave theories, the quantum state plays a role more similar to that of a law in classical mechanics; its role is to provide dynamics for the Bohmian corpuscles, which, according to the theory, compose ordinary objects. See Dürr, Goldstein, and Zanghì (1997), Allori et al. (2008), Allori (2021).

Dürr, Goldstein, and Zanghì (1992) introduced the term “primitive ontology” for what, according to a physical theory, makes up ordinary physical objects; on the de Broglie-Bohm theory, this is the Bohmian corpuscles. The conception is extended to interpretations of collapse theories by Allori et al. (2008). Primitive ontology is to be distinguished from other ontology, such as the quantum state, that is introduced into the theory to account for the behavior of the primitive ontology. The distinction is meant to be a guide as to how to conceive of the nonprimitive ontology of the theory.

Quantum mechanics has not only given rise to interpretational conundrums; it has given rise to new concepts in computing and in information theory. Quantum information theory is the study of the possibilities for information processing and transmission opened up by quantum theory. This has given rise to a different perspective on quantum theory, one on which, as Bub (2000, 597) put it, “the puzzling features of quantum mechanics are seen as a resource to be developed rather than a problem to be solved” (see the entries on quantum computing and quantum entanglement and information ).

Another area of active research in the foundations of quantum mechanics is the attempt to gain deeper insight into the structure of the theory, and the ways in which it differs from both classical physics and other theories that one might construct, by characterizing the structure of the theory in terms of very general principles, often with an information-theoretic flavour.

This project has its roots in early work of Mackey (1957, 1963), Ludwig (1964), and Piron (1964) aiming to characterize quantum mechanics in operational terms. This has led to the development of a framework of generalized probabilistic model. It also has connections with the investigations into quantum logic initiated by Birkhoff and von Neumann (1936) (see the entry quantum logic and probability theory for an overview).

Interest in the project of deriving quantum theory from axioms with clear operational content was revived by the work of Hardy (2001 [2008], Other Internet Resources). Significant results along these lines include the axiomatizations of Masanes and Müller (2011) and Chiribella, D’Ariano, and Perinotti (2011). See Chiribella and Spekkens (2015) for an overview of this burgeoning research area.

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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Feynman, R., Lectures on Physics . These are introductory lectures aimed at physics undergraduates.
• Hardy, Lucien, 2001 [2008], “ Quantum Theory from Five Reasonable Axioms ”, manuscript at arxiv.org originally submitted in 2001, but now is labeled version 4 (2008).
• Lewis, Peter J., “ Interpretations of Quantum Mechanics ”, Internet Encyclopedia of Philosophy .
• Norton, John, “ Origins of Quantum Theory ,” A good introduction to the history of quantum theory, about which little is said in the present entry.
• PhET Interactive Simulations project , University of Colorado Boulder; these pages contain useful simulations of classic quantum experiments.

Bell’s Theorem | physics: holism and nonseparability | quantum mechanics | quantum mechanics: action at a distance in | quantum mechanics: Bohmian mechanics | quantum mechanics: collapse theories | quantum mechanics: consistent histories approach | quantum mechanics: Copenhagen interpretation of | quantum mechanics: Everettian | quantum mechanics: Kochen-Specker theorem | quantum mechanics: many-worlds interpretation of | quantum mechanics: modal interpretations of | quantum mechanics: relational | quantum mechanics: the role of decoherence in | quantum theory: and consciousness | quantum theory: and mathematical rigor | quantum theory: quantum computing | quantum theory: quantum entanglement and information | quantum theory: quantum field theory | quantum theory: quantum gravity | quantum theory: quantum logic and probability theory | quantum theory: the Einstein-Podolsky-Rosen argument in | Uncertainty Principle

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Quantum Physics Overview

How Quantum Mechanics Explains the Invisible Universe

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Quantum physics is the study of the behavior of matter and energy at the molecular, atomic, nuclear, and even smaller microscopic levels. In the early 20th century, scientists discovered that the laws governing macroscopic objects do not function the same in such small realms.

What Does Quantum Mean?

"Quantum" comes from the Latin meaning "how much." It refers to the discrete units of matter and energy that are predicted by and observed in quantum physics. Even space and time, which appear to be extremely continuous, have the smallest possible values.

Who Developed Quantum Mechanics?

As scientists gained the technology to measure with greater precision, strange phenomena was observed. The birth of quantum physics is attributed to Max Planck's 1900 paper on blackbody radiation. Development of the field was done by Max Planck , Albert Einstein , Niels Bohr , Richard Feynman, Werner Heisenberg, Erwin Schroedinger, and other luminary figures in the field. Ironically, Albert Einstein had serious theoretical issues with quantum mechanics and tried for many years to disprove or modify it.

What's Special About Quantum Physics?

In the realm of quantum physics, observing something actually influences the physical processes taking place. Light waves act like particles and particles act like waves (called wave particle duality ). Matter can go from one spot to another without moving through the intervening space (called quantum tunnelling). Information moves instantly across vast distances. In fact, in quantum mechanics we discover that the entire universe is actually a series of probabilities. Fortunately, it breaks down when dealing with large objects, as demonstrated by the Schrodinger's Cat thought experiment.

What is Quantum Entanglement?

One of the key concepts is quantum entanglement , which describes a situation where multiple particles are associated in such a way that measuring the quantum state of one particle also places constraints on the measurements of the other particles. This is best exemplified by the EPR Paradox . Though originally a thought experiment, this has now been confirmed experimentally through tests of something known as Bell's Theorem .

Quantum Optics

Quantum optics is a branch of quantum physics that focuses primarily on the behavior of light, or photons. At the level of quantum optics, the behavior of individual photons has a bearing on the outcoming light, as opposed to classical optics, which was developed by Sir Isaac Newton. Lasers are one application that has come out of the study of quantum optics.

Quantum Electrodynamics (QED)

Quantum electrodynamics (QED) is the study of how electrons and photons interact. It was developed in the late 1940s by Richard Feynman, Julian Schwinger, Sinitro Tomonage, and others. The predictions of QED regarding the scattering of photons and electrons are accurate to eleven decimal places.

