Does spacetime emit and absorb energy?

[Naty1]

Somone in these forums linked to this and I finally got around to reading it and wanted to share the ideas:

What do you think of the overall description...and last paragraph?? Why??

http://blogs.discovermagazine.com/cosmicvariance/2010/02/22/energy-is-not-conserved/

[Mostly quotes but I changed some wording and omitted portions for brevity.]

Sean Carroll:

…..The reason... you thought energy was conserved was time-translation invariance: “the background on which particles and forces evolve, as well as the dynamical rules governing their motions, are fixed, not changing with time.” But in general relativity…. Einstein tells us that space and time are dynamical, and evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved...

The “energy-momentum conservation” equation looks like this:

∇_uT^uv = 0

... the meaning of this equation is straightforward enough: Energy and momentum evolve in a precisely specified way in response to the behavior of spacetime around them. If that spacetime is standing completely still, the total energy is constant; if it’s evolving, the energy changes in a completely unambiguous way.

...Photons redshift losing energy as space expands... If we keep track of a certain fixed number of photons, the number stays constant while the energy per photon decreases, so the total energy decreases. A decrease in energy is just as much a “violation of energy conservation” as an increase in energy, but it doesn’t seem to bother people as much...
the fact that energy is not conserved in an expanding universe is absolutely central to getting the predictions of primordial nucleosynthesis correct...

in my experience, saying “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields” does not actually increase anyone’s understanding — it just quiets them down. Whereas if you say “in general relativity spacetime can give energy to matter, or absorb it from matter, so that the total energy simply isn’t conserved,” they might be surprised but I think most people do actually gain some understanding...

I won't comment on the last paragraph yet, but would note this: We have discussed several related issues elsewhere, like 'do photons redshift or is that a frame related observation'; 'is spacetime a physical entity' or a mathematical artifact; 'how do we ascribe local energy density to the gravitational field' ...so one can see some potentially different perspectives and even theoretical issues.

 

[PeterDonis]

I think I was the one that linked to this a while back. What particular theoretical issues do you see? What Carroll says looks fine to me.

 

[Naty1]

Hi Peter: Well, if it was you who linked this, be careful what you provide, some of us may actually read them [lol]...the 'theoretical issues' include the ones I listed...nothing new nor controversial from Carroll...I did not mean that...but conventional stuff like this:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

when I first read

...“in general relativity spacetime can give energy to matter, or absorb it from matter, so that the total energy simply isn’t conserved,”

I thought it was insightful...then I reconsidered
'well that's just the same as ascribing negative energy to a gravitational field, so it actually isn't...'

But it DOES at least provide something to grab hold of as 'gravitational field' might not be all that clear. Then I wondered if some here who don't like ascribing a physicality to spacetime [seeing it as just a mathematical artifact] would get even more upset...I still bear minor bruises from one of THOSE discussions!

Then I wondered if Carroll's comment applied only to 'expanding spacetime'...he says nucleosynthesis was possible because of 'expansion cooling'...or if we should consider he also included spacetime in a non expanding universe.

Forgetting that a static universe is inherently unstable for a moment, then photons don't redshift in a static universe??...THAT seems different. Why didn't that stop Einstein from assuming a static universe?? something seems different if it prevents cooling...but spacetime curvature is still dynamic anyway...and so maybe emitting/absorbing is an ok way to think about it reagrdless?? Yet something seems different between 'expansion' and say an accordian type changing of spacetime curvature, say, due to solar and galactic orbits?? Is this 'much ado about nothing'??

[PS: You can see how easy it is to confuse an old dude!]\

 

[Ger]

As one might suspect and already addressed, thing do take the point of perspective of the 'observer', observer being the theory in use. A point with the mathematics involved is that, for mathematical reasoning it (should) not matter at which point you start substituting units back to see if there is a 'real' physical interpretation possible

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Woops already posted..

Why can't Energy not pop out of the vacuum sea and dynamically move to a black hole to submerse again into to sea? Energy being quantinized could be just the reasons that onces brought to excistence, it also requires the inverse condition to jump back into the vacuum see: instead of almost complete emptyness, it requires almost infinite energy density to pop back.

Just one thought.

 

[Bill_K]

I disagree with Carroll's last paragraph. Expressing the relation as a conservation law is certainly preferable to the alternative - ignoring the gravitational part and pointing out that (of course) the remaining part is not conserved. The latter approach may generate more enthusiasm among his readers, but at the expense of understanding.

 

[yuiop]

But it DOES at least provide something to grab hold of as 'gravitational field' might not be all that clear. Then I wondered if some here who don't like ascribing a physicality to spacetime [seeing it as just a mathematical artifact] would get even more upset...I still bear minor bruises from one of THOSE discussions!

In cosmology, distant galaxies recede at superluminal velocities relative to us, but relative to the local vacuum or local spacetime the motion of all bodies is restricted to subluminal velocities. However, the concept of velocity relative to a vacuum is nonsense and concept of of the physical motion of bodies being restricted by a "mathematical artefact" is even more silly, so we must conclude that the local spacetime is just the politically correct polite term for something with more substance, i.e. something physical and maybe the vacuum is not just absolutely nothing.

