A Slant on Warped Extra Dimensions

[humanino]

I often read claims that string theory cannot possibly break Lorentz invariance. Whether people have feedback right now, or for future reference, I would like to open a thread on the following paper.

A Slant on Warped Extra Dimensions

We propose an orbifolded, warped, extra dimension scenario in which the visible brane is not parallel to the hidden brane. This leads automatically to Lorentz violation in the visible, four dimensional world. The background solution to the Einstein equations is a function of a parameter that can be identified with the amount of 'tilting' of the brane. The cosmological constant is found to coincide with the classic Randall-Sundrum value to first order in this tilt. Lorentz violating effects induced in the Standard Model are considered. We find that the strongest constraint on the tilt comes from determinations of the electron-proton mass ratio in six quasar spectra (four optical and two radio). Measurements of a third radio source could improve this by an order of magnitude.

 

[Careful]

I often read claims that string theory cannot possibly break Lorentz invariance. Whether people have feedback right now, or for future reference, I would like to open a thread on the following paper.

A Slant on Warped Extra Dimensions

I hinted to this also in my book on page 103. I see it as an inconsistency ... but ok.

 

[marcus]

I hinted to this also in my book on page 103. I see it as an inconsistency ... but ok.

By "my book" I assume you mean the recently posted Noldus book. So you saw the possibility of dispersion as a weakness in string theory? I would be glad to have slightly more explanation.
Since string does not seem to be a monolithic unique theory anyway but something rather flexible and adaptable, wouldn't the possibility of Lorentz bending be an advantage---an additional kind of adaptability?

Here is your book:
http://arxiv.org/abs/1101.5113
Let's see what you said on page 103

==quote Careful page 103==
crucial physical importance (as the reader shall learn in axiom VII) to make the number of geometric degrees of freedom equal to the physical matter degrees of freedom. Actually, by simply counting, the matching of degrees of freedom only occurs in four dimensions which is a proof that no 12 dimensional world can be created without new physical gravitational fields. Indeed, those classical fields need to be gravitational otherwise one would have a breakdown of special relativity in higher dimensions, which is precisely what the Calabi-Yau compactifications do for you (so M theory as it stands appears to be inconsistent to me). How should we interpret this breakdown of Riemannian geometry physically?
==endquote==

 

[humanino]

I hinted to this also in my book on page 103. I see it as an inconsistency ... but ok.

Let me see if I get that right

Actually, by simply counting, the matching of degrees of freedom only occurs in four dimensions which is a proof that no 12 dimensional world can be created without new physical gravitational fields. Indeed, those classical fields need to be gravitational otherwise one would have a breakdown of special relativity in higher dimensions, which is precisely what the Calabi-Yau compactifications do for you (so M theory as it stands appears to be inconsistent to me).

I did not pay enough attention to the other thread to realize it was your book.

 

[Careful]

By "my book" I assume you mean the recently posted Noldus book.

Wow, did you figure that out by yourself ?

So you saw the possibility of dispersion as a weakness in string theory? I would be glad to have slightly more explanation.
Since string does not seem to be a monolithic unique theory anyway but something rather flexible and adaptable, wouldn't the possibility of Lorentz bending be an advantage---an additional kind of adaptability?

Local Lorentz covariance is a principle of nature, no doubt about that (all experimental evidence points in that direction) and the theoretical evidence is compelling (connected to causality, homogeneity, isotropy and the origin of inertia). You may twist whatever you want to (in the most arbitrary fashion), but I am afraid it will only produce garbage instead of good physics. Flexibility is good, provided it is the right kind of flexibility.

 

[marcus]

==quote Careful page 103==
crucial physical importance (as the reader shall learn in axiom VII) to make the number of geometric degrees of freedom equal to the physical matter degrees of freedom. Actually, by simply counting, the matching of degrees of freedom only occurs in four dimensions which is a proof that no 12 dimensional world can be created without new physical gravitational fields. Indeed, those classical fields need to be gravitational otherwise one would have a breakdown of special relativity in higher dimensions, which is precisely what the Calabi-Yau compactifications do for you (so M theory as it stands appears to be inconsistent to me). How should we interpret this breakdown of Riemannian geometry physically?
==endquote==

Local Lorentz covariance is a principle of nature, no doubt about that (all experimental evidence points in that direction) and the theoretical evidence is compelling (connected to causality, homogeneity, isotropy and the origin of inertia). You may twist whatever you want to (in the most arbitrary fashion), but I am afraid it will only produce garbage instead of good physics. Flexibility is good, provided it is the right kind of flexibility.

So M-theory as it stands is garbage? Because of the inconsistency you mentioned?

I hope not. I prefer to think of string/M as a field of mathematics with a wide range of applications and adaptibility, as well as interest to creative mathematicians. It will no doubt have some value to physics although what appears to be not yet decided. I don't want to argue about this, so will bow out.

 

[humanino]

@ Careful : thank you for pointing us to your book. I will put it on my list of things I should read.

You posit that Lorentz violations are a sickness and should be included as one of the consistency conditions for string theory. In the context of this thread, the only important point is that Lorentz violation is not prohibited in principle in string theory, and may exist in the swampland (at least according to you).