Unified Field Theory

Unified field theory is a collection of research paths that are trying to reconcile quantum physics with Einstein's theory of general relativity , often by trying to consolidate the fundamental forces of physics . Some types of unified theories include (with some overlap):

• Quantum Gravity
• Loop Quantum Gravity
• String Theory / Superstring Theory / M-Theory
• Grand Unified Theory
• Supersymmetry
• Theory of Everything

Other Names for Quantum Physics

Quantum physics is sometimes called quantum mechanics or quantum field theory. It also has various subfields, as discussed above, which are sometimes used interchangeably with quantum physics, though quantum physics is actually the broader term for all of these disciplines.

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Quantum physics is a well-established part of many high-school curricula all over the world and the advance of quantum technologies (usually referred to as “second quantum revolution”) may provide an additional boost. At the same time, even some elements of the standard model of particle physics are increasingly included in high school and undergrad syllabi.

Although the integration of these modern topics is welcome, it also poses a challenge for physics education. What is needed, initially, is a proper simplifications and educational reconstructions of the aforementioned topics. However, besides these basics the educational value and individual relevance ascribed by the students also need to be discussed and clarified.

At the high school and undergrad level, one is clearly not aiming at technical mastery of the formalism but more interested in conceptual clarity. This establishes a connection to issues in the philosophy and history of physics. Eventually, one should not lose sight of the established demand to integrate the “nature of science” (roughly speaking over and above the mere scientific facts) into the teaching of physics.  

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Title: topics in weyl geometry and quantum anomalies.

Abstract: The first part of this thesis focuses on the Weyl-covariant nature of holography. We generalize the Fefferman-Graham (FG) ambient construction for conformal geometry to a corresponding construction for Weyl geometry. Through the Weyl-ambient construction, we investigate Weyl-covariant quantities on the Weyl manifold and define Weyl-obstruction tensors. We show that Weyl-obstruction tensors appear as poles in the Fefferman-Graham expansion of the ALAdS bulk metric for even boundary dimensions. Under holographic renormalization in the Weyl-Fefferman-Graham gauge, we compute the Weyl anomaly of the boundary theory in multiple dimensions and demonstrate that Weyl-obstruction tensors can be used as the building blocks for the Weyl anomaly of the dual quantum field theory (QFT). The holographic calculation with a background Weyl geometry also suggests an underlying geometric interpretation of the Weyl anomaly. The second part of this thesis is devoted to understanding the geometric nature of the BRST formalism and quantum anomalies. Using the language of Lie algebroids, the BRST complex can be encoded in the exterior algebra of an Atiyah Lie algebroid derived from the principal bundle of the gauge theory. We showed that the cohomology of an Atiyah Lie algebroid in a trivialization gives rise to the BRST cohomology. We then apply the Lie algebroid cohomology in studying quantum anomalies and demonstrate the computation for chiral and Lorentz-Weyl anomalies. In particular, we pay close attention to the fact that the geometric intuition afforded by the Lie algebroid (which was absent in the traditional BRST complex) provides hints of a deeper picture that simultaneously geometrizes the consistent and covariant forms of the anomaly. In the algebroid construction, the difference between the consistent and covariant anomalies is simply a different choice of basis.

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Quantum Drama: From the Bohr-­Einstein Debate to the Riddle of Entanglement by Jim Baggott and John L. Heilbron. Oxford University Press, 2024 ($32.99)

This meticulous account of the tumultuous evolution of quantum physics spans more than a century, including Albert Einstein and Niels Bohr’s initial standoff at the fifth Solvay conference, in 1927, and recent work on the uncharted modern frontiers of quantum mechanics. Science writer Jim Baggott and professor of history John L. Heilbron balance depth and sophistication with sportscasterlike enthusiasm as they recount how the debate—wisely divided here into four acts—expanded to accommodate “the human passions and social contexts in which the ideas were conceived, debated, refined, accepted or rejected.” The stakes of these theoretical wins and losses are as profound as our understanding of the purpose of science itself. — Dana Dunham

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This Earthly Globe: A Venetian Geographer and the Quest to Map the World by Andrea di Robilant. Knopf, 2024 ($30)

Italian journalist Andrea di Robilant illuminates the geopolitical machinations and heart-pounding voyages of 17th-century explorers who would change how Europeans understood the shape of the world. Di Robilant animates the creation of a world map by recounting the swashbuckling adventures of Marco Polo, al-Hasan ibn Muhammad al-Wazzan, Father Francisco Álvares, and others. We glimpse the tireless work of Venice-based Giovambattista Ramusio, the humanist and editor who translated the explorers’ documents while navigating the “growing climate of intolerance” toward secular writing ushered in by the Counter-Reformation. Scrupulously research­ed, This Earthly Globe reveals the riveting foundations of modern geography and cartography. — Amy Brady

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Scientists observe record-setting electron mobility in a new crystal film

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A material with a high electron mobility is like a highway without traffic. Any electrons that flow into the material experience a commuter’s dream, breezing through without any obstacles or congestion to slow or scatter them off their path.

The higher a material’s electron mobility, the more efficient its electrical conductivity, and the less energy is lost or wasted as electrons zip through. Advanced materials that exhibit high electron mobility will be essential for more efficient and sustainable electronic devices that can do more work with less power.

Now, physicists at MIT, the Army Research Lab, and elsewhere have achieved a record-setting level of electron mobility in a thin film of ternary tetradymite — a class of mineral that is naturally found in deep hydrothermal deposits of gold and quartz.

For this study, the scientists grew pure, ultrathin films of the material, in a way that minimized defects in its crystalline structure. They found that this nearly perfect film — much thinner than a human hair — exhibits the highest electron mobility in its class.

The team was able to estimate the material’s electron mobility by detecting quantum oscillations when electric current passes through. These oscillations are a signature of the quantum mechanical behavior of electrons in a material. The researchers detected a particular rhythm of oscillations that is characteristic of high electron mobility — higher than any ternary thin films of this class to date.

