On Feb 17, 5:12 pm, HW@....(Henri Wilson) wrote:
On 17 Feb 2007 08:54:45 -0800, "PD" wrote:

...
Tell me what is wrong with my derivation...

Nothing is wrong with your derivation. Your conclusion that it implies
circularity is what's wrong.

The rule for combining velocities is not, nor was it ever, used to
assert that the speed of light is constant regardless of reference
frame. The only claim that is made is that the frame independence of
the speed of light is *consistent with* the rule for combining
velocities. Moreover, the experimental evidence in support of the rule
for combining velocities has nothing to do with measuring the speed of
light, but in fact measuring the speed of other particles in different
reference frames -- and it is there that measurements are completely
consistent with the velocity combination rule.

The frame-independence of the speed of light is taken as an unproven
*postulate* in special relativity. It is not necessary in science to
experimentally prove a postulate. One determines the implications of a
postulate (and just as you derived it, the velocity addition rule is
an example of an implication of this postulate) and then tests those
implications against experiment. If the implications match experiment,
and if the postulate is able to generate more successful implications
that match up to experiment than competing postulates, then this is
taken in science to be sufficient grounds for belief in the truth of
that postulate.

In this particular case, the postulate is the frame-independence of
the speed of light. One implication (of numerous implications) is the
rule for combining velocities. The rule for combining velocities has
been tested experimentally in a wide variety of circumstances (without
needing a direct test of the frame-independence of the speed of
light). And because this, and so many other implications, match
experiment so well, we take stock in the truth of the frame-
independence of the speed of light.

....

Well said.

Well, thanks, but Henri will ignore it, since it doesn't feed his
fantasy.

I showed how to derive the formula with trivial mathematical circularity.
Does that make me as great as Einstein ...or greater...?


Well, Henri, as I explained to you in great detail, there is nothing
circular about it. You started with the presumption that c is
constant, independent of the reference frame, and used that derive the
correct rule for the addition of velocities. That is precisely the
right way to do it. Circularity would entail concluding what you
started with, and that is not what you're doing. If you will read my
response quoted above once more, you will perhaps understand that a
little better.

PD