Relativistic Angular Momentum?

[LarryS]

What is the mathematical definition of Angular Momentum in Special Relativity? Is there a definition that does not require knowledge of two-forms, tensors, etc.? As always, thanks in advance.

 

[meopemuk]

What is the mathematical definition of Angular Momentum in Special Relativity? Is there a definition that does not require knowledge of two-forms, tensors, etc.? As always, thanks in advance.

The total angular momentum of any system of massive spinless particles is

$$\mathbf{J} = \sum_{i}^N \mathbf{r}_i \times \mathbf{p}_i$$

where $\mathbf{r}_i$ are particles positions and $\mathbf{p}_i$ are their momenta. This definition is valid in both non-relativistic and relativistic mechanics.

 

[Entropia]

Relativistic angular momentum is the measure of rotational motion in the context of special relativity, which is the theory that describes the relationship between space and time. It takes into account the effects of high speeds and strong gravitational fields on the motion of objects.

In special relativity, the mathematical definition of angular momentum is given by the following formula:

L = r x p

where L is the angular momentum, r is the position vector, and p is the momentum vector. This formula is similar to the classical definition of angular momentum, but it takes into account the relativistic effects of time dilation and length contraction.

This definition does not require knowledge of two-forms, tensors, or other advanced mathematical concepts. It is a simple and intuitive way to understand the concept of angular momentum in special relativity. However, in order to fully understand and apply this definition, a basic understanding of vectors and vector operations is necessary.

In addition to this mathematical definition, there is also a physical interpretation of angular momentum in special relativity. It is defined as the amount of rotational energy that an object possesses due to its motion in a curved space-time. This interpretation is closely related to the concept of spacetime curvature, which is a fundamental aspect of general relativity.

In conclusion, the mathematical definition of angular momentum in special relativity is simple and does not require advanced mathematical knowledge. However, a basic understanding of vectors and spacetime curvature is necessary to fully grasp the concept. Ultimately, the concept of relativistic angular momentum is essential for understanding the behavior of objects in extreme environments, such as near black holes or at high speeds.