**Locality**: The locality assumption is sometimes called "local
causes". It is the requirement that each physical event or change has a
physical cause, and that this cause can be localized in the immediate
space-time neighborhood of its effects. A collision of two billiard
balls, or the mechanical connections between the parts of a steam engine
are clear examples. A more subtle example is the feature of classical
electromagnetism that any change in the velocity of a moving charged
particle can be regarded as being caused by the action upon this
particle of the electric and magnetic fields existing in the immediate
space-time neighborhood of that particle at the moment at which the
change in velocity occurs, and that any change in the electric and
magnetic fields are likewise caused by physically describable properties
that are located very close to where that change occurs.

You could refer here to or even quote some lovely passages in
Einstein/Infeld, The Evolution of Physics (1938), Ch. III, which
specifically discuss classical electromagnetism.

This idea that all physical effects are consequences of essentially
"contact" interactions was part of the intellectual milieu, stemming
from the ideas of Rene Descartes, in which Isaac Newton worked while
creating the foundations of modern physics. However, his universal law
of gravitational attraction was stated as a law of instantaneous action
over astronomical distances, a clear violation of the idea that all
physical effects have local causes. Newton tried unsuccessfully to
devise some local mechanical idea of how gravity worked, but in the end
asserted his famous "hypothesis non fingo" \[I feign (pretend to make)
no hypothesis (about how gravity works)\]. \[Newton 1964/1687, p. 671\]
He relied, instead, on the empirical success of his simple
inverse-square-law postulate to account for a huge amount of empirical
data. Yet as regards basic metaphysics he wrote: " That one body can act
upon another at a distance through the vacuum, without the mediation of
anything else, by and through which their action and force my be
conveyed from one to another, is to me so great an absurdity that I
believe that no man who has in philosophical matters a competent faculty
of thinking can ever fall into it." \[Newton 1964, p. 636\]. This
statement is a trenchant formulation of the notion of locality. It took
more than two centuries of development before Einstein came up with an
explanation, in terms of the idea distortions of space-time, that
allowed the requirement of locality to be met for gravity. Einstein's
special theory of relativity imposes the condition that no localized
measurable output can depend upon the character of a localized physical
input before a point moving at the speed of light can travel from the
smallest region in which the input is localized to the smallest region
in which the output is located. This locality condition is required to
hold in any classical physical theory that is called "relativistic".

This idea of locality is fairly simple and straightforward in classical
physics, because in that setting everything has a material basis and all
causal effect are associated with transfers of momentum or energy, which
moves about in a continuous way. In quantum theory the fundamental
substrate of change is more ephemeral, having the character of
information expressed as changing potentialities for observable events
to occur. These potentialities normally change in a continuous way, but,
in conventional quantum mechanics, they change abruptly in association
with the occurrence of an observable (or actually observed) event. And a
"cause", such as the performance of a freely chosen measurement in one
region, can have an instant faraway effect without any energy or
momentum *traveling* from the region of the cause to the region of the
effect.

In the quantum context a suitable definition of locality pertains to
information: Locality requires that no information about which
measurement is freely chosen and performed in one space-time region can
be present in another space-time region unless a point traveling at the
speed of light or less can get from the first region to the second. Or
in terms of outcomes: no statement whose truth is determined solely by
which outcomes appear in one space-time, under conditions freely chosen
in that region, can be true if one experiment is freely performed in a
region that is space-like-separated from the first region, but be false
if another experiment is freely chosen there. The term "freely chosen"

means only that in the argumentation this choice is not to constrained
in any way.

Locality defined in either of these ways appears to be violated in
relativistic quantum field theory. These violations are discussed the
entries → nonlocality and → Einstein locality.

Primary

Newton, I. (1964/1687): *Principia Mathematica*. Ed. F. Cajori.
Berkeley: University of California Press

Einstein, A. (1948): 'Quantenmechanik und Wirklichkeit', *Dialectica*
**2**, 32-24

Einstein, A./Infeld (1938): *The Evolution of Physics*.

Born-Einstein Letters

Secondary

Cushing, J./E. McMullin (1989): *Consequences of Quantum Theory*

Howard, D. (1993): 'Was Einstein a Realist?' *Perspectives on Science*
**1**, 204-51

Lange, M. (2002): Philosophy of Physics. Ch. I, §4

Maudlin (^2^2002): *Quantum Nonlocality and Relativity*. Ch. I

Note: I have not given the full bibliographic details because they are
my suggestions and you need to be happy with them.

These

Henry P. Stapp, Lawrence Berkeley National Laboratory, University of
California.