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Hi Lubos,
The authors also suggest that "Lorentz symmetry should be viewed as an emergent property of the macroscopic world"; "if a microscopic
theory is constructed such that its horizons always satisfy the second law, Lorentz invariance will always be found on the macroscopic level—regardless of whether the fundamental theory is manifestly Lorentz invariant!"
Do you agree with that?
Dear Q, no. I think that they are confusing words. The word "emerging" should have been "derivable" or "derived".
Yes, their (and Sergei's) particular derivation only rules out macroscopic violations.
But it is virtually impossible to have an exact Lorentz symmetry macroscopically but not microscopically. Even if I am very modest in my statements, no Lorentz-violating system preserving exact Lorentz symmetry macroscopically is intensely studied by any group in the high-energy physics literature. Why? Because no such realistic - and not even semi-realistic - theory is known.
Neither Einstein-aether theory nor ghost theories are examples of that.
Note that even if the temperature difference were suppressed by powers of the Planck mass, it is still nonzero and it would still allow someone to construct the perpetuum mobile machine although the violation would be small.
I am convinced that it is fair to say that we *know* that the ultimate laws of physics must respect exact local microscopic Lorentz symmetry. In perturbative string theory, for example, one can prove this assertion by looking at the short distance (local) limit of the worldsheet action that always exactly reproduces the Polyakov action. The latter is exactly Lorentz invariant. Nonperturbatively, there are no signs that something changes about the conclusion either.
We don't have any sign that it should be violated or that it could be violated. Even if it could be violated, I would prefer Occam's razor here. Beings shouldn't be multiplied unless it is necessary. Microscopically present but otherwise invisible Lorentz symmetry violation is a textbook example how to violate Occam's razor. It would really return us to the aether discussions when Lorentz was trying to mask his own Lorentz symmetry by ever more complex models of a (Lorentz-violating) aether, instead of accepting that it has been shown that the aether couldn't exist.
I would wait for someone to construct a meaningful, useful, or otherwise valuable model that is microscopically Lorentz-violating but macroscopically Lorentz-preserving, and I would be 100:1 that no such useful model will be found in our lifetime and I would prefer not to waste an hour of my life with such things.
Also, there are the constantly repeated claims that Lorentz symmetry violation is predicted by string theory. It is certainly not predicted by any of the 10^{500} vacua that are often referred to when someone talks about the landscape. There are many such vacua but all of them uniformly agree about some extremely strong predictions such as the exact microscopic Lorentz symmetry. All constructions in string theory that are fully stringy as well as realistic preserve Lorentz symmetry.
The phenomenologists who write about Lorentz violation only use some string-inspired tools and words but they are not taking all of them into account and they are not doing full-fledged string theory.
The exact microscopic Lorentz symmetry is one of very many general and universal predictions of string theory. In string theory, it is a derivable fact and thus a prediction, not an assumption. So far it is passing all the tests.
Thanks Lubos for drawing attention to our paper.
Regarding our speculation at the end of our paper, I would like to highlight a couple of qualifying words. First the word "if": we do not assert that such a microscopic theory with the 2nd law but not micro-Lorentz symmetry is possible, but only suggest the consequences if it is possible.
Secondly, the word "manifestly": the scenario does not necessarily presuppose micro-Lorentz violation, but only that in the microscopic theory it is easier to see that the Generalized Second Law is true than that Lorentz symmetry is true.
Aron Wall
...microscopically Lorentz-violating but macroscopically Lorentz-preserving... As such model can serve the model, where the particle density fluctuations (which are violating the LS like micro-gravitational lenses) are forming the less or more flat density gradients (strings?), which are serving for transversal wave spreading. A pretty easy, huh?
http://superstruny.aspweb.cz/ima...r/
foam_part.gif
There's something that confuses me. Now that biology tries to pay more attention to reductionism, some physicists start talking about emergent properties?
LM: Dear rafa, your surprise is shared 
but some physicists have always been talking about the e-word. But nothing technical has really come out of this talk. It remains a philosophical program, a kind of wishful thinking. Some people have distinguished "weak emergence" and "strong emergence". The former is the ability to derive some new effects from the underlying law, as long as this effect requires the number of particles or other elementary building blocks to be high. The latter is the emergence of something completely new that cannot be derived from the elementary blocks at all.
