explain quantum hypothesis

What Is Quantum Physics?

Quantum physics is the study of matter and energy at the most fundamental level. It aims to uncover the properties and behaviors of the very building blocks of nature.

While many quantum experiments examine very small objects, such as electrons and photons, quantum phenomena are all around us, acting on every scale. However, we may not be able to detect them easily in larger objects. This may give the wrong impression that quantum phenomena are bizarre or otherworldly. In fact, quantum science closes gaps in our knowledge of physics to give us a more complete picture of our everyday lives.

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

The Origins of Quantum Physics

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

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

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

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

Mathematics and the Probabilistic Nature of Quantum Objects

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

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

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

Observation of Quantum Objects

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

The Double-Slit Experiment

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

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

Dive Deeper

• History & Society
• Science & Tech
• Biographies
• Animals & Nature
• Geography & Travel
• Arts & Culture
• Games & Quizzes
• On This Day
• One Good Fact
• New Articles
• Lifestyles & Social Issues
• Philosophy & Religion
• Politics, Law & Government
• World History
• Health & Medicine
• Browse Biographies
• Birds, Reptiles & Other Vertebrates
• Bugs, Mollusks & Other Invertebrates
• Environment
• Fossils & Geologic Time
• Entertainment & Pop Culture
• Sports & Recreation
• Visual Arts
• Demystified
• Image Galleries
• Infographics
• Top Questions
• Britannica Kids
• Saving Earth
• Space Next 50
• Student Center
• Introduction

Basic considerations

Planck’s radiation law.

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

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

quantum mechanics

Our editors will review what you’ve submitted and determine whether to revise the article.

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

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

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

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

Historical basis of quantum theory

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

Early developments

By the end of the 19th century, physicists almost universally accepted the wave theory of light. However, though the ideas of classical physics explain interference and diffraction phenomena relating to the propagation of light, they do not account for the absorption and emission of light. All bodies radiate electromagnetic energy as heat; in fact, a body emits radiation at all wavelengths. The energy radiated at different wavelengths is a maximum at a wavelength that depends on the temperature of the body; the hotter the body, the shorter the wavelength for maximum radiation. Attempts to calculate the energy distribution for the radiation from a blackbody using classical ideas were unsuccessful. (A blackbody is a hypothetical ideal body or surface that absorbs and reemits all radiant energy falling on it.) One formula, proposed by Wilhelm Wien of Germany, did not agree with observations at long wavelengths, and another, proposed by Lord Rayleigh (John William Strutt) of England, disagreed with those at short wavelengths.

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

Science Simplified: What Is Quantum Mechanics?

What Is Quantum Mechanics?

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

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

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

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

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

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

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

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

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

What Is Quantum Information Science?

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

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

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

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

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

Related Articles

Science made simple: what is quantum mechanics, breaking the born-oppenheimer approximation – experiments unveil long-theorized quantum phenomenon, quantum fisher information: spilling the secrets of quantum entanglement, quantum breakthrough: how to transform vacancies into quantum information, scientists make pivotal discovery in quantum and classical information processing, experiment shows that light defies the principles of classical physics, “schrödinger’s hat” conceals matter waves inside an invisible container, simulating quantum walks in two dimensions, evidence of elusive majorana fermions raises possibilities for quantum computing.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Save my name, email, and website in this browser for the next time I comment.

Type above and press Enter to search. Press Esc to cancel.

Advertisement

Quantum physics

By Richard Webb

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

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

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

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

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

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

Rethinking reality: Is the entire universe a single quantum object?

In the face of new evidence, physicists are starting to view the cosmos not as made up of disparate layers, but as a quantum whole linked by entanglement

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

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

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

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

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

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

Six ways we could finally find new physics beyond the standard model

Leading physicists explain how they think we will discover the new particles or forces that would complete one of science's greatest unfinished masterpieces

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

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

Sign up to our weekly newsletter

Receive a weekly dose of discovery in your inbox! We'll also keep you up to date with New Scientist events and special offers.

More on Quantum physics

Quantum experiment rewrites a century-old chemistry law

Subscriber-only

How the most precise clock ever could change our view of the cosmos

Quantum holograms can send messages that disappear

Related articles.

People in Science

Richard feynman.

C. V. Raman

Jocelyn Bell Burnell

Quantum Physics Overview

How Quantum Mechanics Explains the Invisible Universe

 traffic_analyzer / Getty Images

• Quantum Physics
• Physics Laws, Concepts, and Principles
• Important Physicists
• Thermodynamics
• Cosmology & Astrophysics
• Weather & Climate

• M.S., Mathematics Education, Indiana University
• B.A., Physics, Wabash College

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.

Major Findings, Experiments, and Basic Explanations

Earliest Findings

• Black Body Radiation
• Photoelectric Effect

Wave-Particle Duality

• Young's Double Slit Experiment
• De Broglie Hypothesis

The Compton Effect

Heisenberg Uncertainty Principle

Causality in Quantum Physics - Thought Experiments and Interpretations

• The Copenhagen Interpretation
• Schrodinger's Cat
• EPR Paradox
• The Many Worlds Interpretation
• The Many Worlds Interpretation of Quantum Physics
• Albert Einstein: What Is Unified Field Theory?
• Introduction to the Dirac Delta Function
• The Copenhagen Interpretation of Quantum Mechanics
• Can Quantum Physics Be Used to Explain the Existence of Consciousness?
• Understanding the "Schrodinger's Cat" Thought Experiment
• What Is Quantum Optics?
• Quantum Entanglement in Physics
• Understanding the Heisenberg Uncertainty Principle
• Using Quantum Physics to "Prove" God's Existence
• Quantum Computers and Quantum Physics
• What Is Quantum Gravity?
• The Basics of String Theory
• The Casimir Effect
• Everything You Need to Know About Bell's Theorem
• The Discovery of the Higgs Energy Field

Quantum Physics Made Simple

Quantum Physics Introduction for Beginners

In this quantum physics introduction for beginners, we will explain quantum physics, also called quantum mechanics, in simple terms. Quantum physics is possibly the most fascinating part of physics that exists. It is the amazing physics that becomes relevant for small particles, where the so-called classical physics is no longer valid. Where classical mechanics describes the movement of sufficiently big particles, and everything is deterministic, we can only determine probabilities for the movement of very small particles, and we call the corresponding theory quantum mechanics.

You may have heard Einsteins saying, “Der Alte würfelt nicht” which roughly means “God does not roll dice”. Well, even geniuses can be wrong. Again, quantum mechanics is not deterministic, but we can in general only determine probabilities. Since we are used to reasonably big objects in our everyday life, quantum mechanics and its laws may initially seem strange and quantum theory is often considered complex. But for example, electrons and photons are sufficiently small that quantum physics is needed, and on this website, we will show you that understanding the basics of quantum physics is easy and fun.

In the following paragraph, we will describe a thought experiment that we perform at two different length scales: With bullets as known from pistols (the large scale) and with electrons (the very small scale). While the experiment is essentially the same but for the size, we will show you how the result is very different. This will be your first lecture in quantum mechanics.

Classical Bullets vs. Electrons in a Two-Slit Experiment

A) classical bullets.

Consider first a machine gun that fires bullets to a wall. Between the wall and the machine gun, another wall has two parallel slits that are big enough to easily allow a bullet to pass through them. To make the experiment interesting, we take a “bad” machine gun that has a lot of spread. This means it sometimes shoots through the first slit and sometimes through the second, and sometimes it hits the intermediate wall.

If we block the second slit, all bullets that reach the outer wall will have come through the first slit. If we count the number of bullets as a function of the distance from the center of the outer wall, we will find a curve distribution that could be similar to a Gaussian curve. We can call this probability curve P1.

If we block the first slit, all bullets that reach the outer wall will have come through the second slit. The probability curve will be mirrored around the center, and we call it P2.

If we open both slits, all bullets at the outer wall will have come through either slit 1 or 2. Typical for classical mechanics in this situation is that the total probability distribution P can be determined as the sum of the previously-mentioned probability distributions, P = P1 + P2.

b) Electrons – Quantum Mechanics

Now consider the same experiment on a much smaller scale. Instead of bullets from a machine gun we consider electrons that for example can stem from a heated wire parallel to the two slits in an intermediate wall. The electron direction will have a natural spread. The slits are also much smaller than before but much broader than a single electron.

