# Relativistic Antiproton Protion

1. Jan 7, 2010

### alex3

This isn't really so much of a homework problem, but I'm reading this webpage, and there's one part of the derivation of the required proton KE needed to produce a static antiproton.

The part that's puzzling me is

"and using... m2inc4 - p2inc2 = m20c4 "

I don't see where this formula is coming from. I can see the resemblance to the invariant, but the RHS deals with the moving proton, and the LHS only has the mass of a single proton, I'm confused as to why it's not (2m0)2c4.

Thanks for any help.

2. Jan 7, 2010

### Staff: Mentor

This is just a rearrangement of the usual Einstein formula:

$$E^2 = m_0^2c^4 + p^2c^2$$

$$m^2c^4 = m_0^2c^4 + p^2c^2$$

$$m^2c^4 - p^2c^2 = m_0^2c^4$$

where m is the 'relativistic mass'.

(This formula is derived on the page just before the one you linked.)

I'm not sure what you mean. This is the invariant. It's true for any proton, including the incoming one.

3. Jan 10, 2010

### alex3

Aha of course, elementary really. Thanks very much for the clarification!