True Background-Independent Particle Physics

[fzero]

Just trying to see if I understand. Does this correspond to the statement that any consistent background for perturbative string theory must be Ricci flat?

Flux vacua need not be Ricci flat, but there is an analogous constraint on the Ricci curvature. There can be further global constraints from anomaly cancellation.

Also, is it true that any Ricci flat background that has the same topology can be obtained from Minkowski spacetime (or in the first place, what are the Ricci flat solutions with the same topology)?

Depends on what you mean by "obtained." The Schwarzschild BH and Minkowski space don't quite have the same topology but the $$m\rightarrow 0$$ limit of the SBH is Minkowski space (to be precise I guess we'd say $$M_4/\{0\}$$).

The classification of Ricci flat metrics in $$D\geq 4$$ is by no means complete. Even for the stronger CY condition (which may be taken as Ricci flat + admits a Kaehler structure), there is no complete classification. At least in the compact case, it's believed that there probably aren't many more inequivalent CYs than have been discovered, but I don't believe this is proven. I believe that noncompact CYs which are resolutions of orbifolds $$\mathbb{C}^n/\Gamma$$ are more or less classified: this is associated to the so-called McKay correspondence.

 

[atyy]

Depends on what you mean by "obtained." The Schwarzschild BH and Minkowski space don't quite have the same topology but the $$m\rightarrow 0$$ limit of the SBH is Minkowski space (to be precise I guess we'd say $$M_4/\{0\}$$).

The classification of Ricci flat metrics in $$D\geq 4$$ is by no means complete. Even for the stronger CY condition (which may be taken as Ricci flat + admits a Kaehler structure), there is no complete classification. At least in the compact case, it's believed that there probably aren't many more inequivalent CYs than have been discovered, but I don't believe this is proven. I believe that noncompact CYs which are resolutions of orbifolds $$\mathbb{C}^n/\Gamma$$ are more or less classified: this is associated to the so-called McKay correspondence.

I was thinking of the picture of strings on a curved background. In some cases, this can also be thought of as strings on a flat background, with the curvature obtained as a coherent state of gravitons (seen as some mode of a string). How far can this dual picture be pushed, ie. can every background with the same topology be seen as a coherent state of gravitons?

 

[fzero]

I was thinking of the picture of strings on a curved background. In some cases, this can also be thought of as strings on a flat background, with the curvature obtained as a coherent state of gravitons (seen as some mode of a string). How far can this dual picture be pushed, ie. can every background with the same topology be seen as a coherent state of gravitons?

That's still a perturbative calculation, so I would say it applies to backgrounds which are close to flat space and wouldn't want to push it much further. The framework of string theory suggests that any geometry can be related to appropriate sources. However, perturbation theory does not generally suffice to make the connection. For instance, we know that there are some exact backgrounds that we can construct by including nonperturbative D-branes. In those cases, we can trust perturbation theory in the weak field far from the source.

 

[rogerl]

The past days. I was rereading String Theory pop-sci books like Trouble With Physics, Philosophy Meets Physics at the Planck Scale, Elegant Universe and re-watching Brian Green PBS 3 part-Elegant Universe to get more ideas about this weird duality where strings move in a fixed background yet they emit gravitons that make spacetime appear curved. I guess this strange behavior is because of the perturbative version of string theory? When we can make it non-perturbative and make it totally background indepedent. I wonder how the gravitons add up to the BI formulation. (?)

Also I wonder. Isn't it that M-theory spacetime should have 11-dimensions. 6 are curled up. In Brian Greene part 3 of the PBS Elegant Universe DVD. There's this part where he dialed up a phone to a parallel brane where live a Grey Alien. Brian was showing how gravitational wave can travel in between branes and if we and they can decode the message. We can communicate with them. Supposed there are other branes that are really inhabited. Would the entire multiverse be still 11 dimensions?? Is Brian saying that each of the brane is 10 dimension and the multiverse being 11 dimensions that can hold all the 10 dimensional parallel branes?

Btw... Brian mentions only gravity can travel between the branes. But said we don't know what is M-Theory yet. What if in the Third Superstring Revolution, a breakthrough would occur that not only gravity can travel in between branes, but another newly discovered field, then the branes are even more accessible to us. This would truly revolutionize the world.