The electron experiment results

Consider again the case that the second slit is blocked. For proper sizes of the slits and distance between the wire and the walls, the probability distribution P1 will be similar to before. Similarly, if we block the slit 1, we will for proper distances find a probability distribution P2 similar to before.

What do you expect will happen if we do not block any slit? Will we find a probability distribution P = P1 + P2 as before? Well, after all we said you may guess that this is not the case. Indeed, we will instead find a probability distribution that has various minima and maxima. That is, for x = 0 there would be the strongest peak of electrons, for a certain +-Delta x there wouldn’t be any electrons at all, but for +-2 Delta x there would be another peak of electrons, and so on.

Explanation of the electron experiment results

How can we explain these results? Well, the explanation is rather straight forward if we assume that electrons in this specific case do not behave as particles, but as waves. “Waves?” you may ask. Well, consider a plain of water, and the same wall as before and the same intermediate wall with a double slit as before. At the place where the machine gun or the wire where, consider a pencil punching periodically downwards into the water. If you do this, you will get concentric waves around the point where you punch the water, until the intermediate plain with the two slits.

Behind each slit, there will be a half circle of concentric waves, up to the point where the new waves from the two slits cross each other. There, the waves from the two slits can add up or eliminate each other. As a function of the periodic punching you will find points where the height of the wave is always the same. There will be other places where the wave is sometimes very high and sometimes very low. At the outer wall, these two phases will be repeatedly following one another. The places where there is a lot of variation correspond to the places where there are the most electrons. The places with no variation correspond to the places where there are no electrons on the wall at all.

So, why do electrons in this case behave like waves and not like particles? Well, this is the thing where you will not find a satisfying answer. You just need to accept it.

c) Photons (light particles)

What if you do not believe this? Well, the thought experiment with the electrons is rather difficult to perform with the proper scale of all elements of the experiment. But there is another very similar experiment that you can do at home. Instead of the electrons you use the photons (light particles) from a laser which you can buy for a few bucks. You let the laser shine through a double slit, darken the room, and look at the outer wall. And boom! What you see is not just two light lines on the outer wall, but a pattern of light line, dark line, light line, dark line, and so on. The intensity of the lighter region becomes less far away from the center. It corresponds exactly to the result of our thought experiments with electrons.

Why does the laser experiment give the same result as the thought experiment with electrons? It is quite easy: Light particles, called photons, are also very small and therefore behave quantum mechanically. And like electrons, they behave like waves in this specific situation. As a side remark, research has shown that light behaves like particles in another respect: If one reduces the intensity a lot, one will find single light spots from single photons on the wall. This means the light behaves like particles as well. One therefore talks about the  particle-wave duality  of photons or electrons.

What do you wait for? Do the experiment, and you will become a believer of quantum mechanics, or more generally phrased, of quantum physics.

Advanced Remarks

Don’t watch.

The pattern with maxima and minima is called an interference pattern, since it comes about by the interference of the waves through slit 1 and slit 2. It has been found that you only get this interference pattern if you do not by other means (some additional measurement instrument) watch through which of the two slits the electrons or photons pass. If you do measure which of the two ways the particles pass by any other means, the interference pattern goes away. You will then find the sum distribution P = P1 + P2 as in the classical experiment.

Uncertainty principle

A measurement device for electrons would typically disturb the electrons. More precisely, their momentum p would typically change due to a measurement device, while the place x of its path would become known more precisely. In general, there will be some uncertainty left in the momentum and in the place of the electron. Heisenberg postulated that the product of these uncertainties can never be lower than a specific constant h: Delta x times Delta p >= h. No one ever managed to disproof this relation, which is at the heart of quantum mechanics. Essentially it says, we cannot measure both momentum and place with arbitrary precision at the same time.

Single Slit Experiments

We said that for proper distributions, you will find a similar result P1 and P2 as in the classical case. However, for other sizes one can achieve an interference pattern even for the single slits. This is the case when the slit is so broad that one can achieve an interference of the wave stemming from one side of the slit with the wave stemming from the other side of the slit.

How Small Is Small?

We said above that quantum physics becomes relevant for small particles — whereby we mean that  naturally , quantum effects are only seen for small particles. However, the theory itself is thought to provide correct results for large particles as well. Why is it then, that quantum effects (which cannot be explained with classical theory) become increasingly difficult to observe for larger particles? Larger compound particles in general experience more interaction both within themselves and with their surroundings. These interactions typically lead to an effect physicists call “decoherence” — which simply put means that quantum effects get lost. In this case (for sufficiently large matter), quantum physics and classical physics yield the same result.

Now you may wonder: “At which size does this happen?”. While one doesn’t naturally observe quantum effects in large particles, ingenious people have managed to specifically prepare test environments that showed quantum effects for an ever-growing size of particles. Already 1999 an experiment showed a quantum superposition in particles as large as C 60  molecules. A 2013  article  already claims to observe quantum superpositions in molecules that weigh more than 10000 atomic mass units. The question of where the achievable limit lies, and whether one can be sure that experiments really demonstrate quantum behavior, is still of interest. That these questions are not finally concluded is also reflected in a more recent  article on the American Physical Society site .  In principle, if one would be able to somehow get rid of decoherence effects in specifically prepared systems, the theory itself imposes no upper size limits on where quantum effects could be shown.

Quantum Effects To a Satellite And Back

The aspect of the length scale for quantum physics that we just discussed was the particle size – which typically is on the microscopic scale. A completely different matter is the length scale of how far you can move or separate such particles after  an initial interaction, without losing quantum effects. You can view the two-slit experiment as showing an interaction between particles at the slit. If you tried out the experiment yourself, you probably realized, that the distance between the slit and the wall were you observe interference patterns can easily be some meters – not microscopic at all!

Other experiments prepare two particles in a special quantum superposition called entanglement — which, by the way, lies at the heart of  quantum computation  — and then separate these particles. In some experiments, it was possible to show interactions between these particles despite a separation over many miles. Essentially, if one measures the state of one such particle, one can thereafter predict the state of the other particle (within errors), despite the large separation between the particles.  A  recent experiment  demonstrated this entanglement effect over extreme distances. Particles were sent to a satellite and back to earth – a fairly large scale distance compared to the size of a human.

Summary of this Quantum Physics Introduction

In this quantum physics introduction, we told you that both photons and electrons behave as both particles and waves. This particle-wave duality is not understandable with classical mechanics. It results in us only being able to predict probabilities, while one classically can make deterministic predictions. You can easily test these results at home by performing the two-slits experiment with a laser pointer. Have fun! We hope you enjoyed this quantum physics introduction for beginners. If you haven’t read it yet, you should continue with our article  What Everyone Should Know About Quantum Physics . And if you want to learn even more, why not have a look at our article Best Quantum Physics Books for Beginners?

quantum theory

• Ivy Wigmore

Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic level. The nature and behavior of matter and energy at that level is sometimes referred to as quantum physics and quantum mechanics. Organizations in several countries have devoted significant resources to the development of quantum computing , which uses quantum theory to drastically improve computing capabilities beyond what is possible using today's classical computers.

In 1900, physicist Max Planck presented his quantum theory to the German Physical Society. Planck had sought to discover the reason that radiation from a glowing body changes in color from red, to orange, and, finally, to blue as its temperature rises. He found that by making the assumption that energy existed in individual units in the same way that matter does, rather than just as a constant electromagnetic wave - as had been formerly assumed - and was therefore quantifiable , he could find the answer to his question. The existence of these units became the first assumption of quantum theory.

Planck wrote a mathematical equation involving a figure to represent these individual units of energy, which he called quanta . The equation explained the phenomenon very well; Planck found that at certain discrete temperature levels (exact multiples of a basic minimum value), energy from a glowing body will occupy different areas of the color spectrum. Planck assumed there was a theory yet to emerge from the discovery of quanta, but, in fact, their very existence implied a completely new and fundamental understanding of the laws of nature. Planck won the Nobel Prize in Physics for his theory in 1918, but developments by various scientists over a thirty-year period all contributed to the modern understanding of quantum theory.