I think that virtually all sane physicists agree that "strong emergence" is incompatible with a scientific picture of reality and a theory involving "strong emergence" could never be accepted as being compatible with the laws describing the elementary particles because those micro-laws are considered to be complete, and if they don't imply some observed effect, they must inevitably be wrong (and replaced by other micro-laws that are expected to be complete, too). We're left with "weak emergence". It is a normal thing in many discoveries in physics: new effects indeed emerge when things become complex. Simple things such as thermodynamics may be counted as examples, in fact. But gravity doesn't emerge from some popular starting points preferred by various people who like the emergent wishful thinking, such as the condensed matter setups. There are various theorems that make emergent gravity (in the same spacetime) impossible and no successful example is thus known.
In this thread, the "emergent" Lorentz invariance is being discussed. While I am probably the only one in this thread who feels certain that such emergent Lorentz symmetry will never enter particle physics, there seems to be a consensus that no such mechanism of emergent (but macroscopically exact) Lorentz symmetry is known. So you are surely right that everything about big emergence words remains hot air - and perhaps an attempt to look sexy, philosophical, open-minded with respect to other disciplines, and original, an attempt supported by no technical content whatsoever.
Dear Aron, thanks for visiting us here. If I read your wording accurately, it is actually agreeable (with me). You even correctly say that it is unknown what tendency might be responsible for getting the macroscopic Lorentz-invariant, 2nd law satisfying limit.
I agree. It is not clear how it could be. In other words, it is very likely that the only good reason why the macroscopic limit is Lorentz-invariant is that the whole theory is Lorentz-invariant even at the microscopic level, or it differs from a Lorentz-invariant one by explicit corrections whose harmlessness for the limit can be easily proven.
It is really the word "emergent" that has caused some excitement of both signs here. But I feel that you agree here that it is a speculation that the property (Lor. symmetry) could emerge from something that doesn't have the property - and no particular mechanism achieving it is known.
Incidentally, I recall an AdS/CFT/condensed_matter talk that argued it wasn't that difficult to get a Lorentz-invariant long distance limit of a condensed-matter-like system of equations but I've never understood what were the truly necessary ingredients and how generic it was. That's why I am keeping my opinion that long-distance Lorentz symmetry requires an infinite amount of tine-tuning of the underlying microscopic theory. The limiting speed for each type of object - each pole of a spectral function etc. - has to be fine-tuned separately.
As model "microscopically Lorentz-violating but macroscopically Lorentz-preserving" can serve the model, where the particle density fluctuations (which are violating the LS like micro-gravitational lenses) are forming the less or more flat density gradients (strings?), which are serving for transversal wave spreading. A pretty easy, huh?
http://superstruny.aspweb.cz/ima...r/
foam_part.gif
Every gravitational lensing violates Lorentz symmetry apparently during light spreading in vacuum and nothing very strange is about.
http://superstruny.aspweb.cz/
ima...ght_gravity.gif
Of course, from the position of observer inside the same effect would serve as a best confirmation of LS, but this example demonstrates, we can always deduce at least two interpretations of the same phenomena.
We can consider emergent phenomena as a process of convergence of understanding in different branches of science due the correspondence principle. I believe, the emergent properties in physics are deeply related to biological evolution and vice versa. For example, the formation of living cells from ancient ocean foam is just a continuation of baryogenesis from vacuum foam and condensation of universe from false vacuum, etc..
http://superstruny.aspweb.cz/
ima...ercritical2.gif
http://www.fz-juelich.de/iff/
src...stingeffect.jpg
Above we can see the example of foam condensation from supercritical liquid and the water-oil mixture. Note the apparent similarity of these processes.
Lubos, you're saying that string theory predicts Lorentz symmetry. Isn't it the other way around, i.e., all the uniqueness of the string theory formalism is based upon the assumption of Lorentz symmetry (and unitarity)?
Historically, it was the way you say - when string theory was being looked for in the late 1960s, they wanted a relativistic theory (and all sensible physicists should want this thing in the first place) - but today it is more logical to say what I am saying.