“Before, what people had achieved in terms of electron mobility in these systems was like traffic on a road under construction — you’re backed up, you can’t drive, it’s dusty, and it’s a mess,” says Jagadeesh Moodera, a senior research scientist in MIT’s Department of Physics. “In this newly optimized material, it’s like driving on the Mass Pike with no traffic.”

The team’s results, which appear today in the journal Materials Today Physics , point to ternary tetradymite thin films as a promising material for future electronics, such as wearable thermoelectric devices that efficiently convert waste heat into electricity. (Tetradymites are the active materials that cause the cooling effect in commercial thermoelectric coolers.) The material could also be the basis for spintronic devices, which process information using an electron’s spin, using far less power than conventional silicon-based devices.

The study also uses quantum oscillations as a highly effective tool for measuring a material’s electronic performance.

“We are using this oscillation as a rapid test kit,” says study author Hang Chi, a former research scientist at MIT who is now at the University of Ottawa. “By studying this delicate quantum dance of electrons, scientists can start to understand and identify new materials for the next generation of technologies that will power our world.”

Chi and Moodera’s co-authors include Patrick Taylor, formerly of MIT Lincoln Laboratory, along with Owen Vail and Harry Hier of the Army Research Lab, and Brandi Wooten and Joseph Heremans of Ohio State University.

The name “tetradymite” derives from the Greek “tetra” for “four,” and “dymite,” meaning “twin.” Both terms describe the mineral’s crystal structure, which consists of rhombohedral crystals that are “twinned” in groups of four — i.e. they have identical crystal structures that share a side.

Tetradymites comprise combinations of bismuth, antimony tellurium, sulfur, and selenium. In the 1950s, scientists found that tetradymites exhibit semiconducting properties that could be ideal for thermoelectric applications: The mineral in its bulk crystal form was able to passively convert heat into electricity.

Then, in the 1990s, the late Institute Professor Mildred Dresselhaus proposed that the mineral’s thermoelectric properties might be significantly enhanced, not in its bulk form but within its microscopic, nanometer-scale surface, where the interactions of electrons is more pronounced. (Heremans happened to work in Dresselhaus’ group at the time.)

“It became clear that when you look at this material long enough and close enough, new things will happen,” Chi says. “This material was identified as a topological insulator, where scientists could see very interesting phenomena on their surface. But to keep uncovering new things, we have to master the material growth.”

To grow thin films of pure crystal, the researchers employed molecular beam epitaxy — a method by which a beam of molecules is fired at a substrate, typically in a vacuum, and with precisely controlled temperatures. When the molecules deposit on the substrate, they condense and build up slowly, one atomic layer at a time. By controlling the timing and type of molecules deposited, scientists can grow ultrathin crystal films in exact configurations, with few if any defects.

“Normally, bismuth and tellurium can interchange their position, which creates defects in the crystal,” co-author Taylor explains. “The system we used to grow these films came down with me from MIT Lincoln Laboratory, where we use high purity materials to minimize impurities to undetectable limits. It is the perfect tool to explore this research.”

The team grew thin films of ternary tetradymite, each about 100 nanometers thin. They then tested the film’s electronic properties by looking for Shubnikov-de Haas quantum oscillations — a phenomenon that was discovered by physicists Lev Shubnikov and Wander de Haas, who found that a material’s electrical conductivity can oscillate when exposed to a strong magnetic field at low temperatures. This effect occurs because the material’s electrons fill up specific energy levels that shift as the magnetic field changes.

Such quantum oscillations could serve as a signature of a material’s electronic structure, and the ways in which electrons behave and interact. Most notably for the MIT team, the oscillations could determine a material’s electron mobility: If oscillations exist, it must mean that the material’s electrical resistance is able to change, and by inference, electrons can be mobile, and made to easily flow.

The team looked for signs of quantum oscillations in their new films, by first exposing them to ultracold temperatures and a strong magnetic field, then running an electric current through the film and measuring the voltage along its path, as they tuned the magnetic field up and down.

“It turns out, to our great joy and excitement, that the material’s electrical resistance oscillates,” Chi says. “Immediately, that tells you that this has very high electron mobility.”

Specifically, the team estimates that the ternary tetradymite thin film exhibits an electron mobility of 10,000 cm 2 /V-s — the highest mobility of any ternary tetradymite film yet measured. The team suspects that the film’s record mobility has something to do with its low defects and impurities, which they were able to minimize with their precise growth strategies. The fewer a material’s defects, the fewer obstacles an electron encounters, and the more freely it can flow.

“This is showing it’s possible to go a giant step further, when properly controlling these complex systems,” Moodera says. “This tells us we’re in the right direction, and we have the right system to proceed further, to keep perfecting this material down to even much thinner films and proximity coupling for use in future spintronics and wearable thermoelectric devices.”

This research was supported in part by the Army Research Office, National Science Foundation, Office of Naval Research, Canada Research Chairs Program and Natural Sciences and Engineering Research Council of Canada.

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Home — Essay Samples — Science — Physics — Quantum Mechanics

Essays on Quantum Mechanics

Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at the smallest scales. It has revolutionized our understanding of the universe, challenging the classical laws of physics and opening up new possibilities for technology and scientific exploration. In this essay, we will explore a wide range of topics in quantum mechanics, from the foundational principles to cutting-edge research and applications.

Importance of the Topic

Advice on choosing a topic.

When choosing a topic for your quantum mechanics essay, consider your interests and the latest advancements in the field. You may want to explore a specific experiment, theory, or application of quantum mechanics, or delve into the philosophical implications of quantum phenomena. It's important to select a topic that you are passionate about and that allows you to engage with the complex and fascinating concepts of quantum mechanics. Additionally, consider the availability of research material and sources to support your chosen topic.