The Development of Quantum Theory

• In 1900, Planck made the assumption that energy was made of individual units, or quanta.
• In 1905, Albert Einstein theorized that not just the energy, but the radiation itself was quantized in the same manner.
• In 1924, Louis de Broglie proposed that there is no fundamental difference in the makeup and behavior of energy and matter; on the atomic and subatomic level either may behave as if made of either particles or waves. This theory became known as the principle of wave-particle duality : elementary particles of both energy and matter behave, depending on the conditions, like either particles or waves.
• In 1927, Werner Heisenberg proposed that precise, simultaneous measurement of two complementary values - such as the position and momentum of a subatomic particle - is impossible. Contrary to the principles of classical physics, their simultaneous measurement is inescapably flawed; the more precisely one value is measured, the more flawed will be the measurement of the other value. This theory became known as the uncertainty principle, which prompted Albert Einstein's famous comment, "God does not play dice."

The Copenhagen Interpretation and the Many-Worlds Theory

The two major interpretations of quantum theory's implications for the nature of reality are the Copenhagen interpretation and the many-worlds theory. Niels Bohr proposed the Copenhagen interpretation of quantum theory, which asserts that a particle is whatever it is measured to be (for example, a wave or a particle), but that it cannot be assumed to have specific properties, or even to exist, until it is measured. In short, Bohr was saying that objective reality does not exist. This translates to a principle called superposition that claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously, as long as we don't look to check.

To illustrate this theory, we can use the famous and somewhat cruel analogy of Schrodinger's Cat . First, we have a living cat and place it in a thick lead box. At this stage, there is no question that the cat is alive. We then throw in a vial of cyanide and seal the box. We do not know if the cat is alive or if the cyanide capsule has broken and the cat has died. Since we do not know, the cat is both dead and alive, according to quantum law - in a superposition of states. It is only when we break open the box and see what condition the cat is that the superposition is lost, and the cat must be either alive or dead.

The second interpretation of quantum theory is the many-worlds (or multiverse theory. It holds that as soon as a potential exists for any object to be in any state, the universe of that object transmutes into a series of parallel universes equal to the number of possible states in which that the object can exist, with each universe containing a unique single possible state of that object. Furthermore, there is a mechanism for interaction between these universes that somehow permits all states to be accessible in some way and for all possible states to be affected in some manner. Stephen Hawking and the late Richard Feynman are among the scientists who have expressed a preference for the many-worlds theory.

Quantum Theory's Influence

Although scientists throughout the past century have balked at the implications of quantum theory - Planck and Einstein among them - the theory's principles have repeatedly been supported by experimentation, even when the scientists were trying to disprove them. Quantum theory and Einstein's theory of relativity form the basis for modern physics. The principles of quantum physics are being applied in an increasing number of areas, including quantum optics, quantum chemistry, quantum computing , and quantum cryptography .

Continue Reading About quantum theory

• 5 quick quantum computing terms to learn
• https://searchdatacenter.techtarget.com/feature/5-quick-quantum-computing-terms-to-learn
• New Scientist explores the quantum world
• New quantum theory could explain the flow of time
• PBS explains quantum mechanics

Related Terms

In general, asynchronous -- from Greek asyn- ('not with/together') and chronos ('time') -- describes objects or events not ...

A URL (Uniform Resource Locator) is a unique identifier used to locate a resource on the internet.

File Transfer Protocol (FTP) is a network protocol for transmitting files between computers over TCP/IP connections.

Network detection and response (NDR) technology continuously scrutinizes network traffic to identify suspicious activity and ...

Identity threat detection and response (ITDR) is a collection of tools and best practices aimed at defending against cyberattacks...

Managed extended detection and response (MXDR) is an outsourced service that collects and analyzes threat data from across an ...

Data storytelling is the process of translating complex data analyses into understandable terms to inform a business decision or ...

Demand shaping is an operational supply chain management (SCM) strategy where a company uses tactics such as price incentives, ...

Data monetization is the process of measuring the economic benefit of corporate data.

Employee self-service (ESS) is a widely used human resources technology that enables employees to perform many job-related ...

Diversity, equity and inclusion is a term used to describe policies and programs that promote the representation and ...

Payroll software automates the process of paying salaried, hourly and contingent employees.

Salesforce Commerce Cloud is a cloud-based suite of products that enable e-commerce businesses to set up e-commerce sites, drive ...

Multichannel marketing refers to the practice of companies interacting with customers via multiple direct and indirect channels ...

A contact center is a central point from which organizations manage all customer interactions across various channels.

• Structure of Atom
• Planks Quantum Theory

Planck's Quantum Theory - Quantization Of Energy

Introduction.

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

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

Table of Contents

Black body radiation, recommended videos.

• Planck’s quantum theory
• Frequently Asked Questions – FAQs

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

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

Black body Radiation

Planck’s Quantum Theory

According to Planck’s quantum theory,

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

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

E = Energy of the radiation

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

ν = Frequency of radiation

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

Related Videos

Electromagnetic radiations & planck’s quantum theory.

Frequently Asked Questions on Black Body Radiation

What is a planck curve.

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

What is Stefan’s law of radiation?

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

How is blackbody radiation produced?

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

What is Planck’s constant in simple terms?

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

What is Planck’s number?

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

To learn more about the  quantum theory of light and other topics you can register with BYJU’S or download BYJU’s – The Learning App.

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

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

Visit BYJU’S for all Chemistry related queries and study materials

Your result is as below

Request OTP on Voice Call

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Post My Comment

i liked your material you have given

Thank you so much.

I like it. It helps with my chemistry homework.

Good job keep it.

It’s good

softly captured, keep it up

thnx a lott

love you BYJU’S FOREVER

thank you so much, helped with my essay on Max Planck

Thank you byjus awesome it helped me a lot in my project

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

• Table of Contents
• Random Entry
• Chronological
• Editorial Information
• About the SEP
• Editorial Board
• How to Cite the SEP
• Special Characters
• Advanced Tools
• Support the SEP
• PDFs for SEP Friends
• Make a Donation
• SEPIA for Libraries
• Entry Contents

Bibliography

Academic tools.

• Friends PDF Preview
• Author and Citation Info
• Back to Top

Many-Worlds Interpretation of Quantum Mechanics

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

1. Introduction

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

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

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

The MWI consists of two parts:

