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 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.