Quantum Mechanics Essay Topics

• The Double-Slit Experiment: An Exploration of Wave-Particle Duality
• The Uncertainty Principle: Understanding Heisenberg's Groundbreaking Theory
• Quantum Entanglement: The Spooky Action at a Distance
• Schrödinger's Cat: A Thought Experiment in Quantum Superposition
• Quantum Tunneling: Breaking the Laws of Classical Physics
• Quantum Computing: The Future of Information Processing
• The Many-Worlds Interpretation: Exploring the Multiverse
• Bell's Theorem: Testing the Limits of Quantum Mechanics
• Quantum Teleportation: The Science of Instantaneous Communication
• Quantum Cryptography: Securing Information with Quantum Principles
• Quantum Chaos: Unraveling the Complex Dynamics of Quantum Systems
• Quantum Gravity: Bridging the Gap Between Quantum Mechanics and General Relativity
• Quantum Biology: Investigating Quantum Effects in Biological Systems
• Quantum Cosmology: Understanding the Origins of the Universe through Quantum Mechanics
• Quantum Field Theory: Describing Elementary Particles and Forces through Quantum Principles
• Quantum Simulation: Using Quantum Systems to Model Complex Phenomena
• Decoherence: Exploring the Loss of Quantum Coherence in Macroscopic Systems
• Quantum Optics: Harnessing Quantum Effects for Advanced Optical Technologies
• Quantum Information Theory: The Study of Quantum Information Processing
• Quantum Mechanics in Everyday Life: Applications and Implications

Quantum mechanics offers a vast array of topics for exploration and study, ranging from foundational principles to cutting-edge research and applications. By delving into these topics, we can gain a deeper understanding of the fundamental nature of the universe and the potential for groundbreaking technological advancements. Whether you are interested in the theoretical aspects of quantum mechanics or its practical applications, there is no shortage of intriguing and thought-provoking topics to explore in this captivating field of physics.

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Role of Physics in The Worldwide Ict Revolution

Quantum game theory: developments in quantum computing, relevant topics.

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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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10 mind-boggling things you should know about quantum physics

From the multiverse to black holes, here’s your cheat sheet to the spooky side of the universe.

1. The quantum world is lumpy

The quantum world has a lot in common with shoes. You can’t just go to a shop and pick out sneakers that are an exact match for your feet. Instead, you’re forced to choose between pairs that come in predetermined sizes.

The subatomic world is similar. Albert Einstein won a Nobel Prize for proving that energy is quantized. Just as you can only buy shoes in multiples of half a size, so energy only comes in multiples of the same "quanta" — hence the name quantum physics.

The quanta here is the Planck constant , named after Max Planck, the godfather of quantum physics. He was trying to solve a problem with our understanding of hot objects like the sun. Our best theories couldn’t match the observations of the energy they kick out. By proposing that energy is quantized, he was able to bring theory neatly into line with experiment.

2. Something can be both wave and particle

J. J. Thomson won the Nobel Prize in 1906 for his discovery that electrons are particles. Yet his son George won the Nobel Prize in 1937 for showing that electrons are waves. Who was right? The answer is both of them. This so-called wave-particle duality is a cornerstone of quantum physics. It applies to light as well as electrons. Sometimes it pays to think about light as an electromagnetic wave, but at other times it’s more useful to picture it in the form of particles called photons. 

A telescope can focus light waves from distant stars, and also acts as a giant light bucket for collecting photons. It also means that light can exert pressure as photons slam into an object. This is something we already use to propel spacecraft with solar sails, and it may be possible to exploit it in order to maneuver a dangerous asteroid off a collision course with Earth , according to Rusty Schweickart, chairman of the B612 Foundation.

3. Objects can be in two places at once

Wave-particle duality is an example of superposition . That is, a quantum object existing in multiple states at once. An electron, for example, is both ‘here’ and ‘there’ simultaneously. It’s only once we do an experiment to find out where it is that it settles down into one or the other. 

This makes quantum physics all about probabilities. We can only say which state an object is most likely to be in once we look. These odds are encapsulated into a mathematical entity called the wave function. Making an observation is said to ‘collapse’ the wave function, destroying the superposition and forcing the object into just one of its many possible states.

This idea is behind the famous Schrödinger’s cat thought experiment. A cat in a sealed box has its fate linked to a quantum device. As the device exists in both states until a measurement is made, the cat is simultaneously alive and dead until we look.

4. It may lead us towards a multiverse

The idea that observation collapses the wave function and forces a quantum ‘choice’ is known as the Copenhagen interpretation of quantum physics. However, it’s not the only option on the table. Advocates of the ‘many worlds’ interpretation argue that there is no choice involved at all. Instead, at the moment the measurement is made, reality fractures into two copies of itself: one in which we experience outcome A, and another where we see outcome B unfold. It gets around the thorny issue of needing an observer to make stuff happen — does a dog count as an observer, or a robot?

Instead, as far as a quantum particle is concerned, there’s just one very weird reality consisting of many tangled-up layers. As we zoom out towards the larger scales that we experience day to day, those layers untangle into the worlds of the many worlds theory. Physicists call this process decoherence.

5. It helps us characterize stars

Danish physicist Niels Bohr showed us that the orbits of electrons inside atoms are also quantized. They come in predetermined sizes called energy levels. When an electron drops from a higher energy level to a lower energy level, it spits out a photon with an energy equal to the size of the gap. Equally, an electron can absorb a particle of light and use its energy to leap up to a higher energy level.

Astronomers use this effect all the time. We know what stars are made of because when we break up their light into a rainbow-like spectrum, we see colors that are missing. Different chemical elements have different energy level spacings, so we can work out the constituents of the sun and other stars from the precise colors that are absent.

6. Without it the sun wouldn’t shine

The sun makes its energy through a process called nuclear fusion. It involves two protons — the positively charged particles in an atom — sticking together. However, their identical charges make them repel each other, just like two north poles of a magnet. Physicists call this the Coulomb barrier, and it’s like a wall between the two protons. 

Think of protons as particles and they just collide with the wall and move apart: No fusion, no sunlight. Yet think of them as waves, and it’s a different story. When the wave’s crest reaches the wall, the leading edge has already made it through. The wave’s height represents where the proton is most likely to be. So although it is unlikely to be where the leading edge is, it is there sometimes. It’s as if the proton has burrowed through the barrier, and fusion occurs. Physicists call this effect "quantum tunneling".

