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## Are we in a black hole?

Are you sure you are calculating this correctly? If you use those units then the dimensions of density should be eV.Mpc-3.

In which case as 1eV = 1.6022x10-12 erg, 1 parsec = 3.0857x1018cms and c2 = 8.9876x1020 (cms/sec)2 then
3.8846x1041 eV.Mpc-3. = 3.8846x1041x1.6022x10-12x8.9876-1x10-20x[3.0857x1024]-3gms/cc = 2.36x10-65 gms/cc; a little less than that required for DE! (By a factor of about 1036)

Garth

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 Quote by hellfire What bothers me, specially in case of the Unruh radiation, is the following: You can get the result of an observer dependent horizon considering only the action of some field (a scalar field for example) in flat spacetime viewed by an accelerated observer. This observer will detect a thermal bath of particles. Calculations and qualitative discussions I am aware of stop at that point. However, a thermal bath of particles should create a gravitational field that should pertub the curvature making it non-vanishing. But, does this make sense? The inertial observer and the accelerated observer, both in the "same" spacetime, would measure different curvatures.
For now, I'm going largely to restrict my comments to this passage.

Most courses in quantum field theory and books like Peskin and Schroeder use inertial observers in a particular solution to Einstein's equation, Minkowski spacetime. In particular, the contribution from quantum fields to the stress-energy tensor in Einstein's equation is not taken into account. Stress-energy tensors of qunatum fields are considered, but they're not fed into Einstein's equation. This is a very useful approximation - quantum fields propagating in Minkowki spacetime without affecting the spacetime background as viewed from inertial frames.

This leads naturally to the idea that doing something similar usiing non-inertial frames and/or non-flat spacetimes might be interesting. Take an interesting solution to Einstein's equation, and consider quantum fields propagating through spacetime without affecting the spacetime background, i.e., don't take into account the contribution from quantum fields to the stress-energy tensor in Einstein's equation.

This results in a big payoff - the Unruh effect, Hawking radiation, and cosmological radiation. The payoff is large, but the effects themselves are usually very small.

After doing this, the "back-reaction" of the stress-energy tensor of the quantum fields on spacetime can be considered, but the methods needed to do this are often quite subtle and difficult. Generalizing renormalization of the expectation values of components of the stress-energy tensor from Minkowski spacetime to other spacetimes is not straightforward because the concept of particle, as formulated in QFT in Minkowski spacetime, often no longer applies. A field (as opposed to particle) interpretation rules! I may talk a little more about this in another post in this thread.

Your point about the consistency required between the views different observers take for the Rindler spacetime Unruh effect is a good one. In this Unruh effect, suppose the quantum field in is the vacuum of the inertial observer. Then, the expectation values of the components of the stress energy tensor for this observer are all zero. Since the stress-energy tensor is a tensor, the values of the components of the stress energy tensor are all zero in every coordinate system, including the coordinate system of the accelerated observer.

What is happening here? How does the non-accelerated observer feel a temperature? To explain this, I'll quote a passage from Birrell and Davies about how an idealized accelerated particle detector reponds to the inertial vacuum.

"The explanation comes from a consideration of the agency that brings about the acceleration of the detector in the first place. As the detector accelerates, its coupling to the field causes the emission of quanta, which produces a resistance against the accelerating force. The work done by the external force to overcome this resistance supplies the missing energy that feeds into the field via the quanta emitted from the detector, and also into the detector which simulaneously makes upward transitions. But as far as the detector is concerned, the net affect is the absorption of thermally distributed quanta."

Of the three effects, I have worked through (a few years ago) the Unruh effect in some detail, looked at some of the details for Hawking radiation from eternal Schwarzschild black holes, and hardly looked at all at cosmological radiation.

As I said before, cosmological radiation is not just associated with expanding universes the have positive acceleration. I think that the point that John Baez makes is as follows.

As pervect noted, cosmological radition is presently very small - much smaller than the cosmic background radiation. As our universe expands, the scale factor (according to present models) will go to infinity, causing the CMB temperature to tend to zero. At some point in the very distant future, cosmological (Unruh) radiation will dominate the CMB radiation.

Regards,
George

 Quote by George Jones For now, I'm going largely to restrict my comments to this passage.
Thank you, I appreciate your efforts here.

I'm following my suspicion that dark energy as well as dark matter may be caused by this acceleration radiation. I've done the calculation that shows that even if all of space has a radiation calculated by assuming that it has the acceleration that the edge of the observable universe has (though places half that distance from us would not be accelerating that much) - this has turned out to be far less than the energy density of the cosmological constant. So now I'm grasping at straws, and it occurs to me that it seems these "acceleration radiation" effects assume one frame of reference accelerating with respect to one other. OK, but we know that every place in the universe is accelerating away from EVERY other place. Not only is a distant point accelerating away from us, but it is accelerating away from every other point as well. Does this mean that we might have to integrate that effect to account for the many different reference frames that each point is accelerating away from? Thanks.
 Recognitions: Gold Member Science Advisor Astrophysics is the science of understanding 'what goes on up there' (astro-) by understanding 'what goes on down here' (-physics) - in the laboratory. Rather than beginning to understand the Unruh effect of the expansion of the universe start with the laboratory. The Unruh effect is observed for non-inertial observers, we are non-inertial observers. This effect predicts that empty vacuum in a suported laboratory should have a non-negative density in that frame of reference. I make this Unruh vacuum density to be ~ 10-113 gms/cc, as a point of interest SSC predicts a vacuum density near the Earth of ~ 10-9 gms/cc, caused by reconciling the divergence of its two field equation solutions for a gravitational field. Garth

