matter into energy at high velocity

ripoli85

hello forum, i got another question:

1st frame of reference:
a proton and its anti matter counter part are next to each other in open space. they have no relative speed to the frame of reference. suddenly they annihilate each other and a burst of energy appears.

2nd frame of reference:
the same proton and its anti matter counter part are next to each other flying through space with a relative speed of 99% the speed of light. from this perspective the two particles have a mass seven times greater then their mass is in the 1st frame of reference. Since energy is being conserved in either of those frames, the annihilation of the two particles should result in a burst of energy that is seven times greater than in the first frame of reference.
My question is: What is accounting for the extra energy in the second frame of reference? Is it that a part of the electromagnetic radiation(of the annihilation) has been shifted to very short wavelength and therefore very high energy radiation?

Mentz114

Yes, it's the frequency shift caused by the relative velocity. Momentum depends on which frame it is measured from.

DrGreg

Energy is a frame-dependent concept: the energy measured in one frame is different from the energy measured in another frame. This is true even in Newtonian physics -- kinetic energy depends on velocity which is frame-dependent.

Conservation of energy applies only when all of the energies are measured in the same frame.

Phrak

To put things in different terms, I think this calls for E=mc². (So we are now presuming relativistic mass for m.)

Both the mass and the energy are there all along. The energy has only changed form upon annihilation. So we don't have to talk about a burst of energy.

In the frame of reference where the center of mass of the particles are moving with respect to an observer, both the energy and mass are greater before and after annihilation.