 

[Careful]

@ Careful : thank you for pointing us to your book. I will put it on my list of things I should read.

You posit that Lorentz violations are a sickness and should be included as one of the consistency conditions for string theory. In the context of this thread, the only important point is that Lorentz violation is not prohibited in principle in string theory, and may exist in the swampland (at least according to you).

No, I just hinted at that, you referred to a paper which made it explicit. The reason why I did not make it explicit is because I am not a specialist in string theory. And all I said is that these versions of string which would break Lorentz covariance should be excluded.

I do not just posit this, I say it with force for compelling reasons as well as from the theoretical as experimental side. People are not sufficiently aware that Lorentz invariance is derived from very basic physical principles which appear to be obvious. So, if you say you don't take Lorentz invariance for granted you have to say which one of these principles are wrong and by what better principle you replace it. Nobody has done this so far
and what people just do is to study ad-hoc deformations within the context of quantum groups. Moreover, you have the enormous experimental constraints on possible violations of it and moreover naturalness implies that Lorentz invariance is exact.

Careful

 

[Careful]

So M-theory as it stands is garbage?

If you do this again, I will report that message for pulling sentences out of context and twisting words to make someone appear bad.

 

[humanino]

if you say you don't take Lorentz invariance for granted you have to say which one of these principles are wrong and by what better principle you replace it.

I do not say that I am interested in Lorentz violating theories. Taking Lorentz invariance as a consistency condition is fine by me. I do however say that insisting on having explicit Lorentz invariance at every step is not necessarily a fruitful theoretical guidance. We do have an example of very fruitful approach in which Lorentz invariance is not manifest, yet allows for a much more efficient calculation of amplitudes : namely the BCFW recursion relation.

 

[suprised]

I often read claims that string theory cannot possibly break Lorentz invariance.

This is not correct as it stands. Any non-trivial classical background, such as a CY compactification or a black hole, breaks Lorentz invariance, and the tilted brane configurations under discussion are an example for this too. This is spontaneous breaking which does not hamper the consistency of the theory; at very high energies Lorentz invariance is restored. This should not be confused with explicit breaking which would ruin consistency.

 

[MTd2]

What you mean, is roughly, like saying that LI is just apparently broken when light goes in an out of refractive media.

 

[humanino]

This is not correct as it stands. Any non-trivial classical background, such as a CY compactification or a black hole, breaks Lorentz invariance, and the tilted brane configurations under discussion are an example for this too. This is spontaneous breaking which does not hamper the consistency of the theory; at very high energies Lorentz invariance is restored. This should not be confused with explicit breaking which would ruin consistency.

Thank you for pointing out this clarification, it is certainly worthwhile. Nevertheless, string theory as it stands would not be inconsistent with observations of Lorentz violations from distant radio sources, in contradiction to what has been said otherwise.

 

[Careful]

I do not say that I am interested in Lorentz violating theories. Taking Lorentz invariance as a consistency condition is fine by me. I do however say that insisting on having explicit Lorentz invariance at every step is not necessarily a fruitful theoretical guidance. We do have an example of very fruitful approach in which Lorentz invariance is not manifest, yet allows for a much more efficient calculation of amplitudes : namely the BCFW recursion relation.

Did I speak about manifest Lorentz covariance ? I spoke about Lorentz covariance; nevertheless, I believe the laws should be formulated in a manifest Lorentz covariant way. Calculations often make it not manifest, we do that even in classical special relativistic theories.

 

[Careful]

This is spontaneous breaking which does not hamper the consistency of the theory; at very high energies Lorentz invariance is restored. This should not be confused with explicit breaking which would ruin consistency.

This may be a confusion on my part, so let me ask you. As far as I know, spontaneous symmetry breaking means chosing a vacuum state which breaks the symmetry of the dynamics. This would imply that somehow the CY compactification needs to be ''quantum mechanical'' like the Higgs is in the standard model (all you do in spontaneous symmetry breaking is chosing an equilibrium point, constructing a different linearization and quantize that perturbatively). So, for the Higgs, the vacuum state which has the full symmetry corresponds to a massless mode, while symmetry breaking gives massive modes. As far as I am aware, what you say, should imply a picture where tunneling between different CY compactifications is possible, I have never seen that (compactifications as far as I know have been treated statically). But again, I am not a specialist in string theory.

 

[suprised]

As far as I know, spontaneous symmetry breaking means chosing a vacuum state which breaks the symmetry of the dynamics. This would imply that somehow the CY compactification needs to be ''quantum mechanical'' like the Higgs is in the standard model (all you do in spontaneous symmetry breaking is chosing an equilibrium point, constructing a different linearization and quantize that perturbatively).

Right - when there is a non-trivial background metric (plus other fields) that corresponds to some CY space for example, then these fields break the 10d Lorentz invariance to 4d spontaneously; spontaneously because it is just the vacuum configuration that breaks it. All this is classical and I am not sure what you mean with quantum mechanical.

So, for the Higgs, the vacuum state which has the full symmetry corresponds to a massless mode, while symmetry breaking gives massive modes.

