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On 2005-08-27, Eugene Stefanovich <eugenev@synopsys.com> wrote:
> Igor Khavkine wrote:
>
> I followed your explanations up to this point:
>
> > When
>> the two observers get together and compare their notes, they find that
>> the recorded numbers are related by a Lorentz transformation (in the
>> sense I outlined above).
>
> Where this statement comes from? Is it a postulate?
It is a consequence of other postulates. Let me break this down for you.
Mathematics:
1) There are two coordinate systems, x-t and x'-t'. The coordinates for
a given space-time point are related by a coordinate Lorentz
transformation. (postulate)
2) There are particle curves embedded in space-time and vector fields
defined on it. (postulate)
3) The particle cuves and vector fields expressed in these two
coordinate systems are related by the appropriate extension of
coordinate Lorentz transformations, which I derived in my previous
post. (consequence)
Physics:
1) Each coordinate system corresponds to space and time measurements by
an inertial observer. The time corresponding axes are the world-lines
of the observers. (postulate)
2) The particle and field measurements for each observer are given by
the expressions for the particle curves and field components
expressed in their respective coordinate systems, as described above.
(postulate)
3) The measurements of two inertial observers are related by a Lorentz
transformation. (consequence)
The last point is what you asked about. It is a direct consequence of
available mathematics and the two physics postulates.
Igor
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