7. It stops dead stars collapsing

Eventually fusion in the sun will stop and our star will die. Gravity will win and the sun will collapse, but not indefinitely. The smaller it gets, the more material is crammed together. Eventually a rule of quantum physics called the Pauli exclusion principle comes into play. This says that it is forbidden for certain kinds of particles — such as electrons — to exist in the same quantum state. As gravity tries to do just that, it encounters a resistance that astronomers call degeneracy pressure. The collapse stops, and a new Earth-sized object called a white dwarf forms. 

Degeneracy pressure can only put up so much resistance, however. If a white dwarf grows and approaches a mass equal to 1.4 suns, it triggers a wave of fusion that blasts it to bits. Astronomers call this explosion a Type Ia supernova , and it’s bright enough to outshine an entire galaxy.

8. It causes black holes to evaporate

A quantum rule called the Heisenberg uncertainty principle says that it’s impossible to perfectly know two properties of a system simultaneously. The more accurately you know one, the less precisely you know the other. This applies to momentum and position, and separately to energy and time.

It’s a bit like taking out a loan. You can borrow a lot of money for a short amount of time, or a little cash for longer. This leads us to virtual particles. If enough energy is ‘borrowed’ from nature then a pair of particles can fleetingly pop into existence, before rapidly disappearing so as not to default on the loan.

Stephen Hawking imagined this process occurring at the boundary of a black hole, where one particle escapes (as Hawking radiation), but the other is swallowed. Over time the black hole slowly evaporates, as it’s not paying back the full amount it has borrowed. 

9. It explains the universe’s large-scale structure

Our best theory of the universe’s origin is the Big Bang . Yet it was modified in the 1980s to include another theory called inflation . In the first trillionth of a trillionth of a trillionth of a second, the cosmos ballooned from smaller than an atom to about the size of a grapefruit. That’s a whopping 10^78 times bigger. Inflating a red blood cell by the same amount would make it larger than the entire observable universe today.

As it was initially smaller than an atom, the infant universe would have been dominated by quantum fluctuations linked to the Heisenberg uncertainty principle. Inflation caused the universe to grow rapidly before these fluctuations had a chance to fade away. This concentrated energy into some areas rather than others — something astronomers believe acted as seeds around which material could gather to form the clusters of galaxies we observe now.

10. It is more than a little ‘spooky’

As well as helping to prove that light is quantum, Einstein argued in favor of another effect that he dubbed ‘spooky action at distance’. Today we know that this ‘quantum entanglement’ is real, but we still don’t fully understand what’s going on. Let’s say that we bring two particles together in such a way that their quantum states are inexorably bound, or entangled. One is in state A, and the other in state B.

The Pauli exclusion principle says that they can’t both be in the same state. If we change one, the other instantly changes to compensate. This happens even if we separate the two particles from each other on opposite sides of the universe. It’s as if information about the change we’ve made has traveled between them faster than the speed of light, something Einstein said was impossible.

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Essays on Quantum Physics

9 samples on this topic

Our essay writing service presents to you an open-access database of free Quantum Physics essay samples. We'd like to emphasize that the showcased papers were crafted by proficient writers with relevant academic backgrounds and cover most various Quantum Physics essay topics. Remarkably, any Quantum Physics paper you'd find here could serve as a great source of inspiration, valuable insights, and content structuring practices.

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Example Of Quantum Computer And Security Research Paper

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Good Essay On Physics In Everyday Life

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Comparison between the cultural impact of Quantum physics to the reaction to the Theory of Natural Selection

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IB Extended Essay Topics: Physics

Stepping into the International Baccalaureate (IB) Diploma program is a significant milestone, and choosing the right Extended Essay topic in Physics can be exciting and daunting. From my years of experience as an IB educator and essay advisor, I’ve seen firsthand how the choice of topic can affect a student’s research. Therefore, in this article, I aim to share insights and ideas on topics for the IB DP Physics Extended Essay.

Understanding the IB Physics Extended Essay

The IB Physics Extended Essay is an independent, self-directed piece of research that culminates in a 4,000-word paper required for the International Baccalaureate Diploma Programme.

According to the IB criteria, this significant academic task involves students independently researching a topic that sparks their interest in IB DP Physics. It’s an excellent opportunity to investigate a question that captivates you and apply theoretical concepts to practical situations.

The primary aim is not merely to produce an essay but to engage in an exhaustive study showcasing your grasp of physics and enthusiasm for the subject. Now, let’s consider the following aspects of the IB Physics Extended Essay:

• Scope of Research . It’s essential to select a topic that allows for an in-depth investigation within the constraints of the available resources and the word limit.
• Application of Theory . The essay should demonstrate how physics theories and concepts can be applied to analyze a specific problem or question.
• Methodology . A clear and systematic approach to conducting your research is critical. It involves choosing appropriate methods for data collection and analysis.
• Critical Thinking . Throughout your essay, you should critically evaluate the information, data, and methodologies used.
• Creativity and Originality . Finding innovative ways to approach your topic can set your essay apart. It’s about posing new questions, exploring novel perspectives, or applying theories in unique contexts.
• Structured Argument . Your essay should present a coherent argument supported by evidence, leading the reader through your findings to a logical conclusion.
• Reflection . Reflecting on what you have learned from the research process and how it has affected your understanding of the subject area is a valuable component of the essay.

Remember, the goal is not just to write an essay but to engage in a thorough investigation demonstrating your understanding and passion for the Physics course.

Topics to Read:

• How IB Prepares Students for University?
• Can You Retake the IB Exams? Guide for IB Students
• Stress Management and Well-Being for IB Students
• How to Manage Time Effectively as an IB Student
• The Benefits of Pursuing the IB Diploma Programme
• IB vs. National Curriculum. The Benefits of an International Perspective
• What Are the Average IB Acceptance Rates? Insights from an IB Expert
• What Are the IB Internal Assessment Deadlines for 2024?
• Does an IB Diploma Help with College Admissions?
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• What to Wear for IB Exams? IB Dress Code

Physics Extended Essay Topics and Research Questions

Let’s talk about some potential extended essay topics in Зhysics. Quantum mechanics, with its paradoxes and mysteries, offers a rich vein of questions to explore. Additionally, investigating the principles of relativity in everyday phenomena can provide a relatable yet profound topic. Renewable energy projects are increasingly relevant and offer a plethora of research opportunities. Lastly, the vastness of astrophysics allows for endless curiosity and exploration, from black holes to the cosmic microwave background.

