Principle of locality

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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. This was stated as follows by Albert Einstein in his article "Quantum Mechanics and Reality" ("Quanten-Mechanik und Wirklichkeit", Dialectica 2:320-324, 1948):

Local realism is the combination of the principle of locality with the "realistic" 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 in the sense used by physicists does not directly equate to realism in metaphysics.^[1] 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). Furthermore, a mind-independent property does not have to be the value of some physical variable such as position or momentum. A property can be dispositional, 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.^[2] 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 relativity and Maxwell's theory, but quantum mechanics largely rejects this principle due to the presence of distant quantum entanglements, most clearly demonstrated by the EPR paradox and quantified by Bell's inequalities.^[3] Any theory, like quantum mechanics, that violates Bell's inequalities must abandon either local realism or counterfactual definiteness. (Some physicists dispute that experiments have demonstrated Bell's violations, on grounds that the sub-class of inhomogeneous Bell inequalities has not been tested or other experimental limitations). Different interpretations of quantum mechanics reject different parts of local realism and/or counterfactual definiteness.

In most of the conventional interpretations, such as the version of the Copenhagen interpretation and the interpretation based on Consistent Histories, where the wavefunction 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 interpretation 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 collapse. 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-lightspeed), 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.

The Bohm interpretation always wants to preserve realism, and it needs to violate the principle of locality to achieve the required correlations.

In the many-worlds interpretation realism and locality are retained but counterfactual definiteness is rejected by the extension of the notion of reality to allow the existence of parallel universes.

Because the differences between the different interpretations are mostly philosophical ones (except for the Bohm and many-worlds interpretations), the 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 the physicists. Such phenomena have never been seen, and they are not predicted by the current theories (with the possible exception of the Bohm theory).

Locality is one of the axioms of relativistic quantum field theory, as required for causality. The formalization of locality in this case is as follows: if we have two observables, each localized within two distinct spacetime 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 covariant or locally Lorentz invariant.

[edit] Notes

1. ^ Norsen, T. - Against "Realism"
2. ^ Ian Thomson's dispositional quantum mechanics
3. ^ Ben Dov, Y. Local Realism and the Crucial experiment.

[edit] See also

• EPR paradox
• Local hidden variable theory
• Nonlocality