On 6/1/2025 6:26 PM, John Clark wrote:
On Sun, Jun 1, 2025 at 8:35 PM Brent Meeker <[email protected]> wrote:
//
/> 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. /
*That's what I said!**If there's a symmetry then there's a
corresponding conservation law, equations remain valid because
something has been conserved, and in the case of time it is energy.
*
What I was objecting to is you wrote, "... if energy is conserved then
the universe should look the same from one time to another..." which is
the converse of your (correct) statement below. This is an interesting
point. Expansion of the universe is a failure of time symmetry that
allows, but does not imply, failure of energy conservation.
Brent
**
/> In your interpretation any process that conserved energy would
leave the system unchanged/
*And I also saidthat if all you know is that there is a conservation
law then Noether's theoremcan you tell you nothing. It only works one
way. *
*
*
*John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
ugg
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.*
*
*
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