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mesouschrist t1_jct3knw wrote

Reply to comment by fr293 in We're often taught that objects travel to lower energy states to reach stability. But the energy of the universe is constant - doesn't that just mean other surrounding things go to higher energy states? What decides which thing gets to have low energy? by SMM-123Sam

The energy of the universe is constant under the assumption that there are laws of physics that apply to the universe across all times (i.e. the motion of things in the universe can be explained without an explicit time dependence, like the gravitational constant shrinking with time without any underlying reason). Energy is the conserved quantity associated with time invariant laws of physics. So if you think energy is decreasing or increasing, you just have the wrong definition of energy (like when a ball rolling across the table slows down, it's lost energy, but really the energy has gone somewhere else).

It doesn't matter whether or not the system is relativistic - certainly energy is still conserved in special and general relativity. But I'd be curious if you could elaborate on what you were thinking there.

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cygx t1_jctjza4 wrote

Due to the metric expansion of space, the universe is not time translation invariant at cosmological scales, hence no energy conservation via Noether's first theorem. However, Noether's second theorem still applies due to general covariance, and you get an 'improper' / 'strict' (terminology differs) conservation law for any time-like vector field (in case of cosmological time, this yields the first Friedmann equation). However, these laws are non-covariant as they include gravitational contributions that cannot be localized via a stress-energy tensor. It's somewhat similar to what happens to energy conservation in rotating frames of reference, except that there's no longer such a thing as inertial frames that make energy conservation manifest. Consequently, a large portion of physicists find it less confusing to just state that energy conservation doesn't hold for the universe at large.

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fr293 t1_jctq3cv wrote

What my man cygx said. But more generally, I wanted OP to articulate the principles that they were using to arrive at their conclusion. It’s a fool’s errand to answer a question without understanding the context that produced it.

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