The best topics for an IB Physics Extended Essay allow you to explore areas where you can apply physical principles, theories, and experimental investigations to answer complex questions. Here are some ideas:

• The Effect of Winglet Angles on Aircraft Efficiency . How do variations in winglet angles on a model aircraft wing affect its lift-to-drag ratio during flight?
• Investigating Solar Panel Orientation for Optimal Power Generation . How do different solar panel orientations and angles impact power output in a specific geographic location?
• Analyzing the Efficiency of Magnetic Levitation in Reducing Friction . How does the use of magnetic levitation affect the frictional forces on a miniaturized model of a maglev train?
• The Physics of Greenhouse Gases and Climate Change . How do different carbon dioxide concentrations affect infrared radiation absorption in a controlled environment?
• Exploring the Properties of Non-Newtonian Fluids under Stress . How does the application of varying stress levels affect the viscosity of a non-Newtonian fluid, such as a cornstarch and water mixture?
• The Role of Antenna Design in Enhancing Wireless Communication . How does the design of a DIY antenna affect the strength and range of wireless signals it receives?
• The Impact of Crater Size on Meteorite Impact Simulations . What relationship exists between the size of a projectile and the crater it creates in sand, simulating meteorite impacts?
• Studying the Effects of Temperature on the Elasticity of Rubber Bands . How does changing the temperature affect rubber bands’ elasticity and tensile strength?
• Investigation into the Optimal Conditions for Hydrogen Fuel Cell Efficiency . Under what conditions does a homemade hydrogen fuel cell operate most efficiently in terms of voltage output?
• Analyzing the Effectiveness of Different Types of Insulators in Minimizing Heat Loss . How do various household materials compare to thermal insulators in preventing heat loss from a container?
• The Physics Behind Efficient Bicycle Gear Ratios . How do different gear ratios affect cyclists’ efficiency and energy expenditure under various conditions?
• Exploring the Influence of Mirror Shape on the Focal Point of Solar Collectors . How does altering the shape of reflective mirrors affect the concentration and temperature at the focal point of a solar collector?
• Investigating the Relationship Between Electric Motor Speed and Load . What is the relationship between the load applied to an electric motor and its rotation speed?
• The Effect of Blade Design on Wind Turbine Efficiency . How does the blade design of a model wind turbine affect its power output under controlled wind conditions?
• Studying the Propagation of Sound Waves in Different Mediums . How do sound waves propagate in various mediums, and how does the medium affect the speed and attenuation of sound?
• The Dynamics of Pendulum Motion in Non-Uniform Gravitational Fields . How does the length of a pendulum affect its period in regions with varying gravitational strengths?
• Investigating the Effects of Surface Roughness on Solar Panel Efficiency . How does the surface roughness of photovoltaic solar panels impact their efficiency in converting sunlight to electricity?
• The Physics of Ice Skating: Friction and Temperature . What is the relationship between the ice’s temperature and the friction coefficient encountered by an ice skate?
• Evaluating the Impact of Air Resistance on Projectile Range . How do the shape and size of projectiles affect their range in the presence of air resistance?
• The Efficiency of Piezoelectric Materials in Energy Harvesting . How effective are different piezoelectric materials in generating electricity from mechanical stress?
• Thermal Conductivity and Building Materials: A Comparative Study . How do different building materials compare in terms of thermal conductivity and energy efficiency in a model house?
• The Effect of Altitude on the Boiling Point of Water . How does changing altitude affect the boiling point of water, and what implications does this have for cooking at high elevations?
• Optimizing the Design of a Parabolic Solar Heater . What is the most efficient design for a parabolic solar heater when considering the focal point and surface area?
• The Role of Resonance in Bridge Oscillations: A Historical Analysis . How have instances of resonance-induced oscillations in bridges influenced modern bridge design?
• Investigating the Photoelectric Effect in Different Metals . How does the photoelectric effect vary across different metals, and what does this reveal about their electronic structure?
• The Physics of Musical Instruments: String Tension and Pitch . How does the tension of strings on different musical instruments affect the pitch and quality of the sound produced?
• The Efficiency of Vertical vs. Horizontal Wind Turbines . Which vertical or horizontal orientation is more efficient for wind turbines in urban settings?
• The Impact of Battery Temperature on Electric Vehicle Performance . How does the operating temperature of batteries affect the performance and range of electric vehicles?
• Studying the Refractive Index of Various Liquids Under Temperature Changes . How does changing the temperature of different liquids affect their refractive index?
• The Physics of Archery: Arrow Dynamics and Material Science . How do an arrow’s material properties and design affect its flight dynamics and accuracy?
• Analyzing the Radiation Shielding Properties of Martian Regolith . Could Martian regolith be effectively used to shield habitats on Mars from radiation?
• The Influence of Magnetic Fields on Plant Growth . How do varying magnetic field strengths affect certain plants’ growth rate and health?
• The Acoustic Properties of Concert Halls . What architectural features contribute most significantly to the acoustic quality of concert halls?
• The Effectiveness of Heat Sinks in Electronic Devices . How do different materials and designs of heat sinks affect the thermal management of electronic devices?
• The Correlation Between Solar Flare Activity and Earth’s Climate . Is there a significant correlation between periods of increased solar flare activity and changes in Earth’s climate patterns?
• The Impact of Wind Turbine Design on Bird Populations . How does the design of wind turbines affect bird mortality rates, and what design modifications can reduce these impacts?
• The Physics of Long-Distance Space Travel: Propulsion Systems . What are the most promising propulsion systems for long-distance space travel, and how do they compare in terms of efficiency and feasibility?
• Optimizing Refrigeration Techniques Using Thermoelectric Coolers . How effective are thermoelectric coolers in small-scale refrigeration applications compared to traditional cooling methods?
• The Physics of Glaciers: Understanding Ice Flow and Melting Patterns . How do the physical properties of glacier ice influence its flow and melting patterns in response to climate change?
• Electromagnetic Interference in Medical Devices . What levels of electromagnetic interference can disrupt the operation of common medical devices?
• Light Absorption and Energy Efficiency in Smart Windows . How does varying the light absorption properties of smart windows affect their energy efficiency in different climates?
• The Dynamics of Satellite Orbits: Stability and Perturbations . What factors most significantly affect the stability of satellite orbits, and how can perturbations be minimized?
• Physics of Firefighting: Water Stream Dynamics and Heat Absorption . How do the dynamics of water streams from firefighting equipment impact heat absorption in different fire scenarios?
• Biophysics of Human Circulation: Arterial Blood Flow Analysis . How does arterial stiffness affect blood flow dynamics, and what implications does this have for cardiovascular health?
• The Role of Physics in Optimizing Solar Cooker Designs . What design elements are crucial for maximizing the efficiency of solar cookers in various environmental conditions?
• The Efficacy of Anti-Reflective Coatings in Optical Devices . How do different anti-reflective coatings improve the performance of optical devices under various light conditions?
• Physics in 3D Printing: Material Properties and Layer Adhesion . How do the physical properties of materials affect layer adhesion and the structural integrity of 3D-printed objects?
• The Efficiency of Different Types of Insulators in High Voltage Applications . What types of insulators offer the most effective performance for minimizing energy loss in high-voltage power lines?
• The Impact of Sound Frequency on Material Fatigue . How do different frequencies of sound waves accelerate material fatigue in metals and polymers?
• The Physics of Virtual Reality: Improving Motion Tracking Accuracy . What key physical principles can improve motion-tracking accuracy in virtual reality systems?

