Elastic relativistic collisions

[Amith2006]

# In a perfectly elastic relativistic collision, which one of the following quantities is not conserved:
a)Momentum
b)Energy
c)Rest mass
d)Angular momentum
In non relativistic elastic collisions, energy and momentum will be conserved. But I don’t know about relativistic elastic collisions. Could anyone please clear my doubt? Can we apply the Newtonian concepts in these cases? Suppose the collision is inelastic (relativistic), then which quantity will be conserved?

 

[quasar987]

I'm puzzled. As far as I know, there is no way to prove conservation of momentum. However, experiments confirm that relativistic momentum is conserved in inelastic collisions (such as particle collisions). Rest mass is conserved by definition of an inelastic collision. Energy is $\sqrt{p^2c^2+m^2c^4}$ so it is conserved since p and m are. Regarding the angular momentum, if you take the coordinate system in which the collision is monitored to have its origin at the point of collision, then angular momentum before and after the collision are 0. So, angular momentum is conserved too.

 

[kyle8921]

In a perfectly elastic relativistic collision, all of the listed quantities are conserved. This includes momentum, energy, rest mass, and angular momentum. This is because in a perfectly elastic collision, there is no loss of energy or mass, and all of these quantities are conserved.

In non-relativistic elastic collisions, we can apply Newtonian concepts to calculate momentum and energy. However, in relativistic elastic collisions, we need to use the principles of special relativity to accurately calculate these quantities.

If the collision is inelastic (relativistic), then only momentum and rest mass will be conserved. Energy and angular momentum may not be conserved due to the loss of energy and changes in direction of motion during the collision. In this case, we would need to use the principles of special relativity to accurately calculate the changes in these quantities.