Re: Instantaneous Action at a Distance
- From: Igor Khavkine <igor.kh@xxxxxxxxx>
- Date: Mon, 17 Jul 2006 23:30:40 +0000 (UTC)
Phil Gardner wrote:
Almost all physicists hold to the view that for any isolated pair of
particles, a and b which have masses, Ma < Mb, interacting elastically:
Information has to continually travel (at speeds not exceeding c)
from one to the other
Hmm, these bullet points look funny. It'd be nice if you could restrict
yourself to the ASCII character set in your posts.
The only acceptable classical interaction models are retarded field
models
The only case in which an interaction potential that is a function
only of the instantaneous distance, R = R(t) = Xa(t) – Xb(t), between
the two can be relied on is that in which the ratio Ma/Mb is so small
that without detectable error we can assume that b is stationary in the
centre of mass reference frame.
Any classical retarded field model of such a system that is accepted by
physicists is explicitly deterministic. Given a complete history of
the motions of the particles for t < 0 it can, at least in principle,
predict to any desired accuracy their positions and momenta as
functions of t for any t > 0. These predictions include R = R(t) and,
provided R is not a constant of the motion, t = t(R). We can thus
transform all the equations of any retarded field model into a set in
which the only independent variable is R. That is we transform the
model into an instantaneous action at a distance model.
There is a subtle flaw in the logic above. There is more information in
a retarded field model than just the positions of the particles coupled
to the field. The reason is that to fully specify the initial
conditions for the equations of motion of the particle + field system,
you need to specify both the particle positions and the field
configuration at some initial time. In other words, because the field
has its own dynamics, specifying just the particle trajectories up to a
certain point is not sufficient to predict their evolution. You never
know when an independent field disturbance will come along and knock
one of the particles "off couse".
The degrees of freedom contained in the field which are not directly
deducible from particle positions are usually referred to as radiation.
In simple problems, radiation is usually swept under the rug by
decreeing that the field has a certain nice value at some instant of
time (for example, zero or the Coulomb potential for one or few
charges). However, this initial condition is only applicable when we
can physically assume that no radiation degrees of freedom are active
near the particles at that instant. But even physically, this
assumption fails for arbitrary large times. We never know if there will
be some radation coming from very far away (think star light).
Is there any way of reconciling this result with the physical
impossibility of instantaneous transfer of information over arbitrarily
large distances? The only way that I can see is to assume that every
particle in the universe has enough (artificial) intelligence, memory
and computing power to deduce from the information it does receive at
some finite speed from any other particle the value of R(t) for the
pair at time, t.
There is a much simpler explanation. Just assume that there is an
externally prescribed field present throughout space, which directs the
particles motions without being affected by them, with the
particle-field interactions being purely local. In other words, the
particles can be thought of as "test particles" for this field. The
trouble comes in when we ask the question "Where did this field come
from"? And that's when we have to realize that the "test particle"
assumption is merely an approximation and that the field has to have
some dynamics of its own and feel some back reaction from the particles
(Newton's third law). But at the same time, we have to realize that the
description of particle interactions described through R(t) can no
longer be exact, because of the possibility of radation.
So, if radation is what tells us that a certain interacting particle +
field theory cannot be expressed in terms of inter-particle potentials
alone, then does every field we know about possess radation? The answer
is Yes. One possible exception is the gravitational field. We have not
yet explicitly detected any gravitational radation, but there are a lot
of people working on that (LIGO, LISA, etc.) There is also indirect
evidence of its existence (decay of a binary pulsar's orbit).
Hope this helps.
Igor
.
- References:
- Instantaneous Action at a Distance
- From: Phil Gardner
- Instantaneous Action at a Distance
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