In cosmological redshifting, photons lose energy because of the expansion of the universe.
Bur what actually happens to this energy? Is it just “lost” or is it physically destroyed (which would seem impossible)? If it is lost, what is it lost to or what does it become?
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The energy is the same, it’s our frame of reference that makes it appear different. Just like a siren sounds higher when coming toward you and lower as it drives away. The siren stays the same, your perception is thrown off by your relative frame of reference.
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Let’s say you and a friend are standing next to a conveyor belt moving at a constant rate.
Every second, your friend takes a cookie and puts it on the belt. The cookies travel down the belt a ways until they reach you. Every time you see a cookie, you take it off the belt and into your cookie jar. With this setup, you are receiving 1 cookie per second.
Now, let’s say your friend gets up and starts walking away from you, against the stream of the belt. But as they walk, they continue to place cookies on the belt. Since they walk away a little further along the belt between cookies, the cookies are now spaced further apart. So you are now getting less than 1 cookie per second.
But hang on. Your friend is still dumping 1 cookie per second onto the belt. But you’re getting less than 1 cookie per second at the other end. Where did all that extra cookie go?
As your friend continues to walk away, there is more belt between you to fill with cookies. That’s where the supposedly missing extra cookie is. All that extra belt your friend is creating by walking away from you is able to store extra cookies. You’re getting less of them per second because some of them are going towards filling that extra belt space.
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This is only part of the puzzle, though. What I’ve described to you is called *non-relativistic* Doppler redshift. It’s decent enough for explaining phenomena like the way an ambulance siren increases in pitch as it’s moving towards you and decreases in pitch as it moves away. But it doesn’t quite cut it for rays of light. For that, we need *relativistic Doppler redshift*.
The relativistic version is the same as the non-relativistic version, but with an extra thing we have to consider. When two things are moving with respect to one another (e.g. your friend is moving away from you), the way the two of you perceive time won’t actually sync up. One of you is going to perceive time passing more slowly from the perspective of other. This is called time dilation.
By convention, we’d say that your friend, since they’re the one emitting the cookies, is the one experiencing “normal time”. From your friend’s perspective, they are still, and *you* are the one moving away. Since you’re moving, that means your perception of time slows down relative to your friend. Because of that, you will be receiving cookies *even slower* than you otherwise would be if we didn’t take relativity into account. That is, this effect stacks with the previous effect. You receive fewer cookies per second because some of them are going towards filling up the extra belt between you, *and* because the very concept of what a “second” is to you has changed due to relativity.
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**EDIT:** Apparently I’ve neglected yet another mechanism that is unique to redshift caused by the expansion of space. Please read the replies.
The explanation above is adequate for relativistic effects in *non-expanding* space, but expanding space is probably what OP actually wanted to know about.
>Bur what actually happens to this energy? Is it just “lost” or is it physically destroyed (which would seem impossible)?
There was a brilliant mathematician around the late 19th and early 20th centuy, called Emmy Noether.
She proved that conservation laws come from symmetries in physics. For example:
* Physics is the same if you move to a different place. This leads to “conservation of momentum”.
* Physics is the same if you face a different direction. This leads to “conservation of angular momentum”
* Physics is the same if you move to a different time. This leads to conservation of Energy.
She even gave an explicit method to translate symmetries into conservation laws.
However, over cosmological timescales, physics isn’t exactly the “same” at different times. At least, not in every way possible. For example, space becomes more stretched out. Since stretching of space represents a breakdown of the time-invariance of normal, classical physics, it means normal classical energy doesn’t have to be strictly conserved. There’s no problem with the stretching of space turning high-energy photons into low-energy ones by stretching them out.
There would be a more sophisticated symmetry *like* time-invariance that is preserved all the way back to the big bang, and that would give (via Emmy Noether’s methods) a conservation law that’s *like* conservation of energy. As another commenter put it, the “energy” goes into the stretched space itself – but then this isn’t classical energy any more, but the more sophisticated “energy” that her maths says is conserved in an expanding universe.
>Is it just “lost” or is it physically destroyed (which would seem impossible)?
There is no global conservation of energy at the cosmological scale, precisely because cosmological expansion breaks time translation symmetry. Check out Noether’s theorem.
