Cosmic Redshift and Photon Energy

[Quadrazar]

When a photon travels cosmomogical distances, it gets a cosmological redshift. Easy to explane it when you think of it as the wavelength being stretched by expanding space, but what if you looked at this from an energy point of view? The energy that went in to creating the photon is smaller than the energy gained by absorbing the photon.

E^emit > E^recieve

Where did the energy go to? To me it seems that the concervation of energy principle is violated, Unless the energy lost by the photon was used to expand the space it moved trough.

ΔEnergy → Δspace

But if this is the case, why isn't all the space expanding? Only the intergalaxtic space seem to expand. (maybe innergalaxtic space is already stretched to the max (a sort of saturation), of gravity prevents it to expand)


For a moment let's assume that the energy loss is (in some degree) contributing to the expansion of space. Could this be a two way process? Could a low energy photon gain some energy when it travels trough expanded space, and in the process contract it a little? In that case a cosmological blueshift is possible for very low energy photons . In this perspective you could see space as the medium that nature creates to stores some of it's energy.

It's a complete crackpot idea, I know, but (to me) it's a fun one to think about. I just wanted to put it on the table for an open discussion, not as an ATM idea. I don't see it colliding with any mainstream theories (maybe it collides with GR, but GR is out of my comfort zone).

[caveman1917]

To me it seems that the concervation of energy principle is violated

There is no global conservation of energy in GR, it is in fact impossible to even unambiguously define a global concept of energy. Conservation of energy only holds locally.

Another way to notice this is to think of dark energy, the energy density of the vacuum. If the universe grows and the energy density remains constant, then the total energy increases. It's related to the principle that energy and momentum are conserved in SR in each reference frame seperately, but in GR those reference frames have only a local extent.

[TooMany]

There is no global conservation of energy in GR, it is in fact impossible to even unambiguously define a global concept of energy. Conservation of energy only holds locally.

So energy can disappear globally? It's curious because the energy was conserved locally when a photon is emitted, but it gradually dissipates due to expansion? On the other hand when the photon arrives and the source was very far away, the photon must have sacrificed some kinetic energy to reach us from a source moving away from us so fast. Is this an equivalent statement? Or is the source not really moving away? GR is hard to get.

Can energy also appear out of nowhere globally? What about matter since it has an energy equivalent?

[Jeff Root]

When someone observes a redshifted photon, he is
moving relative to the object which emitted the photon.
If he matched speed with the object, there would be no
redshift. The photon doesn't lose energy. It is just
that all observers are moving away from all emitters,
giving them all different reference frames, making it
impossible to account for the energy of all the photons
simultaneously.

-- Jeff, in Minneapolis

[Tensor]

So energy can disappear globally? It's curious because the energy was conserved locally when a photon is emitted, but it gradually dissipates due to expansion?

It doesn't disappear. It's simply that different frames of reference "see" different amounts of energy. You may see it explained as a time dilation effect also. But that is also frame dependent. I can point you to several sources that can provide the gory mathematical details, if you want them.

On the other hand when the photon arrives and the source was very far away, the photon must have sacrificed some kinetic energy to reach us from a source moving away from us so fast. Is this an equivalent statement? Or is the source not really moving away?

Again, it's simply a matter of different frames of reference measure different amounts of energy. This is one of the problems of trying to explain the math, using words. Or, how an analogy breaks down when you try to push it too far.

GR is hard to get.

Yes it is. And you will never get it from an "explain it to me with words" type of explanation. It took me four years, part time, just to get the prerequisites to get to the point where I could start studying the math needed for GR. Two more years for that math and then I was finally working on GR. I worked on that for several years on my own until circumstances force me to give it up. And at that point, I knew just enough to be dangerous. Now, after several years on not studying it, I've forgotten quite a bit and know even less and are even more dangerous. You may get through it faster if you have access to an actual university. From my point of view, Caveman seems to have a good grip on it.

Can energy also appear out of nowhere globally?

It would depend on what you mean by energy appearing out of nowhere. In the case of a Big Crunch universe, as the universe collapses, there would be a cosmological blue-shift. Is this what you are talking about? If it is, this would again, simply be a measurement of different energies in different frames of references.

What about matter since it has an energy equivalent?

What about it? You need to be a more specific.

[Quadrazar]

When someone observes a redshifted photon, he is
moving relative to the object which emitted the photon.

hi jeff, thanks for joining the discussion.