Well unless you gauge the symmetry, the Higgs field is a massless Goldstone mode in the broken phase. Similarly moduli fields of brane configurations can be viewed as Goldstone modes, which arise from breaking of the translational position symmetries (ie, it costs no energy to move a brane from A to B in a flat background, so there is a massless mode corresponding to this motion).

The massless modes are actually necessary to implement to broken symmetry; indeed the symmetry is still there but just non-linearly realized (by the Goldstone fields); all sorts of Ward-identities of the broken symmetries still hold and that's why the theory remains consistent.

As far as I am aware, what you say, should imply a picture where tunneling between different CY compactifications is possible, I have never seen that (compactifications as far as I know have been treated statically)

This goes a bit into another direction, but yes, there may be a tunneling between different CY configurations. Simply because different CYs correspond to different vacuum states; but it is not so clear to me right now whether there is actually an energy barrier in-between, since it is known/conjectured that all CY's are continuously connected by so-called extremal transitions.
Indeed most discussions deal with static configurations since a good framework for dealing with off-shell configurations is lacking.

 

[Careful]

Right - when there is a non-trivial background metric (plus other fields) that corresponds to some CY space for example, then these fields break the 10d Lorentz invariance to 4d spontaneously; spontaneously because it is just the vacuum configuration that breaks it. All this is classical and I am not sure what you mean with quantum mechanical.

Ok, I have problems with your use of the word spontaneous. Let me try to clarify myself: again, this may be a confusion on my part. When we speak about spontaneous symmetry breaking in the classical context, we speak about defining particles as perturbations around an equilibrium point which is not invariant under the symmetry of the dynamics. Classical string theory woud start from a bunch of moving strings on a D+1 dimensional Minkowski background. Any compactification of D+1 -> CY + (3+ 1) you perform should be dynamical, otherwise you manifestly break Lorentz covariance, right? For example, the analogy MTd2 pointed out for light traveling at a different speed in a medium requires a dynamical theory of the medium, otherwise you break Lorentz invariance in the hard way. Now, I have never seen a dynamical theory on the space of CY compactifications; actually it is clear that such theory cannot be a field theory because a compactification requires a topology change which at first sight destroys Lorentz covariance directly. So, could you explain why I am wrong here? Another aspect in which this compactification is not dynamical is in the sense that base space isn't ''moving'' and the CY fiber is trivial (that means a direct product structure globally).

Well unless you gauge the symmetry, the Higgs field is a massless Goldstone mode in the broken phase. Similarly moduli fields of brane configurations can be viewed as Goldstone modes, which arise from breaking of the translational position symmetries (ie, it costs no energy to move a brane from A to B in a flat background, so there is a massless mode corresponding to this motion).

The massless modes are actually necessary to implement to broken symmetry; indeed the symmetry is still there but just non-linearly realized (by the Goldstone fields); all sorts of Ward-identities of the broken symmetries still hold and that's why the theory remains consistent.

On the level of the dynamics it doesn't matter what Fock space you choose; it is simply so that the annihilation operators for the ''massless modes'' do not annihilate the vacuum since they are nonlinear compositions of creation and annihilation operators of the massive modes (which do annihilate the vacuum). I guess we are saying the same thing here.

This goes a bit into another direction, but yes, there may be a tunneling between different CY configurations. Simply because different CYs correspond to different vacuum states; but it is not so clear to me right now whether there is actually an energy barrier in-between, since it is known/conjectured that all CY's are continuously connected by so-called extremal transitions.
Indeed most discussions deal with static configurations since a good framework for dealing with off-shell configurations is lacking.

Ok, now then, the Higgs is normally quantum mechanical as is Lorentz covariance. So, I would expect any mechanism for CY compactification (which again cannot be based upon a field theory) to be quantum mechanical too (whatever it means in such generalized context). Again, I have never seen such thing.

 

[suprised]

Ok, I have problems with your use of the word spontaneous.

That's the usual word for having a non-symmetric vacumm state in an otherwise symmetric theory.

Any compactification of D+1 -> CY + (3+ 1) you perform should be dynamical, otherwise you manifestly break Lorentz covariance, right?

You mean dynamical = spontaneous? Then right.

Now, I have never seen a dynamical theory on the space of CY compactifications; actually it is clear that such theory cannot be a field theory because a compactification requires a topology change which at first sight destroys Lorentz covariance directly. So, could you explain why I am wrong here? Another aspect in which this compactification is not dynamical is in the sense that base space isn't ''moving'' and the CY fiber is trivial (that means a direct product structure globally).

I can't really follow… perhaps there is the following confusion. There are various kinds of spontaneous Lorenz symmetry breaking. What was primarily meant here is the breaking of the 10d Lorentz symmetry by the presence of the CY; in the sense of a direct product background X_10 = CY_6 x M_{3,1}. In such a situation the 10d Lorentz symmetry is broken to a 4d one; in the 4d world the Lorentz symmetry is unbroken.

When X_10 is a non-trivial fibration of CY_6 over M_{3,1}, then the properties of the 4d theory depends on where were are in 4d, so the Lorentz symmetry is broken.

