Adding momentum in STR and DSR?

[albatros]

How to add momentums in special theory of relativity? Is there same principle? And how to adding momentum in Double special relativity?

 

[Dale]

How to add momentums in special theory of relativity?

The sum of two four-momenta is the four-momentum formed by summing each component. I.e. standard vector addition.

 

[Entropia]

In special theory of relativity (STR), momentum can be added using the relativistic formula for momentum, p = mv/√(1-v^2/c^2), where m is the mass, v is the velocity, and c is the speed of light. This formula takes into account the effects of time dilation and length contraction, which are the principles of STR.

In double special relativity (DSR), there are two different principles at play - the Planck length and the Planck energy. These principles suggest that there is a maximum energy and a minimum length in the universe. To add momentum in DSR, one can use the modified relativistic equation for momentum, p = mv/√(1-v^2/c^2)(1-EL/E0), where E0 is the maximum energy and EL is the energy of the particle. This equation takes into account the effects of both time dilation and length contraction, as well as the principles of DSR.

In both STR and DSR, the principle of conservation of momentum still holds. This means that the total momentum before and after a collision or interaction must be equal. However, in DSR, this principle is modified to take into account the Planck length and energy.

To summarize, momentum can be added in STR and DSR using the relativistic formula for momentum, taking into account the principles of each theory. In DSR, the modified equation for momentum must be used to account for the Planck length and energy.