Re: C should be called Field Speed instead of Light Speed.
- From: "RP" <no_mail_no_spam@xxxxxxxxx>
- Date: 7 Oct 2006 06:01:56 -0700
Sorcerer wrote:
"RP" <no_mail_no_spam@xxxxxxxxx> wrote in message
news:1160189368.847838.166380@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
|
| rds wrote:
| > Isn't it more proper to call C the speed of field propagation in a
| > vacum ?
|
| c is the speed that "changes in field" propagate.
|
| Richard Perry
How fast does this change in field propagate?
http://www.androcles01.pwp.blueyonder.co.uk/AC/spin.gif
Androcles
c.
Try setting the compass needle 1 light-second away from the magnet.
If we go to the intro of the 1905 paper, Einstein correctly notes:
"Take, for example, the reciprocal electrodynamics action of a magnet
and a conductor. The observable phenomenon here depends only on the
relative motion of the conductor and the magnet...."
Given that changes in field propagate at c we can take this example and
show that clocks in motion wrt each other will not agree on the times
of events, and that simultaneous events in a frame K are no longer
simultaneous wrt a frame K' in motion wrt K.
First let's be sure that you agree that the voltage developed in the
conductor will be independent of the inertial motion of the lab through
space wrt us. The lab being the closed system where the magnet and
conductor are both located. Actually this must follow, since we are
free to take up any observational inertial frame of reference wrt the
lab, and such an arbitrary choice of reference frame shouldn't have any
physical effect on the magnet and conductor. Experience bears this
out, and since you don't subscribe to an aether model, you should have
no problem with this either. At this point in the argument a ballistic
model in Galilean space-time will account for absoluteness of the delay
wrt the source. But that is about to change.
Suppose the conductor is initially at rest and is then accelerated into
its final velocity before it passes through the lines of flux of the
magnet. Since the magnet never moved, the lines of flux are already
present in the space through which the conductor moves, and the
interaction must be instantaneous wrt the frame of the magnet. But now
if we accelerate the magnet instead, then the lines of flux will be
delayed in reaching the conductor, they will trail behind the motion of
the magnet and the conductor will no longer experience that field
instantaneously as the two pass each other. The field will require a
time to reach the conductor at its full strength. And empirically there
is such a delay. However from the frame of reference of the magnet it
is once again at rest, and the conductor is in motion. Thus from the
new frame of the magnet, the force should once again act instantly on
the conductor. There appears to be an asymmetry inherent in the
interaction.
The paradox presented here has its solution in the fact that the
conductor, like the magnet, is composed entirely of charged particles,
each of which also extends a field through the magnet. Thus the field
of the conductor, though neutral on average, is still just as real as
the magnetic field of the magnet. It is a superposition of many fields
which are not themselves neutral. The field of the magnet is similarly
just that of its many charged particles. Thus we really have two sets
of charged particles in motion wrt each other rather than the two
things "magnet" and "conductor".
The force on the magnet, which is supplied by the charges in the
conductor, will thus be as equally delayed as the force on the
conductor, so that wrt a frame in which both are moving in opposite
directions at equal speeds, the opposing forces occur simultaneously
wrt that frame, but are delayed from what was expected given their
current relative positions and an assumption of instantaneous
propagation of force. With respect to the frame of either the magnet or
of the conductor, the forces do not occur simultaneously, since each
experiences an force at a time r/c later than the force impinging on
the other. Recall that wrt the frame of either of these, they have
never moved and their fields are thus already established in the space
of the other. The current generated in the wire occurs instantly wrt
the magnet's frame, but the magnet doesn't experience a recoil force
until a time r/c later. Reciprocally, wrt the conductor's frame the
magnet will recoil first, since from its frame it is the magnet in
motion through its already established field. Thus with a simple
logical argument involving the concept of symmetry and an interaction
that is independent of our observational frame of reference, it has
been derived that simultaneity isn't absolute wrt frames of reference.
In order to get a better perspective on the interactions occurring in
terms of relative motion of point charges see Purcell. The argument
would actually be simplified if we were to replace the magnet and
conductor with two point charges in motion relative to each other. In
such a case the necessary symmetry becomes more apparent.
So even though on the surface a ballistic model in Galilean space-time
seems to work, when put through the rigors of logical argument based
upon empirical evidence, the Galilean view cannot be maintained.
Richard Perry
.
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