As special example for this, sometimes configurations are considered where there are two vacuum states separated by a domain wall (one may think of one side corresponding to a CYa and the other side to a CYb with different tpologies). Then Lorentz symmetry is broken by the presence of the domain wall.

Similarly, Lorentz symmetry may be broken by the presence of black hole at a given point in space; etc.

I didn't read the paper which prompted this thread, but from reading the abstract the situation looks analogous to these examples: some properties of the internal space (D-branes configuration) depend on the location in 4d space time, thus inducing a spatial inhomogeneity which means breaking of Lorentz symmetry.


All this deals with classical static backgrounds, I don't see quantum mechanics or dynamics as important here.

 

[Careful]

That's the usual word for having a non-symmetric vacumm state in an otherwise symmetric theory.

Sure, but that is not what you mean. I am saying that what you do is not this.

You mean dynamical = spontaneous? Then right.

Yes, so let us see now if you do this...

I can't really follow… perhaps there is the following confusion. There are various kinds of spontaneous Lorenz symmetry breaking. What was primarily meant here is the breaking of the 10d Lorentz symmetry by the presence of the CY; in the sense of a direct product background X_10 = CY_6 x M_{3,1}. In such a situation the 10d Lorentz symmetry is broken to a 4d one; in the 4d world the Lorentz symmetry is unbroken.

There are several issues here and we should distinguish them. First of all, this is not a dynamical effect, these compactifications are just put in by hand which results in what you say: that is 10 d Lorentz symmetry is hardly broken to a 4 d symmetry. If you claim it is spontaneous, the please provide us with the dynamical object whose vacuum expectation value gives the CY geometry starting from something living on a different topology. I don't know if you get this right, but the Higgs field is what allows for the symmetry breaking (by means of an atypical vacuum state), so what is the counterpart of the Higgs field in string theory which provides this change of topology and geometry? Second, even if I would accept this hard braking to a residual 4 d Lorentz symmetry, then still this is all ad hoc and kinematical. It is easy to find compactifications to base spaces which do not have Lorentz symmetry, actually this will be generically the case. Why do you exclude them ? What is your rationale for doing so? Ok, this is classical so far.

When X_10 is a non-trivial fibration of CY_6 over M_{3,1}, then the properties of the 4d theory depends on where were are in 4d, so the Lorentz symmetry is broken.

My point exactly, so what about Lorentz symmetry in string theory again ??
You have no dynamical theory to exclude these possibilities and such thing does clearly not exist.

As special example for this, sometimes configurations are considered where there are two vacuum states separated by a domain wall (one may think of one side corresponding to a CYa and the other side to a CYb with different tpologies). Then Lorentz symmetry is broken by the presence of the domain wall.

I can understand that.

Similarly, Lorentz symmetry may be broken by the presence of black hole at a given point in space; etc.

True

All this deals with classical static backgrounds, I don't see quantum mechanics or dynamics as important here.

I do. For the following reasons: if you would finally figure out a ''classical'' dynamical theory for CY compactification and you wouldn't quantize it, then unitarity, the corner stone of string theory, will evaporate. Not that I mind, but I guess Susskind would.

 

[suprised]

I begin to see what our mutual misunderstandings are - it seems to be tied to "dynamical". So you seem expect that there is some dynamical mechanism that _forces_ the Higgs field, or some analog, to some particular, perhaps quantum mechanically required value (like to non-trivial minimum of some potential).

Indeed this is different to what I have in mind, which is much simpler. There no potential to start with, and it is up to you to choose a VEV or background geometry ; this is nothing but the landscape problem. Almost infinitely many choices are possible (and as there are consistency conditions, infinitely many other choices are not possible). So indeed these backgrounds are put in by hand, and this is a kinematical and not dynamical issue; no one claims this being a big deal. The issue here is breaking of Lorentz invariance by backgrounds.

This is called spontaneous breaking, despite all is static and not time dependent. Nothing dynamically happens so far (though one can consider time-dependent situations as well). The important point is that the symmetries are still there, albeit non-linearly realized, which is important for consistency. It is soft breaking, as it disappears at high energies where 10 or 11d Lorentz-invariance is regained.

If you claim it is spontaneous, the please provide us with the dynamical object whose vacuum expectation value gives the CY geometry starting from something living on a different topology…
I don't know if you get this right, but the Higgs field is what allows for the symmetry breaking (by means of an atypical vacuum state), so what is the counterpart of the Higgs field in string theory which provides this change of topology and geometry?

The vev of the metric, g_{mn}; plus other fields like tensor fields. However if you request drastic changes of topology, then the description in terms of an effective action based on classical geometry may break down, and you'd need to formulate the problem in more suitable terms.

It is easy to find compactifications to base spaces which do not have Lorentz symmetry, actually this will be generically the case. Why do you exclude them ? What is your rationale for doing so?

Do I say I exclude this? I am saying here all the time rather the opposite of this.

My point exactly, so what about Lorentz symmetry in string theory again ??
You have no dynamical theory to exclude these possibilities and such thing does clearly not exist.

