Talk:Ultrarelativistic limit

what is E=pc? The energy of a body is equal to its momentum times the speed of light in a vacuum.

The momentum is $p=\gamma mv$. It is a Lorentz invariant. You have also:

$E=\gamma mc^{2}$

$E^{2}=\gamma ^{2}m^{2}c^{4}$

$(1-\beta ^{2})E^{2}=m^{2}c^{4}$ using $\gamma ^{2}={\frac {1}{1-\beta ^{2}}}$ where $\beta =v/c$

$E^{2}-\beta ^{2}E^{2}=m^{2}c^{4}$

$E^{2}=m^{2}c^{4}+\beta ^{2}E^{2}=m^{2}c^{4}+{\frac {v^{2}}{c^{2}}}(\gamma mc^{2})^{2}=m^{2}c^{4}+(\gamma mv)^{2}c^{2}$

$E^{2}=m^{2}c^{4}+p^{2}c^{2}$

When m=0, E=0 using the above trick ! This does not apply to massless stuff !

However it is true to say that when $v\approx c$ , $p\approx \gamma mc$, and of course, $E=\gamma mc^{2}\approx pc$ — Preceding unsigned comment added by Jlpons (talk • contribs) 12:46, 2 December 2023 (UTC)

What does momentum mean?

In planks initial formula, I assume that momentum is NOT rest mass times velocity. This should be explained. Articles that can only be understood by experts that already understand the material are useless. Tuntable (talk) 00:06, 31 March 2011 (UTC)