Question:

When pair production of protons occur, kinetic energy is transformed into the mass of a proton/anti-proton pair.
I would assume that you could work out the numbers by using E=MC^2 and so, (unlike billiard balls whose total speed would be a sum of the initial speed) the resultant speed of the particles produced would not sum to the speed of the original particle.

If the collision occurred within a space ship, the original proton ion would create a backward force on the ship when fired from the accelerator (as a normal ION Drive works) but would an equal and opposite reaction occur at the point of matter creation?

Yes, momentum is conserved in matter creation.

What do you mean by "an equal and opposite reaction" ?

KenG Agreed. Momentum is always conserved in all particle interactions: linear momentum, and angular momentum...part of the hierarchy of conservation laws.
pete

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A second rate theory explains after the fact.
A first rate theory predicts.
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Seems I was forgetting that the initial collision does not create the anti atoms, The Momentum is conserved as the collision makes the pair involved in the collision get extremely hot. The Anti matter is then a by product of this extreme heat.

The Law of the conservation of Momentum states that for every action there will always be an equal and opposite reaction. In the above example the thrust of the particle being fired from the particle accelerator is equal to the thrust of the the target being forced backwards from the recoil of the impact.
Wiki Momentum

Max. Careful with your phrasing there. The momentum of the particle fired from the accelerator is exactly equal to, and opposite in sign to the accelerator itself....that's where the forces occur in pairs, too. Whether the collision is elastic, or inelastic at the target, the total momentum of the incoming particle, and the target (at rest, zero)...is conserved. But in an inelastic collision...say the incoming particle sticks to the target...the recoil of the target itself does not carry it all away, part of it is carried by the particle there...



pete.

__________________
A third rate theory forbids.
A second rate theory explains after the fact.
A first rate theory predicts.
A. Lomonosov