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Thank you George. I was thinking about my question you tried to answer and I am not sure to understand this:
 Quote by George Jones "The explanation comes from a consideration of the agency that brings about the acceleration of the detector in the first place. As the detector accelerates, its coupling to the field causes the emission of quanta, which produces a resistance against the accelerating force. The work done by the external force to overcome this resistance supplies the missing energy that feeds into the field via the quanta emitted from the detector, and also into the detector which simulaneously makes upward transitions. But as far as the detector is concerned, the net affect is the absorption of thermally distributed quanta."
However, I came to another conclusion: The question is not correctly formulated, because it is unclear that spacetime with a scalar field in it should be flat at all. I mean, the usual treatment of Unruh radiation starts with a scalar field in flat spacetime. Radiation in the accelerated frame should induce a back-reaction. However, even in the inertial frame we do not know how to compute the quantum corrections to the flat geometry. Nevertheless spacetime is assumed to be flat (as usual in QFT) per definition. Same should then apply for the accelerated frame. Does this "answer" make sense?

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 Quote by hellfire Radiation in the accelerated frame should induce a back-reaction. However, even in the inertial frame we do not know how to compute the quantum corrections to the flat geometry. Nevertheless spacetime is assumed to be flat (as usual in QFT) per definition.
Sometimes, for simplicity, back-reaction is negelcted, but in the example I gave, there is no back-reaction caused by quantum field because the renormalized stress energy tensor of the field is zero in all frames.

Other examples could start with an excited field for the inertial observer, and then there would be back-reaction.

Regards,
George

Forum,

As I have had a recent post in this thread removed for being too speculative, I wish to resubmit the ideas presented in the removed post as questions. I will include a couple of citations in reference to these questions that I hope will allow it to get by the censors as being in the ballpark of opinions that are "currently held by the scientific community." Here goes:

 The aim of all this activity is, of course, to answer the question, what is the dark energy? If w is about -1, then a cosmological constant might be the solution. If w is more than -1, the right answer might be quintessence. And we cannot rule out a new twist to gravity that even Einstein did not foresee: while most theories that link gravitational and quantum physics predict novel behaviour on microscopic length scales or at very early times in the universe, few, if any, anticipate new effects on the largest length scales in the present day. And what if w is less than -1? Whatever the answer, something mysterious is at work in the cosmos.
Please note particularly where it states: "And we cannot rule out a new twist to gravity that even Einstein did not foresee:"

And in this citation:
 Other ideas Some theorists think that dark energy and cosmic acceleration are a failure of general relativity on very large scales, larger than superclusters. It is a tremendous extrapolation to think that our law of gravity, which works so well in the solar system, should work without correction on the scale of the universe. However, most attempts at modifying general relativity have turned out either to be equivalent to theories of quintessence, or are inconsistent with observations. Other ideas for dark energy have come from string theory, brane cosmology and the holographic principle, but have not yet proved as compelling as quintessence and the cosmological constant.
Note particularly where it states: "Some theorists think that dark energy and cosmic acceleration are a failure of general relativity on very large scales, larger than superclusters. It is a tremendous extrapolation to think that our law of gravity, which works so well in the solar system, should work without correction on the scale of the universe."

So, with these references in mind, I will reitterate the main concepts in my deleted post:

It seems to me that the current thinking in dark energy is to look for an energy density between the galaxies to explain it. My questions are:

What if the energy density between galaxies is irrelevent? What if the galaxies are apparently simply falling outward toward the CEH, rather than being forced outward from an internal pressure?

What if due to a quirk of relativity, the universe appears to be accelerating from all reference frames, but may or may not actually be accelerating? What if the apparent expansion acceleration is simply caused by relativistic effects of very distant mass in motion?

Could these proposed relativistic effects cause an apparent infinite density to the CEH that essentially causes it to behave much like a black hole event horizon in that it emits Unruh and other radiation (that we perceive as the CMBR) and gravity/acceleration (that we perceive as the effects of dark energy)?

That is, (in deference to my citations) could gravity itself be a relativistic effect in the extrenum of the cosmological event horizon?

Note: This post has been edited by ubavontuba
 Recognitions: Gold Member Science Advisor From my calculations above is it not clear that any Unruh coming from the CEH is many orders of magnitude smaller than that required for the CMB? Garth

 Quote by Garth From my calculations above is it not clear that any Unruh coming from the CEH is many orders of magnitude smaller than that required for the CMB? Garth
No, but I've always had trouble paying attention in math.

Anyway, let's think about what's happening at the CEH. Isn't mass heading (falling?) into it?

