Universal expansion vs energy conservation

[martix]

The following thought/problem recently hit me:
What the hell happens to photon energy lost due to the cosmological redshift?

 

[bcrowell]

There is no principle of global conservation of energy in general relativity that applies to all spacetimes: https://www.physicsforums.com/showthread.php?t=506985

 

[Chronos]

Redshifted photons are also time dilated. Their energy is conserved over time.

 

[bcrowell]

Redshifted photons are also time dilated. Their energy is conserved over time.

It's not really an "also." Time dilation is just one way of verbally describing the observed effect.

The second sentence is false.

It may be helpful to compare with energy conservation in a context like the Pound-Rebka experiment: http://en.wikipedia.org/wiki/Pound-Rebka_experiment The Earth's field is well approximated by an asymptotically flat spacetime, so we have globally conserved scalar measures of mass-energy such as the ADM energy or the Bondi energy. A photon released at the bottom and absorbed at the top deposits less energy as measured by a local observer at the top than was released as measured by a local observer at the bottom. However, a distant observer always measures the same total Bondi mass-energy for the earth, and as a corollary we can be assured that, for example, you can't use the Pound-Rebka experiment to make a perpetual motion motion.

But all of this depends on the existence of a conserved scalar measure of mass-energy. Cosmological spacetimes don't have such a thing. For example, they are not asymptotically flat, so they don't have a conserved ADM or Bondi energy.

 

[Chronos]

I see I'm not getting off the hook easily, so, i'll try this except from Lawrence B. Crowell:

[deleted quote from infinite-energy crackpot Lawrence B. Crowell -- bcrowell (not related to Lawrence B. Crowell!)]

 

[bcrowell]

What Lawrence B. Crowell (dunno if he's related to me!) is doing is giving a hand-wavy motivation for the FRW equations. The first sentence should set off alarms: "The Friedman-Lemaitre-Robertson-Walker (FLRW) equations can be derived in an elementary way from Newton’s laws, [...]" Newton's laws are certainly not valid, even in special relativity, much less in GR and cosmology.

Is this quote from a peer-reviewed scientific paper that meets our rules https://www.physicsforums.com/showthread.php?t=414380 for academic references https://www.physicsforums.com/showpost.php?p=2269439&postcount=2 ? If so, could you provide the reference?

Lawrence B. Crowell appears to be a kook: http://www.infinite-energy.com/iemagazine/issue28/inesymposium.html

 

[Chronos]

I will have to check on this, it was from a blog. Ted Bunn also comments:
"Consider the following scenario: I am on a train moving away from you. I throw a ball to you. The speed of the ball as measured by you when you catch it, is less than the speed of the ball as measured by me when I threw it. Where did the energy go?

This situation is precisely the same as the Doppler shift. In both cases, there's no problem with energy conservation, because the energies in question are measured in two different reference frames. Energy conservation says that, in any given reference frame, the amount of energy doesn't change. It says nothing about how the energy in one frame is related to the energy in another frame."

 

[cubzar]

When a ball is thrown on the train, the 'missing' energy goes into pushing the train and the thrower when the ball is thrown. Whilst photons have no rest mass, the do have momentum, and the energy lost when they are red-shifted is used to push whatever emitted them in the opposite direction to the direction in which the photons are moving.

 

[bcrowell]

Chronos, your #7 appears to be in the context of flat spacetime. We all agree that energy is conserved in flat spacetime. It's getting a little frustrating trying to reply to random quotes that you're pulling off the web, presented out of context and without a reference to say where they came from, which don't appear to be from sources that meet PF's rules, and which are sometimes irrelevant and sometimes by crackpots. In #2 I referred you to our FAQ entry on this topic. It has several references to reliable sources of information. Please read one or more of them so that we have a basis for further discussion. If you don't have access to those sources, please say so, and I can try to help you find online sources. (The Weiss-Baez page referenced there is online.) If those sources use math or physics that's beyond your level of expertise, please describe your background in math and physics, and I can try to help you find sources of information that are at the right level for you.

