Is Quantum Geometry the Zero Point Energy?

[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.

 

[MistyMountain]

I think you're on to something.

Please elaborate, and then I will add something to this.

Happy New Year!

 

[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.

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?

 

[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).

 

[Mike2]

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). ...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.

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.

What is IIRC ?

"If I recall correctly"

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

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

 

[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 ...

 

[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

 

[rtharbaugh1]

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

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

 

[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:

 

[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.

 

[Careful]

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

Not at all : two comments to start with
(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

 

[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

 

[rtharbaugh1]

Not at all : two comments to start with
(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

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.

 

[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.

 

[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

 

[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).

Two comments :
(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).

 

[Mike2]

? 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.

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?

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).

What is the title of this book?

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

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?

 

[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.

 

[Mike2]

** 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.

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?

 

[rtharbaugh1]

** 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).
Two comments :
(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).

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

http://physics.nist.gov/cgi-bin/cuu/Value?rp|search_for=proton+radius

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

0601022301 GMT-6 186

 

[Careful]

** 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. **

(a) depends on your particle notion (and therefore your vacuum state). And as you know the latter is a *global* object which does depend on an infinity of observers.
(b) There would probably be corrections to the thermal state. By the way Hawking radiation comes from particle creation and annihilation near the Horizon in the asymtotic region and *not* from the inside of the BH !

** So it can not be the event horizon itself that is causing the Hawking radiation, right? **

Yes it is (with respect to the asymptotic observers in the Hawking effect). It is also the particle horizon which causes the radiation in the Unruh effect (and not the acceleration of the observer as is too often told). Carlo Rovelli and Pierre Martinetti have recently made an (impossible) attempt in arguing that the acceleration is the *cause* of the radiation : the paper was diamond's temperature I think. I say impossible because it is clear from the principles of QFT that such localized interpretation is ruled out.

I advise you to study these things in detail and develop a proper understanding for them.

 

[Careful]

** I am more interested in the concepts than in the details, but it is good to keep things straight. **

You can only get to useful concepts when you know the correct scales. :grumpy:


** In this case you picked out the error in detail and ignored the idea, I am not sure why. Easier target? **

No, I did not (there was simply no well defined idea).

** So, do you agree that classical spacetime is broken by quantum effects or not? **

I don't care: the energy scales which should be involved for that to happen are way too high (PLANCK SCALE) and should not be of any interest yet (in any sensible attempt to unification).

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

Right, so you contradict yourself when you speak about fractal dimensions.

**
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? **

Just caculate the scaling dimension in terms of a length scale and you will observe that it is not an integer.

**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. **

Yes, but this is perhaps not a *perfect* fractal (probably the self similarity breaks down at some scale or another)

**
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. **

The dimension (for a random walker) of space comes out 1,5 on the smallest length scales and increases up to two (for three dimensional spatial building blocks). So you have to thicken out space in the time direction (which you can do in a covariant way - but why care since the whole business of CDT is not covariant anyway).


Same comment to you: you are making wild speculations about the most the most difficult stuff in physics (learn first the conventional material and then go ahead).

Cheers,

Careful

 

[Chronos]

The only way to make any sense of this stuff is to reverse engineer a solution that yields GR and QT at the appropriate scales. Since GR and QT are mutually incompatible, any such effort is currently doomed from the start - sort of like a proof that 1 + 1 = 3. Further complicating matters, there are a 'landscape' of possible mathematical maneuvers that might lead you to this, or almost any other conjecture, if properly tweaked.

 

[selfAdjoint]

Since GR and QT are mutually incompatible, any such effort is currently doomed from the start - sort of like a proof that 1 + 1 = 3.

That has been the conventional wisdom for many years, but with such breakthroughs as asymptotic safety on the table, perhaps it is not so completely impossible after all?

 

[Mike2]

(b) There would probably be corrections to the thermal state. By the way Hawking radiation comes from particle creation and annihilation near the Horizon in the asymtotic region and *not* from the inside of the BH !

Since everything is destroyed by the time it makes it within the BH, it might just be that there is a temperature gradient do to a matter distribution that is a continuation of the Hawking radiation continued inside the BH. I don't think a local observer just outside the horizon would see a discontinuity in radiation as he just enters the horizon.

It is also the particle horizon which causes the radiation in the Unruh effect (and not the acceleration of the observer as is too often told).

