It has been suggested that Quantum mechanics, philosophy and controversy be merged into this article or section. (Discuss)

An interpretation of quantum mechanics is a statement which attempts to explain what quantum mechanics means in terms of how we view nature. Although quantum mechanics is widely considered the most precisely tested and successful theory in the history of science, many feel that the fundamentals of the theory are yet to be fully understood. There are a number of contending schools of thought, differing over whether quantum mechanics can be understood to be deterministic, which elements of quantum mechanics can be considered "real," and other matters. Image File history File links Please see the file description page for further information. ... It has been suggested that this article or section be merged into Interpretation of quantum mechanics. ... Fig. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ... Determinism is the philosophical proposition that every event, including human cognition, decision and action, is causally determined by an unbroken chain of prior occurrences. ...

Although today this question is of special interest to philosophers of physics, many physicists continue to show a strong interest in the subject, though interest has declined with the rise of modern theory of quantum decoherence. Philosophy of physics is the study of the fundamental, philosophical questions underlying modern physics, the study of matter and energy and how they interact. ... In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ...

Historical background

The operational meaning of the technical terms used by researchers in quantum theory (such as wavefunctions and matrix mechanics) progressed through various intermediate stages. For instance Schrödinger originally viewed the wavefunction associated to the electron as the charge density of an object smeared out over an extended, possibly infinite, volume of space. Max Born later proposed its interpretation as the probability distribution in the space of the electron's position. Other leading scientists, such as Albert Einstein, had great difficulty in accepting some of the more radical consequences of the theory, such as quantum indeterminacy. Even if these matters could be treated as 'teething troubles', they have lent importance to the activity of interpretation. An operational definition of a quantity is the description of a specific process, or set of validation tests, accessible to more persons than the definer (i. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ... Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg in 1925. ... Erwin Rudolf Josef Alexander Schrödinger (August 12, 1887 – January 4, 1961) was an Austrian physicist who achieved fame for his contributions to quantum mechanics, especially the Schrödinger equation, for which he received the Nobel Prize in 1933. ... e- redirects here. ... Max Born (December 11, 1882 in Breslau – January 5, 1970 in Göttingen) was a mathematician and physicist. ... In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... Albert Einstein( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is widely considered to have been one of the greatest physicists of all time. ... Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. ...

It should not, however, be assumed that most physicists consider quantum mechanics as requiring interpretation, other than very minimal instrumentalist interpretations, which are discussed below. The Copenhagen interpretation, as of 2007, appears to be the most popular one among scientists, followed by the many worlds and consistent histories interpretations. But it is also true that most physicists consider non-instrumental questions (in particular ontological questions) to be irrelevant to physics. They fall back on Paul Dirac's point of view, later expressed in the famous dictum: "Shut up and calculate" often (perhaps erroneously) attributed to Richard Feynman (see [1]). In the philosophy of science, instrumentalism is the view that concepts and theories are merely useful instruments whose worth is measured not by whether the concepts and theories are true or false (or correctly depict reality), but by how effective they are in explaining and predicting phenomena. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the Anno Domini (common) era. ... The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... ... In philosophy, ontology (from the Greek , genitive : of being (part. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... Richard Phillips Feynman (May 11, 1918 – February 15, 1988; surname pronounced ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ...

Obstructions to direct interpretation

The perceived difficulties of interpretation reflect a number of points about the orthodox description of quantum mechanics, including:

1. The abstract, mathematical nature of the description of quantum mechanics.
2. The existence of what appear to be non-deterministic and irreversible processes in quantum mechanics.
3. The phenomenon of entanglement, and in particular, the higher correlations between remote events than would be expected in classical theory.
4. The complementarity of possible descriptions of reality.