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

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

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

2. Definitions

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

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

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

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

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

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

3. Correspondence Between the Formalism and Our Experience

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

4. Probability in the MWI

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6. Objections to the MWI

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• Adlam, E., 2014, ‘The Problem of Confirmation in the Everett Interpretation’, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics , 47: 21–32.
• Aguirre, A. and Tegmark, M., 2011, ‘Born in an Infinite Universe: A Cosmological Interpretation of Quantum Mechanics’, Physical Review D, 84: 105002.
• Albert, D. and Loewer, B., 1988, ‘Interpreting the Many Worlds Interpretation’, Synthese , 77: 195–213.
• Albert, D., 1992, Quantum Mechanics and Experience , Cambridge, MA: Harvard University Press.
• –––, 1996, ‘Elementary Quantum Metaphysics’, in J. Cushing, A. Fine, and S. Goldstein (eds.), ‘Bohmian Mechanics and Quantum Theory: An Appraisal’, Boston Studies in the Philosophy of Science , 184: 277–284.
• –––, 2010, ‘Probability in the Everett Picture’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 355–368.
• –––, 2013, ‘Physics and Narrative’, in D. Struppa and J. Tollaksen (eds.), Quantum Theory: a Two-Time Success Story. Yakir Aharonov Festschrift , Milan: Springer, pp. 171–182.
• –––, 2015, After Physics , Cambridge, MA: Harvard University Press.
• Albrecht, A. and Phillips, D., 2014, ‘Origin of Probabilities and their Application to the Multiverse’, Physical Review D, 90: 123514.
• Allori, V., Goldstein, S., Tumulka, R., and Zanghi, N., 2011, ‘Many-Worlds and Schrödinger’s First Quantum Theory’, British Journal for the Philosophy of Science , 62: 1–27.
• –––, 2014, ‘Predictions and Primitive Ontology in Quantum Foundations: A Study of Examples’, British Journal for the Philosophy of Science , doi:10.1093/bjps/axs048
• Araújo, M., 2019, ‘Probability in Two Deterministic Universes’, Foundations of Physics , 49(3): 202–231.
• Bacciagaluppi, G., 2002, ‘Remarks on Space-Time and Locality in Everett’s Interpretation’, in Modality, Probability, and Bell’s Theorems , (NATO Science Series).
• Baker, D. J., 2007, ‘Measurement Outcomes and Probability in Everettian Quantum Mechanics’, Studies in History and Philosophy of Science Part B – Studies in History and Philosophy of Modern Physics, 38: 153–169.
• Barnum, H., Caves, C.M., Finkelstein, J., Fuchs, C.A., and Schack, R., 2000, ‘Quantum Probability from Decision Theory’, Proceedings of the Royal Society of London A , 456: 1175–1182.
• Barrett, J. A., 1999, The Quantum Mechanics of Minds and Worlds , Oxford: Oxford University Press.
• –––, 2011, ‘Everett’s Pure Wave Mechanics and the Notion of Worlds’, European Journal for Philosophy of Science , 1: 277–302.
• –––, 2017, ‘Typical Worlds’, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 58: 31–40.
• Barrett, J. A. and Byrne, P., 2012, The Everett Interpretation of Quantum Mechanics: Collected Works 1955–1980 with Commentary , Princeton: Princeton University Press.
• Barrett, J. A. and Huttegger, M., 2020, ‘Quantum Randomness and Underdetermination’, Philosophy of Science , 87: 391–408.
• Becker, L., 2004, ‘That Von Neumann did not Believe in a Physical Collapse’, British Journal for the Philosophy of Science , 55: 121–135.
• Bédard, C. A., 2021a, ‘The ABC of Deutsch-Hayden Descriptors’, Quantum Reports , 3(2): 272–285.
• –––, 2021b, ‘The Cost of Quantum Locality’, Proceedings of the Royal Society A , 477: 20200602.
• Berenstain, N., 2020, ‘Privileged Perspective Realism in the Quantum Multiverse’, in D. Glick, G. Darby, and A. Marmodoro (eds.) The Foundation of Reality: Fundamentality, Space, and Time , Oxford: Oxford University Press, pp. 102–122.
• Belinfante, F. J., 1975, Measurements and Time Reversal in Objective Quantum Theory , Oxford: Pergamon Press, pp. 50–51.
• Bell, J. S., 1987, Speakable and Unspeakable in Quantum Mechanics , Cambridge: Cambridge University Press.
• –––, 1990, ‘Against ‘Measurement’’, Physics World , 3: 33–40.
• Bevers, B.M., 2011, ‘ Everett’s “Many-Worlds” Proposal’, Studies in History and Philosophy of Science Part B – Studies in History and Philosophy of Modern Physics, 42: 3–12.
• Boge, F. J., 2019, ‘The Best of Many Worlds, or, is Quantum Decoherence the Manifestation of a Disposition?’, Studies in History and Philosophy of Science (Part B – Studies in History and Philosophy of Modern Physics), 66: 135–144.
• Bousso, R. and Susskind, L., 2012, ‘Multiverse Interpretation of Quantum Mechanics’, Physical Review D, 85: 045007.
• Bradley, D. J., 2011, ‘Confirmation in a Branching World: The Everett Interpretation and Sleeping Beauty’, British Journal for the Philosophy of Science , 62: 323–342.
• Brown, H. R. and Wallace, D., 2005, ‘Solving the Measurement Problem: de Broglie-Bohm Loses out to Everett’, Foundations of Physics , 35: 517–540.
• Brown, H. R. and Timpson, C. G., 2016, ‘Bell on Bell’s theorem: The Changing Face of Nonlocality’, in Quantum Nonlocality and Reality , Mary Bell and Shan Gao (eds.), Cambridge: Cambridge University Press, 2016, pp. 91–123. Section 9.
• Brown, H. R. and Ben Porath, G., 2020, ‘Everettian Probabilities, The Deutsch-Wallace Theorem and the Principal Principle’, Hemmo M., Shenker O. (eds.) Quantum, Probability, Logic (Jerusalem Studies in Philosophy and History of Science), Cham: Springer, pp. 165–198.
• Brown, H. R., 2020, ‘Everettian Quantum Mechanics’, Contemporary Physics , 60(4): 299–314.
• Buniy, R.V., Hsu, S.D.H. and Zee, A., 2006, ‘Discreteness and the Origin of Probability in Quantum Mechanics’, Physics Letters B , 640: 219–223.
• Byrne, P., 2010, The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family , Oxford: Oxford University Press.
• Cao, J., Cogdell, R.J., Coker, D.F., Duan, H.G., Hauer, J., Kleinekathöfer, U., Jansen, T.L., Mančal, T., Miller, R.D., Ogilvie, J.P. and Prokhorenko, V.I., 2020, ‘Quantum Biology Revisited’, Science Advances , 6(14): 4888.
• Carroll, S. M. and Singh, A., 2019, ‘Mad-dog Everettianism: Quantum Mechanics at its Most Minimal’, in Aguirre A., Foster B., Merali Z. (eds.) What is Fundamental? The Frontiers Collection , Cham:Springer, pp. 95–104.
• Chalmers, D. J., 1996, The Conscious Mind , New York: Oxford University Press.
• Chen, E. K., 2019, ‘Realism About the Wave Function’, Philosophy Compass , 14(7): 12611.
• Collett, B., Pearle, P., Avignone, F., and Nussinov, S., 1995, ‘Constraint on Collapse Models by Limit on Spontaneous X-Ray Emission in Ge’, Foundation of Physics , 25: 1399–1412.
• Cuffaro, M. E., 2012, ‘Many Worlds, the Cluster-State Quantum Computer, and the Problem of the Preferred Basis’, Studies in History and Philosophy of Modern Physics , 43: 35–42.
• Cunningham, A., 2014, ‘Branches in the Everett interpretation’, Studies in History and Philosophy of Modern Physics , 46: 247–262.
• Dawid, R. and Thébault, K. P., 2014, ‘Against the Empirical Viability of the Deutsch Wallace Everett Approach to Quantum Mechanics’, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 47: 55–61
• –––, 2015, ‘Many Worlds: Decoherent or Incoherent?’, Synthese , 192(5): 1559–1580.
• Dawid, R. and Friederich, S., 2020, ‘Epistemic Separability and Everettian Branches: A Critique of Sebens and Carroll’, British Journal for the Philosophy of Science .
• Deutsch, D., 1986, ‘Three Experimental Implications of the Everett Interpretation’, in R. Penrose and C.J. Isham (eds.), Quantum Concepts of Space and Time , Oxford: The Clarendon Press, pp. 204–214.
• –––, 1996, The Fabric of Reality , New York: The Penguin Press.
• –––, 1999, ‘Quantum Theory of Probability and Decisions’, Proceedings of the Royal Society of London A , 455: 3129–3137.
• –––, 2002, ‘The Structure of the Multiverse’, Proceedings of the Royal Society of London A , 458: 2911–2923.
• –––, 2012, ‘Vindication of Quantum Locality’, Proceedings of the Royal Society A , 468: 531–544.
• Deutsch, D. and Hayden, P., 2000, ‘Information Flow in Entangled Quantum Systems’, Proceedings of the Royal Society of London A , 456: 1759–1774.
• Deutsch, D. and Jozsa, R., 1992, ‘Rapid Solutions of Problems by Quantum Computation’, Proceedings of the Royal Society of London A , 439: 553–558.
• De Witt, B. S. M., 1970, ‘Quantum Mechanics and Reality’, Physics Today , 23(9): 30–35.
• Diósi, L., 2015, ‘Testing Spontaneous Wave-Function Collapse Models on Classical Mechanical Oscillators’, Physical Review Letters , 114(5): 050403.
• Dizadji-Bahmani, F., 2015, ‘The Probability Problem in Everettian Quantum Mechanics Persists’, British Journal for the Philosophy of Science , 66(2): 257–283.
• Drezet, A., 2020, ‘Making sense of Born’s rule \(p_\alpha=\lVert\Psi_\alpha\rVert^ 2\) with the many-worlds interpretation’, Quantum Studies: Mathematics and Foundations , 8: 315–336.
