sci.physics.relativity

Timo A. Nieminen wrote in :
> On Thu, 5 Jul 2007, littlejoe wrote:
[...]
> OK, the relativity thing is that _one_ speed is the same in all inertial
> reference frames, and that speed is c. In this context, c is the
> "invariant speed", not necessarily, a priori, the speed of light. As a

I have seen two derivations of SR. In one it is assumed that the speed
of light in a vacuum is constant for all inertial observers and then
you show that all of SR flows from that (along with invariance of
natural law). In the other, it is assumed that there exists a constant
that is the same for all observers and then it is shown that that
constant is the speed of light in a vacuum. It turns out that the two
versions are really the same SR.

> consequence, speeds less than c are less than c in all inertial
> reference frames. Also, speeds greater than c are greater than c in all
> inertial reference frames.

You have to be careful with speeds greater than c. They are excluded
by the topology of space-time in SR. Space and time also loose their
physical meaning for v>c, since you are now outside the domain of the
(abstract) space of SR.

>
> Experimentally, light (in vacuum) travels at c in all inertial reference
> frames so far tested in. This tells us why this is fine for light.
>
> There are (at least) two ways to approach speeds of other objects. One
> is causality. If A causes B, then A must happen before B. If some

Not necessarily. A left-handed space-time can also be Lorentzian and
thus follow a kind of SR. In such a space-time, if A causes B then B
always preceeds A. Usually left-handed space-times are excluded
however, because there is no Lorentz transformation that is consistent
with physics that will transform from a right-handed (observed)
space-time to a left-handed one.

I only mentioned this, because we need to be careful about general
statements.

> "thing" travels slower than c, or at c, from where/when A happens to
> where/when B happens, then the order of the events is the same in all
> inertial frames. If you need to travel at faster than c to get from A to
> B, then in some frames, A will happen first, while in others, B will
> happen first.

Actually, if you travel faster then c, then you are violating energy
constraints, since it will take more energy than is available in the
universe to get you past c.

[...]
> A second approach is to see that you need infinite energy to accelerate
> an object with non-zero rest mass to c.
>

Which is the right answer.

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