When a ball is thrown on the train, the 'missing' energy goes into pushing the train and the thrower when the ball is thrown. Whilst photons have no rest mass, the do have momentum, and the energy lost when they are red-shifted is used to push whatever emitted them in the opposite direction to the direction in which the photons are moving.

The recoil effect you're describing is an effect that exists, but is extremely small and has nothing to do with cosmological redshifts. For example, if we lived in a universe that was undergoing cosmological contraction (a closed universe headed toward a Big Crunch), then we would still have a tiny redshift effect due to the effect you describe, but it would be overwhelmed by a much larger cosmological blueshift. Note that your example involves flat spacetime. We all agree that energy is conserved in flat spacetime. That isn't the issue. The recoil effect you're analyzing also has nothing to do with the situation described in #7.

 

[martix]

In our case the photon redshift does not occur at the moment of departure, thus possibly having some effect on the emitter. It's a different kind of redshift.

However the current line of thought about spacetime geometry is somewhat beyond my level of expertise, which is why I would be grateful if you either come up with a reasonable analogy or point me to an easy to understand/systematic resource, or even just say that it's too advanced for me, just for closure's sake.

I also had a thought, which probably is very far removed from the physical reality, but here goes: Due to expanding space the reference frame for the photon constantly changes or somesuch, which invalidates the conservation idea.

 

[Chronos]

The problem occurs when we try to compare light energy in different inertial frames. In our inertial frame, photons emitted by objects at cosmological distances appear to have lost energy [redshifted]. If you could query these photons about their 'lost' energy, they would reply 'what lost energy?'. The photons would, of course, be correct. We measure redshift using rulers and no one suggests there is any law of conservation of rulers. So, it is meaningless to discuss global energy conservation because energy cannot be universally defined.

[deleted quote from blog; see #16 -- bcrowell]

 

[TrickyDicky]

We all agree that energy is conserved in flat spacetime.

What energy? How do you figure there is energy in a spacetime with no curvature (no gravity) and therefore vanishing stress-energy tensor? Not much to be conserved, right?

 

[WannabeNewton]

What energy? How do you figure there is energy in a spacetime with no curvature (no gravity) and therefore vanishing stress-energy tensor? Not much to be conserved, right?

I think the point is that since the minkowski metric admits a time - like killing vector field, the energy conservation just follows regardless.

 

[TrickyDicky]

I think the point is that since the minkowski metric admits a time - like killing vector field, the energy conservation just follows regardless.

Sure, but precisely in such a flat spacetime universe there would be no energy, at least according to GR. So yes, being a static spacetime implies global energy conservation, but in the special Minkowski case there happens to be no energy to conserve, so it's really trivial to agree about energy conservation in this scenario, like we all agree about hair conservation in a bald man's head.

 

[bcrowell]

What energy? How do you figure there is energy in a spacetime with no curvature (no gravity) and therefore vanishing stress-energy tensor? Not much to be conserved, right?

Energy is conserved in SR.

 

[bcrowell]

We have an ongoing problem in this thread with folks' careless use of bogus sources.

Lawrence B. Crowell (quoted in Chronos's #5) is a crackpot who has co-authored a book with the well known infinite-energy kook Myron Evans.

The papers by Alasdair Macleod appear to be crackpot material, and do not seem to have been published in a journal from our list that may be used as academic references: https://www.physicsforums.com/showpos...39&postcount=2

Please do not pick through random online sources for quotes without verifying whether the source is any good. I've deleted the quotes in Chronos's #5 and #11.

Please do not post out-of-context quotes from blogs, especially without giving the source, as in Chronos's #7.

There are a number of good, reliable print and online sources referenced in the FAQ entry that I linked to in #2. Tl;dr is not an excuse.

Because we do not seem to be making progress in this thread, I'm closing it.