Re: SR Postulate on Speed of Light
- From: dubious@xxxxxxxxxxxxxxxxxxxxxxxxxxxx (Bilge)
- Date: Fri, 20 May 2005 21:06:48 GMT
john_doe_ph_d@xxxxxxxxx:
>I am confused by the typical wording that one finds for the second
>postulate of SR, namely that the speed of light is independent of the
>motion of the source. The speed of any wave depends only on the medium,
>so the motion of the source is not relevent. Consider a horn moving
>through the air. It emits a sound wave. Once the wave leaves the horn,
>its speed depends only on the properties of the air.
The second postuate is completely unnecessary, so you can forget
about aves altogether. The first postulate which states that all
inertial observers are equivalent, is sufficient to derive the lorentz
transforms for an arbitrary velocity, `c', which is not necessarily
the velocity associated with any propagating particle, wave, etc.
The number `c' could be either finite or infinite. In the latter case,
one obtains the galilean relativity of classical mechanics. If `c'
is finite, one has special relativity.
The velocity, `c', is the velocity that a _massless_ particle
propagates. If `c' is infinite, then mass is locally conserved and
radioactive decay cannot occur, thus ruling out the case with
`c' infinite.
Light propagates at `c' if the photon is massless (or equivalently,
if maxwell's equations are correct). Einstein included the second
postulate because his goal was to explain maxwell's equations as
a natural consequence of geometry. Note the title of his paper,
``On the Electrodynamics of Moving Bodies.'' However, einstein
was unaware of other forces like those responsible for radioactive
decay, so he had no reason to think that he was giving light some
special status. However, we know better now, so the question of the
speed of light being equal to `c' is a question that belongs in a
theory of forces, not in relativity. It's straight forward to come
up with a theory of E&M in which light does _not_ propagate at `c',
so the best way to understand relativity is to divorce the meaning
of `c' from the speed of light.
>Now it's true that for someone traveling with the horn, the speed of
>the sound would be greater in the forward direction than the backward
>direction, but this has more to do with the speed of the OBSERVER
>(relative to the medium).
There is a great deal of difference between light and a classical
wave. In particular, there is no wave in any medium with properties
comparable to that of light in vacuum. It's a bad analogy which
came about because that's the only physics that was known 150 years
ago.
>I am more comfortable with an alternate statement of the second
>postulate, namely that the speed of light is the same for all inertial
>observers.
You should think of it as the value `c' is the same for all
inertial observers, since that is true by definition of the
lorentz transforms, i.e., that is what is preserved by a lorentz
transformation.
>Are these two formulations of the second postulate equivalent?
It's equivalent so far as special relativity goes. If you try to
interpret it as motion in a medium neither is correct and you have
to accept the idea that the constant value of `c' is only apparent.
.
- References:
- SR Postulate on Speed of Light
- From: john_doe_ph_d
- SR Postulate on Speed of Light
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