Re: Frame Dragging Post to s.p. research.
From: Androcles (dummy_at_dummy.net)
Date: 11/27/04
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Date: Sat, 27 Nov 2004 17:21:39 GMT
"dar7yl" <no_reply@accepted.org> wrote in message
news:V_Xpd.7244$cE3.5412@clgrps12...
> Einstein created that double-edged sword, that enigmous equation, E =
> m c squared.
No he didn't.
He came close, with E = mc^2 { 1/sqrt(1=v^2/c^2) - 1}
Note the -1.
"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 DE
= 2hu, 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) 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 Dm, where (Dm)u = 2hub/c. Thus, Dm = DE/c2." -J.G.Fox.
Androcles.
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