Sunday, February 01, 2009

Lorentz symmetry and String theory

This post is a polemic to Motl's somewhat nervous defense of Lorentz symmetry (LS), as quoted by italics. It hope, it may be interesting for someone. By AWT the confrontation of ideas in dialectic discussion is driving tensor of new ideas: full agreement cannot serve as a both subject, both object of further thinking and extrapolations.

Moshe Rozali wrote a very sane text about the importance of LS for the search for the fundamental laws of Nature: The Universe is probably not a quantum computer. I agree with every word he wrote. He says that many people who are following the physics blogosphere want to believe that their area of expertise is actually sufficient to find a theory of everything.

.. by the same way, like string theorists and many others.. By AWT whatever theory of your personal preference can become a TOE, if you make it infinitely implicit, i.e. if you compose it from as from minimal number of postulates, as possible. The complex theories mixed from high number of postulates, like string theory would be strongly handicapped by such way, of course.

So Seth Lloyd of the quantum computing fame wants to believe that the world is a quantum computer. Robert Laughlin wants to imagine that quantum gravity is an example of the fractional quantum Hall effect. Other people have their own areas of expertise, too. Peter Woit wants to believe that a theory of everything can be found by mudslinging and defamations while Lee Smolin wants to believe that the same theory can be found by selling caricatures of octopi to the media (following some subtle and not so subtle defamations, too).

..and string theorists are believing in vibrating strings. And so? Live and let live. The world of coexisting theories illustrates the space-time world, being a low energy density projection of it into causual space.

Moshe Rozali correctly tells them that if they are going to ignore the Lorentz symmetry, a basic rule underlying special relativity, they are almost guaranteed to fail. Lorentz symmetry is experimentally established and even if it didn't hold quite accurately, it holds so precisely that a good theory must surely explain why it seems to work so extremely well in the real world.

Lorentz symmetry is violated by quantum mechanics heavily, it's simply based on dual approach be more specific. By AWT even gravitational lensing is rather quantum mechanics phenomena, then the relativity phenomena. To defend Lorentz symmetry you're simply required to fight against quantum mechanics and vice-versa.

It still doesn't mean, Universe computes something for somebody.

Moreover, the state-of-the-art theories of the world are so constrained - i.e. so predictive - exactly because they are required to satisfy the Lorentz symmetry.

Quantum mechanics is based on zero or infinite many radiative time arrows. It's invariant to LS (and other postulates of relativity, based on radiative time arrow causality), while still remains predictive. Aether theory is invariant to both, while still remains predictive. In fact, just because both LS, both quantum mechanics are mutually inconsistent apparently, here's a question, why not to start once again from complete beginning.

Because of this symmetry, quantum field theories only admit a few marginal or relevant deformations. If you assume that they make sense up to extremely high energy scales, you may accurately predict all of their low-energy physics as long as you know a few important parameters. Such a "complete knowledge" of physics in terms of a few parameters would be impossible in non-relativistic theories.

The same is true for relativistic theories. The emergence concept is still required to seamlessly connect both these branches of physics.

String theory is even more constrained than quantum field theory: it has no adjustable dimensionless non-dynamical parameters whatsoever. In some sense, you may view string theory as a tool to generate privileged quantum field theories with some massless spectrum and infinitely many very special, selected massive fields with completely calculable interactions. So all the Lorentz constraints that apply to quantum field theory can do the analogous job in string theory, too.

String theory is like every other quantum field theory in this point. It's true, most of formalism was developed under cover of string theory, because string theory has a good marketing, best experts and some nice faces in front of it. But these approaches can be used in many other theories and the best string theorists, like Ed Witten are doing so without any frustrations.

However, in string theory, the character of LS is even more direct. The very short distance physics of string theory is pretty much guaranteed to respect the LS. Whenever you look at regions that are much smaller than all the curvature radii of a D+1-dimensional spacetime manifold, the dynamics of a closed string reduces to a collection of D+1 free scalars on the worldsheet which manifestly preserves the Lorentz symmetry. And one can show that the interactions respect it, too.

String theory is based on combination of quantum mechanics and special relativity. From this point of view is apparently less general, then any theory based on combination of quantum mechanics and general relativity, like LQG. It's just one of evolutionary steps of physics, no less, no more. It opened many research perspectives, while quantum gravity has opened others.

Open strings may violate the LS spontaneously, for a nonzero B-field or a magnetic field on the brane, and one can enumerate a couple of related ways to spontaneously break the Lorentz symmetry with the presence of branes and their worldvolume fields. But none of these pictures ever hides the fact that the fundamental theory behind all these possibilities is Lorentz-invariant.

This is just one of many perspectives possible. Some others can see an infinitely fractal Universe based upon quantum mechanics units or even particle units. But fractal geometrodynamics, as expressed by double relativity based on Poincare, Cartan and deSitter groups is still in the game as well.

There's a lot of confusion in the public about the fate of the LS in general relativity. Be sure that the LS is incorporated into the very heart of general relativity. General relativity generalizes special relativity; it doesn't deny it. General relativity can be defined as any collection of physical laws that respect the rules of special relativity (including Lorentz invariance) in small enough regions of spacetime - regions that can, however, be connected into a curved manifold. All breaking of LS in general relativity can always be viewed as a spontaneous breaking by long-distance effects and configurations.