Yes, indeed why is our universe not filled with a spaghetti-like mess, rather than with galaxies? I guess no one can answer this. I can only mention the A-word here ;-)

if you would finally figure out a ''classical'' dynamical theory for CY compactification and you wouldn't quantize it, then unitarity, the corner stone of string theory, will evaporate. Not that I mind, but I guess Susskind would.

I guess that's a red herring.

 

[Careful]

Ok, I will react this evening, have to go and entertain my kids now

 

[Careful]

This is called spontaneous breaking, despite all is static and not time dependent. Nothing dynamically happens so far (though one can consider time-dependent situations as well). The important point is that the symmetries are still there, albeit non-linearly realized, which is important for consistency. It is soft breaking, as it disappears at high energies where 10 or 11d Lorentz-invariance is regained.

I guess what you are saying here is that for high frequencies in the CY directions smaller and smaller gaps are going to emerge in the spectrum. But it appears to me that one can have high frequencies in the ordinary dimensions (with low wavelengths in the compactified directions) which do break Lorentz covariance seriously. So, one would think it depends upon what you mean with high energy...

The vev of the metric, g_{mn}; plus other fields like tensor fields. However if you request drastic changes of topology, then the description in terms of an effective action based on classical geometry may break down, and you'd need to formulate the problem in more suitable terms.

Agree

Do1 I say I exclude this? I am saying here all the time rather the opposite of this.

I don't know you, now I do a bit better.

Yes, indeed why is our universe not filled with a spaghetti-like mess, rather than with galaxies? I guess no one can answer this. I can only mention the A-word here ;-)

There are better explanations.

I guess that's a red herring.

No, it isn't. All I want to say is that dynamical symmetry breaking is important for the issue of unitarity, see eg. the standard model. Do you know of a proof that your kinematical compactifications give unitary theories ?

Careful

 

[Fra]

Yes, indeed why is our universe not filled with a spaghetti-like mess, rather than with galaxies? I guess no one can answer this. I can only mention the A-word here ;-)

I hope see how Careful sees this once I get time to check his paper, but here I like to quote Peirce:

"The only possible way of accounting for the laws of nature and for uniformity in general is to suppose them results of evolution. This supposes them not to be absolute, not to be obeyed precisely"
-- http://en.wikiquote.org/wiki/Charles_Sanders_Peirce

So I think the "dynamical explanation" that is seeked is more likely a darwinian style evolution, because otherwise we are back at the same question; why this metalaw.

The question seems to be how to make this into something predictive, rather than using it as an excuse to defend a gigantic landscape.

I don't think the explanation can be conventional dynamics, it seems some new form of evolutionary logic is used even at the level of inference, rather than the more rigid non-flexible deductive logic. (even induction as classical probabilistic deduction is not flexible enough, so I agree that in some generalized sense; some new quantum style logic may need to enter here)

/Fredrik

 

[suprised]

I don't think the explanation can be conventional dynamics, it seems some new form of evolutionary logic is used even at the level of inference, rather than the more rigid non-flexible deductive logic. (even induction as classical probabilistic deduction is not flexible enough, so I agree that in some generalized sense; some new quantum style logic may need to enter here)

Well this problem appears in GR, resp standard cosmology as well: why is space so homogeneous? Also in GR there is an infinity of classical solutions and having such an homogenous universe seemed like a miracle. That's why inflation was invented; more or less conventional dynamics.

So what's about inference, …some quantum style logic.. that's all too abstract for me, unless there are concrete formulas, I can't appreciate it.

 

[Fra]

Well this problem appears in GR, resp standard cosmology as well: why is space so homogeneous? Also in GR there is an infinity of classical solutions and having such an homogenous universe seemed like a miracle. That's why inflation was invented; more or less conventional dynamics.

So what's about inference, …some quantum style logic.. that's all too abstract for me, unless there are concrete formulas, I can't appreciate it.

Ultimately there will be formulas and frameworks of course. But as far as view this, it's still an open problem. I just wanted to acknowledge it, because I've learned that not everyone acknowledge the problem.

One framework for inference is simply bayesian probability theory, and all classical statistics thermodynamics etc. Another inference framwork is quantum theory. The inference lies in how an expectation is inferred from the starting point.

The "logic" in how to compute an expectation rationally, be it via some maxent method, or some extermal action method, including superposition of possibilities etc are IMHO at least all special cases of a class of more general inference frameworks; which are to be seen as a kind of extension to deductive logic.

The very simplest extension to deductive logic, is as we know, simply induction as in probabilistic deduction, or classical probability.

Quantum logic is more complex, and just postulating quantum theory, and without an analysis in terms of it beeing a special case in classes of genereal inference models, we do not undertand it properly. At least this is how I feel.

Probabilit theory can be simply constructed axiomativally like the kolmogorov construction, but the same mathematics can be constructed for example as an extension to quantified reasoning about degrees of beleif. Cox and Jaynes provides other ways to construct the same the same mathematics.

Jaynes also has some ways to construct quantum logic as rules of inference (although I personally don't think it's good enough).

