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A bullet is moving at $0.99 c$. Now we annihilate it by having it collide with an equal mass of antimatter. (assume instant and perfect reaction) This will turn both bullet and antimatter into photons.

But where did the substantial ammount ot kinetic energy carried by the bullet go? Momentum needs to be conserved. Have I just created a radiation beam moving along the vector of the bullet?

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  • $\begingroup$ Depends on what it annihilates into. If it's photons, the photons will be higher in energy than they would have been if the bullet hadn't been moving. $\endgroup$
    – knzhou
    Commented Apr 21, 2019 at 13:02

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Annihilation does not always create photons. However, if photons were created than momentum would have to be conserved. If the bullet and antimatter had equal but opposite momentums, then the simplest case of photon production would be to create two photons going in opposite directions at the same momentum. This is because momentum in the original frame was zero, and a single photon cannot have zero momentum from that frame. Light always moves at the speed of light from all frames.

The mass would be converted to energy through mass-energy equivalence, and additional kinetic energy from before the collision would also have to be conserved. Usually the velocities are so small relative to the speed of light that we ignore the kinetic energy as most of the photon energy is from mass annihilation. If the kinetic energy was significant it would be conserved in the created photons by increasing their frequency and thus momentum. The energy of a photon is known by the equation $E=hf$ with h being Planck's constant and f being the frequency.

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    $\begingroup$ Thanks. So still a spherical "expolsion" but with higher energy photons and no beam? $\endgroup$
    – TheDyingOfLight
    Commented Apr 21, 2019 at 13:29
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    $\begingroup$ Initial momentums determine the photons' "explosion" shape. If the matter/antimatter had equal opposite momentums, a spherical explosion of photons works as symmetry allows the momentums of the photons moving in all directions to cancel (top cancels the bottom, left cancels right, etc.) It may also be possible to have a beam if your initial frame didn't have total momentum at zero. If your bullet going right had more momentum than the leftward antimatter, the photons created would have net momentum to the right (a beam maybe). The less photons you create, the more high energy each one is. $\endgroup$
    – Eliot Behr
    Commented Apr 21, 2019 at 14:21

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