Re: definition of a clock in relativity theory
From: Eric Baird (eric_baird_at_compuserve.com)
Date: 09/27/04
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Date: Mon, 27 Sep 2004 03:41:29 +0000 (UTC)
On Sat, 25 Sep 2004 11:22:03 GMT, "Androcles" wrote:
>"Eric Baird" <eric_baird@compuserve.com> wrote in message
>| On Sat, 18 Sep 2004 16:55:36 -0800, Eric Gisse wrote:
>| >On Sat, 18 Sep 2004 08:52:21 GMT, "Androcles"wrote:
>| >>"Henri Wilson" wrote in message
>| >>
>| >>| Which, when translated, means "light has mass like anything else...
>| >>| but by god,
>| >>| we DHRs will never admit to the fact"!
>
>| >>Mass is E/c^2.
>| >>Light has E/c^2 like anything else?
>| >>That's a little circular, isn't it?
>| >*snicker*
>| >
>| >You say that relativity is wrong yet you use its' predictions in your
>| >spew.
>|
>| FYI, the E=mc^2 relationship (where "m" is rest mass, and "E" is the
>| energy in the rest frame of that mass) also shows up as a consequence
>| of the equations of Newtonian theory.
>|
>| Einstein happened to present his 1905 argument using the equations of
>| LET/SR, but the trick seems to work just about as well either way.
>| (if anything, the "Newtonian" calculation is marginally simpler).
>|
>|
>Indeed it does.
>J.G.Fox writes in the American Journal of Physics, Volume 33 #1 Jan '65.
>==========================================
>The essence and the proven utility of the photon model consists in its
>simple representation of the energy and momentum of radiation. It is more
>than likely that any optical phenomenon which can be explained by making use
>of the momentum of a photon can also be explained rigorously with an
>electromagnetic theory which properly accounts for this property. For the
>rest of this discussion it is assumed that the Ritz theory an indeed take
>proper account of the energy and momentum of light and that what can be
>proved with the photon model could also be proved rigorously with that
>theory.
>
>It may be objected that the photon is a very relativistic particle, i.e., it
>is very closely related to special relativity, and therefore it cannot be
>used to obtain results in support of a theory which denies special
>relativity. In reply, it can be remarked that it was discovered or invented
>before and independently of special relativity and that the ratio of its
>energy and momentum prescribed by electromagnetic theory.
>
>The idea of the inertia of radiant energy, while generally attributed to
>special relativity, also has a certain independence of its own. Hasenohrl
>derived it for blackbody radiation in a moving cavity entirely on the basis
>of electrodynamics before the advent of special relativity. Furthermore, it
>is proved for the familiar photon-in-a-box on the basis of the conservation
>of momentum for the system.
>
>Another proof, more closely related to the present discussion, may be made
>by the following modification of a demonstration due to Langevin. Consider
>a source which is at rest with respect to an observer O and which radiates a
>simultaneous, oppositely directed pair of equal quanta, hu, e.g.,
>annihilation radiation. While the total energy radiated is E = 2hu [u
>represents the greek nu here, which I cannot reproduce], the total momentum
>radiated is zero, so the source remains at rest with respect to O.
>
>Now, consider this phenomenon from the point of view of an observer O' who
>moves with respect to O with the constant velocity v = bc along the line
>defined by the radiation. On account of the first-order Doppler effect O'
>observes two quanta with the frequencies hu(1 + b) [b= beta] and hu(1 - b).
>He thus concludes that a net amount of momentum hu(1 + b )/c - hu(1-b)/c =
>2hub/c is emitted in the direction in which the source and O appear to move
>with respect to him. From the conservation principle for momentum he
>concludes that the source loses this same quantity of momentum. Now the
>velocity of the source with respect to O' does not change since it remains
>at rest with respect to O, as has been seen. Thus O' is forced to conclude
>that the mass of the source has decreased by an amount Delta.m, where
>(Delta.m)u = 2hub/c. Thus, Delta.m = Delta.E/c^2.
>==========================================
>
>Androcles.
>
Woo, a useful quote, from 1965, courtesy of Androcles! :D
Takes an awful long time for "unwanted" information to trickle down to
the masses, doesn't it?
For the benefit of folk here who were only taught the SR arguments, if
you start off with an SR derivation of E=mc^2, based on the way that
the energy and momentum of light and matter are supposed to transform
between frames with SR, and strip out all the Lorentz terms
(correctly!) to produce the corresponding Newtonian calculation, then
the removed Lorentz terms cancel, and the result of the calculation is
unchanged.
For mass, reverting to NM involves making a Lorentz reduction of the
momentum law (back to p=mv), and then we have to perform similar
surgery on SR's momentum of light so that the momentum maps between
frames in the same way irrespective of the form that it takes. This
means reducing SR's predicitons for the energy of light by a Lorentz
term, which gets us to
: E'/E = freq'/freq = c/(c+v) *SQRT[1 - vv/cc] *SQRT[1 - vv/cc]
: = (c-v)/c
, which was the old Newtonian emission-theory relationship.
So if we revert to the original Newtonian relationships, E=mc^2 still
drops out nicely. SR simply takes all the variables that we play off
each other to get E=mc^2 and adds Lorentz terms (compared to NM) that
cancel out and don't appear in the final result.
Maybe if Lorentz had fallen under a bus before publishing his 1904
paper, Einstein might have ended up publishing E=mc^2 as a result of
Newtonian theory, and we'd now have mainstream physicists crossly
telling physics dissidents that Newtonian theory has to be correct, or
else atomic bombs wouldn't work, etc
(Obviously, there are some important differences between NM and SR in
some other areas)
-----------------------
A by-product of trying the "Newtonian" calculation is that we learn
that for momentum conservation to work properly under Newtonian
mechanics (using p=mv), we seem to have the condition that the Doppler
shift law /has/ to yield the emission theory result, E'/E = (c-v)/c ,
even before we start hypothesising how light might propagate, or how
relative motion might alter frequencies, or what shape spacetime is.
This is useful, because it seems to mean that /any/ theory that
assumes p=mv would seem to be locked into that same
: freq'/freq = (c-v)/c
Doppler relationship by default, (and vice versa) by
momentum-conservation considerations, unless it has a damned good
letter from its doctor explaining why the hell not.
That two-way linkage between the momentum and Doppler laws would
/seem/ to have to hold in all other theories with different laws, too,
which drastically cuts down on the theoretical possibilities. It also
seems to mean that the idea that lightspeed is fixed throughout the
observer's /frame/, yielding the different Doppler law
: freq'/freq = c/(c+v)
can't be claimed to be "Newtonian", because /that/ Doppler law is then
incompatible with p=mv (it would seem to instead generate
p=mv* 1/[1- vv/cc), which AFAIK doesn't ever seem to have been
suggested as a serious alternative).
So, experimentally showing that the SR shift law is heaps better than
c/(c+v) doesn't necessarily mean that it's better than NM, because to
move from the NM relationships to that alternative law seems to
require even bigger modifications to NM than moving from NM to SR.
=Erk= (Eric Baird)
: " And one of the children did say unto Moses, look upon thy tablets,
: for upon the third tablet is a spelling mistake
: And on the fourth there is some sloppy workmanship
: And ye have a chisel in thy pocket and a nasty bruise on thy thumb. "
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