Action at a distance

Middle Ages philosopher William of Ockham discussed action at a distance to explain magnetism and the ability of the Sun to heat the Earth's atmosphere without affecting the intervening space.[6]

Efforts to account for action at a distance in the theory of electromagnetism led to the development of the concept of a field which mediated interactions between currents and charges across empty space. According to field theory, we account for the Coulomb (electrostatic) interaction between charged particles through the fact that charges produce an electric field around themselves that can be felt by other charges as a force. Physicist James Clerk Maxwell directly addressed the subject of action-at-a-distance in chapter 23 of his A Treatise on Electricity and Magnetism in 1873.[7] He began by reviewing the explanation of Ampère's formula given by Carl Friedrich Gauss and Wilhelm Eduard Weber. On page 437, he indicates the physicists' disgust with action at a distance. In 1845 Gauss wrote to Weber desiring "action, not instantaneous, but propagated in time in a similar manner to that of light". This aspiration was developed by Maxwell with the theory of an electromagnetic field described by Maxwell's equations, which used the field to elegantly account for all electromagnetic interactions, now also including light (which, until then, had only been suspected as a related phenomenon). In Maxwell's theory, the field is its own physical entity, carrying momenta and energy across space, and action-at-a-distance is only the apparent effect of local interactions of charges with their surrounding field.

Electrodynamics was later described without fields (in Minkowski space) as the direct interaction of particles with lightlike separation vectors. This resulted in the Fokker-Tetrode-Schwarzschild action integral. This kind of electrodynamic theory is often called "direct interaction" to distinguish it from field theories where action at a distance is mediated by a localized field (localized in the sense that its dynamics are determined by the nearby field parameters).[8] This description of electrodynamics, in contrast with Maxwell's theory, explains apparent action at a distance not by postulating a mediating entity (a field) but by appealing to the natural geometry of special relativity.

Direct interaction electrodynamics is explicitly symmetrical in time and avoids the infinite energy predicted in the field immediately surrounding point particles. Feynman and Wheeler have shown that it can account for radiation and radiative damping (which had been considered strong evidence for the independent existence of the field). However, various proofs, beginning with that of Paul Dirac, have shown that direct interaction theories (under reasonable assumptions) do not admit Lagrangian or Hamiltonian formulations (these are the so-called No Interaction Theorems). Also significant is the measurement and theoretical description of the Lamb shift which strongly suggests that charged particles interact with their own field. Fields, because of these and other difficulties, have been elevated to the fundamental operators in quantum field theory and modern physics has thus largely abandoned direct interaction theory.

Since the early twentieth century, quantum mechanics has posed new challenges for the view that physical processes should obey locality. Whether quantum entanglement counts as action-at-a-distance hinges on the nature of the wave function and decoherence, issues over which there is still considerable debate among scientists and philosophers.

One important line of debate originated with Einstein, who challenged the idea that quantum mechanics offers a complete description of reality, along with Boris Podolsky and Nathan Rosen. They proposed a thought experiment involving an entangled pair of observables with non-commuting operators (e.g. position and momentum).[9]

This thought experiment, which came to be known as the EPR paradox, hinges on the principle of locality. A common presentation of the paradox is as follows: two particles interact and fly off in opposite directions. Even when the particles are so far apart that any classical interaction would be impossible (see principle of locality), certain measurements of one particle nonetheless determine the result of corresponding measurements of the other.

After the EPR paper, several scientists such as de Broglie studied local hidden variables theories. In the 1960s John Bell derived an inequality that indicated a testable difference between the predictions of quantum mechanics and local hidden variables theories.[10] To date, all experiments testing Bell-type inequalities in situations analogous to the EPR thought experiment have results consistent with the predictions of quantum mechanics, suggesting that local hidden variables theories can be ruled out. Whether or not this is interpreted as evidence for nonlocality depends on one's interpretation of quantum mechanics.

Interpretations of quantum mechanics vary in their response to the EPR-type experiments. The Bohm interpretation gives an explanation based on nonlocal hidden variables for the correlations seen in entanglement. Many advocates of the many-worlds interpretation argue that it can explain these correlations in a way that does not require a violation of locality,[11] by allowing measurements to have non-unique outcomes.

If "action" is defined as a force, physical work or information, then it should be stated clearly that entanglement cannot communicate action between two entangled particles (Einstein's worry about "spooky action at a distance" does not actually violate special relativity). What happens in entanglement is that a measurement on one entangled particle yields a random result, then a later measurement on another particle in the same entangled (shared) quantum state must always yield a value correlated with the first measurement. Since no force, work, or information is communicated (the first measurement is random), the speed of light limit does not apply (see quantum entanglement and Bell test experiments). In the standard Copenhagen interpretation, as discussed above, entanglement demonstrates a genuine nonlocal effect of quantum mechanics, but does not communicate information, either quantum or classical.

•  This article incorporates text from a free content work. Licensed under CC-BY-SA. Text taken from Newton’s action at a distance – Different views​, Nicolae Sfetcu, .