Every generalization is predestined to violate its roots less or more lately. My personal understanding is, general relativity has nothing to do with LS at all, being even much more general, then many relativists (specially those special ones) may be willing to admit. Anyway, general relativity has nothing to do with string theory, which doesn't uses postulates of general relativity at all. This belongs into realm of quantum gravity.

In fact, even in spacetimes with a lot of curved regions - such as spacetimes with many neutron stars or even black holes - one can use the tools of special relativity in many contexts: either in very small regions that are much smaller than all the curvature radii, or in regions that are much larger than stars and black holes. In the latter description, the stars and black holes may be viewed as local point masses or tiny disturbances that follow the laws of relativistic mechanics at much longer distances, anyway.

That's perfectly right. And the large systems of such particles are following a quantum or newton mechanics at another distances, and so on.

So if someone completely neglects Lorentz invariance, the player that became so essential in 1905, he shouldn't be surprised if theoretical physicists simply ignore him or her. It is not necessary for a theory to be Lorentz-invariant from the very beginning. But a theory only starts to be interesting as a realistic theory of our world after one proves that Lorentz invariance holds exactly (or almost exactly).

It was just Einstein in 1917, who completely omitted Lorentz invariance from further thoughts. Just because string theory has chosen Lorentz invariance as one of its postulates doesn't means, this approach is the only universal approach to physics. Even Einstein has recognized it - so why not some string theorists?

I am personally convinced that theories that try to break Lorentz invariance by small effects are not well-motivated. But even if I insist on the things that have been established only, the "at least almost accurate" Lorentz symmetry that has been demonstrated is an extremely powerful constraint on any theory. If you invent a random theory for which no reason why it should be Lorentz-invariant is known, it is extremely likely that the LS doesn't work at all and the theory is therefore ruled out.

The small breaking of Lorentz invariance we can observe as a quantum chaos. It's not a consequence of violating it, rather applying it in many concurrent time arrows. Because every particle itself is Lorentz invariant, the mutual interaction of many particles brings a causal uncertainty into global view. The theory based on small effects is Kostelecky theory, for example.

There are actually approaches to string theory that are not manifestly Lorentz-invariant. For example, the BFSS matrix model, or M(atrix) theory, is a 0+1-dimensional quantum field theory - a U(N) gauge theory with 16 supercharges. You can also say that it is a quantum mechanical model with many degrees of freedom organized into large Hermitean matrices. It resembles non-relativistic quantum mechanics, with some extra indices and a quartic potential.

Every theory should be defined by its postulate tensor, string theory is no exception. No theory, which is based on Lorentz symmetry can derive the violation of this symmetry by rigorous way.

There is no a priori reason to think that such a seemingly non-relativistic theory - whose symmetry actually includes the Galilean symmetry known from non-relativistic physics - should be Lorentz-invariant. Except that one can defend and "effectively prove" this relativistic symmetry by arguments based on string dualities. Although it can't be completely obvious from the very beginning, the original BFSS matrix model describes a relativistic 11-dimensional spacetime of M-theory. But the relevance of the matrix model for M-theory only began to be studied seriously when arguments were found that these two theories were actually equivalent. You simply can't expect your non-relativistic model to be equally interesting for physicists if you don't have any evidence that your model respects Lorentz invariance - or if it even seems very likely that it cannot respect it. Physicists would be foolish to treat your theory on par with QED or the BFSS matrix model because it seems excessively likely that your theory can't agree with some of the basic properties of the spacetime we know.

This is not true. In AWT the LS is provided by fact, no object can serve both like subject, both like mean of observation at the same space and time (a singular case of observation, based on zero degree causal tensor). Therefore Aether concept cannot violate Lorentz symmetry locally by its definition.

Emergence and the role of Lorentz symmetry in the grand scheme of things.

That's right, but the emergence has no relevant explanation in physics without Aether concept, not a string theory. And they're both theorems of AWT. Aether concept doesn't uses neither require any other ad hoced concepts. While emergence is required both for explanation of relativity, both quantum mechanics, I believe, we can avoid LS safely for future by the same way, like prof. Einstein did.   

The comments above should be completely uncontroversial. But let me add a few more speculations. Because space is emergent in string theory, the LS - a symmetry linking space and time - has to be emergent, too. This symmetry of special relativity is telling us that things can't move faster than light in the newly emergent geometry. What is this constraint good for? Is Nature trying to tell us something deeper than that?

The claim "space is emergent in string theory" simply mean, space is composed of many tiny strings. If you cannot realize it, then you simply don't know, what the emergence is based on. The Nature is just trying to tell us, it doesn't matter, which concept you're use in large quantity, it always loses its conceptual subtleties and becomes a pin-point singularity, i.e. "particle" from sufficiently distant space time perspective. This is what the Aether approach is based on: on particle abstract. The symmetry you're disputing just illustrates, the LS has its principal limits in anti deSitter space. From perspective of observer sitting inside of dense fluctuation of Aether the energy will spread outside of black hole by superluminal speed without problem.