First, the accepted mathematical structure of quantum mechanics is based on fairly abstract mathematics, such as Hilbert spaces and operators on those Hilbert spaces. In classical mechanics and electromagnetism, on the other hand, properties of a point mass or properties of a field are described by real numbers or functions defined on two or three dimensional sets. These have direct, spatial meaning, and in these theories there seems to be less need to provide a special interpretation for those numbers or functions. The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ... In mathematics, a Hilbert space is a real or complex vector space with a positive definite sesquilinear form, that is complete under its norm. ... In mathematics, a linear transformation (also called linear map or linear operator) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... Electromagnetism is the physics of the electromagnetic field; a field encompassing all of space which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... Partial plot of a function f. ... In mathematics, the Lebesgue covering dimension of a topological space is defined to be the minimum value of n, such that any open cover has a refinement with no point included in more than n+1 elements. ...

Further, the process of measurement plays an apparently essential role in the theory. It relates the abstract elements of the theory, such as the wavefunction, to operationally definable values, such as probabilities. Measurement interacts with the system state, in somewhat peculiar ways, as is illustrated by the double-slit experiment. Various meters Measurement is the estimation of a physical quantity such as length, temperature, or time. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ... An operational definition of a quantity is the description of a specific process, or set of validation tests, accessible to more persons than the definer (i. ... Double-slit diffraction and interference pattern The double-slit experiment consists of letting light diffract through two slits producing fringes or wave-like patterns on a screen. ...

The mathematical formalism used to describe the time evolution of a non-relativistic system proposes two somewhat different kinds of transformations: For a system with internal state (also called stateful system), time evolution means the change of state brought about by the passage of time. ...

• Reversible transformations described by unitary operators on the state space. These transformations are determined by solutions to the Schrödinger equation.

• Non-reversible and unpredictable transformations described by mathematically more complicated transformations (see quantum operations). Examples of these transformations are those that are undergone by a system as a result of measurement.

A restricted version of the problem of interpretation in quantum mechanics consists in providing some sort of plausible picture, just for the second kind of transformation. This problem may be addressed by purely mathematical reductions, for example by the many-worlds or the consistent histories interpretations. In functional analysis, a unitary operator is a bounded linear operator U on a Hilbert space satisfying U*U=UU*=I where I is the identity operator. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ... In quantum mechanics, a quantum operation is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. ... The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ...

In addition to the unpredictable and irreversible character of measurement processes, there are other elements of quantum physics that distinguish it sharply from classical physics and which cannot be represented by any classical picture. One of these is the phenomenon of entanglement, as illustrated in the EPR paradox, which seemingly violates principles of local causality. It has been suggested that Quantum coherence be merged into this article or section. ... In quantum mechanics, the EPR paradox is a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory. ...

Another obstruction to direct interpretation is the phenomenon of complementarity, which seems to violate basic principles of propositional logic. Complementarity says there is no logical picture (obeying classical propositional logic) that can simultaneously describe and be used to reason about all properties of a quantum system S. This is often phrased by saying that there are "complementary" sets A and B of propositions that can describe S, but not at the same time. Examples of A and B are propositions involving a wave description of S and a corpuscular description of S. The latter statement is one part of Niels Bohr's original formulation, which is often equated to the principle of complementarity itself. In physics, complementarity is a basic principle of quantum theory closely identified with the Copenhagen interpretation, and refers to effects such as the wave-particle duality, in which different measurements made on a system reveal it to have either particle-like or wave-like properties. ... In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows to establish that certain formulas are theorems of the formal system. ...

Complementarity is not usually taken to mean that classical logic fails, although Hilary Putnam did take that view in his paper Is logic empirical?. Instead complementarity means that composition of physical properties for S (such as position and momentum both having values in certain ranges) using propositional connectives does not obey rules of classical propositional logic. As is now well-known (Omnès, 1999) the "origin of complementarity lies in the noncommutativity of operators" describing observables in quantum mechanics. Hilary Whitehall Putnam (born July 31, 1926) is an American philosopher who has been a central figure in Western philosophy since the 1960s, especially in philosophy of mind, philosophy of language, and philosophy of science. ... Is logic empirical? is the title of two articles that discuss the radical concept, that the empirical facts about quantum phenomena may provide grounds for revising classical logic. ...

