# What is the reason behind why energy must always be conserved, apart from observation? [duplicate]

I know that we see in experiments (physical and thought) that energy is always transformed into something else, but what propels our universe to behave this way? What is happening at small levels that only allows conservation as a possible outcome and not destruction of energy?

Update: Based on a given answer stating that energy is mass, I should probably then expand this question into "Why must mass must always be conserved?"

• How do you define energy at the general level if not as that which is conserved through time translations by Noether's theorem? Feb 27 '16 at 23:51
• @GyroGearloose Mass is the length of the energy-momentum four-vector. The mass of a system is not the sum of the masses of the parts (the length of a sum of vectors isn't of the sum the lengths) and since energy and momentum aren't conserved, neither is mass. So it isn't conserved. Feb 27 '16 at 23:53
• Possible duplicates: physics.stackexchange.com/q/19216/2451 , physics.stackexchange.com/q/2690/2451 and links therein. Feb 28 '16 at 0:14
• Mass is a form of energy; mass alone is not conserved. The Noether theorems, derived from analytical mechanics, tell us that conserved quantities come from symmetries: conservation of momentum comes from translational symmetry (homogeneity of space) ; conservation of angular momentum comes rotational symmetry (isotropy of space); and conservation of energy comes from a temporal symmetry (laws of mechanics do not change with time). So that is the deeper meaning. See en.wikipedia.org/wiki/Noether%27s_theorem Feb 28 '16 at 1:11
• @GyroGearloose If you want a tutorial about what mass is, any book that covers Special Relativity in depth should go into it. If you want a tutorial about the lack of conservation of energy and momentum then any book that covers General Relativity in depth should go into it. The covsriant divergence of the Stress-Energy tensor is zero, but the divergence of the Stress-Energy tensor would give you conservation. But it's worse, energy and momentum don't even exist in General Relativity, only energy density and momentum density fields and there isn't a frame invariant way to add them up. Feb 28 '16 at 1:45

So there isn't an energy of the universe. And there isn't a momentum of the universe. And even if there were, they could be infinite. And even if it when they are finite, then the mass would satisfy $$(mc^2)^2=E^2-(\vec p c)^2$$ and the mass of the universe would not equal the sum of the masses of the parts. And since the energy and momentum would change over time, the mass usually changes over time.