• Duwel, A., 2009, ‘The Many-Worlds Interpretation and Quantum Computation’, Philosophy of Science , 74: 1007–1018.
• Elitzur, A. and Vaidman, L., 1993, ‘Interaction-Free Quantum Measurements’, Foundation of Physics , 23: 987–997.
• Everett, H., 1957, ‘Relative State Formulation of Quantum Mechanics’, Review of Modern Physics , 29: 454–462; see also ‘The Theory of the Universal Wave Function’, in B. De Witt and N. Graham (eds.), The Many-Worlds Interpretation of Quantum Mechanics , Princeton: Princeton University Press, 1973.
• Fein, Y. Y., Geyer, P., Zwick, P., Kiałka, F., Pedalino, S., Mayor, M., Stefan Gerlich, S. and Arndt, M., 2019, ‘Quantum Superposition of Molecules Beyond 25 kDa’, Nature Physics , 15(12): 1242–1245.
• Frauchiger, D. and Renner, R., 2018, ‘Quantum Theory Cannot Consistently Describe the Use of Itself’, Nature communications , 9(1): 1–10.
• Gao, S., 2017, The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics , Cambridge: Cambridge University Press.
• Gell-Mann, M. and Hartle, J. B., 1990, ‘Quantum Mechanics in the Light of Quantum Cosmology’, in W. H. Zurek (ed.), Complexity, Entropy and the Physics of Information , Reading: Addison-Wesley, pp. 425–459.
• Gleason, A. M., 1957, ‘Measures on the Closed Subspaces of Hilbert Space’, Journal of Mathematics and Mechanics , 6: 885–894.
• Graham, N., 1973, ‘The Measurement of Relative Frequency’, in De Witt and N. Graham (eds.), The Many-Words Interpretation of Quantum Mechanics , Princeton: Princeton University Press.
• Greaves, H., 2004, ‘Understanding Deutsch’s Probability in a Deterministic Universe’, Studies in History and Philosophy of Modern Physics , 35: 423–456.
• Greaves, H. and Myrvold, W., 2010, ‘Everett and Evidence’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 181–205.
• Groisman, B., Hallakoun, N., and Vaidman, L., 2013 ‘The Measure of Existence of a Quantum World and the Sleeping Beauty Problem’, Analysis , 73: 695–706.
• Hanson, R., 2003, ‘When Worlds Collide: Quantum Probability from Observer Selection?’ Foundations of Physics , 33: 112–1150.
• –––, 2006, ‘Drift-Diffusion in Mangled Worlds Quantum Mechanics’, Proceedings of the Royal Society A , 462: 1619–1627.
• Harding, J., 2020 ‘Everettian Quantum Mechanics and the Metaphysics of Modality’, The British Journal for the Philosophy of Science , doi:10.1093/bjps/axy037
• Hartle, J. B, 1968 ‘Quantum Mechanics of Individual Systems’, American Journal of Physics , 36: 704–712.
• Hemmo, M. and Pitowsky, I., 2007, ‘Quantum Probability and Many Worlds’, Studies in the History and Philosophy of Modern Physics , 38: 333–350.
• Hemmo, M. and Shenker, O., 2020, ‘Why the Many-Worlds Interpretation of Quantum Mechanics Needs More than Hilbert Space Structure’, in R. Peels, J. de Ridder and R. van Woudenberg (eds.), Scientific Challenges to Common Sense Philosophy , Routledge, pp. 61–70.
• Hewitt-Horsman, C. and Vedral V., 2007, ‘Developing the Deutsch-Hayden Approach to Quantum Mechanics’, New Journal of Physics , 9(5): 135.
• Jansson, L., 2016, ‘Everettian Quantum Mechanics and Physical Probability: Against the Principle of “State Supervenience”’, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 53: 45–53.
• Joos, E., Zeh, H.D., Kiefer, C., Giulini, D., Kupsch, J., and Stamatescu, I.-O., 2003, Decoherence and the Appearance of a Classical World , 2nd edition, Berlin: Springer.
• Kent, A., 1990, ‘Against Many-Worlds Interpretation’, International Journal of Modern Physics A , 5: 1745–1762.
• –––, 2010, ‘One World Versus Many: The Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 307–354.
• –––, 2015, ‘Does it Make Sense to Speak of Self-Locating Uncertainty in the Universal Wave Function? Remarks on Sebens and Carroll’, Foundations of Physics , 45: 211–217.
• Kragh, H., 2009, ‘Contemporary History of Cosmology and the Controversy over the Multiverse’, Annals of Science , 66: 529–551.
• Kuypers S. and Deutsch D., 2021, ‘Everettian Relative States in the Heisenberg Picture’, Proceedings of the Royal Society A , 477(2246): 20200783.
• Lewis, D., 1986, On the Plurality of Worlds , Oxford, New York: Basil Blackwell.
• Lewis, P., 2000, ‘What Is It Like to be Schrödinger’s Cat?’ Analysis , 60: 22–29.
• –––, 2004, ‘Life in Configuration Space’, British Journal for the Philosophy of Science , 55: 713–729.
• –––, 2007, ‘Quantum Sleeping Beauty’, Analysis , 67: 59–65.
• –––, 2010, ‘Probability in Everettian Quantum Mechanics’, Manuscrito , 33: 285–306.
• Lockwood, M., 1989, Mind, Brain & the Quantum , Oxford: Basil Blackwell.
• Lockwood, M., Brown, H. R., Butterfield, J., Deutsch, D., Loewer, B., Papineau, D., Saunders, S., 1996, ‘Symposium: The “Many Minds” Interpretation of Quantum Theory’, British Journal for the Philosophy of Science , 47: 159–248.
• O. Lombardi, S. Fortin, C. López, and F. Holik (eds.), 2019, Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics , Cambridge: Cambridge University Press.
• Mandolesi, A. L., 2018, ‘Analysis of Wallace’s Proof of the Born rule in Everettian Quantum Mechanics: Formal Aspects’, Foundations of Physics , 48(7): 751–782.
• –––, 2019, ‘Analysis of Wallace’s Proof of the Born rule in Everettian Quantum Mechanics II: Concepts and Axioms’, Foundations of Physics , 49(1): 24–52.
• Marchildon, L., 2015, ‘Multiplicity in Everett’s Interpretation of Quantum Mechanics’, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 52: 274–284.
• Maudlin, T., 2010, ‘Can the World be Only Wavefunction?’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 121–143.
• –––, 2019, Philosophy of Physics: Quantum Theory , Princeton Foundations of Contemporary Philosophy, Princeton: Princeton University Press.
• McQueen, K. J., and Vaidman, L., 2019, ‘In Defence of the Self-Location Uncertainty Account of Probability in the Many-Worlds Interpretation’, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 66: 14–23.
• –––, 2020, ‘How the Many Worlds Interpretation brings Common Sense to Paradoxical Quantum Experiments’, in R. Peels, J. de Ridder R. van Woudenberg (eds.), Scientific Challenges to Common Sense Philosophy , London: Routledge, pp. 61–70.
• Monton, B., 2006, ‘Quantum Mechanics and 3N-Dimensional Space’, Philosophy of Science , 73: 778–789.
• Myrvold, W. C., 2015, ‘What is a Wavefunction?’, Synthese , 192: 3247–3274.
• –––, 2016, ‘Lessons of Bell’s Theorem: Nonlocality, yes; Action at a distance, not necessarily’, in Quantum Nonlocality and Reality: 50 Years of Bell’s Theorem , Mary Bell and Shan Gao (eds.), Cambridge, Cambridge University Press, pp. 238–260.
• Ney, A., 2021, The World in the Wave Function: a Metaphysics for Quantum Physics , Oxford: Oxford University Press.
• Ney, A. and Albert, D., 2013, The Wave Function: Essays on the Metaphysics of Quantum Mechanics , Oxford: Oxford University Press.
• Page, D., 1999, ‘Can Quantum Cosmology Give Observational Consequences of Many-Worlds Quantum Theory?’ in C. P. Burgess and R. C. Myers (eds.), General Relativity and Relativistic Astrophysics, Eighth Canadian Conference Montreal, Quebec , Melville, New York: American Institute of Physics, pp. 225–232.
• –––, 2003, ‘Mindless Sensationalism: a Quantum Framework for Consciousness’, in Consciousness: New Philosophical Essays , Q. Smith and A. Jokic (eds.), Oxford: Oxford University Press, pp. 468–506.
• Papineau, D., 2010, ‘A Fair Deal for Everettians’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 181–205.
• Papineau, D. and Durà-Vilà, V., 2009, ‘A Thirder and an Everettian: A Reply to Lewis’s “Quantum Sleeping Beauty”’, Analysis , 69: 78–86.
• Price, H., 2010, ‘Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability?’ in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 369–390.
• Parfit, D., 1986, Reasons and Persons , New York: Oxford University Press.
• Pearle, P., 1986, ‘Models for Reduction’, in R. Penrose and C.J. Isham (eds.), Quantum Concepts of Space and Time , Oxford: Caledonia Press, pp. 204–214.
• Penrose, R., 1994, Shadows of the Mind , Oxford: Oxford University Press.
• Putnam, H., 2005, ‘A Philosopher Looks at Quantum Mechanics (Again)’, British Journal for the Philosophy of Science , 56: 615–634.
• Raymond-Robichaud, P., 2020, ‘A Local-Realistic Model for Quantum Theory’, Proc. R. Soc. A 477: 20200897.
• Read, J., 2019, ‘In Defence of Everettian Decision Theory’, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 63: 136–140.
• Riedel, C. J., 2017, ‘Classical Branch Structure from Spatial Redundancy in a Many-Body Wave Function’, Physical Review Letters , 118(12): 120402.
• Riedel, C. J., Zurek, W. H. and Zwolak, M., 2016, ‘Objective Past of a Quantum Universe: Redundant Records of Consistent Histories’, Physical Review A , 93(3): 032126.
• Rubin, M. A., 2001, ‘Locality in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics’, Foundations of Physics Letters , 14: 301–322.
• –––, 2011, ‘Observers and Locality in Everett Quantum Field Theory’, Foundations of Physics , 41: 1236–1262.
• Saunders, S., 1993, ‘Decoherence, Relative States, and Evolutionary Adaptation’, Foundations of Physics , 23: 1553–1585.
• –––, 1995, ‘Time, Quantum Mechanics, and Decoherence’, Synthese , 102: 235–266.
• –––, 1998, ‘Time, Quantum Mechanics, and Probability’, Synthese , 114: 373–404.
• –––, 2010, ‘Chance in the Everett Interpretation’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 181–205. [ Saunders 2010/Updated 2016 Preprint ]
