what is the difference between relitivistic and nonrelitivistic momuntum?

Answer 1

In classical mechanics, mass, length and time were considered to be absolute.

They will be the same for two observers who are moving relative to each other.

If m0 is the mass of a particle and v is the velocity of the particle, then the momentum is m0v for both the observers, in classical mechanics.

But now, we know that the mass length and time are not absolute and they are relative to each other. Therefore, the mass of any object increases with its speed with respect to an observer who is relatively at rest.

In other words the observer at rest will say that the mass of a moving body increases with its speed.

Therefore according to this observer, the momentum of a moving body with velocity v, whose mass has increased from m0 to m is not m0v but mv.

Though the momentum is mass times the velocity, the mass is not the same which when it was at rest. The new mass is now m0 / sq.root of (1- B^2) where B is the ratio of the speed of the particle with respect to the stationary observer to the speed of light which is the same for all observers.

Thus momentum is {m0 / sq.root of (1- B^2)} x v.

Answer 2

In classical mechanics, momentum is straight forward and relatively simple (no pun intended).

In relativistic theory - time and distance are diluted and mass is increased as the speed of light is approached. Not quite so intuitive compared to our everyday experiences and observations.

And the equations are equally different when speeds become extreme.

Note: Quantum mechanics is often referred to as the non-relativistic theory.

Answer 3

Imagine something weird: the faster you go the heavier you become (at least to a stationary obsever watching you running past him/her).

Paradoxical! You should lose weight when you run.

But this is trully the case! Einstein showed it. This accounts for the relativistic momentum which considers that your mass changes as you increase speed.

In non relativistic momentum, which is wrong, it is assumed that you mass stays constant at any speed.

Answer 4

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Answer 5

classical momentum in the x-direction is just mv.

relativistic momentum in the x-direction is mv/sqrt(1-v^2/c^2)

Answer 6

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