Since both horizon and acceleration co-exist in conjuction, always, it is not possible to say which is the cause and which is the effect. So a derivation claiming the cause is acceleration is just as valid as the claim that the cause is a horizon. Both are different interpretations of the same effect.

 

[Careful]

**Since everything is destroyed by the time it makes it within the BH, it might just be that there is a temperature gradient do to a matter distribution that is a continuation of the Hawking radiation continued inside the BH. I don't think a local observer just outside the horizon would see a discontinuity in radiation as he just enters the horizon. **

You do not seem to grasp the difficulty in defining the fundamental degrees of freedom of the quantum field *inside* the black hole. Neither do you seem to understand that the Hawking effect is only seen by a stationary class of observers with a Killing bifurcation horizon; the observer which crosses the horizon is roughly speaking like the inertial observer in Minkowski and will observe no such thing as a thermal spectrum.


** Since both horizon and acceleration co-exist in conjuction, always, it is not possible to say which is the cause and which is the effect. **

That is utter nonsense. Some observers can accelerate for a while and become inertial later again, there is no particle horizon created in the process.

 

[rtharbaugh1]

** I am more interested in the concepts than in the details, but it is good to keep things straight. **
You can only get to useful concepts when you know the correct scales. :grumpy:
** In this case you picked out the error in detail and ignored the idea, I am not sure why. Easier target? **
No, I did not (there was simply no well defined idea).
** So, do you agree that classical spacetime is broken by quantum effects or not? **
I don't care: the energy scales which should be involved for that to happen are way too high (PLANCK SCALE) and should not be of any interest yet (in any sensible attempt to unification).
**
I believe in trying to make definitive statements. Statements, like theories, that cannot be falsified are not really very useful, are they? **
Right, so you contradict yourself when you speak about fractal dimensions.
**
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? **
Just caculate the scaling dimension in terms of a length scale and you will observe that it is not an integer.
**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. **
Yes, but this is perhaps not a *perfect* fractal (probably the self similarity breaks down at some scale or another)
**
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. **
The dimension (for a random walker) of space comes out 1,5 on the smallest length scales and increases up to two (for three dimensional spatial building blocks). So you have to thicken out space in the time direction (which you can do in a covariant way - but why care since the whole business of CDT is not covariant anyway).
Same comment to you: you are making wild speculations about the most the most difficult stuff in physics (learn first the conventional material and then go ahead).
Cheers,
Careful

** You can only get to useful concepts when you know the correct scales. :grumpy:

This does not seem correct to me. There are many useful concepts which cross all scales. The idea of fractal dimensions is one such concept. Self-similar repetitions in a gradient of scales is common in nature. Are you suggesting that we should all be memorizing tables of numbers rather than looking for patterns?

** In this case you picked out the error in detail and ignored the idea, I am not sure why. Easier target? **
No, I did not (there was simply no well defined idea).

You have avoided the question again. Most respectable researchers, in my limited experience, are not unwilling to admit that they just don't know.

I will restate the idea, and if you feel it is not well-defined, I should expect you to inquire as to the correct definitions. I will make it a positive statement, not because I know it to be a fact, but because that way it will be easier to refute, if there is some error.

QUANTUM EFFECTS VIOLATE THE CLASSICAL SPACETIME MODEL.

** So, do you agree that classical spacetime is broken by quantum effects or not? **
I don't care: the energy scales which should be involved for that to happen are way too high (PLANCK SCALE) and should not be of any interest yet (in any sensible attempt to unification).

I tried to make it clear that quantum effects are not limited to high energy scales, and gave the example of condensed matter. You actually agreed to that, but now seem to be retracting. In another example, electrons escape from quantum wells. This happens at available energies. These things and other quantum effects including virtual particles are not at all beyond our reach. Some of us here feel that we may gain understanding by examining cases where quantum effects seem to contradict the expectations of classical physics.

** I believe in trying to make definitive statements. Statements, like theories, that cannot be falsified are not really very useful, are they? **
Right, so you contradict yourself when you speak about fractal dimensions.

Could you please be specific about where you see a contradiction? I am very interested in useful criticism of my thoughts, and in fact that is the main reason I post them.

Just caculate the scaling dimension in terms of a length scale and you will observe that it is not an integer.

