alt Hacker News> For instance, the fact that the laws of physics are the same today as they were yesterday and will be tomorrow — a symmetry known as time translation symmetry, represented by the Lie group consisting of the real numbers — implies that the universe’s energy must be conserved, and vice versa. “I think, even now, it’s a very surprising result,” Alekseev said.
Maybe I’m misunderstanding the implication here but wouldn’t it be much more surprising if that weren’t the case?
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It's funny you say that, because energy actually isn't conserved in general.
One somewhat trivial example is that light loses energy due to redshift since photon energy is proportional to frequency.
That symmetries imply conservation laws is pretty fascinating (see the Noether theorem). I guess it seems only strange it you assume already that the conservation law holds.
It is surprising that you can derive conversation laws entirely from the symmetry of lie groups, and that every conservation law can be tied to a symmetry.
> For instance, the fact that the laws of physics are the same today as they were yesterday and will be tomorrow
Don’t we just commonly assume this axiomatically but there’s no evidence one way or the other? In fact, I thought we have observations that indicate that the physics of the early universe is different than it is today. At the very least there’s hints that “constants” are not and wouldn’t that count as changing physics.