# Is Quantum Geometry the Zero Point Energy?

1. Dec 31, 2005

### Mike2

I wonder, since the seathing quantum foam of the Zero Point Energy is made up of virtual particles that may be extended objects that have a geometry of their own as strings, branes, etc, could the quantum foam be the quantum nature of spacetime itself that we are looking for? Thanks.

2. Dec 31, 2005

### MistyMountain

I think you're on to something.

Happy New Year!

3. Jan 1, 2006

### Mike2

Well, let me think.... If there is Hawking radiation associated with the curved space of black holes, then maybe this can be taken as a general truth for any curved space. Then there will be virtual particles associated with the tiny worm-holes and tiny black-holes and tiny curved geometry of any quantum spacetime foam. Then perhaps the occurance of these associated virtual particles might just be an equivalent expression for the spacetime quantum foam. The recent paper by Torsten asserts an equivalence between particles and curved spacetime IIRC. And perhaps where the quantum field is more dense there is a greater ability for particles to propagate so that there is an overall effect of acceleration. Your turn, what do you think?

4. Jan 2, 2006

### Careful

** Well, let me think.... If there is Hawking radiation associated with the curved space of black holes, then maybe this can be taken as a general truth for any curved space. **

There are no curvature considerations whatsoever involved in the computation of Hawking radiation (and actually the only nonzero curvature present is to be found in the Weyl tensor). The reason for this is to be found in the choice of Rindler time for the asymptotic observers and the gigantic blueshift of the latter with respect to Minkowski time (in the Lorentz frame of the black hole) in the limit to the Horizon. Therefore, Hawking radiation is only correct for early times (as we call it) : that is for observers which are close´´ to the Horizon at infinity (close in the Lorentz frame). Rigorous results concerning late times are not known AFAIK.

Therefore, Hawking radiation can only serve for quantum gravity if you interpret the latter in the context of a scattering experiment in a ordinary QFT.

** The recent paper by Torsten asserts an equivalence between particles and curved spacetime IIRC. **

What is IIRC ? As far as I am concerned, Torsten did not show anything yet (he must be very ill as he did not return yet).

5. Jan 2, 2006

### Mike2

Could you give a little more on that?

I thought I read somewhere that Hawking radiation was a form of Unruh radiation which involved accelerated reference frames which applied to gravity through the equivalence principle means spacetime is curved. I don't think you can separate curved space from accelerated reference frames from the Unruh effect.

"If I recall correctly"

I did notice that he put off the publishing of his book to June. Perhaps he is prepareing material that addresses your objections.

6. Jan 2, 2006

### Careful

**Could you give a little more on that?
I thought I read somewhere that Hawking radiation was a form of Unruh radiation which involved accelerated reference frames which applied to gravity through the equivalence principle means spacetime is curved. I don't think you can separate curved space from accelerated reference frames from the Unruh effect. **

??? The Unruh effect happens in flat Minkowski spacetime with respect to a congruence of KILLING observers with an event horizon. It is the event horizon, which changes the Minkowski vacuum state into a Rindler thermal state.
Check out the book of Wald on QFT in curved spacetime. Of course, curved spacetime generalizations are possible for the reasons I mentioned previously (see the original black hole calculation of Hawking for example).

Reference frames do not curve spacetime; take any non inertial coordinates in Minkowski and calculate the Riemann tensor - it will stay zero.

** "If I recall correctly"
I did notice that he put off the publishing of his book to June. Perhaps he is prepareing material that addresses your objections. **

Then he might still postpone it even for longer ...

7. Jan 2, 2006

### rtharbaugh1

IIRC...If I Recall Correctly...quantum foam is a conceptual model introduced to describe the difficulty of pinpointing any geometry below the Fermi scale, about 10^-11 meters, in the range of quark and gluon interactions. As such it is a kind of throwing in the towel, a surrender to uncertainty.

Zero Point Energy, as far as I have been able to gather, is the idea that even absolutely empty space has some residual energy.

Branes and strings are models which suggests that the objects we see as point-like particles have structures extended in dimensions we do not see. We only see the point, a kind of cross section of the string, which itself is a kind of cross section of the brane.

Why don't we see the extensions in other dimensions?

1. They are too small to be seen with our technology (Calabi-Yau manifolds).
2. They exist in other universes parallel to our own (Many World theory)
3. They are fractal dimensions and our observational apparatus (consciousness) selects for an integer number of them, disregarding the fractal (virtual) parts.

Number three above is my own current working hypothesis. I like it because it implies that we might make progress by refining our vision.

Any corrections are appreciated.