Please give an example of this so we can get down to particulars. Surely you can't mean to "just caculate" any length scale at all? Are you saying that there is no length scale that is not fractal? Do we then never get integer dimensions? If we never get integer dimensions, then all the calculations of dimension turn out fractal, and then it would seem that there is no especial reason to say that spacetime is fractal near the Planck scale.

My question to you was addressed to the fact that Loll et al say that spacetime is fractal near the Planck scale. Why would they have to say that if they only mean that spacetime is fractal at all scales? I suspect that CDT implies a special fractal nature at small scales, but I have not seen through the math. I was hoping that you had a clearer view.

Yes, but this is perhaps not a *perfect* fractal (probably the self similarity breaks down at some scale or another)

Self similarity is often a recognition feature of fractals, but it is not universal to fractals. Could you explain what you mean by "a *perfect* fractal"? I don't recall seeing that term in Barnsley or in Mandelbrot. I do find that a subset of a metric space is said to be perfect if it contains all of its limit points, but how does that apply to the coastline of England? Are you saying that the coastline of England maybe does not contain all of its limit points? So maybe part of the coastline of England might stick out into Denmark or Dimension X or someplace? Well I am being silly of course, but really I would like to know how to connect the idea of self-similarity to the idea of perfect sets.

**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. **
The dimension (for a random walker) of space comes out 1,5 on the smallest length scales and increases up to two (for three dimensional spatial building blocks). So you have to thicken out space in the time direction (which you can do in a covariant way - but why care since the whole business of CDT is not covariant anyway).

Again you repeat the conclusion without giving me any evidence. As far as I know a random walk is a statistical method for estimating large sums or their averages from a much smaller and more accessible amount of data. One might, for example, estimate the number of bars in Manhattan by randomly walking down a fraction of the streets, counting up the number of bars in your sample, and then multiplying by the appropriate factor to make the fraction equal the known total of streets. This does not provide a precise estimate, and although it may be useful, it tells me nothing about the distribution pattern of bars in Manhattan. I do not see how the drunkard's walk tells me anything about the nature of spacetime at small scales, and still wonder what, exactly, Loll means by this. I don't know what she means. I would like to know. I was hoping that you knew and would be able to comment. Of course, if you just don't care, and are only here to repeat other worker's conclusions, I can hardly expect to get a useful answer.

By the way, strings branes and lqg are all theoretical and beyond the reach of current experiments. If you just don't care about such things, why, exactly, are you so prolific on this board? Personally, I like free association and the creative insights that it gives. Yes, we are working on difficult questions. The mood on this board, at least, has been one of encouraging thinkers, not discouraging them. As far as I know, no one here is a prime authority, and few pretend to be one. You have given some good advice. But your comments have not been very helpful so far. I am left wondering if you have taken it.

cheers

R

 

[Careful]

By the way, strings branes and lqg are all theoretical and beyond the reach of current experiments. If you just don't care about such things, why, exactly, are you so prolific on this board? Personally, I like free association and the creative insights that it gives. Yes, we are working on difficult questions. The mood on this board, at least, has been one of encouraging thinkers, not discouraging them. As far as I know, no one here is a prime authority, and few pretend to be one. You have given some good advice. But your comments have not been very helpful so far. I am left wondering if you have taken it.
cheers
R

Does someone have the time to explain to R what I said before: my answers were crystal clear IMO and I wasn't avoiding any issues AFAIK.

Cheers,

Careful

 

[rtharbaugh1]

You show yourself once again to be interested in insult, not in idea. I am disappointed. I will resume my silence on your behalf.

R

 

[Mike2]

**Since everything is destroyed by the time it makes it within the BH, it might just be that there is a temperature gradient do to a matter distribution that is a continuation of the Hawking radiation continued inside the BH. I don't think a local observer just outside the horizon would see a discontinuity in radiation as he just enters the horizon. **
You do not seem to grasp the difficulty in defining the fundamental degrees of freedom of the quantum field *inside* the black hole. Neither do you seem to understand that the Hawking effect is only seen by a stationary class of observers with a Killing bifurcation horizon; the observer which crosses the horizon is roughly speaking like the inertial observer in Minkowski and will observe no such thing as a thermal spectrum.
** Since both horizon and acceleration co-exist in conjuction, always, it is not possible to say which is the cause and which is the effect. **
That is utter nonsense. Some observers can accelerate for a while and become inertial later again, there is no particle horizon created in the process.

