Editing Principle of locality (section)

== Models for locality ==
[[File:Bell local hidden variables geometry with screening.png|thumb|Diagram for locality in quantum mechanics]]
Simple [[spacetime diagram]]s can help clarify the issues related to locality.<ref name="WhartonArgaman">{{Cite journal |last1=Wharton |first1=K. B. |last2=Argaman |first2=N. |date=2020-05-18 |title=Colloquium : Bell's theorem and locally mediated reformulations of quantum mechanics |url=https://link.aps.org/doi/10.1103/RevModPhys.92.021002 |journal=Reviews of Modern Physics |language=en |volume=92 |issue=2 |page=021002 |doi=10.1103/RevModPhys.92.021002 |issn=0034-6861|arxiv=1906.04313 |bibcode=2020RvMP...92b1002W }}</ref> A way to describe the issues of locality suitable for discussion of [[quantum mechanics]] is illustrated in the diagram. A particle is created in one location, then split and measured in two other, spatially separated, locations. The two measurements are named for [[Alice and Bob]]. Alice performs measurements (A) and gets a result <math>\mathbf{a}</math>); Bob performs (<math>B</math>) and gets result <math>\mathbf{b}</math>. The experiment is repeated many times and the results are compared.

=== Alice and Bob in spacetime ===
[[File:Models of locality Spacetime.png|upright=1.3|thumb|Alice and Bob in spacetime diagram]]
A spacetime diagram has a time coordinate going vertical and a space coordinate going horizontal. Alice, in a local region on the left, can affect events only in a cone extending in the future as shown; the finite speed of light prevent her from affecting other areas including Bob's location in this case.  Similarly we can use the diagram to reason that Bob's local circumstances cannot be altered by Alice at the same time: all events that cause an effect on Bob are in the cone below his location on the diagram. Dashed lines around Alice show her valid future locations; dashed lines around Bob show events that could have caused his present circumstance.  When Alice measures quantum states in her location she gets the results labeled <math>\mathbf{a}</math>; similarly Bob gets <math>\mathbf{b}</math>. Models of locality attempt to explain the statistical relationship between these measured values. 

=== Action at a distance ===
[[File:Models of locality Continuous action.png|thumb|Action at a distance]]
The simplest locality model is no locality: instantaneous action at a distance with no limits for relativity. The locality model for action at a distance is called ''continuous action''.<ref name="WhartonArgaman" /> The gray area (a circle here) is a mathematical concept called a "screen".  Any path from a location through the screen becomes part of the physical model at that location. The gray ring indicates events from all parts of space and time can affect the probability measured by Alice or Bob. So in the case of continuous action, events at all times and places affect Alice's and Bob's model.  This simple model is highly successful for solar planetary dynamics with Newtonian gravity and in electrostatics, cases where relativistic effects are insignificant.

=== No future-input dependence ===
[[File:Models of locality No future continuous action.png|thumb|No future-input dependence]]
Many locality models explicitly or implicitly ignore the possible effect of future events. The spacetime diagram at the right shows the effect of such a restriction when combined with continuous action. Inputs from the future (above the dashed line) are no longer considered part of Alice's or Bob's model. Comparing this diagram with the one for continuous action makes it clear that these are not the same locality model.<ref name="WhartonArgaman" /> Common sense arguments about the future not affecting the present are reasonable criteria but such assumptions alter the mathematical character of the models.

=== Bell's local causality ===
[[File:Models of locality Bell screening.png|thumb|Bell's local causality]]
[[John Stewart Bell]] when discussing his 1975 version of [[Bell's theorem]] used the screening model shown at the right.  Events in the common past of Alice and Bob are part of the model used in calculating probabilities for Alice and for Bob as indicated the way the screen absorbs those events.  However events at Bob's location during Alice measurement and events in the future are excluded. Bell called this assumption '''local causality''', but with the diagram we can reason about the meaning of the assumption without getting tripped up by other meanings of local combined with other meanings of causal.<ref name="WhartonArgaman" /> Dash lines show relativistically valid regions in the past of Alice or Bob. The gray arc is the assumed Bell "screen".