 

[Fra]

to get more ideas about this weird duality where strings move in a fixed background yet they emit gravitons that make spacetime appear curved. I guess this strange behavior is because of the perturbative version of string theory? When we can make it non-perturbative and make it totally background indepedent. I wonder how the gravitons add up to the BI formulation. (?)

The IDEA of how string theory claims BI in despite of the apparent lack of it, IMHO is only consistent if there is some still yet unclear duality between classical and quantum. IE. some deep aspects of the nature of measurement theory seems needed.

Normally, the classical context is defined by the observer. And quantization takes place RELATIVE to this position. If we claim that this choice is gauge, then obviously we are saying that quantum vs classica information is a matter of perspective too. This must extent the choice of observer beyond just classical.

This challanges the foundations of measurement theory IMO.

I am also convinced that confusion arises because perturbation theory either refers to mathematics, or it refers to how you cna consider possible perturbations(*) of a current information state, that is analogous to a tangent plane to a manifold defining the information states.

These are the conceptual things that I think we need to settle.

Unless I missed it, this classical-quantum sort of weird duality is not sometihng I've even seen addressed in ST. I've seen it mentioned as if it was just a philosophical curiousity, but not really analysed. Maybe some of the string experts here knows of any progress here? Then I would really want to read it.

Note. It should be clear that the isssues is much more complicate (due to the observer issue here) that just "perturbation expansion" around one point. One can imagein you can perturb it to a point, and the perturb further from there. It's not that easy.

That confusion would be due to confusion mathematical perturbation theory, and perturbation in the sense of (*), which is more "physical".

/Fredrik

 

[rogerl]

The IDEA of how string theory claims BI in despite of the apparent lack of it, IMHO is only consistent if there is some still yet unclear duality between classical and quantum. IE. some deep aspects of the nature of measurement theory seems needed.

Normally, the classical context is defined by the observer. And quantization takes place RELATIVE to this position. If we claim that this choice is gauge, then obviously we are saying that quantum vs classica information is a matter of perspective too. This must extent the choice of observer beyond just classical.

This challanges the foundations of measurement theory IMO.

I am also convinced that confusion arises because perturbation theory either refers to mathematics, or it refers to how you cna consider possible perturbations(*) of a current information state, that is analogous to a tangent plane to a manifold defining the information states.

These are the conceptual things that I think we need to settle.

Unless I missed it, this classical-quantum sort of weird duality is not sometihng I've even seen addressed in ST. I've seen it mentioned as if it was just a philosophical curiousity, but not really analysed. Maybe some of the string experts here knows of any progress here? Then I would really want to read it.

Note. It should be clear that the isssues is much more complicate (due to the observer issue here) that just "perturbation expansion" around one point. One can imagein you can perturb it to a point, and the perturb further from there. It's not that easy.

That confusion would be due to confusion mathematical perturbation theory, and perturbation in the sense of (*), which is more "physical".

/Fredrik

Hi, I've been researching about this flat spacetime + graviton thing everywhere and I found the following at sci.physics google newsgroup by a guy called Hobba. He said (random passages):

"As Steve Carlip once explained, it is experimentally impossible to tell a theory formulated in flat space-time that makes rulers and clocks behave as if it was curved from a curved one, so the question is basically meaningless at our current level of knowledge."

"Gravity as space-time curvature emerges from spin two gravitons when the underlying geometrical background is not known, but usually assumed to be Minkowskian flat, so the
methods on QFT theory can be applied."

"But the geometry of the background those strings are emersed in, or even if there is such a
background, is unknown. As another poster pointed out no assumption about it is made, so it could be anything. "

(by Bilge)

"The fundamental attraction to string theory is _not_ 10 dimensional minkowski space. The fundamental attraction is that certain Lie groups have unique features which by their very uniqueness, would explain string theory and the 10 dimensional spacetime in which it resides. E8 for example is the largest of the exceptional lie groups. There is no dimensionality bound on SO(N), or SU(N), but there are only a finite number of exceptional groups. It happens that 10 dimensions works for E8 X E8"

------------------

Fred. What the above is saying is that the spacetime where the strings is embedded is unknown. I thought it is supposed to be flat... unless the strings can somehow access beyond Planck scale where it moves and affected by the unknown geometry inside Planck scale? How do you understand this?