Well, I am confident that special relativity is important for life as we know it because motion is very helpful for animals and the equivalence of all inertial frames is the simplest (and maybe the only plausible) method for Nature to guarantee that the very motion won't kill the animals. Imagine that you would feel any motion - you would probably vomit all the time and die almost instantly. ;-)

Stop trolling. Special relativity is important for life of (special) relativists and some fundamentalist string theorists only. Some people can become quite naturalistic, when defeating their pet theories...;-)

The Lorentz symmetry and the Galilean symmetry were the two most obvious realizations of the equivalence of all inertial frames that Nature could choose from, and She chose the LS because it treats space and time more democratically than the Galilean symmetry. (I could probably construct more robust anthropic arguments even though they would probably not be based on the motion of animals only - simply because the low value of "v/c" for animals indicates that the finiteness of "c" is not necessary for life itself.)

Nature doesn't choose the LS, the Prussian academy under Planck leadership has chosen it as its paradigm to avoid influence of Poincare's Sorbonne. This is a difference...;-)

But in the previous two paragraphs, we were talking about the 3+1 large dimensions of spacetime only. String theory has additional dimensions that can emerge in various ways and that are dual to each other - and the LS applies to all these dimensions as long as they become larger than the curvature (and compactification) radii. In some sense, that's quite shocking.

Emergence isn't miracle, it has very simple reason in AWT. Some physicists are becoming a cocooned creationists apparently, because they tend to use the concepts without their firm reasoning. This is a consequence of less or more hidden belief into reality, not the reality understanding by logical implications based on analogies.

The conclusion is, LS violation isn’t supposed to be weak at all. If we consider, particles of matter are all formed by the same vacuum, like the rest of cosmic space, then the LS violation is responsible for refraction index of both black holes, both elementary particles, everything. If LS would be complete universal, we would see anything from Universe - simply because it would be nothing to deflect path of light.

We can call this missunderstanding by proverb “The darkest place is under the candlestick”. Many scientists are spending money and their lives by obstinate search for LS violation - whereas they’re virtually sitting on it all the time. This just illustrates, why is it so important to understand subject at nonformal, conceptual level. It can save the money for all of us.

Every quantum mechanics phenomena is just a manifestation of nearly singular Lorentz symmetry violation from this perspective. Not saying about weaker effects, like CMB, gravitational lensing, photon-photon interactions and pair formation, GZK limit, dark matter… Virtually, if we can observe at least something, then the LS is violated there. We can see just this portion of curved space-time, because the places, where LS remains valid well are transparent for us by definition.

The same, just dual problem exists with quest for hidden dimensions. Because scientists are refuting Aether concept, we are forced to pay them for development of alternative models and for proposal of experiments, which could confirm the presence of hidden dimensions, albeit every quantum chaos or complex long distance interaction is demonstrating them clearly. Such ignorance may appear funny, but it's an innefective and expensive game for the rest of society, because these scientists can get involved in more usefull things.

To be sarcastic regarding string theory, I’d say, it tryies to describe by using of LS just this part of Universe, which violates it most pronouncedly. But this paradox is logical, because we can never use the same aspect of reality both the object of  observation/ description, both the mean of observation/description. We can see, the same logics, which introduces the Aether can be used even for Lorentz symmetry at the another level of reasoning. Theoretical description is dual to experimental observation in this sense. The reality is partly real, partly the consequence of theories and observable reality forms the boundary of both approaches.

Anyway, quantum gravity suffers the same conceptual problem, being dependent on equivalence principle instead of LS. It just means, it becomes wrong/singular in different part of conformal space-time: it can describe the LS violation of free space, assuming a “stringy structure” for it, while it’s missing the complex multidimensional structure of particles.

Whereas string theory depends on LS, it cannot predict the LS violation phenomena by rigorous way, because it doesn’t care about vacuum structure (with exception of string field theory and some other boundary approaches) . But it can describe well the complex structure of particles as such. These nice theories are AdS/CFT dual in fact, being separated by one derivation of Aether gradient in its description (they're mutualy orthogonal each other via Lorentz symmetry group).


Anonymous said...

HAHAHA - Zephir, we don`t give a sh* about your opinion !!

Zephir said...

Yep, this is what the total reflection of information is called. Acceptation of AWT would increase your entropy density too much, so you're reflecting new info like mirror-like bubble. This is the reason, why silly and negatively biased people are especially inert toward new ideas.

Well - if nothing else, we have some fun.. :-)

Zephir said...

Eleanor Roosevelt:
“Great minds discuss ideas.
Mediocre minds discuss events.
Small minds discuss people.”

Zephir said...

Motl, August 2009: "I urge everyone who has some responsibility for these matters to go after Smolin's neck"..
Motl, June 2011: "I have never really understood the psychology of the medieval zealots who would burn people at stake just because those people realized that the Earth wasn't a center of the Solar System or the Universe, for that matter. Where did such extraordinarily obsessed idiots come from, I was asking?"
It's evident, why. One of most important sign of psychopathy is the lack of awareness of own behavior.