Lorentz invariance is a derived fact of string theory. There doesn't exist any string theory prime that would contain some of the required particles and forces but violated the Lorentz symmetry (except for non-relativistic, Galilean symmetric decoupling limits of various stringy vacua).
For example, the perturbative description of string theory - where string theory deserves the name - starts with an embedding of a worldsheet into spacetime. One studies what kinds of actions one can write to get a meaningful theory and the Polyakov action or its equivalents is the only solution. For the Polyakov action, one can show that the theory is (locally) Lorentz-invariant. But it is equally "derived" fact such as the fact that a bilinear function of two variables, such as x^2+y^2, is invariant under rotations of x and y. It is actually pretty much the same thing.
I wouldn't quite claim the same thing about unitarity. "Unitarity" is not really derived, it is an inevitable part of the structure of string theory, much like other postulates of quantum mechanics. The same comment would apply to quantum field theory, not only string theory - there is nothing stringy-specific about having/requiring/deriving unitarity. But on the other hand, I have no idea what on Earth you could mean by a non-unitary string theory (except for some manifestly non-realistic modifications of string theory - such as those with compact time - where the source of unitarity violation is clear). There doesn't exist any preferred non-unitary theory that would deserve to be called "the" counterpart of string theory.
I don't know what such a new term would mean. At any rate, I wouldn't call this fictitious and so-far unknown (and probably universally uninteresting) theoretical structure by the name "string theory" because it is not really string theory.
It might be that in the future, the postulates of QM or relativity will look more derived than they look today. But such comments are about visions and wishful thinking, not about hard results. As far as hard results go, unitarity (and to some extent Lorentz symmetry) are inevitable ingredients to get any at least remotely interesting and remotely realistic theory resembling strings. All the fantastic discoveries such as dualities, mirror symmetry, holography, topology change, supersymmetric non-renormalization theorems, matrix description etc. heavily depend on the properties of the "right" theory, including unitarity and local Lorentz invariance. Neither of these "miraculous" phenomena could be found outside the precise framework we deal with.
So string theorists are certain that unitarity holds. In this sense, it is a prediction of the theory. Those who insist on having a full, complete, predictive models also know that the local Lorentz symmetry is exact in all of the known ones, too.
Just like the local Lorentz symmetry may be viewed as a prediction of string theory, the Lorentz violation can be viewed as a prediction of loop quantum gravity and similar frameworks because no "natural" or "canonical" form of those theories that would respect Lorentz symmetry is known.
Isn't the string theory special relativity based? Then the local Lorentz symmetry becomes one of postulates of string theory, not theorem.
The implication above is logically flawed. If such an implication were possible to be made, one could say the very same thing about every prediction anywhere in science, ending up with the conclusion that predictions don't exist in science.
For example, one can say: "Isn't Darwin's evolutionary biology based on inheritance? Then the existence of intermediate organisms or adapted organisms in certain contexts isn't a prediction but an assumption of evolution." (Well, creationists like to say similar BS because they like to say any nonsense that is "against" evolution, regardless whether it makes any sense.) Or: "Isn't special relativity based on a universal speed limit? Then the universal speed limit (with the speed of light) is one of postulates/assumptions of special relativity, not a theorem/prediction."
Of course, it is not true: the existence of certain organisms and their properties are predictions of evolution and the speed limit is a derived fact of relativity. It can be derived from other starting points - for example from those that Einstein called the postulates (plus old-fashioned causality). Neither of his postulates was the speed limit; once the theory is fully understood, all of the assumptions and theorems belong to it and it is a matter of convention or approach to say which of them is really "starting". But it is impossible to say sharply where the mistake hides in your two sentences because the words are completely vague. What on Earth do you mean "XY is VW based"?
If "XY is VW based" holds whenever XY predicts or requires VW, then indeed, string theory is special-relativity-based. But with this definition of the term "to be based on", you cannot argue that VW or Lorentz symmetry is a postulate, not a theorem, unless you want to redefine the word "postulate" to mean anything true in a theory.
If "XY is VW based" means that there exists a sensible derivation of the theory from a minimal set of postulates and VW is one of these postulates, then sorry, but your statement about string theory is not correct. String theory may be derived from a perturbative string theory starting point and the latter requires one to consider the embedding of worldsheets into spacetime.