The idea of this inference talk is that, the laws of nature, and the action forms of nature, MAY be understood as simply selected rational rules of inductive inference (reasoning based upon incomplete information), and rational action based upong these expectations. The conjecture I hold is that such a route may provide some deep insight.

But this is indeed a very immature field, in the sense I seek it.

As a comparasion, some people has been totaly sold on say geoemtric formulations, and that rephrasing everything in terms of geometry will help us understand things deeper. Yes, geometric methods has been very successful, but there are some (philosophical, but still very good) arguments that inference methods are very fundamental, as they - unlike for example geometriic metohds - are best seen as extensions of logic.

The best examples of the success of this methods in physicvs in the past are statistical physics and modern formulation thermodynamics and entropic methods. Aside from some subtle things like subjectiveness of entropy and ergodic assumptions we pretty much understand this well. Alot of statistical physics almost follows from logical constructions.

Unfortunately QM and QFT does not have the same level of understnading, not to mention the specific actions, where classical physics only can explain diffusion and fluid style interactions as entropic in nature. The other interactions, like EM, strong and weak and gravit are nto so understood yet. Except of course some of the recent entropic papers of verlinde, and some older black hole thermodynamics papers of jacobsson etc.

All these things suggest to me, there is a big nice framework under all this that we do not yet see. And the "inference perspective" is what I call this.

To call it statistical perspecive is misleading as it associates to classical statistics, but this is more. And not only quantum statistics, it's even more. I see quantum statistics again as a special case.

The comment was more targeted to Careful though. I hinted in some of his previous threads and paper that maybe he would address some of these things in his paper. (Though I'm still struggling with my own time to skim it) MAYBE, careful's paper contains something a little bit more explicit than what I have to offer atm, but I'm not sure - this is what I hope to find out, or if he takes some different turns somewhere.

/Fredrik

 

[Careful]

The comment was more targeted to Careful though. I hinted in some of his previous threads and paper that maybe he would address some of these things in his paper. (Though I'm still struggling with my own time to skim it) MAYBE, careful's paper contains something a little bit more explicit than what I have to offer atm, but I'm not sure - this is what I hope to find out, or if he takes some different turns somewhere.

/Fredrik

It is late, so my answer will be short. No, I haven't said about logic anything yet for the very good reason that I first have to work out the full mathematical picture of quantum mechanics on generalized bi-modules (with torsion perhaps). The structure of the yes and no questions will be much weaker than the lattice structure of the hermitean projection operators on Hilbert space. I have referred to the paper of Diederik Aerts in another thread and I think it is at this stage too early to develop the logic (and therefore many axioms in this paper will fail, more than the author mentions). One has to be patient in life and do things in the right order.

Careful

 

[Fra]

I think it is at this stage too early to develop the logic (and therefore many axioms in this paper will fail, more than the author mentions). One has to be patient in life and do things in the right order.

This is more than fair of course as this is really difficult. As long as we do not try to deny the hard questions I have patience.

Personally my approach is starting out like a reconstruction of the rules of inference, but with strong generalisations, where one will ultimately see clearly how classical logic and quantum logic does correspon to different stages of evolution, and one will see why quantum logic is at times peferred over classical logic. I am seeking to develop this as a way to "count evidence", and what needs developing in parallell is the framework for the structure that encodes the counts, as well as the number system itself. What in my view "explains" emergence of quantum logic is that the non-commutative structures for storing information (evidnce counts) spontaneously appear in the evolution for the reason that it is more "economical" and "fit" for the hosting information processing agent (the observer).

So I choose to start here. But I have a lot of work left before I'm near hundre page papers.

Although I don't think you are follwing a pure inference perspective (since you see yourself as realist), I do appreciate a lot of your reasoning and critique of some mainstream thinking (I'll come to later later inthe other thread) so I'm interested to see how you develop the formalism(mathematics&logic).

/Fredrik

 

[Careful]

Although I don't think you are follwing a pure inference perspective (since you see yourself as realist), I do appreciate a lot of your reasoning and critique of some mainstream thinking (I'll come to later later inthe other thread) so I'm interested to see how you develop the formalism(mathematics&logic).

/Fredrik

I am following a pure (higher order) interference perspective, I once said you that everybody is realist. Perhaps we should move this discussion to the correct thread, since it doesn't belong here.

 

[suprised]

Do you know of a proof that your kinematical compactifications give unitary theories ?

Of course; do you seriously think that string theory could possibly be inconsistent for such a reason?

Let me point out how it roughly works, and take for the problem of unitarity the decoupling of the longitudinal modes of the graviton (it works for gauge bosons in the same way). In a consistent theory these modes must decouple, as if they wouldn't, unitarity would be immediately lost. Now, in string theory those modes correspond to BRST exact operators that indeed lead to the vanishing of the relevant amplitudes, by making use of contour deformation arguments. All what is necessary to make these arguments work is that the world-sheet theory is conformally invariant.

So in a nutshell, and generally true, the conformal invariance of the world-sheet theory guarantees certain Ward-identities in the effective space-time theory, which ensure the unitarity of the latter. In the sigma-model approach, the conditions of conformal invariance directly translate into the Einstein eqs of GR. They just follow from the vanishing of the beta-functions of the world-sheet theory; in this sense GR can be viewed as "emergent" from the string theory.