Then I wondered if Carroll's comment applied only to 'expanding spacetime'...he says nucleosynthesis was possible because of 'expansion cooling'...or if we should consider he also included spacetime in a non expanding universe.

Forgetting that a static universe is inherently unstable for a moment, then photons don't redshift in a static universe??...THAT seems different. Why didn't that stop Einstein from assuming a static universe?? something seems different if it prevents cooling...but spacetime curvature is still dynamic anyway...and so maybe emitting/absorbing is an ok way to think about it reagrdless??

Einstein assumed a static and eternal universe perhaps due to religious preconceptions, but of course all that went out the window when Hubble measured the redshift of distant galaxies. In Einstein's static universe there is of course, no big bang, no universal scale cooling, no nucleosynthesis and no redshift, but view was not confirmed by observation. Hence Einstein called it his biggest blunder.

 

[PeterDonis]

I thought it was insightful...then I reconsidered
'well that's just the same as ascribing negative energy to a gravitational field, so it actually isn't...'

Then I wondered if Carroll's comment applied only to 'expanding spacetime'...he says nucleosynthesis was possible because of 'expansion cooling'...or if we should consider he also included spacetime in a non expanding universe.

A bit of clarification: the concept of "spacetime" as a real, dynamical thing applies always in GR. The part about energy "conservation" is more complicated:

* In a stationary spacetime (i.e., one with a time translation symmetry), one can define a conserved "total energy" using the time translation symmetry and Noether's theorem.

* In an asymptotically flat spacetime (i.e., one in which the metric approaches the Minkowski metric at large "distances" from some central region), one can define a conserved "total energy" by finding an effective 4-momentum vector for the system in the asymptotically flat metric. Since this basically amounts to finding an asymptotic time translation symmetry, it ends up being basically equivalent to the stationary case above.

* In a spacetime that is neither stationary nor asymptotically flat, such as the FRW spacetimes used to describe our expanding universe, neither of the above applies, so there is no good way to define a conserved "total energy".

In *all* of the above cases, there are various ways to define "energy stored in the gravitational field", and with at least some of them, you can often come up with a "conservation law" that includes energy being "exchanged between matter and the gravitational field". However, none of these "conservation laws" are relativistically covariant; they all require picking a particular coordinate chart and treating it as "special" somehow. As Bill_K comments, this can often cause more confusion than it solves, compared to the "strict" approach of always focusing on the differential conservation law, that the covariant divergence of the stress-energy tensor is always zero. That law always holds and is always relativistically covariant.

Forgetting that a static universe is inherently unstable for a moment, then photons don't redshift in a static universe??

Correct; there is no "cosmological redshift" in a static universe.

Why didn't that stop Einstein from assuming a static universe??

Because he didn't know about the redshifts of galaxies; nobody did until Hubble discovered it in the late 1920's, IIRC.

maybe emitting/absorbing is an ok way to think about it reagrdless??

The law governing the relationship of emitted to observed photon energies (or frequencies) is general and applies in any spacetime. The 4-momentum of the photon gets determined at the emitter; then it gets parallel transported along the photon's worldline from emitter to observer; then you just contract that 4-momentum with the observer's 4-velocity to get the observed energy (or frequency if you throw in a factor of Planck's constant). That "parallel transport" process is actually where the "redshift" occurs in an expanding universe; the expansion alters the 4-momentum of the photon as it travels (or at least that's one way of looking at it), whereas in a static universe the photon's 4-momentum would "stay the same" as it traveled.

There's another complication here, btw; what about the gravitational redshift of photons in Schwarzschild spacetime? Here the "change" with changing radius is actually in the 4-velocity of the observer; the photon's 4-momentum stays the same, but the 4-velocities of "hovering" observers are different at different radii, so they contract differently with the constant photon 4-momentum.

So yes, there are lots of ways to get confused here.

 

[Naty1]

Why didn't that stop Einstein from assuming a static universe??

Because he didn't know about the redshifts of galaxies; nobody did until Hubble discovered it in the late 1920's, IIRC.

I realized that after posting the comment: it seems rather strange we have learned so much
in such a short time...to realize even I have knowledge that Einstein did not makes me even
more respectful of his contributions. He was operating in a 'near vacuum' of sorts!

 

[PeterDonis]

to realize even I have knowledge that Einstein did not makes me even
more respectful of his contributions. He was operating in a 'near vacuum' of sorts!

In the Feynman Lectures on Gravitation, Feynman comments at one point that he had no idea how Einstein could possibly have arrived at GR at the time he did, given the state of knowledge then about field theory (i.e., very rudimentary at best).

 

[Naty1]

In the Feynman Lectures on Gravitation, Feynman comments at one point that he had no idea how Einstein could possibly have arrived at GR at the time he did, given the state of knowledge then about field theory (i.e., very rudimentary at best).

Of course the factors which are contra to ours is that Einstein had Maxwell's equations and the associated implicit constancy of c' , the 'ether' controversy and attempted explanations, and Lorentz length contraction and Fitzgerald time dilation, or maybe vice versa, but anyway I think they were separate viewpoints at the time. Others have said that SR was 'waiting to be discovered', but that seems a stretch.
What suggests our interpretation may be closer to the truth are Einstein's other discoveries such as Brownian motion and GR. All that was no 'accident'.