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Tyrfing
2009-Jul-27, 07:19 PM
Hello, I am currently halfway through a physics undergrad, and have a question that I can't really find an answer to.

The expansion of the universe clearly causes a redshift different from the Doppler Effect. The specifics of this redshift, as far as I can tell, are explained through General Relativity.

My question is that if all of these photons are being redshifted due to this expansion, where is the photon energy going? It seems like this universal redshift of light must be indicative of some sort of universal energy loss.


Can anyone address this question? Thanks!

ngc3314
2009-Jul-27, 07:40 PM
Hello, I am currently halfway through a physics undergrad, and have a question that I can't really find an answer to.

The expansion of the universe clearly causes a redshift different from the Doppler Effect. The specifics of this redshift, as far as I can tell, are explained through General Relativity.

My question is that if all of these photons are being redshifted due to this expansion, where is the photon energy going? It seems like this universal redshift of light must be indicative of some sort of universal energy loss.


Can anyone address this question? Thanks!

There are probably multiple answers depending on coordinate systems, but one way to view it is exactly that. Conservation of energy, via Noether's Theorem, is equivalent to saying that the properties of space are time-invariant. This is not so in expanding space.

(I await the claws of those well-schooled in the invariant arts).

Jeff Root
2009-Jul-27, 08:08 PM
It seems to me that the energy content of cosmic background radiation
emitted by a small volume of hydrogen atoms at the time of recombination
remains at least equal to what it was at the time it was emitted, relative
to the atoms which emitted it. With the cosmic expansion, that light may
even be gaining energy relative to the atoms which emitted it! So there
is certainly no loss of energy.

-- Jeff, in Minneapolis

George
2009-Jul-28, 12:25 AM
There are several threads from the past that kick this topic around.

Scratching away.... and I could be wrong, but it appears that one can model the redshift as if it were indeed a Doppler shift. We are moving faster and faster away from the more distant objects as time marches onward. This relative velocity increase with time will result in light from more distant objects to appear as if our relative velocities have greatly increased.

Considering how little the expansion effect acts upon local galacitc clusters, it seems odd that some prefer to use the model where the wavelength of light -- an object of electromagnetic strength as opposed to the wimpiness of gravitational forces -- somehow stretches with the expansion, though this approach seems to work, too.

grant hutchison
2009-Jul-28, 12:51 AM
An answer from Edward Harrison's book Cosmology: The Science of the Universe:
The conservation-of-energy-principle serves us well in all sciences except cosmology. In bound regions that do not expand with the universe ... we can trace the cascade and interplay of energy in its multitudinous forms and claim that it is conserved. But in the universe as whole it is not conserved. The total energy decreases in an expanding universe and increase in a contracting universe. Where does the energy go in an expanding universe? And where does it come from in a contracting universe? The answer is nowhere, because in the cosmos, energy is not conserved.Grant Hutchison

Ken G
2009-Jul-28, 01:47 AM
You've had good answers already. I might add, if you're confused about conservation of energy, that energy is never conserved when you change reference frames. In my frame, the Earth has no kinetic energy, in another, it is spinning at about 0.5 km/s, in another, it is orbiting the Sun at about 30 km/s, etc. So conservation of energy means you can bookkeep energy within a particular frame, but that's all.

As ngc3314 said, in cosmology this may depend on coordinate systems (one of publius' "high priests of relativity" could tell you the actual requirements here, I believe I've heard that one can restore conservation of energy in spacetimes that are "asymptotically flat", but whether or not the universe is that I don't know, and it may not be possible to know), because in GR, "reference frame" is a local concept, and the purpose of a coordinate system it to track the connections between reference frames. So as soon as you say you are using "comoving coordinates" (the cosmology standard, where "space expands" and the CMB redshifts continuously with the age of the universe), you are not going to have conservation of energy-- every observer is in a different reference frame, their own little corner of comoving space.

On the other hand, the standard thing we do in physics when energy is not conserved is to make it be conserved by cooking up some "potential" energy. I have heard of efforts to say that the missing energy in the OP is going into "gravitational potential energy" as the universe expands, but it's not the same character as the gravitational potential energy that heats a contracting star or makes an egg splat on the floor. Consult your friendly neighborhood high priest of relativity to inquire about how far you can push this idea, I've heard it said that the total energy in the universe stays zero when you add the "real" energy (rest masses and kinetic energy like photons) to the "potential" energy. I can't say a thing about how true that is.

All I could say is, I do not believe there is any difference between saying that something is happening to the light, than saying something is happening to the detectors of the light. A picture we can use is that all matter (and gravitationally bound systems) are shrinking, and nothing is happening to space or light. That would be a bizarre and unconventional way to say it, but not demonstrably different in the least way. And if you say it like that, it becomes more clear what is happening to the energy-- it is being measured as changing, without "actually" changing. Just like what happens to energy when you change reference frames. Somehow the global gravity and dynamics of the universe are "causing" the change in the instruments, but still nothing is happening to the photons, in that picture. The sole key to all this is that the measurements have to be explained, there is never any guarantee that the explanations have to be unique.

So then, if we can't categorically point to a particular cause, then why does the redshift occur? I'd say that question has no answer that boils down to anything different from "it redshifts because it redshifts" (saying either that the universe is expanding or matter is contracting is not an independent piece of information from the redshifting). We can tell various stories about why it redshifts, but the stories are coordinate dependent, so they are really nothing more than devices for picturing the calculation. So if you need a device for picturing what happens to the energy, just say, as the universe ages, we keep changing the reference frame from which we are observing the CMB, and no energy conservation is required when you change reference frames.