So yes, that energy is destroyed (it doesn’t become anything else, it just disappears).
It is essentially lost. Conservation laws are tied to symmetry. In a universe that is expanding, there is a violation of symmetry. This allows for energy to not be conserved. You could think about it as the energy being diluted, but that is probably a poor analogy when you get into the details.
> Is it just “lost” or is it physically destroyed (which would seem impossible)?
No, the energy isn’t lost. It *contributes* to the expansion of the Universe. Note I stressed the word contributes. The Universe’s expansion has a primary cause, but there are certain things that contribute to it. This is the currently accepted answer by science.
What seems to be getting overlooked in this discussion is that Einstein’s laws only apply to a static, non-expanding Universe. This is fine at most scales, because the expansion of the Universe contributes a trivial amount of error at local scales. Beyond those scales, the error from the expansion of the Universe adds up and it has to be accounted for in order for the results to be accurate. That’s the case with redshifting.
So the answer to your question is that the energy isn’t lost/destroyed, it’s still conserved. The equations we use most often simply don’t account for where it goes, because they assume a static, non-expanding Universe. You have to start using more accurate approximations to understand what happens to the energy at that scale.
This is discussed by the astrophysicist Ethan Siegel in this article. It’s not quite ELI5, but it will hopefully give you a starting point where you can study this further.
https://www.forbes.com/sites/startswithabang/2015/12/19/ask-ethan-when-a-photon-gets-redshifted-where-does-the-energy-go
Here’s a Veritasium video on it [https://www.youtube.com/watch?v=9DrBQg_n2Uo](https://www.youtube.com/watch?v=9DrBQg_n2Uo)
He says it is 100% doppler. Well, really that there is no difference between doppler, gravitational, and cosmological redshift. They are all the same effect due to changing relative velocities of source and observer / accelerating reference frames. Energy and wavelength aren’t intrinsic properties of photons; and it depends on observers. In an expanding universe, every reference frame is changing at far enough distances; and the observers start having high relative velocities.
Photon energy/wavelength being observer dependent is also what causes you to see red (and blue) shift when you travel at relativistic speeds. You’d see blueshift in front, and red in back. But a non relativistic observer would see the same photons as *not shifted*; it is observer dependent. And in an expanding universe; *all directions* are accelerating away from you, so everything is red.
idk why so many posts here are saying energy is lost. I could be wrong and am deferring to the video; I don’t understand these other posts. But, based on this video, no energy is “lost”, because its all relative. If you had something moving at the same relative velocity as a distant galaxy; it would not view its light as red shifted.
Edit: another good point in the video:
People often confuse the fact that “space expands” and “wavelength gets longer”, and associate the two to mean “space stretches photons”. This isn’t true, because, again, wavelength isn’t a property of a photon. And, if it were true, space would stretch everything else as it expands, like atoms. It doesn’t.
Edit 2: here’s another good analogy, I think.
Imagine you’re in deep space, and friend traveling as the same relative velocity as you (i.e. doesn’t appear to be moving) throws something at you. Fast. Say, a baseball at 100 mph. It hits you, and hurts like hell. The ball had a lot of energy.
Now, do the same scenario. But this time, when they throw the ball at 100 mph *relative to themselves*, you start moving away from your friend. By the time the ball catches up to you, it is moving at 5 mph *relative to you*, and when it hits you, it doesn’t hurt. The ball “had less” energy.
The ball “lost energy” according to you, but not your friend. And not according to the universe. The ball didn’t “slow” down, and nothing acted upon it to “slow down”. But the energy it imparted upon you was less than the first scenario.
Same for photons, except they don’t slow down. Their “energy” is still source-observer velocity dependent, like the ball. Instead of “seeing the ball slow down”, you see “the wavelength increase”. Both cause “less relative energy”.
Neither. It’s conserved. Think like taffy. If you have a 1cmx1cm cut of taffy then stretch it out to 2cmx2cm, do you have more or less taffy? Neither, you have the exact same amount of taffy as you had before, it’s now just stretched out. Easier to chew through a corner of a 2cmx2cm cut of taffy than a 1cmx1cm cut of taffy.
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