In

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the

**principle of locality** states that an object is influenced directly only by its immediate surroundings.

Experiments have shownThe Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality...

that quantum mechanically

entangledQuantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

particles must violate either the principle of locality or the form of

philosophical realismContemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....

known as

counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak with meaning of the definiteness of the results of measurements that have not been performed...

.

## Pre-quantum mechanics

In the 17th Century

Newton's law of universal gravitationNewton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

was formulated in terms of

action at a distanceIn physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. This term was used most often in the context of early theories of gravity and electromagnetism to describe how an object responds to the influence of distant...

, thereby violating the principle of locality.

Coulomb's lawCoulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

of electric forces was initially also formulated as instantaneous action at a distance, but was later superseded by

Maxwell's EquationsMaxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

of electromagnetism which obey locality.

In 1905

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

's Special Theory of Relativity postulated that no material or energy can travel faster than the speed of light, and Einstein thereby sought to reformulate physical laws in a way which obeyed the principle of locality. He later succeeded in producing an alternative theory of gravitation,

General RelativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, which obeys the principle of locality.

However a different challenge to the principle of locality subsequently emerged from the theory of

Quantum MechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, which Einstein himself had helped to create.

#### EPR Paradox

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

felt that there was something fundamentally incorrect with

quantum mechanicsQuantum mechanics is the body of scientific principles that explains the behavior of matter and its interactions with energy on the scale of atoms and atomic particles....

since it predicted violations of the principle of locality. Seeking to undermine quantum mechanics, in a famous paper he and his co-authors articulated the

Einstein-Podolsky-Rosen ParadoxThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

. Thirty years later

John Stewart BellJohn Stewart Bell FRS was a British physicist from Northern Ireland , and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.- Early life and work :...

responded with a paper that posited (paraphrased) that no

physical theory of local hidden variablesIn quantum mechanics, a local hidden variable theory is one in which distant events are assumed to have no instantaneous effect on local ones....

, no

*local realism*, can ever reproduce all of the predictions of quantum mechanics (known as

Bell's theoremIn theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...

).

#### Philosophical view

Einstein assumed that the principle of locality was necessary, and that there could be no violations of it. He said:

### Local realism

*Local realism* is the combination of the principle of locality with the

"realistic"Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....

assumption that all objects must objectively have a pre-existing value for any possible measurement before the measurement is made. Einstein liked to say that the Moon is "out there" even when no one is observing it.

### Realism

*Realism* in the sense used by physicists does not equate to

realismContemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....

in

metaphysicsMetaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...

.

The latter is the claim that the world is in some sense mind-independent: that even if the results of a possible measurement do not pre-exist the act of measurement, that does not require that they are the creation of the observer (contrary to the "consciousness causes collapse" interpretation of quantum mechanics). Furthermore, a mind-independent property does not have to be the value of some physical variable such as position or

momentumIn classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

. A property can be

*disposition*A disposition is a habit, a preparation, a state of readiness, or a tendency to act in a specified way.The terms dispositional belief and occurrent belief refer, in the former case, to a belief that is held in the mind but not currently being considered, and in the latter case, to a belief that is...

al (or potential), i.e. it can be a tendency: in the way that glass objects tend to break, or are disposed to break, even if they do not

*actually* break. Likewise, the mind-independent properties of quantum systems could consist of a tendency to respond to particular measurements with particular values with ascertainable probability. Such an ontology would be metaphysically realistic, without being realistic in the physicist's sense of "local realism" (which would require that a single value be produced with certainty).

A closely related term is

counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak with meaning of the definiteness of the results of measurements that have not been performed...

(CFD), used to refer to the claim that one can meaningfully speak of the definiteness of results of measurements that have not been performed (i.e. the ability to assume the existence of objects, and properties of objects, even when they have not been measured).

Local realism is a significant feature of classical mechanics, of

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, and of electrodynamics; but

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

largely rejects this principle due to the theory of distant

quantum entanglementQuantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

s, an interpretation rejected by Einstein in the

EPR paradoxThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

but subsequently apparently quantified by Bell's inequalities. Any theory, such as quantum mechanics, that violates Bell's inequalities must abandon

*either* local realism

*or* counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak with meaning of the definiteness of the results of measurements that have not been performed...

; but some physicists dispute that experiments have demonstrated Bell's violations, on the grounds that the sub-class of inhomogeneous Bell inequalities has not been tested or due to experimental limitations in the tests. Different

interpretations of quantum mechanicsAn interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...

violate different parts of local realism and/or

counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak with meaning of the definiteness of the results of measurements that have not been performed...

.

### Copenhagen interpretation

In most of the conventional interpretations, such as the

Copenhagen interpretationThe Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

and the interpretation based on

Consistent HistoriesIn 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...

, where the

wavefunctionNot to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...

is not assumed to be a

*direct* physical interpretation of reality, it is local realism that is rejected. These interpretations propose that actual definite properties of a physical system "do not exist" prior to the measurement; and the wavefunction has a restricted interpretation, as nothing more than a mathematical tool used to calculate the probabilities of experimental outcomes, hence in agreement with positivism in philosophy as the only topic that science should discuss.

In the version of the

Copenhagen interpretationThe Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

where the wavefunction is assumed to be a physical interpretation of reality (the nature of which is

*unspecified*) the principle of locality is violated during the measurement process via

wavefunction collapseIn quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...

. This is a non-local process because Born's Rule, when applied to the system's wavefunction, yields a probability density for all regions of space and time. Upon actual measurement of the physical system, the probability density vanishes everywhere instantaneously, except where (and when) the measured entity is found to exist. This "vanishing" is postulated to be a

*real* physical process, and clearly non-local (i.e. faster than light) if the wavefunction is considered physically real and the probability density has converged to zero at arbitrarily far distances during the finite time required for the measurement process.

### Bohm interpretation

The Bohm interpretation preserves realism, hence it needs to violate the principle of locality in order to achieve the required correlations.

### Many-worlds interpretation

In the

many-worlds interpretationThe many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...

both realism

*and* locality are retained, but

counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak with meaning of the definiteness of the results of measurements that have not been performed...

is rejected by the extension of the notion of reality to allow the existence of

parallel universesThe multiverse is the hypothetical set of multiple possible universes that together comprise everything that exists and can exist: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them...

.

Because the differences between the different interpretations are mostly philosophical ones (except for the Bohm and many-worlds interpretations), physicists usually employ language in which the important statements are neutral with regard to all of the interpretations. In this framework, only the measurable action at a distance - a superluminal propagation of real, physical information - would usually be considered in violation of the principle of locality by physicists. Such phenomena have never been seen, and they are not predicted by the current theories.

## Relativity

Locality is one of the axioms of relativistic

quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

, as required for

causalityCausality is the relationship between causes and effects. It is considered to be fundamental to all natural science, especially physics. Causality is also a topic studied from the perspectives of philosophy and statistics....

. The formalization of locality in this case is as follows: if we have two

observableIn 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. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value off...

s, each localized within two distinct space-time regions which happen to be at a spacelike separation from each other, the observables must

commuteCommute, commutation or commutative may refer to:* Commuting, the process of travelling between a place of residence and a place of work* Commutative property, a property of a mathematical operation...

. Alternatively, a solution to the field equations is local if the underlying equations are either Lorentz invariant or, more generally,

generally covariantIn theoretical physics, general covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations...

or locally Lorentz invariant.

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