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fluidistic

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Hi guys! I've got 2 extremely simple questions, hence a single thread.

First, I want to know whether the conservation of the 4-momentum in a closed system implies the conservation of the energy and of the 3-momentum.

Let's assume we consider 2 different times, ##t_i## and ##t_f##. Then ##P_i=(E_i/c,\vec p_i)=P_f=(E_f/c, \vec p_f)##. Where the E's are the energy at the 2 different times and the lower capital p's are the 3-momenta at those 2 different times.

Now each component of ##P_i## must be equal to each component of ##P_f## right? If so, it follows that ##E_i=E_f## and that ##\vec p _i = \vec p_f##. Is this correct?

Second question. I've "heard" that the trace of Faraday tensor is 0 and thus its diagonal entries are all 0. However the trace is definied as the sum of all the entries on the diagonal... so the fact that the trace is 0 does not imply that all the diagonal entries are worth 0. Is this correct?

Thanks.

First, I want to know whether the conservation of the 4-momentum in a closed system implies the conservation of the energy and of the 3-momentum.

Let's assume we consider 2 different times, ##t_i## and ##t_f##. Then ##P_i=(E_i/c,\vec p_i)=P_f=(E_f/c, \vec p_f)##. Where the E's are the energy at the 2 different times and the lower capital p's are the 3-momenta at those 2 different times.

Now each component of ##P_i## must be equal to each component of ##P_f## right? If so, it follows that ##E_i=E_f## and that ##\vec p _i = \vec p_f##. Is this correct?

Second question. I've "heard" that the trace of Faraday tensor is 0 and thus its diagonal entries are all 0. However the trace is definied as the sum of all the entries on the diagonal... so the fact that the trace is 0 does not imply that all the diagonal entries are worth 0. Is this correct?

Thanks.

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