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	''Mathematical counterpart: [[Noether's theorems/Applications/Photon energy in an expanding universe\|Photon energy in an expanding universe]].''		''Mathematical counterpart: [[Noether's theorems/Applications/Photon energy in an expanding universe\|Photon energy in an expanding universe]].''
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	''No mathematics is used on this page. The mathematical treatment is on the		''No mathematics is used on this page. The mathematical treatment is on the
	counterpart page named above.''		counterpart page named above.''

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NT>NoetherVolumeBuild: Noether theorems volume, initial import (B-32)

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Noether theorems volume, initial import (B-32)

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{{DISPLAYTITLE:Where the light's energy goes}}

''Mathematical counterpart: [[Noether's theorems/Applications/Photon energy in an expanding universe|Photon energy in an expanding universe]].''

Light from a distant galaxy arrives redder than it left. Redder means less
energetic. So where did the energy go?

The honest answer is that the question is malformed, and seeing why is the best
single illustration of what these theorems actually claim.

== The universe is expanding ==

Distances between galaxies grow. Not because the galaxies are flying apart through
space, but because the space between them is getting bigger. There is a number
that says how much bigger — call it the stretch factor — and it increases with
time.

Now ask which symmetries this universe has, in the sense of
[[Noether's theorems/Explainers/Symmetries of a curved space|the curved space
page]]: which directions can you slide it along without distorting anything?

'''Sliding through space: yes.''' The universe looks the same everywhere. Move to
a different place and nothing about the geometry has changed.

'''Sliding through time: no.''' Move to a different time and the stretch factor is
different, so distances are different. The geometry is not the same. Time
translation is not a symmetry of an expanding universe.

== So there is no conserved energy ==

That is the whole answer, and it is one sentence.

[[Noether's theorems/Explainers/Why energy and momentum are conserved|Energy is
conserved because time is uniform]]. In an expanding universe time is not uniform —
the rules governing how far apart things are genuinely differ between one era and
the next. The condition fails, so the conclusion does not follow.

Nothing broke. A conditional statement was applied to a case that does not meet
its condition, and it correctly returned nothing.

== What is conserved, and what it implies ==

Space is still symmetric, so something does survive.

What survives is momentum measured against the '''grid''' — against the coordinate
labels of the expanding universe, rather than against physical distance. That
quantity is exactly constant, by the result on the curved space page: one symmetry
direction, one conserved quantity along every path.

But physical distances are grid distances multiplied by the stretch factor. So
physical momentum is grid momentum divided by the stretch factor, and as the
universe grows, physical momentum falls in proportion.

For light, energy and momentum are the same thing up to the speed of light. So the
energy of a photon falls in inverse proportion to the stretch factor. Double the
size of the universe and every photon in it has half the energy.

'''That is the redshift, derived from a symmetry count and nothing else.'''

== Where the energy goes ==

Nowhere.

The instinct is to look for it — in the gravitational field, in the expansion, in
some reservoir. That search assumes energy must be conserved and asks where it
went. The theorem says the assumption was the mistake.

It is worth sitting with how unusual that is as a piece of physics. Ordinarily,
when a quantity seems to disappear, you look harder. Here the theorem licenses you
to stop looking, and to say with confidence that there is nothing to find, because
the symmetry that would have guaranteed the conservation is demonstrably absent.

== Not the same as the gravity problem ==

On
[[Noether's theorems/Explainers/Why gravity has no local energy|the gravity page]]
energy conservation also fails, and for a completely different reason: the symmetry
is present but swallowed by a local one, so the conservation law exists and is
empty.

Here the symmetry is simply not there. Same theory, two unrelated failures, and
they are constantly conflated.

== A check you can do ==

The result has a consequence that can be tested against something else you may
know, which is a good sign it is not sleight of hand.

Ordinary matter thins out as the universe expands. Double the size and the same
particles occupy eight times the volume, so the density of matter falls by a
factor of eight — the cube of the stretch.

Radiation thins out faster. Double the size and the density of radiation falls by
a factor of sixteen: the same cube from the volume, and '''one extra factor from
the redshift''', because each photon also carries less energy than before.

Those two rates are different, and the difference is exactly the effect derived on
this page. It is not a separate fact about light; it is the same fact, showing up
in the bookkeeping of the whole universe.

It also has a consequence for history. Going backwards in time, radiation gains on
matter, and far enough back it dominates. The early universe was radiation's, and
matter took over later. That transition is a real, dated event in cosmology, and
its existence traces back to the missing symmetry on this page.

''No mathematics is used on this page. The mathematical treatment is on the
counterpart page named above.''

Noether's theorems/Explainers/Where the light's energy goes - Revision history

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