Problematic status of pictures and interpretations

The precise ontological status, of each one of the interpreting pictures, remains a matter of philosophical argument.

In other words, if we interpret the formal structure X of quantum mechanics by means of a structure Y (via a mathematical equivalence of the two structures), what is the status of Y? This is the old question of saving the phenomena, in a new guise. Scientific formalism is a possible term for two aspects of the presentation of science, particularly relevant to the physical sciences. ...

Some physicists, for example Asher Peres and Chris Fuchs, seem to argue that an interpretation is nothing more than a formal equivalence between sets of rules for operating on experimental data. This would suggest that the whole exercise of interpretation is unnecessary. Asher Peres (born 1934 and died January 1, 2005) was an Israeli physicist, considered a pioneer in quantum information theory. ...

Instrumentalist interpretation

Main article: Instrumentalist interpretation

Any modern scientific theory requires at the very least an instrumentalist description which relates the mathematical formalism to experimental practice and prediction. In the case of quantum mechanics, the most common instrumentalist description is an assertion of statistical regularity between state preparation processes and measurement processes. That is, if a measurement of a real-valued quantity is performed many times, each time starting with the same initial conditions, the outcome is a well-defined probability distribution over the real numbers; moreover, quantum mechanics provides a computational instrument to determine statistical properties of this distribution, such as its expectation value. This article aims at proposing a non-interpretative description of some key quantum experiments, based as far as possible on genuine facts, although there is no criterion for deciding whether this goal has been fully achieved or not (should it be feasible). ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects as the outcome of the random trial when identical odds are...

Calculations for measurements performed on a system S postulate a Hilbert space H over the complex numbers. When the system S is prepared in a pure state, it is associated with a vector in H. Measurable quantities are associated with Hermitian operators acting on H: these are referred to as observables. In mathematics, a Hilbert space is a real or complex vector space with a positive definite sesquilinear form, that is complete under its norm. ... The complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots. ... The term pure state refers to several related concepts in physics, particularly quantum mechanics and in functional analysis. ... In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ... On a finite-dimensional inner product space, a self-adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose. ... In physics, particularly in quantum physics, a system observable is a property of the system state that can be determined by some sequence of physical operations. ...

Repeated measurement of an observable A for S prepared in state ψ yields a distribution of values. The expectation value of this distribution is given by the expression

This mathematical machinery gives a simple, direct way to compute a statistical property of the outcome of an experiment, once it is understood how to associate the initial state with a vector, and the measured quantity with an observable (that is, a specific Hermitian matrix).

As an example of such a computation, the probability of finding the system in a given state is given by computing the expectation value of a (rank-1) projection operator Template:Unite See also projection (linear algebra). ...

The probability is then the non-negative real number given by

By abuse of language, the bare instrumentalist description can be referred to as an interpretation, although this usage is somewhat misleading since instrumentalism explicitly avoids any explanatory role; that is, it does not attempt to answer the question of what quantum mechanics is talking about.

Summary of common interpretations of QM

Properties of interpretations

An interpretation can be characterized by whether it satisfies certain properties, such as:

• Realism
• Completeness
• Local realism
• Determinism

To explain these properties, we need to be more explicit about the kind of picture an interpretation provides. To that end we will regard an interpretation as a correspondence between the elements of the mathematical formalism M and the elements of an interpreting structure I, where: In physics, the principle of locality is that distant objects cannot have direct influence on one another: an object is influenced directly only by its immediate surroundings. ... Determinism is the philosophical proposition that every event, including human cognition, decision and action, is causally determined by an unbroken chain of prior occurrences. ...

• The mathematical formalism consists of the Hilbert space machinery of ket-vectors, self-adjoint operators acting on the space of ket-vectors, unitary time dependence of ket-vectors and measurement operations. In this context a measurement operation can be regarded as a transformation which carries a ket-vector into a probability distribution on ket-vectors. See also quantum operations for a formalization of this concept.
• The interpreting structure includes states, transitions between states, measurement operations and possibly information about spatial extension of these elements. A measurement operation here refers to an operation which returns a value and results in a possible system state change. Spatial information, for instance would be exhibited by states represented as functions on configuration space. The transitions may be non-deterministic or probabilistic or there may be infinitely many states. However, the critical assumption of an interpretation is that the elements of I are regarded as physically real.