 

[Fra]

"As Steve Carlip once explained, it is experimentally impossible to tell a theory formulated in flat space-time that makes rulers and clocks behave as if it was curved from a curved one, so the question is basically meaningless at our current level of knowledge."

This sounds like something you could say in the context of classical physics and GR. It would be a lame comment in the context of QG. I suspect you took it out of context? Although there are people that maintain this view also in QG - I personally think that's a fallacy, because then you aren't taking the essence of measurement theory seriously.

My point is that things get much more complicated in a measurement theory.

The main conceptual problem does not lie in wether that the background space is flat or curved, the main issue is that it's CLASSICAL. And that you make a SPLIT (which is as per the argument above arbitrary classicaly) but then you quantize one part and keep the other part classical.

If we are talking about "perturbations" of a flat classical background, to a curved classical one. Or perturbing one classical BG into another one, then of course that is a different - much simpler story. But the issue here is much deeper.

So again, the big issue is not about curved vs flat SPLIT (perturbation analogy), it's about quantum vs classical SPLIT; and in particular how the statistics transforms - this is the interesting (and hard) part.

Ie. how to understand how a quantum part, condenses into the classical part. I have my own thinking of this independent of ST.

Somehow I think it's an assumption or conjecture of ST that some kind of such duality exists, but it's not yet understood. Why is it assumed, if it's not understood? That's a good question, but it seems that IF you think string theory must make sense, then somehow this duality must also be there (at least IMHO).

However, such duality can still exists without having anthing to do with string theory. This problem has in it's core nothing to do with string theory.

The whole issue has to do with observables, and context dependent measurement theory and how to combine that with the invariance of observer frames you have in GR.

/Fredrik

 

[Fra]

What the above is saying is that the spacetime where the strings is embedded is unknown.

Unknown as in constrained by a big landscape of backgrounds on which there is not even a probability measure.

There seems to be no consensus even within ST on what this means. One idea could then be to view the string background almost like a gauge choice. But if the symmetry is broken, a background is singled out. How and why does this breaking work?

My picture (non-specific to strings) is that this has to be understood in terms of a generic theory scaling picture - replacing or generalizing RG theory. Thus background independence is generalized into no-prior master theory. There IS no such thing. Other theories can only be described in terms of another theory. A sort of relational thinking, for theories. Thus theree seems to be a need for FULL unification of RG and any front line theory. Since they are in fact no different, just holographically connected.

/Fredrik

 

[rogerl]

Unknown as in constrained by a big landscape of backgrounds on which there is not even a probability measure.

There seems to be no consensus even within ST on what this means. One idea could then be to view the string background almost like a gauge choice. But if the symmetry is broken, a background is singled out. How and why does this breaking work?

My picture (non-specific to strings) is that this has to be understood in terms of a generic theory scaling picture - replacing or generalizing RG theory. Thus background independence is generalized into no-prior master theory. There IS no such thing. Other theories can only be described in terms of another theory. A sort of relational thinking, for theories. Thus theree seems to be a need for FULL unification of RG and any front line theory. Since they are in fact no different, just holographically connected.

/Fredrik

What Hobba is saying is that the spacetime inside the Planck length is unknown. Somehow the spacetime inside Planck can affect the string even if the string is as large as Planck size (?) But the internal part of the string is smaller than Planck size, hence it can be affected by what kind of space time is inside the Planck. What do you think?

 

[Fra]

What Hobba is saying is that the spacetime inside the Planck length is unknown. Somehow the spacetime inside Planck can affect the string even if the string is as large as Planck size (?) But the internal part of the string is smaller than Planck size, hence it can be affected by what kind of space time is inside the Planck. What do you think?

I'm sorry but I don't quite follow your core questioning. Maybe you could ask the guy who wrote it.

/Fredrik

 

[rogerl]

I'm sorry but I don't quite follow your core questioning. Maybe you could ask the guy who wrote it.

