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## Is energy momentum tensor symmetric?

The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy-momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime.

### What is the relativistic relation between energy and momentum?

The energy–momentum relation is consistent with the familiar mass–energy relation in both its interpretations: E = mc2 relates total energy E to the (total) relativistic mass m (alternatively denoted mrel or mtot ), while E0 = m0c2 relates rest energy E0 to (invariant) rest mass m0.

#### Is stress energy tensor always symmetric?

The stress-energy tensor is a symmetric matrix. If we have a nonzero Ttx, it represents a flux of mass-energy (pt) through a three-surface perpendicular to x. This means that mass is moving in the x direction.

Is momentum equal to energy?

Therefore, we can say that a body’s kinetic energy is equal to the product of momentum and half its velocity. It is the relation between linear momentum and kinetic energy of a substance.

What’s the difference between momentum and energy?

One of the most obvious differences between kinetic energy and momentum is that kinetic energy depends quadratically on velocity (it increases as v2), while momentum depends linearly on velocity (it increases as just v). This means that kinetic energy actually increases way faster with velocity as momentum does.

## Why is energy momentum a tensor?

The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.

### Is momentum a energy?

Common mistakes and misconceptions. Some people think momentum and kinetic energy are the same. They are both related to an object’s velocity (or speed) and mass, but momentum is a vector quantity that describes the amount of mass in motion. Kinetic energy is a measure of an object’s energy from motion, and is a scalar …

#### What is the physical meaning of the energy-momentum tensor?

This is the energy-momentum tensor, also known as the stress-energy tensor for the dust. Physical meaning of the energy-momentum tensor Because the stress–energy tensor is of order two, its components can be displayed in 4 × 4 matrix form: As seen previsouly, T tt represents the density of relativistic mass, i.e the energy density.

Where does the energy-momentum relation come from?

Origins and derivation of the equation. The Energy–momentum relation was first established by Paul Dirac in 1928 under the form = + +, where V is the amount of potential energy. The equation can be derived in a number of ways, two of the simplest include:

How are the components of the stress-energy tensor represented?

Because the stress–energy tensor is of order two, its components can be displayed in 4 × 4 matrix form: As seen previsouly, T tt represents the density of relativistic mass, i.e the energy density. But what can represent all the other 15 components of the energy momentum tensor?

## How is invariant mass related to energy and momentum?

Total energy is the sum of rest energy and kinetic energy, while invariant mass is mass measured in a center-of-momentum frame. , where total energy in this case is equal to rest energy (also written as E0 ). The Dirac sea model, which was used to predict the existence of antimatter, is closely related to the energy–momentum relation.