On Wednesday, September 4, 2019 at 10:03:44 AM UTC-5, John Clark wrote:
>
> On Tue, Sep 3, 2019 at 11:01 PM Alan Grayson <[email protected]
> <javascript:>> wrote:
>
> *> Just sum over the estimated total of 10^80 particles, using mc^2 by
>> first estimating the average mass of those particles for the rest energy,
>> adding their average potential gravitational energy and their average
>> kinetic energy. Why not? AG*
>>
>
> What about the energy in light, it's being redshifted by the expanding
> universe and thus becoming weaker, where did all that energy go? I would
> maintain the energy went nowhere it was just destroyed. When looked at
> at the scale of the entire universe why would anyone even expect energy to
> be conserved? Noether's Theorem says if there is time-translation
> invariance, that is to say if things generally look about the same from one
> time period to another, then matter-energy is conserved, but in our
> expanding accelerating universe things don't look the same. So it might be
> better to say that in general relativity spacetime can create energy, as it
> does when it accelerates the expansion of the universe, or destroy energy,
> as it does when it redshifts photons in a expanding universe). So energy
> simply isn’t conserved globally at the level of the entire cosmos, although
> it is locally at least approximately.
>
> John K Clark
>
I would argue it goes into the gravity field. The expansion of space
stretches the wavelength of photons and the loss of energy in the photon is
taken up by gravitation in the form of Λg_{ab} for Λ the cosmological
constant.
The lack of Killing vectors in a type O spacetime of a cosmology, which
also happens with type N and III, just means there is no Noether principle
of symmetry associated with time translation. That is what conserves
energy. This does have some odd prospects, such as for k = 1 spacetime with
positive spatial curvature, where space is a sphere, then the expansion of
that space means for a constant vacuum energy density that vacuum energy is
being generated out of nothing. For k = 0 the spatial surface is flat and
infinite and while expanding the vacuum energy adjusts by a multiplier of
"infinity," which is not observable. In fact either way a local observer is
bounded by the cosmological horizon and that will bound observations to a
finite vacuum energy.
LC
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