• Saunders, S. and Wallace, D., 2008a, ‘Branching and Uncertainty’, British Journal for the Philosophy of Science , 59: 293–305.
• –––, 2008b, ‘Reply’, British Journal for the Philosophy of Science , 59: 315–317.
• Saunders, S., Barrett, J., Kent, A. and Wallace, D. (eds.), 2010, Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press.
• Schlosshauer, M., 2006, ‘Experimental Motivation and Empirical Consistency in Minimal No-Collapse Quantum Mechanics’, Annals of Physics , 321: 112–149.
• –––, 2007, Decoherence and the Quantum-to-Classical Transition , Heidelberg and Berlin: Springer.
• –––, 2019, ‘Quantum Decoherence’, Physics Reports , 831: 1–57.
• Schwarz, W., 2015, ‘Belief Update Across Fission’, British Journal for the Philosophy of Science , 66(3): 659–682.
• Sebens, C.T. and Carroll, S.M., 2018, ‘Self-locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics’, British Journal for the Philosophy of Science , 69(1): 25–74.
• Skyrms, B., 1976, ‘Possible Worlds, Physics and Metaphysics’, Philosophical Studies , 30: 323–332.
• Susskind, L., 2016, ‘Copenhagen vs Everett, Teleportation, and ER= EPR’, Fortschritte der Physik , 64(6–7): 551–564.
• Steane, A. M., 2003, ‘A Quantum Computer Only Needs One Universe’, Studies in History and Philosophy of Modern Physics , 34: 469–478.
• Stoica, O. C., 2019, ‘Representation of the Wave Function on the Three-Dimensional Space’, Physical Review A , 100: 042115.
• Tappenden, P., 2000, ‘Identity and Probability in Everett’s Multiverse’, British Journal for the Philosophy of Science , 51: 99–114.
• –––, 2008, ‘Saunders and Wallace on Everett and Lewis’, British Journal for the Philosophy of Science , 59: 307–314.
• –––, 2011, ‘Evidence and Uncertainty in Everett’s Multiverse’, British Journal for the Philosophy of Science , 62: 99–123.
• –––, 2017, ‘Objective Probability and the Mind-Body Relation’s Multiverse’, Studies in History and Philosophy of Science (Part B), 57: 8–16.
• –––, 2019a, ‘Everettian Theory as Pure Wave Mechanics Plus a No-Collapse Probability Postulate’, Synthese , 14: 1–28.
• –––, 2019b, ‘Everett’s Multiverse and the World as Wavefunction’, Quantum Reports , 1(1): 119–129.
• Tegmark, M., 2014, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality , New York: Vintage.
• Timpson C. J., 2005, ‘Nonlocality and Information Flow: The Approach of Deutsch and Hayden’, Foundations of Physics , 35: 313–343.
• Tipler, F. J., 1986a, ‘The Many-Worlds Interpretation of Quantum Mechanics in Quantum Cosmology’, in R. Penrose and C.J. Isham (eds.), Quantum Concepts of Space and Time , Oxford: The Clarendon Press, 1986, pp. 204–214.
• –––, 1986b, ‘Interpreting the Wave Function of the Universe’, Physics Reports , 137: 231–275.
• –––, 2012, ‘Nonlocality as Evidence for a Multiverse Cosmology’, Modern Physics Letters A , 27: 1250019.
• –––, 2014, ‘Quantum Nonlocality Does Not Exist’, Proceedings of the National Academy of Sciences A , 111(31): 11281–11286.
• Vaidman, L., 1994, ‘On the Paradoxical Aspects of New Quantum Experiments’, Philosophy of Science Association 1994 , pp. 211–217.
• –––, 1998, ‘On Schizophrenic Experiences of the Neutron or Why We should Believe in the Many-Worlds Interpretation of Quantum Theory’, International Studies in the Philosophy of Science , 12: 245–261.
• –––, 2001, ‘Probability and the Many Worlds Interpretation of Quantum Theory’, in A. Khrennikov, (ed.), Quantum Theory: Reconsidereation of Foundations , Sweeden: Vaxjo University Press, pp. 407–422.
• –––, 2010, ‘Time Symmetry and the Many-Worlds Interpretation’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 582–596.
• –––, 2012, ‘Probability in the Many-Worlds Interpretation of Quantum Mechanics’, in Ben-Menahem, Y. and Hemmo, M. (eds.), Probability in Physics , The Frontiers Collection XII Springer, pp. 299–311.
• –––, 2013, ‘Past of a Quantum Particle’, Physical Review A , 87: 052104.
• –––, 2014, ‘ Quantum Theory and Determinism’, Quantum Studies: Mathematical and Foundations , 1: 5–38.
• –––, 2016a, ‘All is \(\Psi\)’, Journal of Physics: Conference Series , 701: 1.
• –––, 2016b, ‘Bell Inequality and Many-Worlds Interpretation’, in Quantum Nonlocality and Reality: 50 Years of Bell’s Theorem , Mary Bell and Shan Gao (eds.), Cambridge: Cambridge University Press, pp. 195–203.
• –––, 2019, ‘Ontology of the Wave Function and the Many-Worlds Interpretation’, O. Lombardi, S. Fortin, C. López, & F. Holik (eds.), Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics , Cambridge: Cambridge University Press, 93–106.
• –––, 2020, ‘Derivations of the Born rule’, Hemmo M., Shenker O. (eds.), Quantum, Probability, Logic , Jerusalem Studies in Philosophy and History of Science. Cham: Springer, pp. 567–584.
• Van Wesep, R., 2006, ‘Many Worlds and the Appearance of Probability in Quantum Mechanics’, Annals of Physics , 321: 2438–2452.
• Vinante, A., Carlesso, M., Bassi, A., Chiasera, A., Varas, S., Falferi, P., Margesin, B. Mezzena, R. and Ulbricht, H., 2020, ‘Narrowing the Parameter Space of Collapse Models with Ultracold Layered Force Sensors’, Physical Review Letters , 125(10): 100404.
• von Neumann, J., 1932, Mathematische Grundlagen der Quantenmechanik , Berlin: Springer; R. T. Beyer (trans.) Mathematical Foundations of Quantum Mechanics , Princeton: Princeton University Press, 1955.
• Waegell, M., 2018, ‘An Ontology of Nature with Local Causality, Parallel Lives, and Many Relative Worlds’, Foundations of Physics , 48(12): 1698–1730.
• Waegell, M. and McQueen, K. J., 2020, ‘Reformulating Bell’s Theorem: The Search for a Truly Local Quantum Theory’, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 70: 39–50.
• Wallace, D., 2002, ‘Worlds in the Everett Interpretation’, Studies in History & Philosophy of Modern Physics , 33B: 637–661.
• –––, 2003, ‘Everettian Rationality: Defending Deutsch’s Approach to Probability in the Everett interpretation’, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 34: 415–438.
• –––, 2007, ‘Quantum Probability from Subjective Likelihood: Improving on Deutsch’s Proof of the Probability Rule’, Studies in History and Philosophy of Science (Part B: Studies in the History and Philosophy of Modern Physics), 38: 311–332.
• –––, 2010a, ‘ Decoherence and Ontology (Or: How I Learned to Stop Worrying and Love FAPP)’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 53–72.
• –––, 2010b, ‘How to Prove the Born Rule’, in S. Saunders, J. Barrett, A. Kent and D. Wallace (eds.), Many Worlds? Everett, Quantum Theory, & Reality , Oxford and New York: Oxford University Press, pp. 227–263.
• –––, The Emergent Multiverse , Oxford: University Press.
• Wallace, D. and Timpson, C. J., 2007, ‘Non-locality and Gauge Freedom in Deutsch and Hayden’s Formulation of Quantum Mechanics’, Foundations of Physics , 37: 951–955.
• –––, 2010, ‘Quantum Mechanics on Spacetime I: Spacetime State Realism‏’, British Journal for the Philosophy of Science , 61: 697–727.
• Weissman, M. B., 1999, ‘Emergent Measure-Dependent Probabilities from Modified Quantum Dynamics without State-Vector Reduction’, Foundations of Physics Letters , 12: 407–426.
• Wheeler, J., 1957, ‘Assessment of Everett’s “Relative State” Formulation of Quantum Theory’, Reviews of Modern Physics , 29: 463–465.
• Wigner, E. P., 1961, ‘Remarks on the Mind-Body Question’, in I. J. Good, (ed.), The Scientist Speculates , Heinemann, pp. 284–302.
• Wilson, A., 2013, ‘Objective Probability in Everettian Quantum Mechanics’, British Journal for the Philosophy of Science , 64: 709–737.
• –––, 2014, ‘Everettian Confirmation and Sleeping Beauty’, British Journal for the Philosophy of Science , 65: 573–598.
• –––, 2017, ‘The Quantum Doomsday Argument’, British Journal for the Philosophy of Science , 68: 597–615.
• –––, 2020, The Nature of Contingency: Quantum Physics as Modal Realism , New York: Oxford University Press.
• Zeh, H. D., 1981, ‘The Problem of Conscious Observation in Quantum Mechanical Description’, Epistemological Letters , 63.
• Zurek, W. H., 2003, ‘Decoherence, Einselection, and the Quantum Origins of the Classical’, Review of Modern Physics , 75: 715–775.
• –––, 2005, ‘Probabilities from Entanglement, Born’s rule \(p_k =|\psi_k |^2\) from Envariance’, Physical Review A , 71: 052105.
• –––, 2018, ‘Quantum Theory of the Classical: Quantum Jumps, Born’s Rule and Objective Classical Reality via Quantum Darwinism’, Philosophical Transactions of the Royal Society A , 376: 20180107.
• Cuffaro, M. E., forthcoming, ‘The Philosophy of Quantum Computing’, in E. Miranda (ed.), Quantum Computing in the Arts and Humanities: An Introduction to Core Concepts, Theory and Applications , Dordrecht: Springer, [ Cuffaro forthcoming preprint ].
• Parrochia, D., 2020, ‘Are there Really Many Worlds in the “Many-Worlds Interpretation” of Quantum Mechanics?”, [ Parrochia 2020 preprint ].
• Saunders, S., forthcoming-a, ‘The Everett Interpretation: Structure’, The Routledge Companion to the Philosophy of Physics , E. Knox and A. Wilson (eds.), London: Routledge, [ Saunders forthcoming-a preprint ].
• –––, forthcoming-b, ‘The Everett Interpretation: Probability’, The Routledge Companion to the Philosophy of Physics , E. Knox and A. Wilson (eds.), London: Routledge, [ Saunders forthcoming-b reprint ].

