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Re: [Phys-L] long-range forces, short-range couplings

In the context of:

"How can you have a "long-range" force at all, given that special
relativity and basic notions of causality require everything to be
local in space and time?"

On 07/29/2015 07:51 AM, Moses Fayngold wrote:

I have never met such a requirement explicitly formulated in any
known formulation of SR.

It's discussed explicitly, in accessible non-technical terms,
in Feynman _The Character of Physical Law_.

The argument goes like this: If A were to cause B via some
nonlocal interaction, i.e. separated by a spacelike interval
in some frame, then in some other frame the effect would
occur before the cause ... violating the most basic notions
of causality.

It's just that simple. Pretty much bulletproof.

On the contrary, one of the basic concepts of SR such as distance (or
proper length) is non-local in space.

Sure, you can define such a distance, and you can have
object A separated by object B by such a distance ... but
then A cannot be the cause of B, nor vice versa.

This is what people mean when they say there is no action
at a distance: No effect is separated from its cause by a
spacelike interval.

The language of cause-and-effect is tricky; we can avoid
some of that by saying event A can send /information/ to
any point in its forward light-cone, and not otherwise,
i.e. not to the past, and not to any point at a
spacelike separation.

The equations of electrostatics are time-independent, and
appear to describe action-at-a-distance ... which is how
you know they cannot be entirely correct. At some point,
you need to replace the Coulomb potential with the Liénard-
Wiechert potential. The chain of causation is embodied by
propagating waves.
https://www.av8n.com/physics/lienard-wiechert.htm

Similarly, at some point you need to replace the Newtonian
gravitational potential with general relativity. Again,
the chain of causation is embodied by propagating waves.
All the couplings are local.