These topics and questions provide a starting point for an in-depth exploration of physical concepts, encouraging critical thinking and problem-solving skills in the context of real-world applications.

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Essay on Quantum Physics

Students are often asked to write an essay on Quantum Physics in their schools and colleges. And if you’re also looking for the same, we have created 100-word, 250-word, and 500-word essays on the topic.

Let’s take a look…

100 Words Essay on Quantum Physics

Introduction to quantum physics.

Quantum physics, also known as quantum mechanics, is a branch of physics that deals with phenomena on a very small scale, like molecules, atoms, and subatomic particles.

Quantum Particles

In the quantum world, particles can exist in multiple places at once. This is called superposition. Particles can also be linked across space, known as entanglement.

Wave-Particle Duality

Quantum physics suggests that particles can behave both like particles and waves. This is known as wave-particle duality.

Uncertainty Principle

The Heisenberg Uncertainty Principle states that it is impossible to accurately measure both the position and momentum of a particle at the same time.

250 Words Essay on Quantum Physics

Quantum superposition and entanglement.

Two of the most intriguing principles in quantum physics are superposition and entanglement. Superposition refers to the quantum phenomenon where a particle can exist in multiple states at once, only collapsing into one state when observed. This is best exemplified by the famous Schrödinger’s cat thought experiment.

Quantum entanglement, on the other hand, describes the inexplicable interconnectedness of particles regardless of distance. If two particles are entangled, the state of one immediately influences the state of the other, even if they are light-years apart.

Quantum Physics and Reality

Quantum physics challenges our perception of reality. The Copenhagen interpretation, one of the earliest and most commonly taught interpretations of quantum mechanics, suggests that a quantum particle doesn’t exist in one state or another, but in all of its possible states at once. It’s only when we observe its state that a quantum particle is essentially forced to choose one probability, and that’s the state that we observe.

Quantum physics, while complex and counterintuitive, provides a more accurate description of the universe at microscopic scales. It has revolutionized our understanding of the physical world and continues to inspire new technologies, from quantum computing to quantum teleportation.

500 Words Essay on Quantum Physics

Quantum physics, also known as quantum mechanics, is a branch of physics that deals with phenomena on a very small scale, such as molecules, atoms, and even smaller particles. It is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.

The Birth of Quantum Mechanics

Key principles of quantum physics.

One of the most intriguing aspects of quantum physics is the principle of superposition, which holds that a physical system—such as an electron—can exist in multiple states simultaneously. This principle is illustrated by the famous Schrödinger’s cat thought experiment.

Another fundamental principle in quantum physics is wave-particle duality. This concept suggests that all particles also have properties of waves. It’s an idea that was first introduced by Louis de Broglie in 1924.

Quantum Physics and the Modern World

Quantum physics has been instrumental in the development of many technologies that we use today. Semiconductors, the building blocks of modern electronics, function due to principles of quantum mechanics. The field has also given rise to technologies like lasers and magnetic resonance imaging (MRI). More recently, quantum physics has become essential in the developing field of quantum computing, which has the potential to revolutionize technology.

Challenges and Future Directions

Despite its successes, quantum mechanics also presents several philosophical and practical challenges. The interpretation of quantum mechanics remains a contentious issue among physicists. Additionally, the unification of quantum mechanics with general relativity, to create a single theory that can describe all of the fundamental forces in nature, remains an unsolved problem in theoretical physics.

If you’re looking for more, here are essays on other interesting topics:

Apart from these, you can look at all the essays by clicking here .

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Extended Essay IB - Quantum Physics Oriented

• Thread starter Eliot_Abramo
• Start date May 19, 2020
• Tags Essay Extended essay Ib Physics Quantum Quantum physics
• May 19, 2020
• Physicists develop method to detect single-atom defects in semiconductors
• Searching for dark matter with the coldest quantum detectors in the world
• New theory reveals fracture mechanism in soft materials

Eliot_Abramo said: If possible I wanted to do something regarding Quantum Mechanics and Electricity/ electrical components.

Eliot_Abramo said: I've been asked to pick a topic for my IB Extended Essay.

Eliot_Abramo said: Quantum Mechanics is a vast domain

• May 20, 2020

Vanadium 50 said: That's your assignment. Are you asking us to do your work for you?

PeterDonis said: Yes. What parts of it have you looked at already?

