<berry@pop.networkusa.net> wrote in message
news:1125103706.305300.122520@g43g2000cwa.googlegroups.com...
>
> Eugene Stefanovich wrote:
> > berry@pop.networkusa.net wrote:
> >
> > >>Maxwell's theory and Einstein's relativity give precise expressions
for the
> > >>transformations of p and e (we keep only terms up to the first order
in
> > >>transformation parameters; v.p denotes the scalar product of two
vectors;
> > >>c=1 is assumed for simplicity):
> > >>
> > >>Boost[v] p = p - ve (1)
> > >>Boost[v] e = e - v.p (2)
> > >
> > >
> > >>Shift[a] p = p
> > >>Shift[a] e = e
> > >
> > >
> > > These equations are wrong. You need to take into account the force
> > > acting on the particle as well.
> > > For example,
> > >
> > > Shift[a] e = e + a.L
> > >
> > > instead of what you have above.
> >
> > So, you say that the energy of a particle looks different to two
> > observers shifted in space wrt each other. I don't think such a
> > difference has been ever seen in experiments.
> >
>
> Sorry, I thought you were talking about translating and boosting the
> particle; since you seem to mean translation of the observer, there is
> either no effect from either time translation or space translation, or
> an effect from both (different from the one I gave), depending on
> whether e is supposed to represent the energy of the particle at a
> fixed event, or on its intersection with the observer's lightcone. If
> on the third hand you want it to represent the particle's energy at
> time 0, then your boost equations are wrong, because they don't take
> into account the fact that the two observers have different time 0s.
>
Let me explain my definitions:
Observer K at time t=0 (by his clock) measures momentum of the particle p
and the energy of the particle e.
Observer K' is moving wrt K with velocity v. Her clock is
adjusted to show t'=0 when axes of K and K' coincide and the clock of
observer K
shows t=0. At time t'=0 (by observer's K' clock) she measures momentum p'
and energy e' of the particle. These measurements I denote by
p' = Boost[v] p
e' = Boost[v] e
Observer K'' is shifted wrt K by the distance a. At time t''=0 (by his
clock)
he measures momentum p'' and energy e'' of the same particle
p'' = Shift[a] p
e'' = Shift[a] e
Eugene.