Four Momentum
Created | Updated Nov 4, 2010
History
Four momentum is mentioned in Einstein's special theory of relativity.
When he published his theory of relativity, Einstein realised that he could have defied one of the oldest branches of physics and mathematics. Vector mechanics. He worked to find a solution and four
momentum was it.
Concept
The concept is that a translation to occur in space would not be of a vector, as space-time is 4 dimensional so you could not be able to translate an object in space without moving it in time aswell.
This requires a new type of vector that specifies each of these dimensions, the 3 of motion and the 1 of time. Four momentum created a new type of vector so it did not defy vector mechanics.
Notation
The way a standard 2 dimensional vector works is when translating an object accross a 2 dimensional sheet or graph. They are notated with a movement upwards or downwards and a movement of sideways.
A 2d vector telling you to go up 2 units of distance and left 3 units of distance would be- (2/-3). The minus is used to bring an object to the inverse of the default.
A four momentum vector states upward, sideward, diagonal and temporal movement. Therefore a vector for 2 up, 3 left, 4 diagonal left and 3 timeparts forward would read- (2/-3/-4/3).
Proving
We know that if you move an object further away it travels in time. For instance we know that it takes about 8 minutes for the Sun's light to reach the Earth meaning that the Earth is 8 light minutes away from the Sun. But if we were further out, then it would take longer for the Sun's light to reach us, so it is further away temporally aswell as spatially.
What Exactly Is It?
Four momentum is a way of explaining regular momentum in four dimensional space. The problem was that regular momentum didn't explain the 1 dimension of time. So a new type of momentum was discovered to explain the temporal dimension according to Einstein's laws, it was called four momentum.
