Are momentum and energy together conserved?

  • $\begingroup$ try reading up hyperphysics.phy-astr.gsu.edu/hbase/conser.html $\endgroup$ – anna v Jun 18 '18 at 15:43
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    $\begingroup$ Do students study landau lifshitz pseudotensor in class 12 nowadays? If you understand that, why are you asking for a simple answer? $\endgroup$ – sammy gerbil Jun 18 '18 at 17:19
  • $\begingroup$ Possible duplicate of How can momentum but not energy be conserved in an inelastic collision? $\endgroup$ – sammy gerbil Jun 18 '18 at 17:26
  • $\begingroup$ I had seen a video on noethers theorem and in that video this landau lifshitz pseudotensor was mentioned so i just wanted to know what it is $\endgroup$ – Ayu Jun 20 '18 at 5:06
  • $\begingroup$ In relativity, energy and momentum can have different values from frame to frame, but $E^2-p^2$ is always $m^2$, m is mass and it is an invariant quantity. $\endgroup$ – Andrei Geanta Jun 20 '18 at 6:32

Your question says that momentum and energy are together conserved.

The question does not specify if you are asking about a closed system's (like a galaxy cluster) total energy level or about micro interactions (particle) energy level as per QM.

  1. First, let's take the micro interactions as per QM:

This is only true for an elastic interaction, like elastic scattering. It is the typical case when a photon hits an atom and the photons energy is conserved, only its direction is changed. Rayleigh scattering is like that.

For an inelastic interaction, like inelastic scattering, Compton scattering, only momentum can be conserved, but energy not. When a photon hits an atom, and the photon gets inelastically scattered, its energy will change, but its momentum could be conserved.

Please see here:


  1. Now let's take a closed system's total energy level:

Though our universe is not closed, so its energy level is not conserved, we can select areas of space, like a galaxy cluster, which we can say is a local area as per GR, and so it's total energy level will be conserved.

  • $\begingroup$ Kinetic energy may not be conserved, but in a closed (local) system, total energy is always conserved. $\endgroup$ – PM 2Ring Jun 19 '18 at 6:59
  • $\begingroup$ @PM 2Ring this is only true for a closed universe, but the one we are living in, on the universe's level, total energy is not conserved, and on the micro level, only elastic interactions can do that. $\endgroup$ – Árpád Szendrei Jun 19 '18 at 17:05
  • $\begingroup$ That's why I said "(local)". In GR, energy is conserved locally. $\endgroup$ – PM 2Ring Jun 19 '18 at 17:11
  • $\begingroup$ I think the OP is asking about interactions, and not systems, but that should be clarified more whether the question is about a system's energy level as per GR, or a micro interaction's energy level as per QM. I will edit my answer. $\endgroup$ – Árpád Szendrei Jun 19 '18 at 17:23
  • $\begingroup$ The universe is composed of these galaxy cluster and if these galaxy's energy is conserved then why the total energy of universe not conserved $\endgroup$ – Ayu Jun 20 '18 at 5:27

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