What Happens in a Relativistic Particle Collision?

[itsjustme]

Suppose 2 particles are heading towards each other at a speed very close to the speed of light (relative to a stationary observer). Relative to the observer they would collide at a given point. But if you look at it relative to one or the other particle, the collission would happen elsewhere. What exactly happens?

 

[JesseM]

Suppose 2 particles are heading towards each other at a speed very close to the speed of light (relative to a stationary observer). Relative to the observer they would collide at a given point. But if you look at it relative to one or the other particle, the collission would happen elsewhere. What exactly happens?

Why do you think the collision would happen elsewhere? Suppose in the stationary observer's frame the two particles are at equal distances from the observer, so they both collide at the same position the observer is standing. Either particle sees the stationary observer coming toward it at close to the speed of light in its own frame, and the other particle coming toward it in back of the stationary observer at even closer to the speed of light, with both the stationary observer and the other particle reaching the first particle's position at the same moment, so they also agree that all three come together at the same point in space and time.

 

[itsjustme]

Well i was thinking that seeing as Particle A is moving at a speed close to that of light, relative to Particle A, both the observer and Particle B would appear to be going at that speed seiing as it is impossible to go faster than the speed of light.

 

[JesseM]

Well i was thinking that seeing as Particle A is moving at a speed close to that of light, relative to Particle A, both the observer and Particle B would appear to be going at that speed seiing as it is impossible to go faster than the speed of light.

You can use the velocity addition formula...if both particles are moving at speed v relative to the middle observer, then in the particle's own frame the observer will be coming towards it at v while the second particle will come towards it a bit faster, at (v + v)/(1 + v*v/c^2). No matter what frame you choose the timing will work out so they all meet at the same spot though.

 

[itsjustme]

ok, thanks