/Fredrik

I just saw it at sci.physics and the poster is no longer available. Anyway. I read it more details for more than an hour. I think I kinda understood what it was saying. It's like this. The strings gravitons makes emergence our General Relativity as a limit. But the spacetime where the strings are imbedded are not known.. meaning.. it could be 10 dimensional with p-branes and stuff. Since we don't know what it is. There is no sense to explore its curvature and how the strings interact with it causing gravity. Instead what we do is apply some dualities which you mentioned (?) and let it produce gravitons which produce our GR. Of course this is the way I understood it. Do you agree with the following?

"A membrane as a continuum and treated by the methods of continuum mechanics emerges as a limit from the atomic structure of an actual membrane - yet does not imply it is a continuum at the level of individual atoms. The same with GR. Gravity as space-time curvature emerges from spin two gravitons when the underlying geometrical background is not known, but usually assumed to be Minkowskian flat, so the methods on QFT theory can be applied"

 

[rogerl]

I just saw it at sci.physics and the poster is no longer available. Anyway. I read it more details for more than an hour. I think I kinda understood what it was saying. It's like this. The strings gravitons makes emergence our General Relativity as a limit. But the spacetime where the strings are imbedded are not known.. meaning.. it could be 10 dimensional with p-branes and stuff. Since we don't know what it is. There is no sense to explore its curvature and how the strings interact with it causing gravity. Instead what we do is apply some dualities which you mentioned (?) and let it produce gravitons which produce our GR. Of course this is the way I understood it. Do you agree with the following?

"A membrane as a continuum and treated by the methods of continuum mechanics emerges as a limit from the atomic structure of an actual membrane - yet does not imply it is a continuum at the level of individual atoms. The same with GR. Gravity as space-time curvature emerges from spin two gravitons when the underlying geometrical background is not known, but usually assumed to be Minkowskian flat, so the methods on QFT theory can be applied"

Fredrik, I guess you don't get what I'm talking about because in your mind, string theory is modeled in a fixed background. But look at this paper for instance:

http://arxiv.org/abs/0909.1861

"Space does not exist, so time can"

Fotini is a colleague of Lee Smolin. She was suggesting that in Planck scale.. space doesn't even exist. So it's possible the spacetime even slightly above the Planck scale doesn't contain space. What do you think? Pls. try to read the paper. It may be the ultimate cause of background independence. Pls. refute the paper if you can I'm looking for a critical flaw.

 

[Fra]

http://arxiv.org/abs/0909.1861

"Space does not exist, so time can"

Fotini is a colleague of Lee Smolin. She was suggesting that in Planck scale.. space doesn't even exist. So it's possible the spacetime even slightly above the Planck scale doesn't contain space. What do you think? Pls. try to read the paper. It may be the ultimate cause of background independence. Pls. refute the paper if you can I'm looking for a critical flaw.

I'll need to read that to comment, but judging from the abstract he argues that there is some paradox in the problem of time.

I've got a reasonably clear opinion on the problem of time, and it's that time DOES dissapperar in the limiting theory of a small subsystems. Time does NOT dissappear in arbitrary theories. These are the two KINDS of time, cosmological time or entropic time, vs microscopic time.

So my opinon on the "paradox" is that the confusion is that we are confusing two limits of theories. It's is a mistake to think that the oversall QG theory has to be timeless. In that respect I agree. But there are still open questions. I think just because there is time, doesn't mean there is an objective time. I think even cosmological time is subjective, but not relative like in SR. The distinction is wether the observer invariance is a fixed constraints or emergent and evolving with undecidable parts.

He seems to have a different argument and I need to read that in order tocomment.

/Fredrik

 

[rogerl]

I'll need to read that to comment, but judging from the abstract he argues that there is some paradox in the problem of time.

I've got a reasonably clear opinion on the problem of time, and it's that time DOES dissapperar in the limiting theory of a small subsystems. Time does NOT dissappear in arbitrary theories. These are the two KINDS of time, cosmological time or entropic time, vs microscopic time.

So my opinon on the "paradox" is that the confusion is that we are confusing two limits of theories. It's is a mistake to think that the oversall QG theory has to be timeless. In that respect I agree. But there are still open questions. I think just because there is time, doesn't mean there is an objective time. I think even cosmological time is subjective, but not relative like in SR. The distinction is wether the observer invariance is a fixed constraints or emergent and evolving with undecidable parts.

He seems to have a different argument and I need to read that in order tocomment.

