On Wed, 07 May 2008 12:52:09 +0200, "Paul B. Andersen"
wrote:

Albertito wrote:
On May 6, 8:11 pm, "Paul B. Andersen"
wrote:
Albertito skrev:

Hi all,
In recent threads I was trying to show velocities
do not add as Einstein's addition formula states,
but strictly as euclidean vectors,
w = u + v,
Have you done the one thing that can prove
Einstein's formula wrong?

If you have, why don't you tell us about
the experiment that falsified Einstein's formula?

[..]

--
Paul

http://home.c2i.net/pb_andersen/

Someone has already pointed out to you that the
Pioneer anomaly may be very well a experiment that
can falsify Einstein's formula.

Not really.
There are too may open questions to do that.

But you said you have tried to show that velocities
do not add as Einstein's addition formula states,
but strictly as euclidean vectors w = u + v

Don't you know of any experiments testing how
velocities transform?
How did Einstein's velocity transform and
the Galilean velocity transform do in those tests?
Were any of them falsified?

I think that one of the problems with discussing velocity addition
under SR vs "older models", and then talking about experimental
verification, is that people tend to forget that lots of the older
models could also generate their own velocity-addition formulae.

Any model that assumes that the velocity of light is somehow mangled
by the motion of objects tends to generate these sorts of formulae.
The //status// of velocity-addition under SR is unusual, but the
associated phenomenology isn't especially new. The significance of the
match between Fizeau's experiment and SR sometimes gets exaggerated, I
don't think the match was supposed to be any better than the match
between Fizeau and Fresnel's old aether-dragging model (which Fizeau's
experiment was seemingly meant to test).

If we're sticking to strictly optical effects, we find that quite a
few theories have "non-Galiean" relationships when composite shifts
are involved.
For instance, with ancient emission theory, the Doppler shift law for
a recedign object was f'/f = (c-v)/c , so if you watched an object
receding at half the speed of light, it's frequency would be halved.

If there was then a second object beyond it, also receding, at half
lightspeed wrt /it/, then you'd normally tend to say that that second
object was receding from you at exactly the speed of light ... but it
wouldn' t be receding at the speed of //its own// light.

For a signal passed from the more distant object, to the intermediate
object, to you, the frequency of the light (according to old emission
theory) would be freqOriginal×0.5×0.5 , so you'd expect to see the
furthest object's signals, relayed vie the intermediate object, to
have one quarter of their original frequency, as we'd expect under
emission theory if we'd observed it directly while it was only
receding at 0.75c, rather than c.
The "effective" recession velocity calcualtion for the
indirectly-observed object under emission theory would then be
0.5c+0.5c = 0.75c


Similar "non-Galilean" patterns show up under other models where
lightspeed is variable, and can be justified by pointing out that a
relative "velocity", defined as a fraction of the speed of light, can
end up being assigned a different nominal value when the speed of the
light-signal that's being used as a reference changes.


Obviously, a lot of the old models were pretty stinky in places, but
we have to remember that the main advantage of the Galiean transforms
isn't perhaps so much their historical relavance, as their narrative
value in explaining the thought-processes that take us from (a)
assuming that the speed of light is globally fixed in the laboratory
frame (fixed stationary absolute aether), to (b) arriving at a
"relativised" version of that global-c description, provided by
special relativity.

If we're going to try to make a fair comparison, the Galilean
transforms themselves arguably don't correspond to the relationships
that appear in all pre-SR theories, or even to all the //major//
pre-SR theories.


SR does (however) seem to depart from older models in how its
velocity-addition formula is applied and interpreted:
In older theories, the appearance of a "special" v.a.f. would
typically have been taken as solid evidence that the motion of bodies
was altering the propagation of light (but that no single body's state
of motion could be used to absolutely dictate the speed of all light
in an experiment).
Under special relativity, the motion of nearby bodies is assumed to
have no effect on the propagation of light "in vacuo", so instead of a
v.a.f. documenting local lightspeed variations caused by the relative
velocities between intermediate objects in the signal path, the //SR//
v.a.f. applies even when no physical bodies corresponding to those
intermediate stages are present, and has to be taken instead as as a
structural quality inherent to spacetime itself.

=Erk= (Eric Baird)
www.relativitybook.com