Principle of locality

The principle of locality in physics states that an object is only directly influenced by its immediate surroundings. A physical theory is said to be a local theory if it is consistent with the principle of locality. An alternative to the earlier concept of instantaneous "action at a distance", locality evolved as a property of the field theories of classical physics. The concept of locality is that, for an action at one point to have an influence at another point, something in the space between the points, such as a field, must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, to carry the influence.

Quotes

• [C]onsider the scalar Aharonov-Bohm effect... the change in the electrons' interference pattern is a nonlocal effect of the electric field in the capacitor. This nonlocal effect is action at a distance! The electric field, acting at a distance on the electrons, yields a measurable effect (the change in the electrons' interference pattern). So quantum nonlocality does permit action at a distance.
  There is a constraint similar to the one we guessed. It is called (relativistic) causality. The principle of causality states that there is no way to send a message faster than light. We do not expect nonrelativistic quantum mechanics to obey this principle, because in nonrelativistic quantum mechanics there is no maximum speed. However... Nonlocal quantum correlations obey causality, because they are useless for sending messages. The Aharonov-Bohm effect, too, obeys causality: ...the change in the electrons' interference pattern - lies within the future light cone of the field. In each example we find that quantum nonlocality obeys causality.
  • Yakir Aharonov, Daniel Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (2005) p. 87.

• For several centuries, there has been a strong feeling that nonlocal theories are not acceptable in physics. ...Newton felt very uneasy about action-at-a-distance and... Einstein regarded it as 'spooky'. But... one can see nothing basically irrational about such an idea. Rather it seems to be most reasonable to keep an open mind on the subject and therefore allow oneself to explore this possibility. If the price of avoiding nonlocality is to make an intuitive explanation impossible, one has to ask whether the cost is not too great.
  • David Bohm, Basil Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory (1993)

• In the long debate about action at a distance versus contact action we also find a concern with the effective individuation of particles and subsystems and with distant action. Belief in contact action goes back to Aristotle and Eudoxes, based on the self-evident regulative principle that a thing cannot act where it is not. For them, causal explanations were essential for true science. For Descartes too, there could be no vacuum and what may appear to be empty is actually filled with an aether. After the Principia, there were basically two camps on the "gravity dilemma." The one, among whose members were the Cartesians, Leibniz, and Huygens, maintained that an ether was required to allow any intelligible explanation of gravitational phenomena. The other, notably represented by Newton's ally... Samuel Clarke, took gravity to be evidence for God's action. ...God is everywhere and, hence, "instantaneous" action... is no mystery. The basic motivating factor in demanding contact action was that of intelligibility. Maxwell put the matter quite succinctly when he argued for "a force of the old school—a case of vis a tergo—a shove from behind.
  • James T. Cushing, Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony (1994) p. 19.

• Frans van Luteren (1991), in his extensive... study of conceptions of gravity in the eighteenth and nineteenth centuries, demonstrates that a quest for intelligibility was uppermost for several physicists who attempted [to challenge the absolute non-locality doctrine with] ether-type explanations for action-at-a-distance.
  • James T. Cushing, Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony (1994) Footnote, p.

• Classical electrodynamics is generally understood to be the paradigm of a local and causal physical theory. ...[A] theory with real fields realistically appears to be a local theory. ...But what, exactly, is it for a theory to be local or nonlocal? ...Informally, locality principles are often introduced in causal terms. Newtonian graviational theory... is said to be nonlocal because it allows action-at-a-distance, while the theory of special relativity is often said to imply the locality condition that there can be no superliminal causal propogation. According to a widespread view, however, the notion of causation should have no place in fundamental physics... Thus, Bertrand Russell famously argued that in the advanced sciences the notion of functional dependency has replaced that of causation... "a relic of a bygone age..." ...Russell was wrong. ...I will appeal to Dirac's classical theory of the electron ....the most promising candidate for a fully consistent theory of classical charged particles, is causally nonlocal. ...[T]he theory allows for forces to act where they are not and for superliminal causal propogation.
  • Mathias Frisch, Inconsistency, Asymmetry, and Non-Locality: A Philosophical Investigation of Classical Electrodynamics (2005) Ch. 4 Nonlocality.