This argument is completely independent as to what the internal theory corresponds to, ie flat space M9,1 or CY_6xM3,1 or whatever - all what matters is conformal invariance (incl modular invariance).

This is what is meant when people say that string theory implies Lorentz invariance/general covariance. As I was saying here before, this does NOT mean that string theory necessary implies flat homogeneous Minkowski space-time. Similarly, the Einstein eqs of GR are generally covariant, but nevertheless have solutions that are not Lorentz invariant (like a black hole at a given location).

So nothing is a priori wrong with the paper that promped this thread (which postulates a non-Lorentz invariant background), nor does it contradict standard string theory wisdom.

 

[suprised]

Ultimately there will be formulas and frameworks of course. But as far as view this, it's still an open problem.

Well I have seen plenty of philosophical ideas as to what the nature of GR and QM "should" be. But there _is_ indeed a difference between philosophy and phyics. Unless one can present a concrete mathematical formulation (lets not even ask for physical predictions), one still is stuck at level zero. The step from words to meaningful formulas is a trillion times more complicated, in fact that's the real problem - there was never a lack of ideas, but of ideas that actually can be shown to concretely "work".

 

[Careful]

Of course; do you seriously think that string theory could possibly be inconsistent for such a reason?

My comment was more inspired by my own line of thought (that is, the insights coming from my own work which I believe to be more correct). Therefore, I was careful in mentioning it, I didn't deem it worthwhile to investigate it properly since this is the task of string theorists, not mine.

Let me point out how it roughly works, and take for the problem of unitarity the decoupling of the longitudinal modes of the graviton (it works for gauge bosons in the same way). In a consistent theory these modes must decouple, as if they wouldn't, unitarity would be immediately lost. Now, in string theory those modes correspond to BRST exact operators that indeed lead to the vanishing of the relevant amplitudes, by making use of contour deformation arguments. All what is necessary to make these arguments work is that the world-sheet theory is conformally invariant.

Hmm, I thought you were playing with D-branes which have no conformal invariance I guess and moreover, one could even drop the requirement of an anomaly free Virasoro algebra and work in the non-critical dimensions. This is called non-critical string theory as far as I remember, so how would your argument apply to that? Moreover, conformal invariance forces your background to satisfy an equation with an infinite number of terms. As far as I know, nobody has ever made sense out of this from a nonperturbative point of view and therefore it might even well be that no exact solutions exist (apart from a few trivial ones like local Minkowski). Therefore, is it really known that these CY compactifications give a unitary theory beyond say - third order perturbation theory in the string coupling constant? The devil usually is in the details. I don't know, so I ask.

This is what is meant when people say that string theory implies Lorentz invariance.

This is then an abuse of language as far as I can see...

Btw. Decoupling is a necessary condition, do you also know it is a sufficient one? You did not give a proof yet as far as I see.

 

[Careful]

Well I have seen plenty of philosophical ideas as to what the nature of GR and QM "should" be. But there _is_ indeed a difference between philosophy and phyics. Unless one can present a concrete mathematical formulation (lets not even ask for physical predictions), one still is stuck at level zero. The step from words to meaningful formulas is a trillion times more complicated, in fact that's the real problem - there was never a lack of ideas, but of ideas that actually can be shown to concretely "work".

Sure, but ad hoc formula's without good philosophical insight are equally meaningless... That is what is usually forgotten too

 

[Fra]

Well I have seen plenty of philosophical ideas as to what the nature of GR and QM "should" be. But there _is_ indeed a difference between philosophy and phyics. Unless one can present a concrete mathematical formulation (lets not even ask for physical predictions), one still is stuck at level zero.

If you are referring to MY personal ideas, then I will do my best. I need many many years from now before I am ready to present in terms of explicit predictive models. I wouldn't speak if I didn't think that I had a chance at doing better, in despite of the odds.

Other than that you are right, but I would like to add an important point. Not only are their plenty of philosophical ideas as to what physics and reality should be; there are also plenty of mathematics as to what what reality must be, that consumes a lot of research resources. I am as impressed with a random mathematical model that lacks connection to reality as I am with philosophical ramblings. One isn't better than the other, not from the point of view of physics as I see it.

But the task isn't to come up just with mathematics, the task is to find the RIGHT framework or at least some optimally rational framework, here the philosophical style analysis or the logic is a guide.

I have always had the opinion that there are a lot of brilliant technical mathematicians doing physics, but the people that in addition to the basic skills neede AND have the deeper insight and capability to see the mathematics required by nature are the rare geniouses. In that perspective, I do not see what is wrong with also analysing the way mathematical models has evolved and been constructed. IT does in neither way contradict the goal that we seek explicit mathematics for computing and simulating systems in our environment in a way that allows predictions.

/Fredrik

 

[suprised]

Hmm, I thought you were playing with D-branes which have no conformal invariance

They do have!