You are beginning to sound like a detractor. "accelerate and decelerate to an inertial reference frame again" - that's not what I was talking about, and you know it. I was talking about acceleration only, and you know it. Show me any instance where one is accelerating and where there is no horizon involve. True, for small accelerations the horizon may be far away indeed, such as the cosmological event horizon. But still where there is one there is always the other.
And I don't understand your objection to Torsten, either. Didn't we already know that singularities were solutions to Einsteins equation, which also gave curved spacetime around them? And didn't we already know that integrating the gravitational field on a closed surface give us the mass inside, no matter what size the surface is? And isn't this another discription of a Dirac Delta function?

 

[Careful]

** You are beginning to sound like a detractor. "accelerate and decelerate to an inertial reference frame again" - that's not what I was talking about, and you know it. **

You said that acceleration is equivalent to the existence of an horizon, you never added that the acceleration had to be constant for an infinite amount of time! Such situation is highly idealized and never occurs in practice.

** I was talking about acceleration only, and you know it. Show me any instance where one is accelerating and where there is no horizon involve. **
Very simple (if the acceleration is not necessarily constant) : take a sheet of paper and draw a global congruence of curved timelike curves.

** True, for small accelerations the horizon may be far away indeed, such as the cosmological event horizon. But still where there is one there is always the other. **

Nope, what I wanted to learn you is that the Unruh effect is a *global* result and has nothing to do with the local acceleration of a rocket. Therefore, I do not believe it is a meaningful *physical* result - at least not in its present form.

** And I don't understand your objection to Torsten, either. Didn't we already know that singularities were solutions to Einsteins equation, which also gave curved spacetime around them? **

Yes, but the question is whether Torsten's construction gives rise to that kind of singularities. If you would take his definition of the mixed connection and do the math, then you easily see that there is no curvature effect outside the body, so an observer from outside wouldn't notice anything. Therefore, there is no physical matter source involved - and actually it is no so difficult to understand why but for the moment I leave the matter up to Torsten.

Look, mike2, I am always trying to stay polite but I just cannot understand why certain people do not *listen* to what I say such as R (if he actually reads my previous answers carefully, he will see that many of his ``objections´´ are flawed) and constantly argue using quotes they have read in some magazines. On the other hand, you cannot expect me to type out entire courses with all definitions included: if R wants to know the details I mentioned about CDT, he should in the first place look them up in the papers of Loll and Ambjorn instead of bothering me with that.

You, on the other hand, might also benifit from the references I gave you : otherwise I do not understand the purpose of your questioning in the first place.

Cheers,

Careful

 

[Mike2]

** You are beginning to sound like a detractor. "accelerate and decelerate to an inertial reference frame again" - that's not what I was talking about, and you know it. **
You said that acceleration is equivalent to the existence of an horizon, you never added that the acceleration had to be constant for an infinite amount of time! Such situation is highly idealized and never occurs in practice.

Infinity has nothing to do with it, and I think you know this too. Only where there is acceleration there is a horizon. True or false.

** I was talking about acceleration only, and you know it. Show me any instance where one is accelerating and where there is no horizon involved. **
Very simple (if the acceleration is not necessarily constant) : take a sheet of paper and draw a global congruence of curved timelike curves.

I would assume that if the acceleration changed, then so does the horizon. For example the point at which the universe went from deceleration to acceleration, the horizon's distance began to shrink.

** True, for small accelerations the horizon may be far away indeed, such as the cosmological event horizon. But still where there is one there is always the other. **
Nope, what I wanted to learn you is that the Unruh effect is a *global* result and has nothing to do with the local acceleration of a rocket. Therefore, I do not believe it is a meaningful *physical* result - at least not in its present form.

Where did you get "global" from the equations? The equation gives temperature for a given acceleration, that's all. The equation does not ask for the accelerating particle's mass or charge or spin or distance from any other particles, etc. It applies to acceleration, period. I simply assume that the equivalence principle gives an acceleration that can be entered into that equation. This seems straightforward to me.

** And I don't understand your objection to Torsten, either. Didn't we already know that singularities were solutions to Einsteins equation, which also gave curved spacetime around them? **
Yes, but the question is whether Torsten's construction gives rise to that kind of singularities. If you would take his definition of the mixed connection and do the math, then you easily see that there is no curvature effect outside the body, so an observer from outside wouldn't notice anything. Therefore, there is no physical matter source involved - and actually it is no so difficult to understand why but for the moment I leave the matter up to Torsten.