Now let's think about the CEH like how we might think about black holes. In this case, let's think about black holes with halos of matter around and falling into them. They emit a lot more energy in IR than simply the Unruh and Hawking radiation, don't they?

P.S. It looks to me like the expansion model must still hold, but the universe needn't be quite as young or old as we might measure. Also, it isn't the concept of expansion that is in question, but rather the acceleration effect known as dark energy. In other words, is it possible that even a linear expansion might be perceived as an acceleration in the extrenum of relativity and the CEH?

 Quote by George Jones ... "The explanation comes from a consideration of the agency that brings about the acceleration of the detector in the first place. As the detector accelerates, its coupling to the field causes the emission of quanta, which produces a resistance against the accelerating force. The work done by the external force to overcome this resistance supplies the missing energy that feeds into the field via the quanta emitted from the detector, and also into the detector which simulaneously makes upward transitions. But as far as the detector is concerned, the net affect is the absorption of thermally distributed quanta."
Is the cosmological constant or dark energy considered to be the due to the acceleration of spacetime? Or is it the other way around? Is the cosmological constant considered to be due to the acceleration of the expansion rate or the acceleration of a constant expansion rate as more distant objects recede more quickly as they recede?

I wonder if acceleration radiation is the same as vacuum energy of the cosmological constant? If so, then it would seem that since zero acceleration gives zero energy density, then inertial frames traveling arbitrarily close to any point in space (even with zero velocity) would feel no temperature and would prove that there is no zero point energy/vacuum energy/cosmological constant. I could use some clarification on this. Thank you.

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 Quote by Mike2 Is the cosmological constant or dark energy considered to be the due to the acceleration of spacetime? Or is it the other way around?
The latter
 Is the cosmological constant considered to be due to the acceleration of the expansion rate or the acceleration of a constant expansion rate as more distant objects recede more quickly as they recede?
The cosmological constant is one possible cause of cosmic acceleration.
 I wonder if acceleration radiation is the same as vacuum energy of the cosmological constant?
As in a previous post above any acceleration radiation (if it exists in the first place) is many many orders of magnitude smaller than the CMB or the cosmological constant energy density
 If so, then it would seem that since zero acceleration gives zero energy density, then inertial frames traveling arbitrarily close to any point in space (even with zero velocity) would feel no temperature and would prove that there is no zero point energy/vacuum energy/cosmological constant. I could use some clarification on this. Thank you.
The temperature we "feel" is that of the CMB radiation, 2.70K, a real temperature of radiation emitted by real hot gas (at z >1000). It might indeed be the case that there is no cosmological constant but that possibility would not be proven by the non-observance of cosmological Unruh radiation.

Garth

 Quote by Garth As in a previous post above any acceleration radiation (if it exists in the first place) is many many orders of magnitude smaller than the CMB or the cosmological constant energy
I wonder if particle creation (virtual or real) might be types of acceleration radiation - even the zero point energy or the cosmological constant. What I mean is this: force itself is described in terms of mass(energy) and the acceleration. Even with virtual particles, they are produced in pairs (and only pairs?) that move away from each other and then come back together. So even there they are accelerating with respect to each other. So there seems to be some sort of accelerating reference frames even at the local scale that produces particles (or is at least associated with particle production). Any thoughts on this? Thanks.

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 Quote by Mike2 I wonder if particle creation (virtual or real) might be types of acceleration radiation - even the zero point energy or the cosmological constant. What I mean is this: force itself is described in terms of mass(energy) and the acceleration. Even with virtual particles, they are produced in pairs (and only pairs?) that move away from each other and then come back together. So even there they are accelerating with respect to each other. So there seems to be some sort of accelerating reference frames even at the local scale that produces particles (or is at least associated with particle production). Any thoughts on this? Thanks.
You are mixing up Quantum effects and GR gravitational effects. As we do not yet have a quantum gravity theory your speculation cannot be assessed. In virtual particle pair production there is no sum total change of momentum and no overall acceleration so there is no Unruh radiation, or are you claiming to have detected it?

Garth

 Quote by Garth You are mixing up Quantum effects and GR gravitational effects. As we do not yet have a quantum gravity theory your speculation cannot be assessed. In virtual particle pair production there is no sum total change of momentum and no overall acceleration so there is no Unruh radiation, or are you claiming to have detected it? Garth
I'm just marvelling at the fact that acceleration produces radiation, thus particles. OK.... how many ways are there to produce "particles". It would seem to me that there would have to be only one way of producing particles. Some fundamental transformation is involved. If it is acceleration in one instance, could it be acceleration in all instances? So I remembered that virtual particles do appear in pairs, they first separate, and then come back together in a brief enough time so as to not violate the uncertainty principle. Separating and coming back together involves a change in velocity, thus it involves acceleration as well. The only alternative is to suppose particles can be produced in many different inequivalent ways, when they all end up having the same properties.

This would give us a connection between the properties of spacetime and the properties of matter, so that QFT might lead to QG.
 Forum, Hey, take a look at this article in the current issue of NewScientist! Apparently life inside a black hole, isn't quite such an absurd notion afterall.