Richard

8. Jan 2, 2006

### rtharbaugh1

I think the interesting point here is that a moving observer experiences Unruh radiation....that may be interpreted as a change of virtual particles to real particles in the acceleration process, in the frame of the accelerated observer. Just a thought.

R

9. Jan 2, 2006

### Careful

** IIRC...If I Recall Correctly...quantum foam is a conceptual model introduced to describe the difficulty of pinpointing any geometry below the Fermi scale, about 10^-11 meters, in the range of quark and gluon interactions. **

Euhh ??? You mean the Planck scale I guess which is 10^{-24} times smaller

**
Zero Point Energy, as far as I have been able to gather, is the idea that even absolutely empty space has some residual energy. **

Precisely why the QFT notion of vacuum is ridiculous. SED gives at least a more intelligent answer to this

** Why don't we see the extensions in other dimensions? **

Because they might not exist. You forgot to mention the most plausible option.

**
3. They are fractal dimensions and our observational apparatus (consciousness) selects for an integer number of them, disregarding the fractal (virtual) parts. Number three above is my own current working hypothesis. I like it because it implies that we might make progress by refining our vision. **

No, it is absolutely horrible. It is a travesty against Occam's razor and therefore belongs in the world of science fiction.

**Any corrections are appreciated.**

I hope so :tongue2:

10. Jan 2, 2006

### rtharbaugh1

Well, I am just an interested person, not an authority, but I like to think about things.
But I did intend to say Fermi scale, not Planck. Quantum effects are visible even at large scales (cm) in condensed matter for example. The Fermi scale, as I remember, is thought to be the scale at which quantum effects begin to predominate. The Planck scale is a kind of absolute in itself, a horizon if you will, beyond which discussion of space and time is not meaningful.
I hope you do not think I am referring to science fictional ideas of other dimensions. Dimensions are merely systematic application of the rules of measurement.
What is SED?

I have a notation for Fermi coupling at 10^-15cm
R.

Last edited: Jan 2, 2006
11. Jan 2, 2006

### Careful

(a) The derivation of the Unruh effect does *not* prove at all that an accelerated observer is immersed in a thermal bath wrt to the Minkowski vacuum
(b) an accelerating observer at infinity would not even notice the Unruh radiation in practice (if it would exist at all): characteristic times for observation are the order of one year for realistic accelerations. There are zillions of other reasons which could account for this.

Let me tell you, moreover, that the construction of the Rindler vacuum can be seen as a problem for QFT instead of a virtue.

Cheers,

Careful

12. Jan 2, 2006

### Careful

**Well, I am just an interested person, not an authority, but I like to think about things. **

We all do like to think about things.

** Quantum effects are visible even at large scales (cm) in condensed matter for example. **

True

** The Fermi scale, as I remember, is thought to be the scale at which quantum effects begin to predominate. **

Yes, but that has nothing to do with quantum foams. Quantum foams is a name people give to the breakdown of classical spacetime structure.

**I hope you do not think I am referring to science fictional ideas of other dimensions. Dimensions are merely systematic application of the rules of measurement. **

??? It seemed to me pretty clear that you meant that. So what do you mean then, I do not understand.

** What is SED? **

Stochastic electrodynamics, a semiclassical theory which postulates the zero point field to be a real (stochastic) radiation field.

Cheers,

Careful

13. Jan 2, 2006

### rtharbaugh1

I am a humble student and don't have the math to discuss QFT.

I don't know if we can talk about proof of much of anything at these scales.

I'm not sure what you mean by Rindler vacuum. I can put it on my list of things to study.

It seems to me that an observer at infinity doesn't notice much of anything. What can you tell me that you have observed "at infinity"? All of this, as far as i know, is theory, not really observation. The best we can do is make sure our theories account for what the experimentalists observe.

R.

14. Jan 2, 2006

### rtharbaugh1

Classical spacetime structure is broken by quantum effects. Classical theory is not useful below about 10^-9 cm, the proton diameter.

As for what I mean by other dimensions, that is the opening of a long discussion which I will not have time to pursue right now. I will just say that it has nothing to do with the supernatural, but has everything to do with interpretation of observations of reality based on geometry. I begin with questioning the nature of time, assume a strong spacetime equivalence, and attempt to understand, visually, what we mean by four and higher dimensionalities.

Sorry I have to go offline. I hope to return to this tonight or tomorrow.

R.

Last edited: Jan 2, 2006
15. Jan 2, 2006

### Careful

** I am a humble student and don't have the math to discuss QFT.
I don't know if we can talk about proof of much of anything at these scales. **

Sure we can, but that was not the point.

**
I'm not sure what you mean by Rindler vacuum. I can put it on my list of things to study. **

It is the vacuum state determined by the *global* congruence of accelerating observers.