In this sense, an interpretation can be regarded as a semantics for the mathematical formalism. Bra-ket notation is the standard notation for describing quantum states in the theory of quantum mechanics. ... On a finite-dimensional inner product space, a self-adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose. ... In quantum mechanics, a quantum operation is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. ... Semantics (Greek semantikos, giving signs, significant, symptomatic, from sema, sign) refers to the aspects of meaning that are expressed in a language, code, or other form of representation. ...

In particular, the bare instrumentalist view of quantum mechanics outlined in the previous section is not an interpretation at all since it makes no claims about elements of physical reality.

The current use in physics of "completeness" and "realism" is often considered to have originated in the paper (Einstein et al., 1935) which proposed the EPR paradox. In that paper the authors proposed the concept "element of reality" and "completeness" of a physical theory. Though they did not define "element of reality", they did provide a sufficient characterization for it, namely a quantity whose value can be predicted with certainty before measuring it or disturbing it in any way. EPR define a "complete physical theory" as one in which every element of physical reality is accounted for by the theory. In the semantic view of interpretation, an interpretation of a theory is complete if every element of the interpreting structure is accounted for by the mathematical formalism. Realism is a property of each one of the elements of the mathematical formalism; any such element is real if it corresponds to something in the interpreting structure. For instance, in some interpretations of quantum mechanics (such as the many-worlds interpretation) the ket vector associated to the system state is assumed to correspond to an element of physical reality, while in others it does not. In quantum mechanics, the EPR paradox is a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory. ...

Determinism is a property characterizing state changes due to the passage of time, namely that the state at an instant of time in the future is a function of the state at the present (see time evolution). It may not always be clear whether a particular interpreting structure is deterministic or not, precisely because there may not be a clear choice for a time parameter. Moreover, a given theory may have two interpretations, one of which is deterministic, and the other not. Partial plot of a function f. ... For a system with internal state (also called stateful system), time evolution means the change of state brought about by the passage of time. ...

Local realism has two parts:

• The value returned by a measurement corresponds to the value of some function on the state space. Stated in another way, this value is an element of reality;
• The effects of measurement have a propagation speed not exceeding some universal bound (e.g., the speed of light). In order for this to make sense, measurement operations must be spatially localized in the interpreting structure.

A precise formulation of local realism in terms of a local hidden variable theory was proposed by John Bell. In quantum mechanics, a local hidden variable theory is one in which distant events are assumed to have no instantaneous effect on local ones. ...

Bell's theorem and its experimental verification restrict the kinds of properties a quantum theory can have. For instance, Bell's theorem implies quantum mechanics cannot satisfy local realism. Bells theorem is the most famous legacy of the late Irish phyisicist John Bell. ...

Ensemble Interpretation, or Statistical Interpretation

Main article: Ensemble Interpretation

The Ensemble Interpretation, or Statistical Interpretation is an interpretation that can be viewed as a minimalist interpretation. That is, it is a quantum mechanical interpretation, that claims to make the fewest assumptions associated with the standard mathematical formalization. At its heart, it takes the statistical interpretation of Born to the fullest extent. The interpretation states that the wave function does not apply to an individual system, or for example, a single particle, but is an abstract mathematical, statistical quantity that only applies to an ensemble of similar prepared systems or particles. Probably the most notable supporter of such an interpretation was Einstein: The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation. ... The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation. ...

"The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems."

Einstein - Albert Einstein: Philosopher-Scientist, ed. P.A. Schilpp (Harper & Row, New York)

To date, probably the most prominent advocate of the Ensemble Interpretation is Leslie E. Ballentine, Professor at Simon Fraser University, and writer of the graduate level text book "Quantum Mechanics, A Modern Development".

