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cmb

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

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In summary: The ADM and Bondi energies are not well defined, and the ADM energy is no longer conserved. This is due to the expansion of the universe, which breaks the symmetries that allow for the conservation of these energies. In summary, the energy of the universe is not conserved due to the expansion of the universe and the lack of well-defined symmetries.

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cmb

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

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mfb

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cmb

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

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Vanadium 50

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

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cmb

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timmdeeg

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http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/cmb said:If so, do we have estimates of what that is.

You might be interested to read this article.

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kimbyd

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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.cmb said:

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

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

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Buzz Bloom

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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?kimbyd said:The easy answer is simply no, energy is not conserved at all.

Regards,

Buzz

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mfb

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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.kimbyd said: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.

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256bits

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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.kimbyd said: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 foranyfluid, not just radiation

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timmdeeg

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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 said: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.

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kimbyd

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That doesn't make any sense. The classical box has rigid walls made of some kind of insulated material.256bits said: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.

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.

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.timmdeeg said: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?

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PAllen

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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

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timmdeeg

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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?kimbyd said: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.

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PAllen

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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.timmdeeg said: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?

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PeterDonis

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PAllen said: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.

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PeterDonis

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timmdeeg said:As the distance between two subsequent flashes depends linearly on the development of ##a##

No, the

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.

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kimbyd

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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.timmdeeg said: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 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).

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Flisp

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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.PeterDonis said: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.

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PeterDonis

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Flisp said: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.

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Flisp

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Buster59

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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.cmb said:

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

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.

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Ibix

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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.Buster59 said:The total energy within reality (everything in existence) is constant, since energy can't be created or destroyed.

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timmdeeg

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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?Buster59 said:The total energy within reality (everything in existence) is constant, since energy can't be created or destroyed.

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timmdeeg

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PeterDonis said: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.

Agreed, thanks for your comments and corrections.kimbyd said: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.

@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.

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PeterDonis

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

The total energy of the observable universe refers to the sum of all forms of energy present in the observable universe, including matter, radiation, and dark energy.

According to the law of conservation of energy, the total energy of a closed system remains constant over time. Therefore, it is believed that the total energy of the observable universe is also constant.

The total energy of the observable universe is calculated by measuring the amount of matter and radiation present and estimating the amount of dark energy, which is currently the largest contributor to the total energy of the universe.

One theory, known as the "Big Rip" theory, suggests that the total energy of the universe may not be constant and could potentially increase over time due to the accelerating expansion caused by dark energy.

The concept of total energy of the observable universe is an important aspect of cosmology, as it helps scientists understand the overall structure and evolution of the universe. It also plays a role in theories and models that attempt to explain the origin and fate of the universe.

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