- #31

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1. Why would we bother with [tex]V[/tex], when we have all the measurable quantities [tex]v_i[/tex] ?I'm not following that.

Anyway, both your formula andDr Greg's formula are simply working out energy/momentum for a system of particles without any mention of the velocity, V, of the systemas a whole.

2. I think I pointed out that the quantity :

[tex]E^2-(\textbf{P}c)^2[/tex] is wrong because it produces terms in [tex]v_i v_j[/tex]. This can be seen as well from the example . In this example, [tex]M[/tex] is clearly not an invariant due to the term [tex]p_1p_2[/tex]

3. I am of the opinion that the correct quantity is:

[tex]E^2-c^2 \Sigma ||\textbf{p}||^2[/tex]

4. DrGreg is of the opinion that the correct quantity is :

[tex]E^2 -c^2 ||\Sigma \textbf{p}||^2 [/tex]

Note that both formulas need to include [tex]|| \textbf{p}||[/tex] instead of [tex] \textbf{p}[/tex] from the wiki page. There is nothing stopping you from using [tex] \textbf{p}[/tex] as long as you realize that it will produce a frame-variant value for the total mass of the system. If this is what you want, fine, it is all a matter of definitions.

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