I Is the total energy of the observable universe constant?

[cmb]

If so, do we have estimates of what that is.

Also, if we have estimates of that, what will the final entropy of the universe be, in J/K?

 

[mfb]

There is no unambiguous way to define "total energy of the universe at a given point in time". You can measure the local energy density (where "local" is still a volume large enough to not care about individual galaxy clusters). That goes down, but not as fast as volumes go up - dark energy seems to keep its energy density.

 

[cmb]

I'll go with one ambiguous way, and why it is probably not that one, to kick off the conversation.

 

[Vanadium 50]

If you don't have an unambiguous definition, how can you tell if it is conserved or not?

"kick off the conversation" is not a good way to fix a bad question.

 

[cmb]

How about the latter question, then? In J/K, what will the entropy of the universe asymptote towards, or will it not? Estimates and ambiguities are fine, I am an engineer, putting error bars on it is fine.

 

[timmdeeg]

If so, do we have estimates of what that is.

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
You might be interested to read this article.

 

[kimbyd]

If so, do we have estimates of what that is.

Also, if we have estimates of that, what will the final entropy of the universe be, in J/K?

The article that timmdeeg posted above is good and recommended. The easy answer is simply no, energy is not conserved at all. Take the super simple example of a thermal gas of photons in an expanding universe. As the universe expands, the temperature of the gas drops as $1/a$. And since the energy in a volume of a thermal gas of photons is proportional to $T$, the energy in that expanding volume also drops.

In a classical system, the drop in energy of the thermal radiation would come from the gas being confined to a box and the size of the box getting bigger. The thermal radiation exerts pressure on the walls of the box as it expands, which transfers energy from the thermal radiation to the walls of the box. In an expanding universe, there are no walls of the box, so there's nothing to dump energy into. It's just gone.

Though curiously, the math in this analogy works for any fluid, not just radiation.

 

[Buzz Bloom]

The easy answer is simply no, energy is not conserved at all.

Is it not also the case that over time the boundary (radius) of an OU increases faster that the scale factor to include more and more stuff? Wouldn't this additional stuff add to the total energy within the boundary?

Regards,
Buzz

 

[mfb]

In a classical system, the drop in energy of the thermal radiation would come from the gas being confined to a box and the size of the box getting bigger. The thermal radiation exerts pressure on the walls of the box as it expands, which transfers energy from the thermal radiation to the walls of the box. In an expanding universe, there are no walls of the box, so there's nothing to dump energy into. It's just gone.

As another difference: Radiation slows the expansion of the universe (both from its energy and pressure), while it would speed up expansion of a classical box filled with radiation.

 

[256bits]

In a classical system, the drop in energy of the thermal radiation would come from the gas being confined to a box and the size of the box getting bigger. The thermal radiation exerts pressure on the walls of the box as it expands, which transfers energy from the thermal radiation to the walls of the box. In an expanding universe, there are no walls of the box, so there's nothing to dump energy into. It's just gone.

Though curiously, the math in this analogy works for any fluid, not just radiation

Are you saying in the classical system the gas is doing work on the box walls, even if the walls are a vacuum, and massless, and thus the temperature drops? I am not sure I understand the description.

 

[timmdeeg]

The thermal radiation exerts pressure on the walls of the box as it expands, which transfers energy from the thermal radiation to the walls of the box. In an expanding universe, there are no walls of the box, so there's nothing to dump energy into. It's just gone.

Isn't it enough to say that the wavelength of a photon and hence it's energy scales with the scale factor so that it decreases in an expanding universe and increases in a contracting universe?

 

[kimbyd]

Are you saying in the classical system the gas is doing work on the box walls, even if the walls are a vacuum, and massless, and thus the temperature drops? I am not sure I understand the description.

That doesn't make any sense. The classical box has rigid walls made of some kind of insulated material.

What I'm saying is that the energy of the stuff inside the expanding box changes based upon how much work is done on the walls of the box. And the change in energy is the same change in energy you get in an expanding universe.

Isn't it enough to say that the wavelength of a photon and hence it's energy scales with the scale factor so that it decreases in an expanding universe and increases in a contracting universe?

I don't think it's immediately obvious that expansion and photon wavelengths should be linearly-related. They are, but I don't think the link between the two is as obvious as many seem to think.

 

[PAllen]

I think there is more to it than the @kimbyd example. Consider such an expanding thermal gas isolated in a region of an asymptotically flat spacetime rather than in a box (which is also equivalent, to very high accuracy, to a expanding gas blob reasonably isolated between galaxies. In this case (the asymptotically flat spacetime), the energy is exactly conserved as long as radiation is accounted for. The ADM energy, which includes the radiation, remains constant. The Bondi energy, which excludes escaping radiation (EM plus gravitational), decreases.

However, our universe is not asymptotically flat. Neither ADM energy nor Bondi energy can be defined for a realistic cosmology. In simple terms, for a closed universe, there is no outside boundary to sum over, and for an open universe, there is no 'quiescence at infinity' to allow an invariant summing up.

The key point, IMO is that conservation of energy is 'essentially' exact in GR up to scales considerably bigger than a galaxy, over long time scales, but breaks down over cosmological distances and times, because the approximation of asymptotically flat spacetime embedding becomes less and less accurate.

Thus, to my mind, the correct statement isn't 'energy conservation is violated' (which is not what @kimbyd said, but some careless authors have), but that total energy cannot be meaningfully defined over very large scales in a realistic cosmology (FLRW, or anything else that is not asymptotically flat).

 

[timmdeeg]

I don't think it's immediately obvious that expansion and photon wavelengths should be linearly-related. They are, but I don't think the link between the two is as obvious as many seem to think.