This sounds similar to how they calculate the gravitational field at the surface of a sphere by using the mass inside that surface. It seems just as strange that all the mass outside the surface does not enter the equation (and seems to have no effect) on the gravitational field at a point on the sphere.
Also, it seems you are worried about things outside the support within which quantities are defined. I'm not so sure that it is valid to question results because of undefined quantities. If Torsten leaves undefined quantities outside the support, then nothing right or wrong can be based on undefined things. If a field is defined on a curve and results obtained from the field, then it is not valid to denouce those results because the field in not defined elsewhere.

 

[Careful]

**Infinity has nothing to do with it, and I think you know this too. Only where there is acceleration there is a horizon. **

No, there is not, you clearly did not take your sheet of paper. Do you know the derivation or not?

**
I would assume that if the acceleration changed, then so does the horizon. **

You simply do *not* seem to get that a vacuum state and the associated Fock particle notion are *global* concepts and in the Uruh effect, there is no point in throwing the low frequences away by making a cutoff on lab scale (since the very long wavelengths are all we get). Did you read the paper of Rovelli which I suggested to you ?? I guess not, since you would have understood my comments otherwise.

**
Where did you get "global" from the equations? The equation gives temperature for a given acceleration, that's all. **

Question : what does temperature mean and how is it related to the ergodic hypothesis ?

**The equation does not ask for the accelerating particle's mass or charge or spin or distance from any other particles, etc. It applies to acceleration, period. I simply assume that the equivalence principle gives an acceleration that can be entered into that equation. This seems straightforward to me. **

Again, this is the THIRD time that I urge you to see HOW the equation is DERIVED which requires a proper understanding of QFT. Please, have some respect for people who refer you to this work in good faith.


** Also, it seems you are worried about things outside the support within which quantities are defined. I'm not so sure that it is valid to question results because of undefined quantities. If Torsten leaves undefined quantities outside the support, then nothing right or wrong can be based on undefined things. If a field is defined on a curve and results obtained from the field, then it is not valid to denouce those results because the field in not defined elsewhere. **


I beg you pardon ! The gravitational field is stilll well defined by the metric outside the body (and as I said before, this remains invariant under Torsten's construction). Please give the honor to Torsten for a reply, I remember having said something similar (to you ?) previously : it seems I was right from the very beginning (and I might be just right again, imagine yourself ).

Cheers,

Careful

 

[Mike2]

**Infinity has nothing to do with it, and I think you know this too. Only where there is acceleration there is a horizon. **

No, there is not, you clearly did not take your sheet of paper. Do you know the derivation or not?

The question was: in what physical situation is there an acceleration without a horizon?

The Black Hole event horizon is inside a gravity well that is an accelerated reference frame with respect to far away. With the Cosmological Event Horizon there is faster speed of expansion with distance (an acceleration). And with the acceleration of a particle there is a distance behind the particle at which light cannot reach the particle (assuming it continues to accelerate at that rate).

**
Where did you get "global" from the equations? The equation gives temperature for a given acceleration, that's all. **

Question : what does temperature mean and how is it related to the ergodic hypothesis ?

AFAIK you can get a temperature from the speed of one particle, and this is a local effect.

 

[Careful]

** The question was: in what physical situation is there an acceleration without a horizon? **

An inertial observer which puts on his rocket engine for a while and then switches it off again is a nice example (which I gave you already). But, to avoid any cunfusion : what definition of horizon do you use ?

** The Black Hole event horizon is inside a gravity well that is an accelerated reference frame with respect to far away. **

That does not make any sense, where did you get that from (I guess I know what you want to say but you state it miserably) ?

**
AFAIK you can get a temperature from the speed of one particle, and this is a local effect. **

? This is entirely false and moreover, you did not seem to grasp that the notion of a particle *itself* is a global one which effectively extends over a great distance in this case since the Unruh temperature is terribly close to the absolute zero point.

Again, you might want to study this paper of Rovelli. There, you will see that some extra physical *assumption* (that of thermal time) is needed to even make (remotely) sense of the Unruh effect in terms of ``localized´´ acceleration. I do not remember the exact details anymore but I definately was far from happy about it.

Cheers,

Careful