In
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
, 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, also called the quantum non-local connection, is a property of a quantum mechanical state of a system of two or more objects in which the quantum states of the constituting objects are linked together so that one object can no longer be adequately described without full...
particles must violate either the principle of locality or the form of
philosophical realismContemporary philosophical realism is the belief in a reality that is completely ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc. Philosophers who profess realism also typically believe that truth consists in a belief's correspondence to reality...
known as
counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak meaningfully about the definiteness of the results of measurements, even if they were not performed....
.
Albert EinsteinAlbert Einstein was a theoretical physicist. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion advance of Mercury, prediction of the deflection of...
felt that there was something fundamentally incorrect with quantum mechanics since it predicted violations of locality. In a famous paper he and his co-authors articulated the
Einstein-Podolsky-Rosen ParadoxIn 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...
.
In
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
, 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, also called the quantum non-local connection, is a property of a quantum mechanical state of a system of two or more objects in which the quantum states of the constituting objects are linked together so that one object can no longer be adequately described without full...
particles must violate either the principle of locality or the form of
philosophical realismContemporary philosophical realism is the belief in a reality that is completely ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc. Philosophers who profess realism also typically believe that truth consists in a belief's correspondence to reality...
known as
counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak meaningfully about the definiteness of the results of measurements, even if they were not performed....
.
EPR Paradox
Albert EinsteinAlbert Einstein was a theoretical physicist. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion advance of Mercury, prediction of the deflection of...
felt that there was something fundamentally incorrect with quantum mechanics since it predicted violations of locality. In a famous paper he and his co-authors articulated the
Einstein-Podolsky-Rosen ParadoxIn 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...
. Thirty years later
John Stewart BellJohn Stewart Bell was a physicist, and the originator of Bell's Theorem, one of the most important theorems in quantum physics.- Life and work :...
responded with a paper which stated (paraphrased) that no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics (
Bell's theoremBell's theorem is a no-go theorem, loosely stating that:It is the most famous legacy of the late physicist John S. Bell. The theorem has important implications for physics itself and philosophy of science as well.- Overview :...
).
Philosophical view
Einstein assumed that principle of locality was necessary, and 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 in a reality that is completely ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc. Philosophers who profess realism also typically believe that truth consists in a belief's correspondence to reality...
assumption that all objects must objectively have pre-existing values for any possible measurement before these measurements are 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 directly equate to
realismContemporary philosophical realism is the belief in a reality that is completely ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc. Philosophers who profess realism also typically believe that truth consists in a belief's correspondence to reality...
in
metaphysicsMetaphysics investigates principles of reality transcending those of any particular science. Cosmology and ontology are traditional branches of metaphysics. It is concerned with explaining the fundamental nature of being and the world...
.
The latter is the claim that there is in some sense a mind-independent world. Even if the results of a possible measurement do not pre-exist the measurement, that does not mean they are the creation of the observer (as in the "consciousness causes collapse" interpretation of quantum mechanics). [citation?] Furthermore, a mind-independent property does not have to be the value of some physical variable such as position or
momentumIn classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section "modern definitions of momentum" on this page...
. A property can be
dispositionA 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, 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 certain measurements with certain values with some probability. Such an ontology would be metaphysically realistic without being realistic in the physicist's sense of "local realism" (which would require that single value be produced with certainty).
Local realism is a significant feature of classical mechanics,
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. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a...
and Maxwell's theory, but
quantum mechanicsQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
largely rejects this principle due to the presence of distant
quantum entanglementQuantum entanglement, also called the quantum non-local connection, is a property of a quantum mechanical state of a system of two or more objects in which the quantum states of the constituting objects are linked together so that one object can no longer be adequately described without full...
s, most clearly demonstrated by the
EPR paradoxIn 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...
and quantified by Bell's inequalities. Any theory, like 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 meaningfully about the definiteness of the results of measurements, even if they were not performed....
. (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 other experimental limitations). Different
interpretations of quantum mechanicsAn interpretation of quantum mechanics is a statement which attempts to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has received thorough experimental testing, many of these experiments are open to different interpretations...
reject different parts of local realism and/or
counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak meaningfully about the definiteness of the results of measurements, even if they were not performed....
.
Copenhagen interpretation
In most of the conventional interpretations, such as the version of the
Copenhagen interpretationThe Copenhagen interpretation is an interpretation of quantum mechanics. A key feature of quantum mechanics is that the state of every particle is described by a wavefunction, which is a mathematical representation used to calculate the probability for it to be found in a location or a state of...
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
wavefunctionA wave function or wavefunction is a mathematical tool used in quantum mechanics to describe any physical system. It is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics describe how the wave function evolves over time...
is not assumed to have a
direct physical interpretation of reality, it is realism that is rejected. The 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, in agreement with positivism in philosophy as the only topic that science should discuss.
In the version of the
Copenhagen interpretationThe Copenhagen interpretation is an interpretation of quantum mechanics. A key feature of quantum mechanics is that the state of every particle is described by a wavefunction, which is a mathematical representation used to calculate the probability for it to be found in a location or a state of...
where the wavefunction is assumed to have 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 process by which a wave function, initially in a superposition of different eigenstates, appears to reduce to a single one of the states after interaction with an observer...
. This is a non-local process because Born's Rule, when applied to the system's wave function, yields a probability density for all regions of space and time. Upon measurement of the physical system, the probability density vanishes everywhere instantaneously, except where (and when) the measured entity is found to exist. This "vanishing" would be a
real physical process, and clearly non-local (faster than light) if the wave function is considered physically real and the probability density converged to zero at arbitrarily far distances during the finite time required for the measurement process.
Bohm interpretation
The
Bohm interpretationThe Bohm or Bohmian interpretation of quantum mechanics, which Bohm called the causal, or later, the ontological interpretation, is an interpretation postulated by David Bohm in 1952 as an alternative to the standard Copenhagen interpretation. The Bohm interpretation grew out of the search for...
preserves realism, and it needs to violate the principle of locality to achieve the required correlations.
Many-worlds interpretation
In the
many-worlds interpretationThe many-worlds interpretation is an interpretation of quantum mechanics.It is also known as MWI, the relative state formulation, theory of the universal wavefunction, parallel universes, many-universes interpretation or just many worlds.Many-worlds asserts the objective reality of the...
realism
and locality are retained but
counterfactual definitenessIn some interpretations of quantum mechanics, counterfactual definiteness is the ability to speak meaningfully about the definiteness of the results of measurements, even if they were not 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 physically exists: the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and constants that govern them...
.
Because the differences between the different interpretations are mostly philosophical ones (except for the Bohm and many-worlds interpretations), physicists usually use the language in which the important statements are independent of the interpretation we choose. In this framework, only the measurable action at a distance - a superluminal propagation of real, physical information - would usually be considered in violation of locality by physicists. Such phenomena have never been seen, and they are not predicted by the current theories (with the possible exception of the Bohm theory).
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 described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
, as required for
causalityCausality describes the relationship between causes and effects, is fundamental to all natural science, especially physics, and has a basis in logic. It is also studied from the perspectives of philosophy, computer science, and statistics. In physics it is useful to interpret certain terms of a...
. 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 commute. 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.