The Polyakov action is the only set of dynamical laws for such an embedding that allows interactions to be expressed by mathematically meaningful equations - more technically, it is the only action involving the spacetime coordinates that is conformally invariant - and then the Lorentz symmetry is a consequence.
So very generally, in perturbative string theory, it is the (super)conformal symmetry on the worldsheet that is the main postulate - a condition that has almost nothing to do with spacetime - and all other usual things are derived facts or "theorems", if you wish, including the existence of bosons, fermions, gauge forces and gauge symmetry, gravity following general relativity at long distances, the precise masses and coupling constants describing all these particles and forces, local Lorentz symmetry, the absence of spacetime anomalies, the existence of black holes and their thermodynamics, and unitarity of the S-matrix. All of these things are derived.
This is how string theory works. All technical features of spacetime and matter are predicted, they are derived from a different, more elementary starting point. Perturbatively it is conformal symmetry on the worldsheet, the non-perturbative generalization of this universal starting principle is not yet described by well-understood words but we know that a set of conditions different from those well-known from field theories exists in nonperturbative string theory, too.
At any rate, the combination of two sentences you wrote is a typical verbal exercise of a layman who doesn't understand what any of these words mean. It is an exact counterpart of the silly things that creationists say about evolutionary biology. I think it is obvious that one must actually understand how a theory works to be able to say which of its true facts can be derived from other facts and which facts. There is no rational "universal" method to say that some things are always derived or never derived. And I told you the correct answer. All the well-known spacetime rules including local Lorentz symmetry are consequences of conformal symmetry on the worldsheet.
This leads me to one of the most solid methods - working in 90+ percent of cases - to quickly figure out who is not a real scientist in a field but a crackpot. The latter people say things like:
Evolution cannot be disproved. http://www.newscientist.com/chan...-
disproved.html
Evolution is not predictive. http://www.newscientist.com/
chan...predictive.html
Other nuts say similar things about physics etc. Of course, it is always a complete nonsense. Any theory that says anything physical and/or quantitative about the real world, its history, its structure at any scale, etc. always has a nontrivial physical content that must be either correct or wrong. It can't be otherwise. It can sometimes take time and effort to find out the correct answer but that's what scientists are expected to do. Whoever says something else is a crackpot.
But special relativity isn't based on "universal speed limit". It's based on Lorentz symmetry, because the "universal speed limit" doesn't belong to postulates of SR.
Therefore every theory based on special relativity depends on special relativity postulates on the background and it cannot derive the very same as a theorem.
"that must be either correct or wrong. It can't be otherwise"
This is apparent BS (Black-or-White Stance).... :-D Every theory has a certain scope of validity - no less, no more. As we already know, many predictions of relativity or quantum mechanics are violating each other or they violate some experiments, some others not. For example, the quantum mechanics isn't very good in cosmological constant prediction.
Lubos,
What a fascinating exchange. This is why I keep returning to TRF. Thanks!
You said,"But it is virtually impossible to have an exact Lorentz symmetry macroscopically but not microscopically."
From my naive viewpoint the transition from microscopic to macroscopic is continuous and, therefore, any symmetry that is broken microscopically cannot be exact macroscopically either. If this were the case there would have to be a sort of phase transition in the progression from the small to the large with the exact symmetry only on one side and this would violate the idea, at least, of a continuous transition from microscopic to macroscopic.
So, why the word "virtually" in the quoted statement?
The derivation of some postulate by using of theory, which such postulate depends on is what the cyclical reasoning exactly means.
Snapper,
You are a splendid example of circular (cyclical) reasoning!
LOL. Why do you mean?
Snapper,
Sorry. Please ignore my statement. I was confused by what you were saying and still am.
We would expect that at the center of a blackhole there is some shell where the matter, due to compaction, ceases to move at a microscopic level. This is the state of energy we would expect in a zero kelvin temperature environment, but does it have to necessarily be cold in the core of a blackhole?
BTW is it a Lorentz violation between the solar photosphere and the corona? I have read many times that the corona is millions of degrees and the photosphere is a measly 6000.