• To soothe the theologians, who in his time were pressing so hardly upon Galileo, Descartes was content to say that the operation by which God maintains the world is similar to that by which he created it; so that, if it had pleased him, instead of creating it instantaneously, to allow these laws of evolution to operate, the result would have been what we now see. He began by assuming space to be occupied by perfectly homogeneous and continuous matter. He then supposed this solid substance to be divided into parcels of various shape and size, each of them animated by motion in various directions. These would observe the laws of motion as Descartes defines them:—1. Each would maintain its own condition of rest or motion or magnitude, until altered by contact with another. 2. In such contact the gain or loss of motion to one body would be exactly compensated by the loss or gain to another—the total quantity of motion in the world remaining invariable. 3. Owing to constant contacts, motion would be usually in curved lines, the moving body tending always to follow the tangent to the curve.
  The result after a period of time would be the differentiation of primitive matter into three kinds. The moving portions of matter, by constant attrition, would be for the most part converted into spheroidal molecules of various sizes. Some larger masses of irregular shape would amalgamate into solid masses; the finer particles rubbed off from the molecules would insert themselves between them, vibrating with far more rapid motion than they. This vibrating ethereal substance would collect towards the centre of a vortex, and form a sun or star: round it would revolve aërial matter, and plunged amidst this, at various distances, the solid masses of the planets. How by degrees yet further differentiation took place... so that the various metals and crystals arose, and finally plant life, and animal life... is described in the Principia and in the Treatise on Man.
  • Frederic Harrison, The New Calendar of Great Men: Biographies of the 558 Worthies of All Ages (1892) Ch. XI Modern Philosophy, p. 483.

• [L]ocality... reflects our ability to construct the "big picture" like a jigsaw puzzle, starting with a description of the most basic interactions among elementary particles.
  • Mario Livio, Is God a Mathematician? (2009)

• In fact every theory in the history of physics before quantum theory was EPR-local. So the discovery that the world is not EPR-local (i.e. that any physical theory that makes accurate predictions cannot be EPR-local) would mark a radical break in the history of physics.
  • Tim Maudlin, "What Bell Did", Journal of Physics A: Mathematical and Theoretical (2014)

• I must ask you to go over very old ground, and to turn your attention to a question which has been raised again and again ever since man began to think.
  The question is that of the transmission of force. We see two bodies at a distance from each other exert a mutual influence on each other's motion. Does this mutual action depend on the existence of some third thing, some medium of communication, occupying the space between the bodies, or do the bodies act on each other immediately, without the intervention of anything else?
  The mode in which Faraday was accustomed to look at phenomena of this kind differs from that adapted by many modern inquirers, and my special aim will be to enable you to place yourselves at Faraday's point of view, and to point out the scientific value of that conception of lines of force which, in his hands, became the key to the science of electricity. ...
  Why... should we not admit that the familiar mode of communicating motion by pushing and pulling... is the type and exemplification of all action between bodies, even in case in which we can observe nothing between...
  • James Clerk Maxwell, "On Action at a Distance" (1873) from the Proceedings of the Royal Institution of Great Britain, Vol. VII (1890) p. 311.

• The generation that grew up with Newtonian gravity found the theory entirely natural. For millennia, natural philosophers recoiled from nonlocality; in the eighteenth century, they embraced it. ...And no sooner did scholars get used to Newtonian nonlocality when along came another U-turn and a new generation went back to thinking that the world had to be—just had to be—local, thereby setting up our present predicament. ...Naturalistic explanations tend to be local. In our experience, when you want something to move... you need to go over and push on it... Thales suggested that earthquakes occur [not by the arbitrary will of gods, but] because the land is floating on a subterranean ocean... occasionally rocking back and forth. The cause is in direct contact with the effect. ...The concept of space was the atomists' [e.g., Democritus and Lucretius] creation. ...matter needs a venue to exist and move. ...If atoms were the athletes and space the playing field, locality was the rulebook. ...The atomists held that atoms interact only by direct contact.
  • George Musser, Spooky Action at a Distance: The Phenomenon That Reimagines Space and Time... (2015)

• Descartes' objective was comprehensibility—to make the workings of nature completely transparent. Locality was essential to this goal. Objects interacted strictly locally: they moved in straight lines until they collided; only then did they change course. Like Democritus and Aristotle, Descartes offered no real evidence for this principle.
  • George Musser, Spooky Action at a Distance: The Phenomenon That Reimagines Space and Time... (2015) p. 54.

• It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation, in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body can act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent is material or immaterial, I have left to the consideration of my readers.
  • Isaac Newton, Letter to Richard Bentley (February 25, 1693) as quoted in The works of Richard Bentley, Vol. 3, pp. 211-212.

