The idea that space-time might not be higher-dimensional on short distances but instead be lower-dimensional has been around for some while, inspired by results from causal dynamical triangulation. In a paper last year, Anchordoqui et al proposed to examine the possibility of lower dimensionality at small distances for its phenomenology in their paper

*Vanishing Dimensions and Planar Events at the LHC*

Luis Anchordoqui, De Chang Dai, Malcolm Fairbairn, Greg Landsberg, Dejan Stojkovic

arXiv:1003.5914v2 [hep-ph]

Greg Landsberg gave a talk about this work on our last year's workshop on Experimental Search for Quantum Gravity (recording of the talk here). The basic idea is that the dimensionality of space changes with distance in such a way that it is 3-dimensional on scales we have tested it, lower dimensional on distances shorter than we have probed yet (about 1/1000 of a femtometer) and possibly higher-dimensional on distances larger than we can observe. The picture suggested is that of a (one-dimensional) string being knitted, and the knitted sheet (2-dimensional) being crumpled to a ball (3-dimensional). The authors dubbed this "evolving dimensionality." The merit of having a smaller number of space-like dimensions at small distances or high energies is that it improves the renormalizability of quantum field theories and esp. that of quantum gravity. (In contrast to additional dimensions which actually make the problem worse.)

The above paper as well as two recent follow-up papers, arXiv:1012.1870 [hep-ph] and arXiv:1102.3434 [gr-qc], looked at the phenomenological consequences of the evolving dimensions. Most interesting, they predict that at high energies the outgoing particles in scattering events should have an increased probability of being aligned in a plane. And the latest paper investigates the modification of the gravitational wave background. This modification is due to the early universe having been lower-dimensional if the idea is true, which would prohibit the propagation of gravitational waves. Both predictions are for all I know unique to this particular model.

But the question that springs to mind immediately is: What about Lorentz invariance? If one has a lower number of dimensions at short distances, these dimensions need to be oriented somehow relative to the four-dimensional continuum that must be reproduced at large distances. This orientation necessarily breaks Lorentz invariance. The problem is then that violations of Lorenz invariance are extremely tightly constrained already. I was thus curious to see how the model of evolving dimensions avoids these constraints.

The way this is achieved is that there is no model. Instead, it's in the authors words "not a concrete model, but rather a conceptual new paradigm." The papers offer pictures and analogies instead of a mathematical description of the new fundamental structure of space-time and the dynamics of quantum fields in it. The most recent paper addresses the issue of Lorenz invariance as follows:

"For random orientation of lower-dimensional planes/lines (see e.g. Fig. 2 ), violations of Lorentz invariance induced by the lattice become non-systematic, and thus evade strong limits put on theories with systematic violation of Lorentz invariance."

Unfortunately, this claim is not backed up by any argument and the figure does not represent a Lorentz-invariant random orientation. (The average spacings are approximately of the same size which is not boost invariant). From Causal Sets we know there are Lorentz-invariant 'sprinklings,' but these are sets of points and not distributions of planes. I also don't see from the picture if and how these planes end when they meet and it remains unclear how the length scales on which the dimensionality changes, supposedly a property of the space-time structure, is defined Lorenz-invariantly. Most problematic however is that the previous paper (arXiv:1012.1870) talked about the loss of energy into the background. This necessitates an interaction and that interaction should be described by an operator coupling the fields to the, oriented, background. I would then suspect this interaction falls among the already highly constrained Lorenz-invariance violations. It doesn't matter if these orientations average out on large distances if the effect that one looks for necessitates one is in a regime where one is sensitive to the distance it is not averaged out. This is very difficult to say though without a model.

However, in the recent paper on gravitational waves, one doesn't actually need Lorenz-invariance since one is concerned with cosmology and has a preferred frame - the restframe of the CMB - at hand anyway. So I wrote to one of the authors of the paper, Dejan Stojkovic from the University of Buffalo, who explained that they consider the model to be breaking boost-invariance but not rotational invariance. With that, the length scales on which dimensionality changes can be well defined without much effort. The question of Lorentz invariance violating operators however remains open. Dejan also readily admits that their new paradigm still needs work and explains how the first paper came about:

"I had this idea since 2003 while intensively working on higher dimensional theories. It crossed my mind that instead of making things more complicated at high energy (and hoping that the problems will miraculously disappear) we could instead make things less complicated - thus evolving dimensions (at short distances we have less dimensions, while at large distances we have more). However, I could not come up with a Lagrangian and would not dare to make it public.