/Fredrik

In Bell's Theorem. The spirit of relativity is violated. Even if no information is being transmitted. There would be frames where it is instantaneous. This means in other frames one would seem to occur backward in time. We know nature uses seemingly unhackable random encryption, but still the spirit of relativity is violated.

Another possibility. What if these randomness is just default mode. Meaning superluminal signal is possible. Then we will have utmost violation of causality where some frames would be seem to occur backward in time. However. If geometric time is not real, there may be some kind of Lorentz-like transformation where it can be transferred to fundamental time. Meaning even if superluminal signalling was true, no causation is violated because it uses fundamental time below the metric. Do you think this is possible? How do you make Bell's Theorem work in a spacetime where the fabric is continuous. Again. Even if no information is being transmitted. There would be frames where it is instantaneous. This means in other frames one would seem to occur backward in time. Hence the of relativity (continuousness of the fabric of spacetime) is violated

 

[Fra]

In Bell's Theorem. The spirit of relativity is violated. Even if no information is being transmitted. There would be frames where it is instantaneous. This means in other frames one would seem to occur backward in time. We know nature uses seemingly unhackable random encryption, but still the spirit of relativity is violated.

Another possibility. What if these randomness is just default mode. Meaning superluminal signal is possible. Then we will have utmost violation of causality where some frames would be seem to occur backward in time. However. If geometric time is not real, there may be some kind of Lorentz-like transformation where it can be transferred to fundamental time. Meaning even if superluminal signalling was true, no causation is violated because it uses fundamental time below the metric. Do you think this is possible? How do you make Bell's Theorem work in a spacetime where the fabric is continuous. Again. Even if no information is being transmitted. There would be frames where it is instantaneous. This means in other frames one would seem to occur backward in time. Hence the of relativity (continuousness of the fabric of spacetime) is violated

Are you discussing different things at once?

I honestly don't quite understand what you say.

Bell's theorem is said to rule out local realism. I personally keep locality and toss realism. I don't qute see what you mean this has to do with relativity.

Correlations in a prepared system is something completely different than causality.

What do You take to be the "spirit of relativity"? Let's not forget that relativity is a classical realist theory. IMHO, we need so translate the principles to a higher stantadard when we're talking about measurement theory.

/Fredrik

 

[rogerl]

Are you discussing different things at once?

I honestly don't quite understand what you say.

Bell's theorem is said to rule out local realism. I personally keep locality and toss realism. I don't qute see what you mean this has to do with relativity.

Correlations in a prepared system is something completely different than causality.

What do You take to be the "spirit of relativity"? Let's not forget that relativity is a classical realist theory. IMHO, we need so translate the principles to a higher stantadard when we're talking about measurement theory.

/Fredrik

Why do you think Bell mentioned the following about the spirit of relativity seemingly violated by the non-locality inherent in EPR for example. Bell said (what is wrong in his reasoning?):

"I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare ´ thought that there was an aether – a preferred frame of reference – but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether. . . . that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant. . . . what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincare ´, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether – that is a perfectly coherent point of view. . . . The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backward in time. . . . [this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether. (‘‘John Bell,’’ interview with Davies and Brown)

 

[rogerl]

Why do you think Bell mentioned the following about the spirit of relativity seemingly violated by the non-locality inherent in EPR for example. Bell said (what is wrong in his reasoning?):

"I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare ´ thought that there was an aether – a preferred frame of reference – but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether. . . . that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant. . . . what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincare ´, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether – that is a perfectly coherent point of view. . . . The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backward in time. . . . [this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether. (‘‘John Bell,’’ interview with Davies and Brown)

I think a simple answer is that Bell is holding on to realism. By denying realism, there is nothing to be non-local about because reality doesn't exist.. at least according to the definition.

Anyway. In a C60 buckyball molecule sent from the emitter in a double slit experiment, it still interferes. In your opinion, what do you think happen to the C60 buckyball halfway? Do you believe it is still whole or disappear altogether? If still whole, how can it still interfere with itself (beside Many World Intepretation)? If disappear (and Copenhagen prefers this.. hence they reject realism), how can spacetime track the particle position which doesn't even exist? Any ideas especially this latter?

Before measurement of quantum object, position properties don't exist. So how do spacetime track something that doesn't exist??