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.

• Search in Physics Preprint Archive
• Search in PhilPapers
• Search in Pittsburgh Philosophy of Science Archive
• Search in Google Scholar
• Search in YouTube

Dutch book arguments | quantum mechanics | quantum mechanics: action at a distance in | quantum mechanics: Everettian | quantum mechanics: relational | quantum mechanics: the role of decoherence in | quantum theory: philosophical issues in | quantum theory: quantum computing | quantum theory: quantum entanglement and information | quantum theory: the Einstein-Podolsky-Rosen argument in

Acknowledgments

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

Copyright © 2021 by Lev Vaidman < vaidman @ post . tau . ac . il >

• Accessibility

Support SEP

Mirror sites.

View this site from another server:

• Info about mirror sites

The Stanford Encyclopedia of Philosophy is copyright © 2023 by The Metaphysics Research Lab , Department of Philosophy, Stanford University

Library of Congress Catalog Data: ISSN 1095-5054

Physical Review Letters

• Collections
• Editorial Team
• Open Access

Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large- N c Expansion

Anthony n. ciavarella and christian w. bauer, phys. rev. lett. 133 , 111901 – published 9 september 2024.

• No Citing Articles

Supplemental Material

• ACKNOWLEDGMENTS

Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we show how the Hilbert space and interactions can be expanded in inverse powers of N c . At leading order in this expansion, the Hamiltonian simplifies dramatically, both in the required size of the Hilbert space as well as the type of interactions involved. Adding a truncation of the resulting Hilbert space in terms of local energy states we give explicit constructions that allow simple representations of SU(3) gauge fields on qubits and qutrits. This formulation allows a simulation of the real time dynamics of a SU(3) lattice gauge theory on a 5 × 5 and 8 × 8 lattice on ibm_torino with a CNOT depth of 113.

• Received 28 February 2024
• Revised 26 July 2024
• Accepted 5 August 2024

DOI: https://doi.org/10.1103/PhysRevLett.133.111901

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP 3 .

Published by the American Physical Society

Physics Subject Headings (PhySH)

• Research Areas

Authors & Affiliations

• 1 Physics Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, USA
• 2 Department of Physics, University of California , Berkeley, Berkeley, California 94720, USA
• * Contact author: [email protected]
• † Contact author: [email protected]

Article Text

Vol. 133, Iss. 11 — 13 September 2024

Authorization Required

Other options.

• Buy Article »
• Find an Institution with the Article »

Download & Share

Calculation of ( 1 / T ) ∫ 0 T d t ⟨ ψ ( t ) | H ^ E | ψ ( t ) ⟩ on a 4 × 1 lattice with periodic boundary conditions and g = 1 . The blue line shows the simulation for a SU(3) lattice gauge theory truncated at p + q ≤ 1 , using the formalism introduced in Ref. [ 48 ]. The purple line shows the time evolution computed with the large N c truncated Hamiltonian in Eq. ( 8 ). The black line underneath shows the ratio of the large N c electric energy to the SU(3) electric energy.

Average probability of a plaquette being excited from the electric vacuum as a function of time on a 4 × 4 and 7 × 7 plaquette lattice with open boundary conditions and g = 1 . The dark green points are an exact classical simulation. The dark blue points were obtained by tensor network simulations of up to two Trotter steps. The light blue and green points are the error mitigated results from ibm_torino.

Graphical representations of Young diagrams in terms of arrows.

