That's not what Noether's theorem says. Time symmetry means that if you
put a time shift in the equations of evolution, then equations remain
valid. Not that the system state is static. In your interpretation any
process that conserved energy would leave the system unchanged and
explosions wouldn't conserve energy.
Brent
On 6/1/2025 4:38 AM, John Clark wrote:
On Sun, Jun 1, 2025 at 3:16 AM Alan Grayson <[email protected]>
wrote:
/> But the question persists; when photons redden as the universe
expands, where does the lost energy go? AG/
*The energy doesn't go anywhere, it's just destroyed, energy is not
conserved at the cosmic level. Noether's theorem says if there's a
symmetry, then there's a corresponding conservation law (but the
reverse does not necessarily hold, if there is a conservation law
there may or may not be a corresponding symmetry). *
*
*
*In the case of energy Noether says the corresponding symmetry is
time, at the cosmic scale if energy is conserved then the universe
should look the same from one time to another, but if the universe is
expanding it doesn't look the same from one time to another, and if
the universe is accelerating then time is even less symmetrical. So
energy is not conserved globally, however it's still true that at the
local level if things are at thermal equilibrium then the amount of
energy entering a finite volume of space will equal the amount of
energy leaving that volume.*
*
*
*John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
7ma
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