Then at the meeting in Heidelberg, after diner and several beers, I told our friends, who intensively worked on extra dimensions, that the LHC is much more likely to find less rather than more dimensions, and after first 10 minutes of disbelief, they liked the idea and convinced me that in order to make a prediction rather than post-diction, the paper must go out NOW."

**In summary:**The idea of evolving dimensions is very interesting and makes predictions that are, for all I know, unique to this particular setting. At present it however lacks a mathematical model for the new fundamental structure and the dynamics of quantum fields in it.

## 90 comments:

The idea of evolving dimensions is very interesting and makes predictions that are, for all I know, unique to this particular setting. At present it however lacks a mathematical model for the new fundamental structure and the dynamics of quantum fields in it.Then maybe QFT has run it's course, as in Weinberg's introduction to his Vol. 1 The Quantum Theory of Fields book, our current QFT may be emergent.

Or ... maybe we we need better Mathematics. Something of a

notation revolution, so to speak.Dayam, I had NO idea my last question at your last post would be begun to be answered at your next one (this one), Bee. ;-) Serendipity? Doesn't happen often, but I'll take it. Ciao.

/* ... space-time might not be higher-dimensional on short distances but instead be lower-dimensional.. */

...stringy or even particle like, something like the aether gas...;-) Actually it could be both lower-dimensional, both higher-dimensional at the same moment (compare the black hole complementarity stuff)

illustrationIt seems to me that quantum gravity theorists are searching for quite exotic answers to the question of how quantum gravitation works, but are completely ignoring the simplest and most natural concept: discrete conformal dilation invariance.

You get to keep GR and a 4-D spacetime at all scales, but you reject absolute scale and absolute gravitational coupling in favor of relative scale and discrete scaling for gravitational coupling.

The resistance to this simple and natural idea, and its related extension of group theory, which would give you a discrete self-similar cosmos, is incomprehensible to me.

Why invent extra dimensions, or invent the concept that known dimensions disappear in the microcosm before thoroughly exploring discrete scale relativity?

RLO

BTW this stuff is nothing, which couldn't be interpreted with trivial classical physics, compare the dispersion of ripples at the water surface.

imageAs we can see, the wavelength of ripples decreases with distance from source, because they're dispersing into additional dimensions of underwater. But the same dispersion leads into formation of invisible longitudinal waves, which are spreading through underwater and their wavelength gradually increases.

imageThe mutual interference of longitudinal and transverse waves formed with dispersion should lead into formation of supersymmetric particles, which we probably cannot observe, because they're too close of event horizon, formed with such a dispersion.

The red/shift (Pioneer anomaly) are examples of dimensionality decrasing with distance scale. The light is spreading gradually more slowly through dispersing space-time, which creates an illusion of accelerated space-time expansion with distance from observer (note that the wavelength of ripples collapses with increasing speed on the above picture). The dark matter is the same stuff, just observed from outside - the source of waves appears surrounded with invisible "matter", which slows down the ripple propagation.

/*...discrete conformal dilation invariance...*/

Why not, but at first it's somewhat ad-hoced concept from my perspective, at second, Universe maintains conformal dilation of dilation invariance and all higher orders of such transform at the same moment, at third, we cannot observe all levels in the same way. At fourth, such dilation invariance is heavily violated at the human scale. Which object from your neighbourhood actually maintains such dilation invariance? The heads of brocolli? It's not enough for considering it as an universal approach.

I admit I don't have time to study or the "wherewithal" to adequately evaluate these claims in detail, but at first take they seem a bit confusing. Sure, "strings" are themselves one-dimensional

per sebut I thought they "lived" in a higher dimensional space, for which we're treated to cute trouser diagrams and loops and snail or inner-ear-like diagrams of Calabi-Yau manifolds etc. Now to hear that things "really are" lower dimensional at short range, but higher at large scale (!?) is really weird.Well I have an open mind, just saying it's jarring to those brought through the traditional multi-dimensions, M-theory etc. story. And what now for "other universes" etc? Wow, what a roller coaster ride.