There is more then one possible cause for photons to get redshift.
- redshift due to movement (as you described)
- gravitational redshift (redshift of overcomming a gravitational field)
- cosmic redshift. (redshift created by expanding space)

If he matched speed with the object, there would be no
redshift. The photon doesn't lose energy.

I know and I agree but concider this:
Galaxies drift appart due to te expansion of space, not because they are moving appart. In a sense they remain stationary¹. Otherwise some galaxies would 'speed away' from us at speeds greater then the speed of light. (general concensus is that no reference frame would allow the speed to be greater then 'c', I believe).

If there is no significant speed between us and distant galaxies, the photons shouldn't loose energy. Just like you you said.
(I would dare to say that for a cosmic redshift, energy is getting dumped somewhere along the road the photon takes).


¹ when I say stationary, it includes the 'minor' movement of galaxies relative to eachoter like the one we can detect in our local cluster of galaxies.

[Jeff Root]

Cosmic redshift is what I was talking about. The idea
that galaxies are not moving relative to each other is a
convention which makes some analysis techniques more
convenient. Galaxies do get farther apart from each
other, whether the reason is expansion of space or not.
I assume here that it is.

I'm not sure whether there is a gravitational redshift due
to the decreasing density of the Universe or not. If there
is, that should be included too, but I believe it would be
a fairly small factor (about 1 or 2 percent).

In order to match speeds with a distant object, one would
have to take into account the expansion of space between
the object and the observer over the path the light took.
That automatically accounts for all of the observed cosmic
redshift except possibly the little bit due to gravity.

-- Jeff, in Minneapolis

[Quadrazar]

Galaxies do get farther apart from each
other, whether the reason is expansion of space or not.
I assume here that it is.

Cosmological timedilation observed on distant supernova's is a very convincing data to accept that space is expanding. (so we are on the same line here)

In order to match speeds with a distant object, one would
have to take into account the expansion of space between
the object and the observer over the path the light took.
That automatically accounts for all of the observed cosmic
redshift except possibly the little bit due to gravity.

the redshift observed from distant galaxies (z_total) is the sum of three parts:

z_total = z_grav + z_{relative dopler} + z_comological (EDIT: should be product see post12)


If you isolate the z_comological and zoom in to it, it facinates me

1+z_comological = a_now / a_then

a = the expansion factor of the universe


It's possible to state, that te expansion of space changed the Electromagnetic Energy of the photon. It's a cause and effect sitiation. But can we be shure that it is cause and effect? Could it be that the energy leaving the photon is the cause of space expanding. (or that it is just a proces that happens, that neither is the prefered cause).

[caveman1917]

So energy can disappear globally?

Putting it that way is slightly misleading, energy cannot be unambiguously defined globally in general.

I'll try an explanation.

What we consider "conservation laws" are in fact symmetries of the spacetime (the "fabric of the universe" we are considering).

The term symmetry of the spacetime basically means that the universe looks the same if i do something. For example, if i turn around the universe keeps looking the same, so we term this a rotational symmetry (along the axis from my head to my feet, there are 3 such axes in a 3 dimensional space of course). Another example would be if i go towards some direction the universe also keeps looking the same, this we then call a translational symmetry along that direction (translational in this context just means moving to a different point, there are of course also 3 directions in which to do that).

Each of these symmetries can be represented by a vector, which is basically an arrow pointing in a certain direction that has a certain length, called the norm of the vector. If this vector represents such a symmetry we call it a Killing vector.

Alright, so much for the terminology

Each of those symmetries corresponds to a certain conservation law, showing this is quite daunting mathematically so you'll just have to believe me on it, or you could look up Noether's theorem which is the basis for that. They are conservation of momentum in 3 directions for translational symmetry in those directions, conservation of angular momentum on 3 axes for rotational symmetry on those axes and conservation of energy for translational symmetry in the time direction. This last one, translational symmetry in the time direction may seem a bit strange, but it merely means that if i go forward/backward in time the universe keeps looking the same.

Representing these symmetries with Killing vectors enables us to define the related concept. For example energy is the norm of the Killing vector pointing in the time direction, etc. Since this vector represents a symmetry, its norm is constant and can be used to quantify the concept used. So we can define energy as the norm of the timelike Killing vector, and since that is constant we have conservation of energy. Likewise for all the other conservation laws.

