Energy-Momentum Relation | Learn Physics

[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?

 

[vanesch]

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"

 

[charng]

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.