Let me just point out the relevant feature of the physics of Special
Relativity and let you ponder:
Consider a point light source originating a spherical light pulse into the
vacuum at x=x'=t=t'=0. (The proper frame of the light source is
irrelevant to what follows.):
This generates a myriad of events characterized by a light pulse arriving
at a space-time point. To the unprimed observer, a set of such events
satisfying x^2 + y^2 + z^2 = (c^2)(t^2) are simultaneous (i.e.. he sees a
spherical wave front centered on his location x=y=z=0 and advancing at the
speed c ). To the primed observer, a set of (different) events satisfying
the same equation with primed x,y,z,t are simultaneous ( i.e.. he sees a
spherical wave front centered on his location x'=y'=z'=0 and advancing at
the speed c). The Lorentz transformation is rigged to make this so - if
you reach a different conclusion by manipulating the Lorentz equations,
you have mis-calculated and/or mis-interpreted.
Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net http://www.velocity.net/~trebor
----- Original Message -----
From: "pvalev" <pvalev@BAS.BG>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, June 06, 2003 11:58 AM
Subject: Re: Teaching logic is urgent (the only reasonable transformatio
| --- Bob Sciamanda <trebor@VELOCITY.NET> wrote:
| > Pentcho,
| > Ken included your statement t' = (pv + q)t in his reply to my post:
| > " . . . and a symmetric argument shows that t =
| > gamma t' for events such that x' = 0 "
| >
| > Please carefully read the posts which answer your assertions!
|
| I assume you would agree that an event such that x' = 0 could be the
| movement of the front of a beam along the y'-axis. For this event, we
| can substitute x = vt in Lorentz second equation and obtain indeed
|
| t' = (1 / gamma)t /1/
|
| However take another event - the movement of the front of a beam
| along the y-axis. For this event, x = 0, x' = -vt' and by
| substituting these in Lorentz first equation we obtain
|
| t' = gamma*t /2/
|
| The first event is slower in the primed (train) frame than in the
| track frame, the second event is faster in the train frame than in
| the track frame. In my view, the conclusion that, for some events,
| time dilation in the primed frame turns into time constriction is
| absurd. Since /1/ was obtained from Lorentz second and /2/ from
| Lorentz first equation, the absurd conclusion implies that the two
| Lorentz equations are incompatible. This can easily be checked - in a
| previous posting, I expressed x from them:
|
| x = (tc^2 - t'*c^2*sqrt)/v (second Lorentz)
|
| x = vt + x'*sqrt (first Lorentz)
|
| I think it is obvious that in the second Lorentz x is almost
| inversely proportional to v whereas in the first Lorentz x increases
| almost linearly with v (the "almost" is due to the sqrt). I don't
| know what other argument could show more convincingly that the two
| Lorentz equations are incompatible.
|
| Pentcho