I think it's quite obvious if one considers instead light flashes emitted with constant frequency. As the distance between two subsequent flashes depends linearly on the development of $a$ one doesn't have to think about boxes and their walls. Isn't this reasoning much more natural?

 

[PAllen]

I think it's quite obvious if one considers instead light flashes emitted with constant frequency. As the distance between two subsequent flashes depends linearly on the development of $a$ one doesn't have to think about boxes and their walls. Isn't this reasoning much more natural?

Actually, this gets to my argument that the real issue with energy in cosmology is inability to define it due to global geometry. The FLRW family of solutions includes the case of linear scale factor growth, which corresponds to flat spacetime (not space - the spatial slices are hyperbolic in this case), and conservation of energy is exact in this case - total energy is exactly zero.

 

[PeterDonis]

The FLRW family of solutions includes the case of linear scale factor growth, which corresponds to flat spacetime (not space - the spatial slices are hyperbolic in this case), and conservation of energy is exact in this case - total energy is exactly zero.

Actually, even for a general curved spacetime, one can define an "energy" using the Hamiltonian constraint in the ADM formalism; but this constraint gives the same unhelpful answer, that total energy is zero.

 

[PeterDonis]

As the distance between two subsequent flashes depends linearly on the development of $a$

No, the time between the reception of two subsequent flashes, if both emitter and receiver are comoving observers, depends linearly on the development of $a$. As $a$ gets larger, the time gets longer. So cosmological redshift in this sense is a direct observable.

The problem comes when you try to convert this direct observable into a statement about the "wavelength" of the photons. There is no invariant way to do that.

 

[kimbyd]

I think it's quite obvious if one considers instead light flashes emitted with constant frequency. As the distance between two subsequent flashes depends linearly on the development of $a$ one doesn't have to think about boxes and their walls. Isn't this reasoning much more natural?

I'm not seeing how this leads to that conclusion. What you've argued here relies upon the assumption that wavelength scales by the scale factor.

I know that you can reach this conclusion by using a semiclassical approach: consider the light, as it travels through the expanding universe, to be traveling through a bunch of small patches, each described by flat space-time. Then you can use Special Relativity in many small steps to figure out the light travel path, and you'll get the right redshift factor too, I believe.

Or you can just do the math using conservation of stress-energy and the pressure that a photon gas has (the hypothetical expanding box matches this description well).

 

[Flisp]

Actually, even for a general curved spacetime, one can define an "energy" using the Hamiltonian constraint in the ADM formalism; but this constraint gives the same unhelpful answer, that total energy is zero.

From a philosophical point of view, this is actually the only answer that makes sense. Somehow our "existing" universe came into being from a state of total "non-existance" (either directly or via an evolution of universes or within some construct of multiverses). That its energy is zero makes it possible that something came from nothing, because even this something is basically nothing. And it gives the intuitively best answer to the original question: Yes, the energy is constant. As it should be.

 

[Demystifier]

One possible definition of energy is the canonical Hamiltonian. In general relativity the full Hamiltonian (gravity + matter) is always zero, so in this sense the energy is conserved.

 

[PeterDonis]

this is actually the only answer that makes sense. Somehow our "existing" universe came into being from a state of total "non-existance" (either directly or via an evolution of universes or within some construct of multiverses). That its energy is zero makes it possible that something came from nothing, because even this something is basically nothing.

This answer only "makes sense" if you are willing to accept that our universe "is basically nothing", which is a hard pill for many people to swallow.

 

[Flisp]

I guess every philosophy and religion struggles with the 2 problems that, what ever you do, who ever you are, one day you and what ever you have built are gone and that the ultimate origin of life, the universe and everything out of nothing is simply inconceivable (even if you try to blame god for it, only pushing the problem to the question of HIS origin). That existence is a polarized version of non-existance makes it somehow imaginable. Like streching a rubber band in both directions and the let go again. Everything goes back to zero. From our point of view we are on one side of that streched rubber band and only see existence. Untill that day, of course...

 

[Buster59]

If so, do we have estimates of what that is.

Also, if we have estimates of that, what will the final entropy of the universe be, in J/K?

The total energy within reality (everything in existence) is constant, since energy can't be created or destroyed. What percentage of reality this universe is appears to be unknowable.

My view: Something had to have always been in existence in order for anything to exist. That means reality is eternal - no beginning and no end. It's just energy interacting with itself in a complex manner.

 

[Ibix]

The total energy within reality (everything in existence) is constant, since energy can't be created or destroyed.

I'd suggest reading the link in post #6 before making this claim so boldly. It isn't at all clear that it is true globally.

 

[timmdeeg]

The total energy within reality (everything in existence) is constant, since energy can't be created or destroyed.

Think of an expanding box which contains a certain energy. This particular energy shall maintain it's density during expansion. Is the total energy within this box constant?

 

[timmdeeg]

The problem comes when you try to convert this direct observable into a statement about the "wavelength" of the photons. There is no invariant way to do that.

I know that you can reach this conclusion by using a semiclassical approach: consider the light, as it travels through the expanding universe, to be traveling through a bunch of small patches, each described by flat space-time. Then you can use Special Relativity in many small steps to figure out the light travel path, and you'll get the right redshift factor too, I believe.

Agreed, thanks for your comments and corrections.

@kimbyd Yes, as JohnA.Peacock points it out in "Cosmological Physics", "... it is correct to think of the effect [cosmological redshift] as an accumulation of the infinitesimal Doppler shifts ...".

Coming back to "the distance between two subsequent flashes ", shouldn't it be possible to show such distances in a spacetime diagram? That they are constant over time in flat Minkowsky spacetime where Special Relativity holds but not in an expanding universe? - I'm thinking here of the famous spacetime diagram shown in the thesis of Tamara Davis.

 

[PeterDonis]

The thread has degenerated into personal speculation and is now closed.