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From: glird on 3 Apr 2010 15:05
On Apr 1, 8:00 am, "Androcles" <Headmas...(a)Hogwarts.physics_x> wrote:
>
> Einstein decided a = 1.
> Now
> @tau/@t = delta tau /delta t =
> @t/@tau =
> delta t /delta tau =
> dt/dtau =
> dtau/dt = 1

> Goodbye gamma.
> Goodbye babbling cretin.

Dear John Babble Walker,
The REASON "Einstein decided a = 1" is that in
Lorentz's 1904 paper, he (Lorentz!) said that the ONLY effect
of a system's motion would be a deformation of its lengths,
Given that, then there would be no change in rates of anything;
including the rate at which clocks beat.
Therefore, dt'/dt = 1 WOULD be the ratio of rates, dt' : dt,
of clocks of two differently moving systems.
Given that his equations would "be linear on account of the
properties of homogeneity" E attributed "to space and time",
you are right insofar as "@tau/@t = delta tau /delta ... = 1"
is concerned.
In P1! @t/@tau = delta t /delta tau = dt/dtau = a = 1.
However, the little detail you slipped in and on is that rather
than dt/dtau = dtau/dt - 1, as in your greasy equation (which is
precisely
what tripped up Einstein), if a = dt/dtau = 1 as measured by system
k',
then dtau/dt IS NOT equal to a = 1 as measured by system K!!

You, John W, are the only one on these newsgroups who pinpointed the
small bimp in Einstein's paper, "Hence, if x' be chosen
infinitesimally
small,"
Although you still don't know it, eqs 4 and 5 were not derived from
eq 3; nor was eq 7 derived from anything in P2. It was put there to
bridge
the unbridgeable gap (*) in his treatment.
Although it is the most brilliant equation in his entire paper, it
was and is a HUGE {though heretofore invisible} bimp -- an invention
to join what came before and what came after it.

* Even though a = dt/dt' DID equal 1 in P1, and a = dtau/dt DOES
equal sqrt(1-v^2/c^2) in P2, (both of which satisfy eq 7!); there is
no
logical or mathematical way to let it be both.

Regards,
glird
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