Re: Article: A Century of Einstein

From: RP (no_mail_no_spam_at_yahoo.com)
Date: 08/30/04 

Date: Sun, 29 Aug 2004 22:03:33 -0500

Tom Roberts wrote:

> RP wrote:
>
>> Let me put it this way, [...]. If the PoR is to be strictly
>> maintained, then frames won't enter into the laws of physics. By this
>> I mean, "no transformations".
>
>
> Sure. That's what we do in modern physics. The equations of all modern
> fundamental theories of physics are completely independent of "frame"
> (i.e. coordinates).
>
> Perhaps you should put down your comic books and actutally LEARN some
> modern physics....
>
> Transformations between coordinate systems only arise when
> one considers tensors projected onto specific coordinate
> systems. But the equations of the theory relate the tensors
> themselves, not their components projected onto some
> coordinates (though some older treatments did so -- there is
> an equivalence here, but it hides the underlying structure).
>
>
>> IOW, if you have valid laws of physics, then you will never perform a
>> transformation between frames, you'll simply plug in the values that
>> are frame invariant. Covariance doesn't cut it.
>
>
> Sure. You can do that. But usually one uses rulers and clocks (etc.) to
> make measurements, and they intrinsically PROJECT the quantity being
> measured onto themselves. As we usually need to make an array of such
> measurements over a defined region in space and time, it is simplest to
> erect a coordinate system using a convenient set of clocks and rulers,
> and to reference all measurements to those coordinates. Doing that
> inherently means everything is projected onto those coordinates.
>
> So while the theory is coordinate independent, actual measurements are
> not -- every measuring apparatus inherently projects the quantity being
> measured onto itself.
>
>
>> Look at my electromagnetic equations: [...]
>
>
> I don't know what "your" equations are, but look at the standard
> equations of classical elecrodynamics:
>
> dF = 0
> *d*F = J
>
> All quantities therein are tensors (differential forms), and therefore
> independent of coordinates.
>
>
>> Have I made myself clear yet on what the PoR must be, on a logical basis?
>
>
> Sure. But you seem utterly ignorant of its relationship to modern
> physics. Your central idea is valid in modern physics, but you get the
> details wrong.
>
>
>> IOW, The E and B fields have no place in the real laws of
>> electromagnetism, they are simply arbitrary divisions of a single field.
>
>
> Look at the equations above. F is a single field encompasing both E and
> B. But E and B are not "arbitrary", they are PROJECTIONS of F onto a
> specific coordinate system.
>
>
>> Thus once again I state unequivocally that "On the Electrodynamics of
>> Moving Bodies", was contradictory to the central idea that is the PoR.
>
>
> You are wrong. That paper showed how to restore the PoR to
> electrodynamics. As has been remarked elsewhere, perhaps a better name
> for relativity would have been "theory of invariances". For instance,
> note that Einstein's two postulates are both statements of invariance.
>
>
>> Light speed is no more required by the PoR to be invariant than is the
>> speed of sound.
>
>
> Sure. That's why Einstein had to have a second postulate.

A second postulate, yes, one that leads to contradiction. More on that
later.
As for your essay on invariance, it was very elegant, though you still
didn't get my point.
Ironically, I read today in the Sept. Scientific American pretty much
what you said above. Almost word for word.

But you still haven't registered what I've been stating. You are of the
opinion that no form of the electromagnetic laws can be scripted that
aren't Galilean invariant. If you abandon the E and B fields, and the
macroscopic terms used by Maxwell/Heaviside (e.g. charge density,
current density, etc.) then automatically you must opt for a treatment a
bit less statistical in nature. IOW, the relativistic treatment of
electromagnetism is macroscopic in its approach, as is QM.
When you attempt to relate the behaviors of individual quanta of charge,
then both Maxwell/Lorentz and QM are insufficient, i.e. neither can
describe the fluid interaction between two particles. This is the very
reason that these two approaches are incompatible, each describes large
numbers of events on average, but within different systems. Attempting
to unify them is a bit synonymous with an attempt to unify gravitational
orbits and the gas laws. Neither can be derived directly from the
other, though both are accurate, and both are subsets of the more
fundamental Newtonian thermodynamic laws.

Neither special relativity nor QM are a subset one of the other, they
are both special cases of another yet more fundamental theory. There
is no symmetry of the sort necessary to fully satisfy the PoR in
Einstein's derivations.
He begins by pondering the motion of particles through each others
fields, in conjunction with the PoR, in the sense that I described
earlier. He reasoned correctly that the laws must be invariant wrt the
respective frames of the charges, and wrt all frames whatsoever. Since
Maxwell derived c without consideration of frames of reference, then
Einstein reasoned that lightspeed must be invariant, and thus framed his
conclusions upon that premise. He thus automatically assumed that c and
lightspeed were synonymous. I disagree. No doubt his approach was an
improvement in that engineers no longer needed to fret over where to
begin with systems not in the lab frame. OTOH, the approach is
cumbersome, and not only so, it isn't correct. Though he has symmetry,
and he has internal consistency, he does not have a one to one
correspondence to reality, nor even to the broader "system of logic" of
which the math is a small subset.