** It seems to me that an observer at infinity doesn't notice much of anything. What can you tell me that you have observed "at infinity"? **

Infinity is a mathematical construct, we mean by this : far enough from the bifurcation horizon.

You might want to read the book of Wald which is self contained enough for any good student.

Cheers,

Careful

16. Jan 2, 2006

### Careful

** Classical spacetime structure is broken by quantum effects. Classical theory is not useful below about 10^-9 cm, the proton diameter.**

The proton diameter is around 10^{-15} metre and not 10^{-11} (which is not possible - the Bohr radius is around 5,3 10^{-11} metre).

(a) it is not known wheter classical theory is useful below these scales or not (actually the stable ground state of the H - atom can be obtained from a (semi) classical theory)
(b) Quantum theory uses classical spacetime as a background and is also expected to breakdown at Planck scale energies.

For being a humble student, your are making pretty definite, albeit incorrect, statements.

** I begin with questioning the nature of time, assume a strong spacetime equivalence, and attempt to understand, visually, what we mean by four and higher dimensionalities. **

That does not make sense at all to me, but go ahead... (PS: fractal dimensions are already dynamically generated in CDT for your information).

17. Jan 2, 2006

### Mike2

I thought the event horizons of black hole were characterized by curves spacetimes. So are you admitting that the there is a ZPE that could give rise to this Hawking radiation?

What is the title of this book?

What I really would like to know is whether the ZPE increases in deeper gravitational wells. Of course it would seem that there is more ZPE when the universe was small and tightly curved up. Is that a prove of the generality of curved space having greater ZPE?

If so, then do particles propagate faster in more dense quantum fields? I'm thinking that higher density quantum fields have more states available in a region of space which would make it easier for particles to find states as they pass through them. This would seem to appear as an acceleration in those regions, right?

18. Jan 2, 2006

### Careful

** I thought the event horizons of black hole were characterized by curves spacetimes. **

The Kerr spacetimes are solutions to the VACUUM field equations and therefore have a vanishing ricci tensor. The only Riemann curvature is therefore in the Weyl tensor (which gives the gravitational force). However, the *derivation* of Hawking radiation does not depend upon these features at all. Check out a real textbook or paper which provides the details.

** So are you admitting that the there is a ZPE that could give rise to this Hawking radiation? **

Might be, might not be. If I were to believe SED, then probably yes.

** What is the title of this book? **

Quantum field theory in curved spacetime and black hole thermodynamics.

** What I really would like to know is whether the ZPE increases in deeper gravitational wells. **

Free QFT's in curved spacetimes are to my knowledge only rigorously developped with respect stationary observers. Ah, I remember now to have seen a paper which also develops free QFT in de Sitter, look into that (but I think that the effects due to particle production were neglible) - if you really insist I will look it up in my pile.

19. Jan 2, 2006

### Mike2

AFAIK, a local observer does not notice that he has fallen behind an event horizon, but he would feel the heat of the Hawking radiation. So it can not be the event horizon itself that is causing the Hawking radiation, right? What else could be causing the radiation if not the acceleration that he feels?

20. Jan 2, 2006

### rtharbaugh1

Yes, I see that you have the details down correctly. NIST website at

has proton radius as .8750 x 10^-15 m. I am more interested in the concepts than in the details, but it is good to keep things straight. In this case you picked out the error in detail and ignored the idea, I am not sure why. Easier target? So, do you agree that classical spacetime is broken by quantum effects or not?

Well I suppose I may as well assume you will not like my choice of words to portray this idea. Broken. Violated. Not useful. The uncertainty principle causes the classical idea of 3 dimensions of space and one of time to break down, give wrong results, etc. Virtual particles appear from what should be nothing, go back into nothing without leaving any trace, except as a kind of field effect. It seems reasonable to me to wonder if Hawking and Unruh radiation give evidence that differences in position (in relation to a black hole) and velocity (in relation to another observer) may result in changes in which and how many particles are "real" and which and how many are virtual.

I believe in trying to make definitive statements. Statements, like theories, that cannot be falsified are not really very useful, are they?

What is it exactly that I have said that does not make any sense to you?

I am glad that you are aquainted with CDT. I have tried to read as much of it as I can understand. Perhaps you can resolve a mystery for me. In what way is spacetime near the Planck scale fractal, and what leads Loll et al to this conclusion? Of course, spacetime has fractal features at any scale. Mandelbrot's first paper, IIRC, has to do with the fractal nature of the coastline of England. But it seems to me now that Loll has implied there is something special about very small scales that results in some especial fractal behavior. What would that be? I hope your mastery of the maths is such that you can enlighten me a little on this question.

Thanks,

Richard

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Last edited: Jan 2, 2006