Consistent histories

Main article: Consistent histories

The consistent histories generalizes the conventional Copenhagen interpretation and attempts to provide a natural interpretation of quantum cosmology. The theory is based on a consistency criterion that then allows the history of a system to be described so that the probabilities for each history obey the additive rules of classical probability while being consistent with the Schrödinger equation. In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... In theoretical physics, quantum cosmology is a young field attempting to study the effect of quantum mechanics on the earliest moments of the universe after the Big Bang. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ...

According to this interpretation, the purpose of a quantum-mechanical theory is to predict the relative probabilities of various alternative histories.

Many worlds

Main article: Many-worlds interpretation

The many-worlds interpretation (or MWI) is an interpretation of quantum mechanics that rejects the non-deterministic and irreversible wavefunction collapse associated with measurement in the Copenhagen interpretation in favor of a description in terms of quantum entanglement and reversible time evolution of states. The phenomena associated with measurement are explained by decoherence which occurs when states interact with the environment. As result of the decoherence the world-lines of macroscopic objects repeatedly split into mutally unobservable, branching histories -- distinct universes within a greater multiverse. The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome... The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome... In certain interpretations of quantum mechanics, wavefunction collapse is one of two processes by which quantum systems apparently evolve according to the laws of quantum mechanics. ... Quantum decoherence is the general term for the consequences of irreversible quantum entanglement. ... A multiverse (or meta-universe) is the hypothetical set of multiple possible universes (including our universe) that together comprise all of physical reality. ...

Many minds

Main article: Many-minds interpretation

The many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. The many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. ... Fig. ... The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome...

The Copenhagen Interpretation

Main article: Copenhagen interpretation

The Copenhagen interpretation is the "standard" interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. Bohr and Heisenberg extended the probabilistic interpretation of the wavefunction, proposed by Max Born. The Copenhagen interpretation rejects questions like "where was the particle before I measured its position" as meaningless. The measurement process randomly picks out exactly one of the many possibilities allowed for by the state's wave function. The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ...

Objective collapse theories

Main article: Objective collapse theory

Objective collapse theories differ from the Copenhagen interpretation in regarding both the wavefunction and the process of collapse as ontologically objective. In objective theories, collapse occurs randomly ("spontaneous localization"), or when some physical threshold is reached, with observers having no special role. Thus, they are realistic, indeterministic, no-hidden-variables theories. The mechanism of collapse is not specified by standard quantum mechanics, which needs to be extended if this approach is correct, meaning that Objective Collapse is more of a theory than an interpretation. Examples include the Ghirardi-Rimini-Weber theory^[1] and the Penrose interpretation. ^[2] Objective collapse theories are an approach to the interpretational problems of quantum mechanics. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... This article or section is in need of attention from an expert on the subject. ...

Quantum Logic

Main article: Quantum logic

Quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. This research area and its name originated in the 1936 paper by Garrett Birkhoff and John von Neumann, who attempted to reconcile some of the apparent inconsistencies of classical boolean logic with the facts related to measurement and observation in quantum mechanics. In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ... In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ... Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA - November 22, 1996, Water Mill, New York, USA) was an American mathematician. ... John von Neumann (Hungarian Margittai Neumann János Lajos) (born December 28, 1903 in Budapest, Austria-Hungary; died February 8, 1957 in Washington D.C., United States) was a Hungarian-born mathematician and polymath who made contributions to quantum physics, functional analysis, set theory, topology, economics, computer science, numerical analysis...