Lubos, you seem to completely deny the notion of teleology in physics. But there is one controversial law called the principle of least action, which requires teleology. If a particle wants to take the shortest possible way, it must already know beforehand, which way is the shortest. (I read the Feynman´s book about quantum electrodynamics and there he used this law to explain phenomena like light refraction between two optical media, why the angle of incidence is equal to the angle of reflection, or the mirage effect)
http://plus.maths.org/issue44/fe...lson/
index.html
In the above link the author claims the following
"The principle of least action and variational calculus seem to suggest that the behaviour of everything in the universe is dictated by the future. A particle can only take a path of least action if it "knows" where it is going to end up — different endpoints will yield different paths. But how can that be the way the universe actually operates? How can the universe depend on knowing where the system ends up in order to work out how it got there? It doesn't make any sense ... yet the method of variational calculus works. This issue goes beyond the teleological notion that there is a plan or design in the universe. It invokes perfect knowledge of the future for the entire universe — everything is done and dusted and things like free will, morality and scientific endeavour become meaningless."
What is the truth about this law?
Dear Mephisto, let me admit that I had to look what teleology really was, http://en.wikipedia.org/wiki/Teleology
After reading a portion of the article, the answer is that you are almost certainly right. The t-word means to put form above the existence, the purpose above structure. Well, yes, I deny teleology and not only in physics.
In the article, teleology is presented as the opposite of metaphysical naturalism. http://en.wikipedia.org/wiki/
Met...ical_naturalism Is that really so surprising that I would prefer to pick metaphysical naturalism and most scientific skeptics would do the same thing? Events don't really have a purpose. With some intelligence, one can *plan* things but without intelligence and usually even with it, things evolve as they are dictated by the laws of Nature.
Your statement about particles' choosing their path in advance has been proven impossible by the free will theorem we discussed previously. The decision about an outcome otherwise described by quantum probabilities only cannot be determined by the data in its past light cone. Some statements of teleology or yours are even more obviously impossible because they violate simple causality itself.
So in this sense you can be sure that teleology is falsifiable and it has already been falsified. In theology and philosophy, teleology may be a valuable approach that swallows 1/2 of the souls or more. In physics, it is a testable conjecture that can be ruled out within a minute and we don't have to waste another minute with it. And Phil Wilson's is a philosophical babbling of a person who has no idea about physics. Great to learn that besides a dangerous climate change denier, I am also a teleology denier. I guess it is an equally serious sin.
Lubos, teleology is concerned with purpose. It was a heated topic in evolutionary theory. Consider these two views: "we have eyes so that we could see" - this is the teleological view, and "we have eyes therefore we see" - this is the realist view.
http://www.iscid.org/
encyclopedi...n_and_Teleology
or try to google teleology + evolution
Of course I am not a physicist, so it would be stupid to argue about physics, but isn´t it in the QM so, that every particle always travels all possible paths and in the end always chooses the shortest or quickest in accordance with the principle of least action? ie Light from point A to point B always travels all possible paths as a wave but only the direct route as a photon? Isn´t the Path integral formulation of QM exactly about this puzzle?
http://en.wikipedia.org/wiki/
Pat...ral_formulation
Where is the teleology in it? If a particle wants to take the shortest possible way, it must already know beforehand, which way is the shortest - and this it knows, because it travels all the possible paths. Sorry if I sound confusing but QM fascinates me
LM: Dear Mephisto, that's a cute debate. I agree that in some sense we have eyes in order to see. But every process that allowed that to happen has a more concrete reason. For example, the first ur-eye evolved because of aminoacid chaos. It evolved by mutations. The better eyes survived because it gave the animals evolutionary advantages. And so on. So it's perhaps a synthesis of the philosophies, after all.
Lubos,
This paper doesn't actually show that any theory that breaks Lorentz symmetry leads to a violation of the 2nd law of thermodynamics, ...
LM: It does. Please learn how to read before you make comments on this blog. Warning: the rest of the comment below is based on wrong assumptions.
... just that you have to be very, very careful when you're constructing theories that break Lorentz symmetry, and that all the attempts to do so thus far have been failures.
Hi Lubos,
Let me quote from the paper itself.
"We will therefore focus on the case of theories where different fields travel at different speeds, bearing in mind that exceptional LV theories may exist where our analysis does not apply."
Are Jacobson and Wall wrong about the content of their own paper?