/*..now to hear that things "really are" lower dimensional at short range, but higher at large scale (!?) is really weird. ..*/

Actually the very same perspective you would observe, if you would density fluctuation of some dense fluid and you would interact with another fluctuations around you, both larger, both smaller ones. With increasing difference in distance scale the dimensionality (complexity) of your interactions will gradually decrease. On this aspect the AWT is based, after all: the particle gas model is extrapolated from this dependence, not ad-hoced here.

Illustratively speaking, try to imagine, you're observing objects around you inside of landscape under haze. The more remote object will appear less and less detailed, the 3D shapes will change into 2D ones and the most remote objects will appear only like fuzzy 1D blobs.

An observation of streaks of dark matter illustrates it clearly - at proximity we can see all its complexity, but at large distance only foamy density fluctuations (2D "strings") will prevail and at the most distance scale the Universe is composed only from pin-point galaxies without apparent shape. The blurring of light during its long travel through CMBR noise vanishes all details of space-time geometry. I presume, the space-time behaves in the same way at short scales with decreasing distance scale.

RLO,

While we disagree on some (not so minor) details I agree with what you said.

Hi Eric,

Thanks, you may be the only person on the planet to see some merit in what I am talking about.

If you change one assumption about gravitation, and it is verifiably no more than an assumption, then you get a radically different model of the cosmos, and one that bears a very strong resemblance to the observed portion of the cosmos.

With just GR, EM and DSR you can retrodict almost everything observed without invoking anything weird or improbable - just two well-tested dynamical interactions and discrete self-similar scaling.

I would not expect people to immediately fall on their knees and worship the idea, but I would expect to see scientists show more interest in the theory, since simplex sigillum veri.

Paradigm change is a bitch.

Same as it ever was.

RLO

I really doubt that I'm the only one who agrees with the broad outlines of what you are saying. People forget what they knew inherently as kids, that is, to be direct in one's interactions with world. As you get older you can't help but see that the ones getting to the top of the heap usually aren't getting there by pure ability. Usually it's more saying the right things in a framework in which people are willing to listen.

But after a while you find out there is NEVER a right time to say things people don't want to hear, even if it's true. I think most people don't realize that it is a real advantage to be an outsider in that way. You and me don't have nearly as much to lose as they do so we can speak our minds. Actually I think a lot of people agree with your common sense but they don't see any of the up and

comers getting in line to agree so they just keep there mouths shut. I think a few odd souls might actually agree with me also, heaven help them.

Zephir:

It's enough now. This post is about the papers by Anchordoqui et al. One more off-topic remark and all your comments go into the trashbin. I've told you some hundred times: no self-advertisement. Why do I have to repeat this over and over again? Best,

B.

Robert,

If you want to discuss something else than the papers I wrote about in my post, please do so elsewhere. Thanks,

B.

Hi Bee,

Thanks for the run down and pointing out the relevant papers. This lesser rather than greater dimensional concept is interesting and yet as you point out seems to create as many problems as it solves. However with that said I’ve always had a gut feeling things might shake out this way in the end. Then again perhaps it’s just that I’m an Occam’s razor fellow, who favours what’s the consistently lesser as being the better bet rather then more. One thing for certain there appears to be an ever broadening spectrum of ideas now coming forward and that can only be a good thing, even if any particular one might not be correct. Actually what I like most of all is they have included consequential predictions with their hypothesis and thus nature can be the decider as to its worth; thus I’ll keep an eye on this one.

Best,

Phil

Hi Phil,

I'd argue simplicity doesn't necessarily mean less of something. Often things also get simpler if one takes more and more. Think thermodynamics. Not so suprising then the efforts to express gravity through thermodynamics. Best,

B.