The Bohm interpretation

Main article: Bohm interpretation

The Bohm interpretation of quantum mechanics is an interpretation postulated by David Bohm in which the existence of a non-local universal wavefunction allows distant particles to interact instantaneously. The interpretation generalizes Louis de Broglie's pilot wave theory from 1927, which posits that both wave and particle are real. The wave function 'guides' the motion of the particle, and evolves according to the Schrödinger equation. The interpretation assumes a single, nonsplitting universe (unlike the Everett many-worlds interpretation) and is deterministic (unlike the Copenhagen interpretation). It says the state of the universe evolves smoothly through time, without the collapsing of wavefunctions when a measurement occurs, as in the Copenhagen interpretation. However, it does this by assuming a number of hidden variables, namely the positions of all the particles in the universe, which, like probability amplitudes in other interpretations, can never be measured directly. The Bohm interpretation of quantum mechanics, sometimes called the Bohmian Mechanics or Ontological interpretation is an interpretation postulated by David Bohm in 1952, which was an extension of the de Broglie-pilot-wave theory of 1927. ... The Bohm interpretation of quantum mechanics, sometimes called the Bohmian Mechanics or Ontological interpretation is an interpretation postulated by David Bohm in 1952, which was an extension of the de Broglie-pilot-wave theory of 1927. ... David Bohm. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892–March 19, 1987), was a French physicist and Nobel Prize laureate. ...

Transactional interpretation

Main article: Transactional interpretation

The transactional interpretation of quantum mechanics (TIQM) by John G. Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward-in-time) and advanced (backward-in-time) waves. The author argues that it avoids the philosophical problems with the Copenhagen interpretation and the role of the observer, and resolves various quantum paradoxes. The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ... The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ... John G. Cramer (born 1934) is a Professor of Physics at the University of Washington in Seattle, USA. When not teaching, he works with the STAR detector at the new Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, and the particle accelerator at CERN in Geneva, Switzerland. ...

Consciousness causes collapse

Main article: Consciousness causes collapse

Consciousness causes collapse is the speculative theory that observation by a conscious observer is responsible for the wavefunction collapse. It is an attempt to solve the Wigner's friend paradox by simply stating that collapse occurs at the first "conscious" observer. Supporters claim this is not a revival of substance dualism, since (in a ramification of this view) consciousness and objects are entangled and cannot be considered as distinct. The consciousness-causes-collapse theory can be considered as a speculative appendage to almost any interpretation of quantum mechanics and most physicists regard it as a non-scientific concept, claiming that it is 1) unverifiable and 2) introduces unnecessary elements into physics. Supporters could reply that this simply assumes what is at issue, namely whether or not consciousness is a necessary element in physics. Consciousness causes collapse is the theory that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics. ... Consciousness causes collapse is the theory that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics. ... Wigners friend is a thought experiment proposed by the physicist Eugene Wigner; it is an extension of the Schrödingers cat experiment designed as a point of departure for discussing the mind-body problem as viewed by the Copenhagen interpretation of quantum mechanics. ...

Relational Quantum Mechanics

Main article: Relational quantum mechanics

The essential idea behind relational quantum mechanics, following the precedent of Special Relativity, is that different observers may give different accounts of the same series of events: for example, to one observer at a given point in time, a system may be in a single, "collapsed" eigenstate, while to another observer at the same time, it may be in a superposition of two or more states. Consequently, if quantum mechanics is to be a complete theory, Relational Quantum Mechanics argues that the notion of "state" describes not the observed system itself, but the relationship, or correlation, between the system and its observer(s). The state vector of conventional quantum mechanics becomes a description of the correlation of some degrees of freedom in the observer, with respect to the observed system. However, it is held by Relational Quantum Mechanics that this applies to all physical objects, whether or not they are conscious or macroscopic. Any "measurement event" is seen simply as an ordinary physical interaction, an establishment of the sort of correlation discussed above. Thus the physical content of the theory is to do not with objects themselves, but the relations between them [2]. For more information, see Rovelli (1996). // Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, the state is the relation between the observer and the system. ... // Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, the state is the relation between the observer and the system. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... Quite literally, quantum state describes the state of a quantum system. ...

Modal Interpretations of Quantum Theory

Modal interpretations of Quantum mechanics were first conceived of in 1972 by B. van Fraassen, in his paper “A formal approach to the philosophy of science.” However, this term now is used to describe a larger set of models that grew out of this approach. The Stanford Encylopedia of Philosophy describes several versions:

• The Copenhagen Variant
• Kochen-Dieks-Healey Interpretations
• Motivating Early Modal Interpretations, based on the work of R. Clifton, M. Dickson and J. Bub.