Symmetry must begin with the particle/particle interaction, then
expanded to macroscopic situations after the dynamics of this system are
established logically and empirically. The reason for this is that
macroscopic systems are rarely symmetric in nature. As I noted in a
short logical argument in a previous thread, there can be no delay in
the fields of these particles wrt each other, not without abandoning
symmetry, i.e. not without abandoning the PoR. As two electrons
approach along parallel paths, then each considers itself to be at rest.
The other is then moving through a field that is already established,
i.e. not delayed. Though this is a simple and obvious result of
symmetry, it could not have appealed to Einstein, since from this
conclusion the magnetic force cannot be derived. IOW, he must have
reasoned that the field must be geometrically contorted in some respect
in order that the particles experience a force in addition to the
Coulomb force when in motion wrt each other. Without this latter
premise, he couldn't have accounted for the magnetic interaction, and
thus his insistence on a transform other than the Galilean transform.

There is an alternative approach that doesn't require space-time
distortions, but so far in this thread it hasn't been my intent to go
into that theory. Just let it be noted that Einstein provided
covariance, not invariance, since nulling the fields against each other
isn't quite as symmetric as it is put forth to be. IOW your argument is
simply incorrect. Invariance-wrt-a-specific transform isn't equivalent
to invariance. The symmetry is much more complete when there is one
field with one aspect, not a "unified of field" with two aspects.

As for the contradiction, it's quite simple, and regardless of attempts
to iron out the details for me, not a single coherent response to the
following argument has ever been provided. A form of the argument goes
as such:

If two observers have identical light clocks oriented so that the faces
of the mirrors are perpendicular to the y axis and move along the x
axis, then regardless of relative motions, or even boosts, given
constancy of c in all frames, then each of these clocks will always see
the other clock as ticking slower since the other beam is taking a
zig-zag path. Though with manipulations of the lorentz transform you
can provide internal consistency, that doesn't change the fact that
these observers cannot actually see this happening in reality, i.e. it
is necessarily empirically inconsistent.
You are free to rationalize.

Observer A is located at the right end of a platform that is at rest in
an inertial frame.
Observer B is moving parallel to the platform to the right at .5c along
the x axis directly toward A.
If the platform is 1 light second in length in the rest frame, then wrt
B the platform is shorter by a factor 1/gamma.
As B intercepts the leading end of the platform a toggle on his clock is
flipped and his clock begins ticking. At the same instant a light signal
is sent along toward A at a speed of c. The signal must arrive at t =
1sec. Upon arrival of the signal A sets his clock to 1 sec, thus he can
get an accurate comparison of their ticking rates when B arrives at A,
that is, he knows that B started across the surface at t = 0.

B is moving at .5c, thus he will arrive at A's position in a time of
2seconds. Since wrt A, B's clock is ticking slow by a factor 1/gamma,
which is confirmed by the pythagorean theorem, i.e.. the beam is moving
in a zig-zag pattern wrt A, and thus takes longer to travel between the
mirrors than the beam in his own clock. B's clock will show
(2/gamma) seconds upon arrival. IOW B's clock ticked slower.

Now from B's frame the light signal takes a time 1/gamma seconds to get
to A, simply because wrt him the beam moves at c, and because the
platform is shorter by a factor 1/gamma wrt B. Thus according to B, A's
clock is set to 1 at the same instant that B's clock ticks
(1/gamma)seconds. Now since B takes a total time (2/gamma) seconds to
cross the platform, then he must be exactly at the midpoint of the
platform when A's clock is set to 1.

Now wrt him, it is A's clock that is ticking slow by virtue of the same
geometrical argument made above. Thus during the second half of the trip
his clock will advance by another (1/gamma)seconds, while A's clock
advances by
((1/gamma)/gamma) seconds. Thus in B's frame A's clock does not read 2
seconds upon their meeting.
Now if we had let A's clock tick faster than B's clock by a factor
gamma, then we would have resolved the contradiction. OTOH, this
requires the beam in A's clock to be moving faster than c wrt B's frame.
Thus it was Lorentz who was correct in his interpretation of the MMX. No
wonder he viewed Einstein as quite the idiot.

Now if perchance I've made some grievous oversight in this argument, and
lord knows I have done so in past arguments, please illuminate me,
because I've gone over this a thousand times and I don't see any mistakes.

PS, note that there are no boosts in this thought experiment, which BTW
is an aspect that introduces contradictions of its own. What we have
above is an argument between two observers who happen upon each other
without a clue as to either of their acceleration histories. Thus "which
clock will be the one ticking slower?" is a valid question.

Richard Perry

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