LM: They say that these theories "may exist" (they certainly don't say that these theories "do exist", even though you incorrectly suggest this misinterpretation) which means that they don't know a proof that they don't exist. I know the proof.
Lorentz violation is equivalent to having at least 1 pair of particles or bound states with a different speed limit. The implication to the left side is obvious and the implication in the opposite direction can be proven by spectral functions. If all particles and bound state respect the speed of light at large momenta, it means that the behavior of all the dynamics at high energies and high momenta - i.e. short distances and times - is equivalent to the behavior of a Lorentz-invariant theory. By the usual causality, this speed limit is then respected at all distance scales (if signals propagate within light cones at short distances, it must be so at all distances). Any breaking of Lorentz symmetry must then be spontaneous and any spontaneous Lorentz breaking may be seen to slow down at least one particle, otherwise the breaking is zero.
The only person who is wrong here is you. And please stop this dumb quotation of verses that you read somewhere and that you don't understand - a procedure that reminds me of a madrassah. If you can't follow the science and say something relevant yourself, couldn't you please just shut your mouth? I will do it for you if you're unable to do it yourself.
Hi Lubos
I am hardly able to add anything into disussion but will still try to put my 5 cents...
1) I think, it is indeed wrong to say that string theory predicts Lorentz violation at high energies. Lorentz invaiance is built into the theory; at high energies gravity is described in terms of dual theory - weakly coupled YM, which is of course Lorentz invariant. It is meaningless to talk in this regime about effective disersion relation for the graviton, because there is simply no such fundamental degree of freedom there (let us be consistent and, say, also discuss what happens with its width as quantum state in high energy regime, in other words, how well the graviton can be described as a particle).
Am I correct here?
2) Suppose that string theory has nothing to do with objective reality (doubt that) and Lorentz violation does take place beyond Planckian scale, as, say, in models of emergent gravity Grigory Volovik likes to talk about (so that effective dispersion relation is omega = k (1 + (k^alpha / M_P^alpha ))). First trivial thing to notice - if the theory is effectively non-interacting there (i.e., we delt with asymptotically free theory in the IR, and there is no UV-IR phase transition), then one does not have to care whether 2nd law of thermodynamics holds or not. The form of distribution of particles (species etc.) over energy is frozen, nothing thermalizes.
Second thing - in the opposite case, when interaction is important at higher energies (like in QED), troubles begin. 2nd law of thermodynamics is broken down -> theory there is strongly out of equilbrium (take a look on the name of this blog 
), thermodynamic unstability develops. It badly messes with everything: even if we say that 2nd law of thermodynamics is effectively valid at low energies and IR degrees of freedom are thermalized quickly, IR dynamics should be influenced by strongly non-equilibrium UV dynamics - phase volume of UV degrees of freedom in Boltzmann integral is large, and they constantly source deviations from thermal equilibrium in the IR.
So, the bottom line, I guess, is that if Lorentz violation may be allowed by some strange flip of Nature, it will be allowed in asymptotically free theories. On the other hand, there are _always_ phase transitions in asymptotically free theories, and IR degrees of freedom are not quite the same as UV ones, so it is not very smart to write corrections to dispersion relations
Cheers,
Dmitry.
Dear Dmitry, thanks for your refreshing points but anyway, here's my comments:
1) YM is the dual of some superselection sectors of string theory only, not a universal "high energy" dual. Moreover, I don't quite see why you say that YM is "high energy" dual. Weakly coupled YM is the "high curvature" dual of AdS backgrounds of string theory. Also, the Lorentz symmetry of YM is not the same thing as the Lorentz symmetry in the gravity dual. In this particular case, the YM Lorentz symmetry is a subgroup: in this case, the whole isometry of the AdS spacetime - namely the generalized/curved (super)Poincare symmetry - is the (super)conformal symmetry of the YM theory.
2) If you turn off the interactions, indeed, you may make the perpetuum mobiles impossible and the paradox goes away. But turned-off interactions are forbidden in quantum gravity themselves, see e.g. the weak gravity conjecture http://arxiv.org/abs/hep-th/0601001 saying that all forces must be stronger in some proper counting - otherwise you would encounter other paradoxes analogous to this perpetuum mobile paradox here.