Having that we can see which conservation laws exist for the universe. If we go forward/backward in the time the universe certainly looks different (it expanded or contracted), so time symmetry and thus conservation of energy is out. If we turn around on all 3 axes the universe does keep looking the same, so we have all rotational symmetries and conservation of angular momentum on all axes. If we move to some other location in all 3 directions the universe keeps looking the same, so we have all spatial translational symmetries and conservation of momentum in all directions. With this last one it should be noted that the norm of the translational Killing vector is constant in comoving coordinates, not proper coordinates, so there appears to be a "loss of momentum" tied to the expansion of the universe.

The reason why we have all conservation laws locally, is because locally we can think of the universe as flat. Compare this to a map of the earth, if you stay local (eg within a single city) then a flat map is an accurate representation. However globally this fails, since all flat maps will start to have distortions on a global scale. So when we consider a local patch of the universe, we need to only consider a flat spacetime without any bells and whistles, known as minkowski space. This one has all symmetries, thus all conservation laws, and so locally we will have conservation of energy.

This doesn't mean that it's impossible to have global conservation of energy, it just depends on the "thing" you're considering. For example consider a black hole (in an otherwise empty universe). If we go forward/backward in time, the black hole just keeps sitting there looking exactly the same. So in that case we do have global conservation of energy, even though the spacetime around a black hole is highly warped. The set of all spacetimes that have global conservation of energy is called stationary spacetimes, to throw in some more terminology.

You can even have some stranger spacetimes. Take for example a rotating black hole, it "drags" space long with it along its equatorial region. This means that you have rotational symmetry along the axis the black hole is rotating, but not along the other axes. Just think of it as an oblate spheroid, there's only one axis you can rotate it around so that it looks the same. So this means we have conservation of angular momentum but only along one axis, not along the other two.

Of course all possible spacetimes will have full local conservation laws, because no matter how warped the spacetime is, if you go to a small enough patch it will look flat there, it's just a matter of scale. This is what i meant by that in GR reference frames are local.

[caveman1917]

In order to match speeds with a distant object, one would
have to take into account the expansion of space between
the object and the observer over the path the light took.
That automatically accounts for all of the observed cosmic
redshift except possibly the little bit due to gravity.

That's a bit meaningless. Let's assume 3 observers. The first is on a galaxy far away emitting a photon. The second receives it and says "it is cosmologically redshifted". What you now say is that the third observer can match speed wrt the second in such a way that the resulting doppler effect will make him perceive that photon at the same wavelength as the first one emitted it, effectively "erasing" the redshift. While this is true, it doesn't mean that the original redshifting has anything to with the doppler effect, it just means that we can use the doppler effect to "undo" the cosmological redshift.

You could argue this just as well with gravitational redshift. If an observer falls into a black hole and emits a photon it will be redshifted to the outside observer. So you could argue that this outside observer could match speed in such way as to "undo" that redshift by doppler shifting, but that doesn't at all imply that graviational redshift is "really a doppler effect".

[caveman1917]

When someone observes a redshifted photon, he is
moving relative to the object which emitted the photon.
If he matched speed with the object, there would be no
redshift. The photon doesn't lose energy. It is just
that all observers are moving away from all emitters,
giving them all different reference frames, making it
impossible to account for the energy of all the photons
simultaneously.

To go further on this, neither the recessional speed at the time of emittence nor at the time of reception would work. You'd have to calculate a speed based on the calculation of cosmological redshift to get the speed you need to undo that redshift with the doppler effect, and it's not even clear that the speed required was ever attained as a recessional speed by the two galaxies. That is completely ad hoc and doesn't explain anything. Cosmological redshift has nothing to do with relative motion.

[caveman1917]

the redshift observed from distant galaxies (z_total) is the sum of three parts:

z_total = z_grav + z_{relative dopler} + z_comological

It's the product, not the sum. They combine as

[Strange]

I'll try an explanation.

Fantastic explanation. Thanks!

[Tensor]

Putting it that way is slightly misleading, energy cannot be unambiguously defined globally in general.

I'll try an explanation.

snip...

Of course all possible spacetimes will have full local conservation laws, because no matter how warped the spacetime is, if you go to a small enough patch it will look flat there, it's just a matter of scale. This is what i meant by that in GR reference frames are local.

See, I told you caveman has a good grip on this.