.. one could even drop the requirement of an anomaly free Virasoro algebra and work in the non-critical dimensions. This is called non-critical string theory as far as I remember, so how would your argument apply to that?

Those indeed break Lorentz symmetry due to the Virasoro anomaly, and are not consisered as consistent (I mean the usual non-critical strings, there are other ones not based on a world-sheet formulation).

Alas… there were attempts to invent different quantization schemes which do not know about anomalies, and it has been claimed that with these one could quantize the non-critical string consistently. AFAIK this is not taken serious by many; this is similar to certain quantization schemes in LQG which also do not see anomalies (and thus, do not even quantize the harmonic oscillator correctly…).

Moreover, conformal invariance forces your background to satisfy an equation with an infinite number of terms. As far as I know, nobody has ever made sense out of this from a nonperturbative point of view and therefore it might even well be that no exact solutions exist (apart from a few trivial ones like local Minkowski).

Well the higher expansion terms are strongly suppressed by inverse powers of the Planck scale so there is all reason to expect that they would represent small corrections when away from singularities. The situation is expected to be significantly different near singularities; ie they might not exist etc. Moreover, the convergence of the perturbation series is a hard issue, but probably a red herring.

Therefore, is it really known that these CY compactifications give a unitary theory beyond say - third order perturbation theory in the string coupling constant? The devil usually is in the details.

Indeed it is in the details. So let me spell this out. Lorentz invariance is in fact coming from conserved world-sheet Kac-Moody currents that exist on all higher genus Riemann surfaces, so naively it can't be violated. But what still could happen is that the longitudinal components don't decouple, and then there would be an anomaly which destroys unitarity. Again naively these decouple because the usual contour arguments should go through on arbitary Riemann surfaces, this means at arbitrary loop order.

But there is the devil in the details. The contour argument can fail for singular Rieman surfaces, and this is where potential anomalies could come from. This is a complicated issue and requires a careful analysis of the various degeneration limits of Rieman surfaces. AFAIK this issue is rigorously settled to one-loop order and convincingly settled to some higher orders, like 2 or 3. At higher orders there are problems as to how to rigorously define the measure on supermoduli space, I am not sure what the status is. So AFAIK there is no rigorous proof that anomalies do not appear at say, 5th loop order. On the other hand, this is pretty unlikely as anomalies usually appear at lowest order, ie 1 loop, I never have seen something else.

. Decoupling is a necessary condition, do you also know it is a sufficient one?

I guess so… the symmetries are preserved at tree level and also at the quantum level, assuming the absence of anomalies. Violation of unitarity can arise only from degeneration limits of (super-)Riemann surfaces, which is what we discussed above. AFAIK there are no hard proofs at arbitrary loop orders; I didnt follow the literature on this recently. But there has always been circumstantial evidence that this works, there are no concrete indications that it ever goes wrong; the issue is rather to prove it rigorously.

 

[Careful]

They do have!

Ok, thanks for your detailed answer . Just a simple question about your first comment which is somewhat mysterious to me: I always thought conformal invariance was somehow thightened to 2 d unless you use Weyls trick of course. So I guess the action depends upon the Weyl tensor and not the simple area ? Or do you add another field which transforms appropriately under Weyl rescalings ?

Cheers,

Careful

 

[suprised]

Just a simple question about your first comment which is somewhat mysterious to me: I always thought conformal invariance was somehow thightened to 2 d unless you use Weyls trick of course.

True… now I understand what your aim is. The issue is not to quantize the world-volume of general branes, for which indeed there is all sorts of problems. Specifically D-branes are "dual" representatives of branes that can be represented perturbatively, which means in terms of 2d CFT with boundaries. So the trick behind D-branes is that instead quantizung solitonic world-volumes, one can describe the non-perturbative closed string dynamics by perturbative open strings based on boundary CFTs, and similar computational techniques can then be applied as for closed strings.

Note that not all p-branes are equivalent to D-branes, like the NS fivebrane, and for those these methods fail.

 

[Careful]

True… now I understand what your aim is. The issue is not to quantize the world-volume of general branes, for which indeed there is all sorts of problems. Specifically D-branes are "dual" representatives of branes that can be represented perturbatively, which means in terms of 2d CFT with boundaries. So the trick behind D-branes is that instead quantizung solitonic world-volumes, one can describe the non-perturbative closed string dynamics by perturbative open strings based on boundary CFTs, and similar computational techniques can then be applied as for closed strings.

Note that not all p-branes are equivalent to D-branes, like the NS fivebrane, and for those these methods fail.

Well, as I said, I do not know enough details to make a definite statement about string theory (I studied it only intensely for like three months) ; I can only judge it from the perspective where I am standing (about the other approaches like CDT, LQG and causal set, I do know all the fine print). Actually, the reason why I would say that my approach is not so far from string is because it treats gravity in a similar dual way and insights such as the holographic principle appear to show up directly (also, my black holes do not have an horizon, so they are not perfectly black). On the other hand, the geometry and quantum theory I develop is far more general (and sophisticated) and locality on spacetime is a sacred principle for me (altough the construction is nonlocal on the tangent bundle). So, we will see what happens in the future...

Careful