• The principle of locality states that no instantaneous transmission of physical influences between spatially separated physical systems ("action at a distance") is allowed, or... that physical systems can only be physically influenced by their immediate environment. ...[The] broader principle states that any possible definitive determinations concerning any given system—its physical state; the application of technology (such as a measurement, which, rather than a prediction, definitely determines a physical state of a quantum system); the falsifiability of claims concerning quantum systems, and so forth—is local.
  • Arkady Plotnitsky, The Principles of Quantum Theory, From Planck's Quanta to the Higgs Boson (2016) p. 32.

• [T]he view that the ultimate theory... should be more in accord with the fundamental principles of quantum theory need not imply that such a theory will be any form of quantum theory currently known, such as quantum mechanics or quantum field theory. ...[These] are far from complete or free of deficiencies even within their proper scope. Some new or perhaps now unimaginable theories and very likely new principles may be required to approach the ultimate constitution of nature. Will these theories retain the locality principle? My Bayesian bet would be that this will more likely than not to be the case, but one cannot be certain.
  • Arkady Plotnitsky, The Principles of Quantum Theory, From Planck's Quanta to the Higgs Boson (2016) pp. 35.

• Quantum mechanics has an axiomatic structure, exposed by von Neumann, Dirac and others. The axioms... tell us that every state of a system corresponds to a vector in a complex Hilbert space, every physical observable corresponds to linear hermitian operator acting on that Hilbert space, etc. ...Special relativity can be deduced... from two axioms: the equivalence of inertial reference frames, and the constancy of the speed of light. Both axioms have clear physical meaning. By contrast, the numerous axioms of quantum mechanics have [none]... the new axioms are hardly more natural than the old.
  Abner Shimony offers hope... a remarkable property of... nonlocality. ...Bell showed, quantum correlations could not arise in any theory in which all variables obey relativistic causality. On the other hand, quantum correlations themselves obey relativistic causality—we cannot exploit quantum correlations to transmit signals at superliminal speeds (ar at any speed). That quantum mechanics combines nonlocality and causality is wondrous... Shimony has aptly called the nonlocality manifest in quantum correlations "passion at a distance"... [and] has raised the question whether nonlocality and causality can peacefully coexist in any other theory besides quantum mechanics.
  • Sandu Popescu, Daniel Rohrlich, "Action and Passion at a Distance: an essay in honor of Professor Abney Shimony", Potentiality, Entanglement and Passion-at-a-Distance: Quantum Mechanical Studies for Abner Shimony (2013) Vol. 2

• The results of experiments on Bell-type arrangements have forced the conceptual issue of quantum non-locality into focus. ...[A]ny physically adequate quantum theory must violate the Principle of Locality. Yet the idea... still sits uncomfortably with most of us. ...The kind of non-locality... has been described as 'benign' since it cannot be used for any kind of signalling... and therefore does not explicitly violate Special Relativity. It is fortunate that parts of the universe do not constantly exhibit non-local behaviors so that we can continue to use established scientific methods to investigate the world. However... non-locality does not necessitate a causality.
  • Peter J. Riggs, Quantum Causality: Conceptual Issues in the Causal Theory of Quantum Mechanics (2009) pp. 104-105, Studies in the History and Philosophy of Natural Science 23.

• What is the 'means' by which the non-local connection is actualized? ...[S]ome possible responses ...(1) The connection is mediated ...by particles or fields that propogate at superliminal fields. ...(2) The connection propogates backward in time. ...(3) Physical space has more than three spatial dimensions. ...(4) [P]hysical space is not simply connected. ...
  Option (2) violates the Principle of Causality. ...
  Based on the results of tests of Bell-type inequalities... non-local connections have at least the features... (a) not decreasing with distance; (b) cannot be shielded against; and (c) are highly selective in what they effect. The[se] features are consistent with Option (4)...
  • Peter J. Riggs, Quantum Causality: Conceptual Issues in the Causal Theory of Quantum Mechanics (2009) pp. 106-107, Studies in the History and Philosophy of Natural Science 23.

See also

• On Action at a Distance by James Clerk Maxwell
• John Stewart Bell
• David Bohm
• Causality
• René Descartes
• Paul Dirac
• Albert Einstein
• EPR paradox
• Boris Podolsky
• Quantum mechanics

External links

• Quantum nonlocality vs. Einstein locality by H. D. Zeh.