Some ideas I had in mind was to discuss the Meissner Effect in Superconductors when cooled down to a critical temperature with liquid nitrogen and investigate how it can be used for future applications, as a new way to transmit energy frictionless, not allowing the material to waste any of its energy into heat. I am unsure if this idea is a feasible one, so I would appreciate if someone could point me in the right direction. Thank you for any help.  

Eliot_Abramo said: I am unsure if this idea is a feasible one

Eliot_Abramo said: I would appreciate if someone could point me in the right direction.

• May 21, 2020

Eliot_Abramo said: Some ideas I had in mind was to discuss the Meissner Effect in Superconductors when cooled down to a critical temperature with liquid nitrogen and investigate how it can be used for future applications, as a new way to transmit energy frictionless, not allowing the material to waste any of its energy into heat. I am unsure if this idea is a feasible one, so I would appreciate if someone could point me in the right direction. Thank you for any help.

Related to Extended Essay IB - Quantum Physics Oriented

1. what is the purpose of an extended essay in ib.

The Extended Essay is a mandatory research project that is a core component of the International Baccalaureate (IB) Diploma Programme. Its purpose is to allow students to engage in independent, in-depth research on a topic of their choice, developing essential skills such as critical thinking, time management, and communication.

2. What is quantum physics and how is it related to the Extended Essay?

Quantum physics is a branch of physics that studies the behavior of matter and energy at a microscopic level. It is related to the Extended Essay in IB because it is a complex and fascinating topic that allows students to explore the fundamental principles of the universe and develop a deeper understanding of the world around us.

3. What are some potential research topics for an Extended Essay in quantum physics?

Some potential research topics for an Extended Essay in quantum physics include the study of quantum mechanics, quantum entanglement, quantum computing, and the applications of quantum physics in various fields such as medicine, technology, and energy.

4. What are the key components of a successful Extended Essay in quantum physics?

A successful Extended Essay in quantum physics should have a clear research question, a well-defined methodology, and a strong theoretical framework. It should also include relevant and reliable data, critical analysis, and a logical conclusion that answers the research question.

5. How can I ensure that my Extended Essay in quantum physics meets the IB requirements?

To ensure that your Extended Essay in quantum physics meets the IB requirements, it is important to carefully read and follow the guidelines provided by the IB. You should also seek guidance from your supervisor, conduct thorough research, and use appropriate referencing and citation methods.

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Searching for dark matter with the coldest quantum detectors in the world

by Lancaster University

One of the greatest mysteries of science could be one step closer to being solved. Approximately 80% of the matter in the universe is dark, meaning that it cannot be seen. In fact, dark matter is passing through us constantly—possibly at a rate of trillions of particles per second.

We know it exists because we can see the effects of its gravity, but experiments to date have so far failed to detect it.

Taking advantage of the most advanced quantum technologies, scientists from Lancaster University, the University of Oxford, and Royal Holloway, University of London are building the most sensitive dark matter detectors to date.

Their public exhibit entitled "A Quantum View of the Invisible Universe" is showcased at this year's Royal Society's flagship Summer Science Exhibition from 2–7 July 2024. Related research is also published in the Journal of Low Temperature Physics .

The researchers include Dr. Michael Thompson, Professor Edward Laird, Dr. Dmitry Zmeev and Dr. Samuli Autti from Lancaster, Professor Jocelyn Monroe from Oxford and Professor Andrew Casey from RHUL.

EPSRC Fellow Dr. Autti said, "We are using quantum technologies at ultra-low temperatures to build the most sensitive detectors to date. The goal is to observe this mysterious matter directly in the laboratory and solve one of the greatest enigmas in science."

There is indirect observational evidence of the typical dark matter density in the galaxy, but the mass of the constituent particles and their possible interactions with ordinary atoms are unknown.

Particle physics theory suggests two likely dark matter candidates: new particles with interactions so weak we haven't observed them yet, and, very light wave-like particles termed axions. The team are building two experiments, one to search for each.

Of the two candidates, new particles with ultra-weak interactions could be detected through their collisions with ordinary matter. However, whether these collisions can be identified in an experiment depends on the mass of the dark matter being searched for. Most searches so far would be able to detect dark matter particles weighing between five and 1,000 times more than a hydrogen atom, but it is possible that much lighter dark matter candidates may have been missed.

The Quantum Enhanced Superfluid Technologies for Dark Matter and Cosmology (QUEST-DMC) team aims to reach world-leading sensitivity to collisions with dark matter candidates with mass between 0.01 to a few hydrogen atoms. To achieve this, the detector is made of superfluid helium-3, cooled into a macroscopic quantum state and instrumented with superconducting quantum amplifiers. Combining these two quantum technologies creates the sensitivity to measure extremely weak signatures of dark matter collisions.

By contrast, if dark matter is made from axions, they will be extremely light—more than a billion times lighter than a hydrogen atom—but correspondingly more abundant. Scientists would not be able to detect collisions with axions, but they can search instead for another signature—an electrical signal that results when axions decay in a magnetic field.

This effect can only be measured using an exquisitely sensitive amplifier that works at the highest precision allowed by quantum mechanics. The Quantum Sensors for the Hidden Sector (QSHS) team is therefore developing a new class of quantum amplifier that is perfectly suited to search for an axion signal.

The stand at this year's exhibition will enable visitors to observe the unseeable with imaginative hands-on exhibits for all ages.

Demonstrating how we infer dark matter from observing galaxies, there will be a gyroscope-in-a-box that moves in surprising ways due to the unseen angular momentum. There will also be glass marbles that are transparent in liquid, showing how invisible masses may be observed using clever experimentation.

A light-up dilution refrigerator will demonstrate how the team achieve ultra-low temperatures, and a model dark matter particle collision detector will show how our universe would behave if dark matter behaved like normal matter.

Visitors can then search for dark matter with a model axion detector by scanning the frequency of a radio receiver, and they can also create their own parametric amplifier using a pendulum.

Cosmologist Carlos Frenk, Fellow of the Royal Society and Chair of the Public Engagement Committee, said, "Science is vital in helping us understand the world we live in—past, present and future. I urge visitors of all ages to come along with an open mind, curiosity and enthusiasm and celebrate incredible scientific achievements that are benefiting us all."

Provided by Lancaster University

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