Graphical representations of basis states on a point-split lattice.

Graphical method to obtain the scaling of the overlap matrix ⟨ { L i } | { P p , P ¯ p } ⟩ . The top example contains two loops, each encircling a single plaquette m 1 = m 2 = 1 , while the bottom example has a single loop encircling 2 loops m 1 = 1 . This gives for the top example q 1 = q 2 = 1 + 3 × 1 = 4 and v 1 = v 2 = 2 + 2 × 1 = 4 , giving the final scaling N c 0 . For the bottom example we have q 1 = 1 + 2 × 3 = 7 and v 1 = 2 + 2 × 2 = 6 , giving the final scaling 1 / N c .

Sign up to receive regular email alerts from Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

• Forgot your username/password?
• Create an account

Article Lookup

Paste a citation or doi, enter a citation.

• Scientists have developed a groundbreaking theory that unifies Einstein's theory of general relativity and quantum physics, potentially solving some of the universe's greatest mysteries.
• This mathematical framework redefines the mass and charge of fundamental particles, offering a unified explanation for everything from dark matter to photons.
• This could help us understand why black holes don't collapse, the conditions of the Big Bang, and the workings of space-time entanglement.

Unified quantum physics, relativity theory may unlock universe's greatest mysteries

In a groundbreaking development, scientists have successfully established a mathematical link between Einstein's theory of general relativity and quantum physics. The researchers stated, "We proved that the Einstein field equation from general relativity is actually a relativistic quantum mechanical equation." This innovative framework bridges the gap between macroscopic and microscopic scientific principles, potentially revolutionizing our understanding of physical phenomena.

The theory could explain all physical observations

The researchers behind this groundbreaking theory believe it could challenge existing physics principles and transform our understanding of the universe. They stated, "To date, no globally accepted theory has been proposed to explain all physical observations." The new framework offers a unified explanation for everything from the enigmatic dark matter in space to the photons emitted by everyday devices like smartphones .

Bridging the gap between relativity and quantum physics

Einstein's theory of general relativity provides an understanding of gravity, explaining how massive objects like planets and stars warp space-time around them. On the other hand, quantum physics delves into the peculiar behavior of minuscule particles in the universe. Until now, these two theories have remained separate due to their fundamentally different descriptions of the universe. When applied together—for instance, in black hole studies—they often yield contradictory results.

The need to unify the two

The unification of general relativity and quantum physics is crucial for two primary reasons. First, it could offer a comprehensive understanding of the universe across all scales. Second, without this connection, it's challenging to fully comprehend phenomena like quantum gravity, Hawking radiation, string theory among others. To bridge this gap, researchers have developed a mathematical framework that redefines the mass and charge of leptons (fundamental particles), in terms of interactions between field energy and spacetime curvature.

The equation could answer various mysteries

The newly developed equation has demonstrated that the Einstein Field Equation from relativity theory is equivalent to a quantum equation. This discovery could potentially answer long-standing scientific mysteries. For instance, it might elucidate why black holes don't collapse, what conditions prevailed during the Big Bang, and how space-time entanglement operates.

Quantum Effects Explain the Twist Angle in the Helical Structure of DNA

• CC BY-NC-ND 4.0

• This person is not on ResearchGate, or hasn't claimed this research yet.

Abstract and Figures

Discover the world's research

• 25+ million members
• 160+ million publication pages
• 2.3+ billion citations

• CHEMPHYSCHEM
• Johannes Henrichsmeyer
• Michael Thelen

• PHYS CHEM CHEM PHYS
• Kevin Carter-Fenk
• John M. Herbert

• Jiří Šponer
• J BIOL SYST

• DEVANATHAN RAGHUNATHAN

• J CHEM INF MODEL

• Georg Jansen
• BIOPOLYMERS

• Recruit researchers
• Join for free
• Login Email Tip: Most researchers use their institutional email address as their ResearchGate login Password Forgot password? Keep me logged in Log in or Continue with Google Welcome back! Please log in. Email · Hint Tip: Most researchers use their institutional email address as their ResearchGate login Password Forgot password? Keep me logged in Log in or Continue with Google No account? Sign up

Students get quantum computing mentorship and research experience

Fellowship covers theory, programming and hands-on projects.

September 10, 2024

Twenty-one students got hands-on experience working with the Lab's quantum computing experts and the opportunity to program on actual quantum computers, a unique opportunity for them to work on cutting-edge research and for the Lab to build a pipeline to advance the mission.

In existence since 2018, the Quantum Computing Summer School attracts students from around the world with diverse academic backgrounds, including physics, chemistry, computer science and applied mathematics. The summer school is one of the world’s top quantum computing internships available to undergraduate and graduate students. Applications to the 10-week, research-intensive program reached an all-time high of nearly 700 this year, though only 21 students can be accepted.

School co-lead Marco Cerezo said many students discover that Los Alamos is a great place to do quantum science, and they want to stay longer after the summer program ends. Some extend their fellowships to continue their research, while others return as graduate research assistants or postdoctoral researchers. Still others land long-term positions at the Lab.

“Deep expertise in quantum science will be essential for advancing national security, material science and other critical aspects of our mission. The school is a great way to grow our effort, build expertise and attract future workforce,” said school co-lead Lukasz Cincio, a physicist who won IBM’s quantum coding challenge in 2020.

The Quantum Computing Summer School is supported by the Lab’s Information Science and Technology Institute and Theoretical division.

Quantum explained

Fundamentally different from classical computers, quantum processors use a variety of approaches to process quantum information, including superconducting and quantum photonic circuits as well as trapped ions. They rely on quantum properties of their constituents such as superposition and entanglement.

Quantum computing technology has the potential to solve certain kinds of complex problems faster than classical computers, but its powers and pitfalls are still being studied. At the Lab's summer internship, each student is paired with a mentor who has the expertise to guide them through projects that explore burning questions and help them learn quantum coding.

The summer school's maturation is reflected in the participation this summer of researchers from Xanadu, a Canadian company that is a longtime collaborator with the Lab.

“Researchers from Xanadu extended our mentor pool and allowed us to pursue projects that we would not be able to execute on our own,” Cincio said.

Max West, a student from the University of Melbourne in Australia, worked on two projects with Xanadu mentorship — one concerned with efficiently learning properties of unknown quantum states via “classical shadows” and the other optimizing quantum circuits in the presence of symmetries.

“I think attending the summer school will be extremely helpful career-wise due to the opportunity not only to work on some really cool projects, but also to meet and work with some of the leading people in quantum computing,” West said.

Productive problem-solvers

This summer, students worked on a variety of subjects, including quantum machine learning, quantum error mitigation, applications of quantum computing to material science and high-energy physics, classical simulations of quantum systems, optimization problems and many more. Their Los Alamos mentors were staff scientists and postdoctoral researchers from four divisions.

Summer student Alice Barthe, who is affiliated with the Lab’s Theoretical division and two European institutions, has already finished writing a manuscript that explores a central question: “What are problems that a quantum computer can efficiently solve, but that would be intractable for their classical counterparts?”

Many other projects will finish with a paper, published months out from now.

“The school is very productive. Over the seven years we've been running it, students have published over 40 papers, many of them in high-impact journals. Their work assists many scientific projects at LANL,” Cincio said.

In lectures open to Lab employees, leading researchers from academia and industry discussed their latest work: Miles Stoudenmire (Flatiron Institute), Robert Huang (Caltech), Rolando Somma (Google), Bob Coecke (Oxford, Quantinuum) and Vedran Djunko (Leiden University).

And in an ongoing tradition, the program brought back a former student who has achieved significant success and with whom the Lab continues to collaborate. This time it was Supanut Thanasilp of Chula University, Thailand.

“Attending LANL Quantum Computing Summer School was without a doubt the most valuable experience during my Ph.D. and had a life-changing impact on my academic career path, leading to me securing a faculty position at the top university in my home country,” Thanasilp said.

LA-UR-24-29589

Brian Keenan (505) 412-8561 [email protected]

Related Stories

Browse by topic.

• Awards and Recognitions
• Climate Science
• Environmental Stewardship

More Stories

Subscribe to our newsletter.

Sign up to receive the latest news and feature stories from Los Alamos National Laboratory