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My mistake about Lorentz transformations (addition)



--- pvalev <pvalev@bas.bg> wrote:
--- Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU> wrote:
pvalev wrote:



You say (A) and (C) are compatible and lead to the Lorentz
transformations. If I take
one of those transformations, namely

x = (x' + vt')/sqrt(1-v^2/c^2)

and substitute x' = -vt', I get x=0, which is your statement
(B).

You have chosen a version of Lorentz transformations that agrees
with
(B) but does not agree with (A). Substitute x=vt and you will
not
obtain x'=0.


???? The standard complementary transformation back from x,t to
x',t',
namely x'=(x+vt)/sqrt(1-v^2/c^2), immediately gives x'=0.

Even if one restricts oneself to the transformations from x',t' to
x,t,
namely x=(x'+vt')/sqrt(1-v^2/c^2) and t=(t'+vx'/c^2)/sqrt(1-
v^2/c^2) and
then substitute x=vt, one still gets x'=0. At this very elementary
level,
your statements (A), (B) and (C) appear logically compatible when
the
Lorentz transformations are used.

You proposed this as a question to be presented to students. Could
you
please present what you would consider an acceptable student
solution -
something more detailed than simple assertions that (A), (B) and
(C) are
incompatible.

You are right - (A), (B) and (C) are indeed compatible within the
Lorentz transforations. For the moment, I am not quite sure how I
made this naive mistake. I remember starting from

x' = ax + by + cz + dt

x' = 0 <-> x = vt

x = 0 <-> x' = -vt'

Addition: The above three conditions give

t' = at /1/

and so I decided to take the opportunity to introduce a constant (v-
dependent) time dilation, in accordance with experimantal data. The
transformations I obtained were incompatible with

x = ct <-> x' = ct' /2/

and I presented them on the forum. However there must have been some
path leading to Lorentz transformations compatible with /2/. I still
think that, according to Lorentz equations, the time change on the
train is variable - some processes go faster than in the track frame,
others go slower. In the transformations I obtained all processes on
the train go slower.

Pentcho