# Adding momentum in STR and DSR?

• albatros
In summary, momentum is a physical quantity that describes an object's motion and is calculated as the product of its mass and velocity. It affects an object's resistance to change in motion, with higher momentum making it harder to change velocity. In the Special Theory of Relativity (STR), momentum is calculated as p = mv for non-relativistic speeds. In Dual-Speed Relativity (DSR), the modified equation p = (m0v)/√(1-v^2/c^2) is used to account for relativistic speeds. Momentum is important in both theories to explain the behavior of objects in motion.

#### albatros

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

albatros said:
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.

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.

## 1. What is momentum in physics?

Momentum is a physical quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity.

## 2. How does momentum affect an object's motion?

Momentum is a measure of an object's inertia, or resistance to change in motion. The more momentum an object has, the harder it is to change its velocity.

## 3. How is momentum calculated in Special Theory of Relativity (STR)?

In STR, momentum is calculated using the equation p = mv, where p is momentum, m is mass, and v is velocity. However, this equation only applies to objects with non-relativistic speeds.

## 4. How is momentum calculated in Dual-Speed Relativity (DSR)?

In DSR, momentum is calculated using the modified equation p = (m0v)/√(1-v^2/c^2), where p is momentum, m0 is the rest mass of the object, v is velocity, and c is the speed of light. This equation accounts for relativistic speeds and is a more accurate representation of momentum in DSR.

## 5. Why is momentum important in both STR and DSR?

Momentum is an important concept in both STR and DSR because it helps us understand the behavior of objects in motion. In STR, momentum is used to explain the effects of mass and velocity on an object's motion. In DSR, momentum is crucial to accurately describe the motion of objects with relativistic speeds.