Principle of locality

Principle of locality

Discussion
Ask a question about 'Principle of locality'
Start a new discussion about 'Principle of locality'
Answer questions from other users
Full Discussion Forum
 
Encyclopedia
In physics
Physics
Physics 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 shown
Bell test experiments
The 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 entangled
Quantum entanglement
Quantum 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 realism
Philosophical realism
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....

 known as counterfactual definiteness
Counterfactual definiteness
In 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 gravitation
Newton's law of universal gravitation
Newton'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 distance
Action at a distance (physics)
In 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 law
Coulomb's law
Coulomb'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 Equations
Maxwell's equations
Maxwell'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 Einstein
Albert Einstein
Albert 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 Relativity
General relativity
General 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 Mechanics
Quantum mechanics
Quantum 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 Einstein
Albert Einstein
Albert 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 mechanics
Introduction to quantum mechanics
Quantum 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 Paradox
EPR paradox
The 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 Bell
John Stewart Bell
John 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 variables
Local hidden variable theory
In 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 theorem
Bell's theorem
In 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"
Philosophical realism
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 realism
Philosophical realism
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....

 in metaphysics
Metaphysics
Metaphysics 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 momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

. A property can be disposition
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 definiteness
Counterfactual definiteness
In 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 relativity
General relativity
General 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 mechanics
Quantum mechanics
Quantum 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 entanglement
Quantum entanglement
Quantum 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 paradox
EPR paradox
The 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 definiteness
Counterfactual definiteness
In 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 mechanics
Interpretation of quantum mechanics
An 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 definiteness
Counterfactual definiteness
In 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 interpretation
Copenhagen interpretation
The 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 Histories
Consistent histories
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...

, where the wavefunction
Wavefunction
Not 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 interpretation
Copenhagen interpretation
The 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 collapse
Wavefunction collapse
In 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 interpretation
Many-worlds interpretation
The 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 definiteness
Counterfactual definiteness
In 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 universes
Multiverse (science)
The 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 theory
Quantum field theory
Quantum 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 causality
Causality (physics)
Causality 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 observable
Observable
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. 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 commute
Commute
Commute, 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 covariant
General covariance
In theoretical physics, general covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations...

 or locally Lorentz invariant.

External links