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We know from the first law of thermodynamics that the amount of energy in the universe is conserved. However, doesn't this law presuppose that the amount of energy in the universe is a finite quantity of Joules?

As David Hume reasoned, all of science depends on inductive generalization. But wouldn't it be a fallacy of hasty generalization to conclude from models and experiments where the quantity of joules are finite and contained by an adiabatic wall that therefore the universe at large is like this?

ArtIntoNihonjin.
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Ideally, yes. Energy is conserved, so all interactions just release (e.g. chemical reactions) shift and distribute energy around. But the sum should stay the same. All stored chemical energy sources will eventually be exhausted, heat exchanges between any bodies at different temperatures will keep happening until the whole universe is in thermal equilibrium. Maximum entropy. No more thermal exchanged. Heat death of the Universe.

However, energy is not conserved in the Universe.

This is because of General Relativity and the (accelerated) expansion of the Universe. The universe is expanding, which means that something is driving the expansion - dark energy. But the expansion is accelerating, so this dark energy is somehow increasing. From where? Nobody really knows.

If you have physics background, then you will know that energy conservation is linked to time invariance of the Hamiltonian. From Noether's theorem, the conserved charge in time translations is the energy of the system. Since the accelerated expansion of the universe breaks the time translation invariance of the system (i.e. the whole universe), energy in said system is not conserved.

SuperCiocia
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