If I understand you, I agree that the asymptotically free example could lead to unexpected (and generic) consequences in the IR if you do something dangerous in the UV and even the relevant degrees of freedom change. More concretely, you almost certainly get a high Lorentz violation in the IR if you introduce it in the UV, right?
Best
Lubos
Hi Lubos
1) Thanks for clarification! I was just thinking in too broad Polyakov-like pre-AdS/CFT sense: any gauge theory is dual to some string theory, and the latter necessarily contains gravitation in its low energy effective action. Such a generic statement is most probably wrong.
2) As for quantum gravity, also agree, you are not allowed to turn all the interactions off, of course, if gravity itself survives at high energies. As I remember, Lorentz-violating people like to say that it does not have to (only spin degrees of freedom survive, in the spirit of LQG you love so much ). On the other hand, nobody among them was ever able to introduce a working model providing Einstein-Hilbert in the IR.
Qualitatively, I think, IR influence depends on how rapidly coupling decreases with decreasing energy (Boltzmann integral is proportional to the coupling squared), and in order for UV physics to decouple, this decrease should be very rapid (thermodynamic instability develops exponentially).
Cheers,
Dmitry.
Dmitri and Lubos,
I understand only a small part of what you are saying but it is so very refreshing to read your comments!
I do hope this kind of exchange continues because it seems to me to be central to the way that real science is actually done.
Lubos wrote:
>
> All the fantastic discoveries such as dualities, mirror symmetry, holography, topology change, supersymmetric non-renormalization theorems, matrix description etc. heavily depend on the properties of the "right" theory, including unitarity and local Lorentz invariance. Neither of these "miraculous" phenomena could be found outside the precise framework we deal with.
They might be features of a framework, but is there any guarantee they might not also apply in more general settings that include that framework as a mere part or special case?
For example, I've been reading up on mirror symmetry (as best I can) and my impression is the experts are plagued by extra rogue "spherical manifolds" that pop up, and which they try to ignore.
But suppose those apparently unwelcome intruders are telling them something? Isn't it the mark of a good scientist or mathematician to be on the lookout for anomalies rather then sweep them under the carpet?
(I'm not disputing anything said here about Lorentz symmetry BTW. But as you may recall in a screed you kindly reviewed, I believe there's no such thing as a "fundamental" string or brane, and strings are composed of chains of smaller compact branes, most likely spherical, linked by others like beads on a wire, and it's only dual stringy images of these or other branes that may appear fundamental.)
Feynman found a model for the electron called the "Feynman checkerboard". It worked in 1+1 dimensions. The massive electron propagator is built from two massless propagators runing in opposite directions, with random changes in direction and a complex phase at each turning point.
Originally the checkerboard was discrete but it is obvious how to make it continuous. In this model, there is no Lorentz violation because the electron is built from two propagators that also travel at speed c.
There is a natural, though little known generalization of the Feynman checkerboard to 1+3. The problem with the generalization? You guessed it. The electron ends up built from stuff that is massless, but travels at speed c sqrt(3).
As a theory, this gives mass to the electron in a perfectly valid way, but in direct violation of Lorentz invariance. Sure it's not being studied by many people, but that doesn't mean that Lorentz violating microscopic theories do not exist.
It seems that "c sqrt(3)" for electron pops up as a problem from time to time, I have seen it very long ago in one very old Fock's textbook, but I do not remember the title, it was "Introduction to QM" or something ("Mir publishers" translation), with editors note concerning the status of velocity as an operator in QM and explaining why actually it is not a problem. Unfortunatelly, I am not in a mood today to elaborate this issue.
Interesting stuff about the electron models. Thanks Carl and A.M.
I googled on "electron zitterbewegung", and one of the first results was an interesting looking recent paper by David Hestenes at http://arxiv.org/abs/0802.3227v1
Although it's in General Physics Hestenes is no kook, as the paper makes clear. (He's also a leading expert in Geometric Algebra.)
I went ahead and gathered together most of the stuff that has to do with the 3+1 Feynman checkerboard at the "HomePage" link:
Not sure if I'm the right person to mention it, but Carl has also prepared a fascinating and instructive review of Hestenes's paper and related topics, at http://carlbrannen.wordpress.com...electron-model/
