# Energy-Momentum Relation | Learn Physics

• actionintegral
In summary, the energy-momentum relation in physics states that the energy of a particle is equal to its momentum multiplied by the speed of light. It is derived using the principles of special relativity and is significant in understanding high-speed particle behavior. It cannot be violated as it is a fundamental principle in physics and is closely related to the concept of mass-energy equivalence.
actionintegral
Gentlemen,

I see where there is a relationship between energy and momentum in

$$E=\frac{p^2}{2m}$$

Ok. And I also see where there is a different relationship between energy and momentum in

$$E^2 = p^2c^2 + (m_{0}c^2)^2$$

fine. So there must be some abstract concept where E=E(p) in general. What is that concept called? And what do I search on to learn about it?

actionintegral said:
So there must be some abstract concept where E=E(p) in general. What is that concept called? And what do I search on to learn about it?

"dispersion relation"

The concept you are looking for is called the energy-momentum relation. It is a fundamental principle in physics that relates the energy and momentum of a particle. This relation is derived from the principles of special relativity and is described by the equations you have mentioned: E=\frac{p^2}{2m} and E^2 = p^2c^2 + (m_{0}c^2)^2. These equations show that the energy and momentum of a particle are closely related and cannot be considered separately. To learn more about this concept, you can search for "energy-momentum relation" or "relativistic energy-momentum relation" in physics textbooks or online resources.

## 1. What is the energy-momentum relation in physics?

The energy-momentum relation in physics is a fundamental concept that describes the relationship between energy and momentum of a particle. It states that the energy of a particle is equal to its momentum multiplied by the speed of light (c), according to Einstein's famous equation E=mc².

## 2. How is the energy-momentum relation derived?

The energy-momentum relation is derived using the principles of special relativity. It is based on the fact that the laws of physics are the same for all inertial observers and the constant speed of light in a vacuum. By applying these principles, we can derive the relationship between energy and momentum for a particle.

## 3. What is the significance of the energy-momentum relation?

The energy-momentum relation is significant because it helps us understand the behavior of particles at high speeds, close to the speed of light. It also plays a crucial role in many areas of physics, including particle physics, nuclear physics, and cosmology.

## 4. Can the energy-momentum relation be violated?

No, the energy-momentum relation cannot be violated. It is a fundamental principle in physics that has been extensively tested and proven to hold true in all physical processes. Any violation of this relation would contradict the laws of physics as we know them.

## 5. How does the energy-momentum relation relate to the concept of mass-energy equivalence?

The energy-momentum relation and the concept of mass-energy equivalence, as described in Einstein's equation E=mc², are closely related. Both concepts stem from the principles of special relativity and describe the relationship between energy and mass. The energy-momentum relation shows that a particle's energy is directly proportional to its momentum, while mass-energy equivalence shows that a particle's energy is also directly proportional to its mass.

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