By the way, the difference between "devices for picturing calculations" and "descriptions of what is really happening" crops up all over relativity. This fact is kind of slow to percolate through the literature you find on relativity-- many places continue to take these stories a bit too literally, missing what must be considered one of the core lessons of relativity: reality is whatever emerges intact from the smoke of all the one-sided stories we tell about it.

Spaceman Spiff
2009-Jul-28, 02:41 AM
Well, I've got to pipe in with my usual list of references on the topic:

Is Energy Conserved in General Relativity? (http://www.math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html)
It's a bit technical, but I bet the poster can take most of it in, and in any case the narrative is excellent. It discusses and explains this issue in a bit more detail, but reaches similar conclusions as Ken G.

A favorite article of mine, and one that you'll sure want to read:
Expanding Space: the Root of All Evil? (http://arxiv.org/abs/0707.0380)

A teaser quote from page 4:

This is the central issue and point of confusion. Galaxies move apart because they did in the past, causing the density of the Universe to change and therefore altering the metric of spacetime. We can describe this alteration as the expansion of space, but the key point is that it is a result of the change in the mean energy density, not the other way around. The expansion of space does not cause the distance between galaxies to increase, rather this increase in distance causes space to expand, or more plainly that this increase in distance is described by the framework of expanding space. There is therefore no need to look for Newtonian analogues to the expansion of space, since it is an effect rather than a cause.(my emphasis)

And this excellent blog (http://blogs.discovermagazine.com/cosmicvariance/2008/10/06/does-space-expand/) by young(ish) physicists and astrophysicists expounds a bit on the issue of "expanding space", and also providing links to the above paper and two other related ones. Many of the comments below the blog article are also enlightening.

Dittoing Ken G's suggestion -- if you're really interested in this topic, do a search for related posts in the Q&A area by Publius -- he knows a heck of a lot about GR and its intricacies, and has taught me a lot. :)

And good luck on your budding career in physics or perhaps astrophysics(?).

Simona
2009-Jul-29, 07:55 PM
Does the expansion somehow affect the use of the Dopper shift when searching for exoplanets?

George
2009-Jul-29, 08:02 PM
Does the expansion somehow affect the use of the Dopper shift when searching for exoplanets? No, exoplanets are all very close realtive to the distances necessary to observe redshifts due to expansion.

Simona
2009-Jul-29, 08:10 PM
That makes sense. Thanks a lot.

publius
2009-Aug-06, 06:45 AM
I'm getting lazy and not watching threads I ought to paying attention to. Bad boy am I.

And we would need a high priest to properly explain all the details and dot the i's and cross the t's, etc, etc. But the truth is, in the general case, energy cannot be conserved globally in GR. That may sound shocking at first blush, like the rug has been pulled out from everything you think you know, but it's really no big deal. Energy is conserved locally, absolutely -- it's just that in the global picture, you have some coordinate depedent trouble with trying to integrate the total global energy.

In a static (actually just stationary, I think) there is no problem with global energy conservation. But in a non-stationary, dynamic space-time (basically, in coordinate language, no coordinates can be found where the metric is not varying with time) you have problems.

If the space-time is asymptotically flat, I think that may be just asymptotically stationary (there are several different ways to define a global total energy, and they may have different limits, so one way may require asympotica flat status, but another way may not have as many limits, but will be more complicated), one can define some invariant notion of global total energy.

If the spacetime doesn't meet those restrictions, then it doesn't work. Any observer can construct a notion of gravitational energy, and say the missing or gained energy with time goes into the gravitational field, but that concept cannot be made invariant. And I caution that this GR notion of gravitational energy is very different than the Newtonian notion. Very different, indeed! For example, in Schwarzschild, there is no gravitational energy at all. That only comes with gravitational radiation, or dynamic space-times where the energy appears to be coming in or going away from a global system.

One way to see this is to consider two observers in Schwarzschild, one high up, nearly flat, and the other deep down in the well looking at the energy of some test particle. They will disagree on that energy. Either can say his is the correct value, and the other observer's clock is just screwed up. Both will predict the same invariant behavior of the test particle, of course, but they will disagree on how much energy it has, although they will say it is conserved.

Now, imagine that situation where the metric is varying with time. That energy they come up with will then vary with time itself. If that time-varying behavior can't be transformed away, then there's no way to calibrate it to a constant baseline so to speak. But there, locally, since our (by very definition of how this works) local frame following us along and always Lorentz, everything close to us in unchanging and everything works locally.

The problem is just trying to integrate all those local frames into one global whole. Curvature just throws a monkey wrench in that in the general case.

-Richard

Jeff Root
2009-Aug-06, 02:18 PM
So, in your view, Hank, the Universe consists of uncountably many caveats?

-- Jeff, in Minneapolis

publius
2009-Aug-06, 08:26 PM
So, in your view, Hank, the Universe consists of uncountably many caveats?

-- Jeff, in Minneapolis

Is that some kind of reference to County Agent Hank Kimball? Well, maybe not a reference, but more of an allusion. No, it's a metaphor. Well, no, it's a malapropism.

Who?


-Richard

Jeff Root
2009-Aug-07, 04:52 AM
:) :) :) :) :)

-- Jeff, in Minneapolis

.

WayneFrancis
2009-Aug-07, 05:11 AM
You've had good answers already...
Well put.