Incomplete Measurements

Main article: Theory of incomplete measurements

The theory of incomplete measurements (TIM) derives the main axioms of quantum mechanics from properties of the physical processes that are acceptable measurements. In that interpretation: The Theory of Incomplete Measurements (TIM) is an attempt to unify Quantum Mechanics and General Relativity by focusing on physical measurement processes. ... The Theory of Incomplete Measurements (TIM) is an attempt to unify Quantum Mechanics and General Relativity by focusing on physical measurement processes. ...

• wavefunctions collapse because we require measurements to give consistent and repeatable results
• wavefunctions are complex-valued because they represent a field of "found/not-found" probabilities
• eigenvalue equations are associated with symbolic values of measurements, which we often choose to be real numbers.

The TIM is more than a simple interpretation of quantum mechanics, since in that theory, both general relativity and the traditional formalism of quantum mechanics are seen as approximations. However, it does give an interesting interpretation to quantum mechanics. In certain interpretations of quantum mechanics, wavefunction collapse is one of two processes by which quantum systems apparently evolve according to the laws of quantum mechanics. ... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ...

Comparison

At the moment, there is no experimental evidence that would allow us to distinguish between the various interpretations listed below. To that extent, the physical theory stands, and is consistent with, itself and with reality; troubles come only when one attempts to "interpret" it. Nevertheless, there is active research in attempting to come up with experimental tests which would allow differences between the interpretations to be experimentally tested.

Some of the most common interpretations are summarized here (however, the assignment of values in this table is not without controversy, for the precise meanings of some of the concepts involved are unclear and, in fact, the subject of the very controversy itself):

Each interpretation has many variants. It is difficult to get a precise definition of the Copenhagen Interpretation — in the table above, two variants are shown — one that regards the waveform as being a tool for calculating probabilities only, and the other regards the waveform as an "element of reality".

See also

Bells theorem is the most famous legacy of the late Irish phyisicist John Bell. ... The Bohm interpretation of quantum mechanics, sometimes called the Bohmian Mechanics or Ontological interpretation is an interpretation postulated by David Bohm in 1952, which was an extension of the de Broglie-pilot-wave theory of 1927. ... Niels Bohr with Albert Einstein at Paul Ehrenfests home in Leiden (December 1925) The Bohr-Einstein debates is a popular name given to what was actually a series of epistemological challenges presented by Albert Einstein against what has come to be called the standard or Copenhagen interpretation of quantum... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... The many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. ... The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome... The measurement problem is the key set of questions that every interpretation of quantum mechanics must answer. ... This article or section is in need of attention from an expert on the subject. ... Classical Newtonian physics has, formally, been replaced by quantum mechanics on the small scale and relativity on the large scale. ... The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers. ... Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. ... Fig. ... Quantum metaphysics is concerned with exploring the nature of all reality by using quantum mechanical theories and idea. ... In 1925, modern quantum mechanics came into being through the work of Werner Heisenberg and Erwin Schrödinger. ... // Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, the state is the relation between the observer and the system. ... The Pondicherry interpretation of quantum mechanics (PIQM) was developed by Ulrich Mohrhoff, who teaches at the Sri Aurobindo International Centre of Education in Puducherry (formerly Pondicherry), India — hence the name. ... The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ... The Theory of Incomplete Measurements (TIM) is an attempt to unify Quantum Mechanics and General Relativity by focusing on physical measurement processes. ... In certain interpretations of quantum mechanics, wavefunction collapse is one of two processes by which quantum systems apparently evolve according to the laws of quantum mechanics. ...

Related lists

• List of physics topics
• Unsolved problems in physics

This page aims to list all Wikipedia articles that are related to physics. ... This is a list of some of the unsolved problems in physics. ...

References

• Bub, J. and Clifton, R. 1996. “A uniqueness theorem for interpretations of quantum mechanics,” Studies in History and Philosophy of Modern Physics, 27B, 181-219
• R. Carnap, The interpretation of physics, Foundations of Logic and Mathematics of the International Encyclopedia of Unified Science, University of Chicago Press, 1939.
• D. Deutsch, The Fabric of Reality, Allen Lane, 1997. Though written for general audiences, in this book Deutsch argues forcefully against instrumentalism.
• Dickson, M. 1994. Wavefunction tails in the modal interpretation, Proceedings of the PSA 1994, Hull, D., Forbes, M., and Burian, R. (eds), Vol. 1, pp. 366-376. East Lansing, Michigan: Philosophy of Science Association.
• Dickson, M. and Clifton, R. 1998. Lorentz-invariance in modal interpretations The Modal Interpretation of Quantum Mechanics, Dieks, D. and Vermaas, P. (eds), pp. 9-48. Dordrecht: Kluwer Academic Publishers
• A. Einstein, B. Podolsky and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47 777, 1935.
• C. Fuchs and A. Peres, Quantum theory needs no ‘interpretation’ , Physics Today, March 2000.
• Christopher Fuchs, Quantum Mechanics as Quantum Information (and only a little more), arXiv:quant-ph/0205039 v1, (2002)
• N. Herbert. Quantum Reality: Beyond the New Physics, New York: Doubleday, ISBN 0-385-23569-0, LoC QC174.12.H47 1985.
• R. Jackiw and D. Kleppner, One Hundred Years of Quantum Physics, Science, Vol. 289 Issue 5481, p893, August 2000.
• M. Jammer, The Conceptual Development of Quantum Mechanics. New York: McGraw-Hill, 1966.
• M. Jammer, The Philosophy of Quantum Mechanics. New York: Wiley, 1974.
• W. M. de Muynck, Foundations of quantum mechanics, an empiricist approach, Dordrecht: Kluwer Academic Publishers, 2002, ISBN 1-4020-0932-1
• R. Omnès, Understanding Quantum Mechanics, Princeton, 1999.
• K. Popper, Conjectures and Refutations, Routledge and Kegan Paul, 1963. The chapter "Three views Concerning Human Knowledge", addresses, among other things, the instrumentalist view in the physical sciences.
• H. Reichenbach, Philosophic Foundations of Quantum Mechanics, Berkeley: University of California Press, 1944.
• C. Rovelli, Relational Quantum Mechanics; Int. J. of Theor. Phys. 35 (1996) 1637. arXiv: quant-ph/9609002 [3]
• M. Tegmark and J. A. Wheeler, 100 Years of Quantum Mysteries", Scientific American 284, 68, 2001.
• van Fraassen, B. 1972. A formal approach to the philosophy of science, in Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain, Colodny, R. (ed.), pp. 303-366. Pittsburgh: University of Pittsburgh Press.
• John A. Wheeler and Wojciech Hubert Zurek (eds), Quantum Theory and Measurement, Princeton: Princeton University Press, ISBN 0-691-08316-9, LoC QC174.125.Q38 1983.

John Archibald Wheeler (born 1911) is an American theoretical physicist. ... Wojciech Hubert Zurek is a well-known physicist, as a Laboratory Fellow at Los Alamos National Laboratory. ...

External links

• Willem M. de Muynck Broad overview, realist vs. empiricist interpretations, against oversimplified view of the measurement process
• Comparative interpretations
• Skeptical View of "New Age" Interpretations of QM
• The many worlds of quantum mechanics
• Erich Joos' Decoherence Website Basic and in-depth information on decoherence
• Quantum Mechanics for Philosophers An argument for the superiority of the Bohm interpretation.
• Many-Worlds Interpretation of Quantum Mechanics
• Numerous Many Worlds-related Topics and Articles
• Relational Quantum Mechanics
• This Quantum World What is quantum mechanics trying to tell us about the nature of Nature?
• Theory of incomplete measurements Deriving quantum mechanics axioms from properties of acceptable measurements.
• Schreiber, Z. - The Nine Lives of Schrodinger's Cat (overview of interpretations)