Hi Bee,

I would agree, although with the case of thermodynamics it’s not so much one has increased the number of fundamental elements to be considered, yet rather the resultantly dynamic complexity they manifest. For instance when I look at the simplicity of the operative elements of the Mandelbrot set and then look to the complexity it manifests when executed it has me to appreciate the essential difference. In the end what counts is what one comes up with agree with nature as it presents itself and not how one would like it to present. That is why I was so pleased they included predictions so such could be determined.

"The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience"-Albert Einstein, “Ideas and Opinions”, Crown Publishing(1954)

Best,

very interesting, thanks Sabine.

(it's a shame that the video suddenly stops at 11 minutes though..)

Question: is this really that far from the current standards of publications in this field? I mean, how many papers on extra dimensions or discretization can claim to have a "mathematical model for the new fundamental structure and the dynamics of quantum fields in it." ?

T.

"The merit of having a smaller number of space-like dimensions at small distances or high energies is that it improves the renormalizability of quantum field theories and esp. that of quantum gravity. (In contrast to additional dimensions which actually make the problem worse.)".. SaBEEnius

D'oH! That's Great! Instant classic. :-)

Hi T,

Sorry about the video :-( I hadn't watched it, so didn't notice the recording hadn't worked.

The models with extra dimensions make qft in higher dimensional spacetime with some matter fields confined to a submanifold. Very straight forward. With Causal Sets the spacetime structure is, well, a causal set. They're working on putting classical and quantum fields on it, see e.g.. Point I was trying to make is that the 'new paradigm' of evolving dimensions doesn't even attempt to explain what the spacetime looks like or how fields propagate on it. Best,

B.

Hi Steven,

Not sure what you mean there. Note that I was referring to qft. If your fundamental theory isn't a qft, then the question of renormalizability can look entirely different. Best,

B.

Since I don't have a handle on the particulars of QFT at very small scales, let's look in the other direction. (Btw, I question the "fantastic success of the cosmological standard model ... the particle standard model is a fantastic success, but the cosmological one ... ?!).

On the large scale if the number of dimensions increase are they implying compacted ones as in String theory, because I seem to member reading about the original CDT experiments (tabletop, using inkspots!) that there is a curve where the number of dimensions maxes out at 3, and asymptotically so.

Hi Steven,

Can't recall they said anything about whether they imagine compactification on large scales or not. It would have to be on super-horizon scales anyway. Best,

B.

I believe you recall correctly bee as I didn't see any mention either, but I just skim-read. Yes, I like that it would occur at a super-horizon as you put it. Would that then allow AdS/CFT to be brought in?

I apologize for asking so many questions but CDT always fascinated me most of all in this QG stuff; I can't get enough of it. I remember reading that when it came out BOTH stringers AND loopers were all over it, one of the few times they seemed to climb the same tree, and then ... a "desert" so to speak where I heard little.

Bee:That the space-time of Einstein's Special and General Relativity might not be fundamental plays a central rĂ´le in our quest for quantum gravity.Of course then this would then eliminate certain models. To have something like space-time emerge out of, then one cannot ignore it arising out of a complex issue?

The caveat might be then, your interpretation of extra dimensions, and I appreciate the evolving dimensions summary.

I might fall under a false pretense conceptualization of a Q<->Q measure(please correct if it appears wrong) and the amount of energy of such an environ.

It would have us question with regard to that relation of extra dimension as an environ laced with energetic valuations as particulates of the standard modelthat amount too, parts of the whole energy valuation?

Then I have trouble thinking again about how the real world looks and how something one can pass through it, as easily as a boat that could cut through water.

A number system like Riemann's Hypothesis, "like a sieve" eventually an arrow snakes out of as if contained within the Ulam spiral. This is a larger perspective on that valuations of a chain reaction, yet it is par and parcel of the defining substrates of reality as an example.

Best,

The basic idea is that the dimensionality of space changes with distance in such a way that it is 3-dimensional on scales we have tested it, lower dimensional ondistances shorter than we have probed yet (about 1/1000 of a femtometer)and possibly higher-dimensional on distances larger than we can observe.(emphasis mine)

So 1/1000 of a femotometre = 1 Attometre = 1 x 10^-18 m = the sensitivity of the LIGO detector for gravitational waves, yes?

The smallest "thing" we know of then must have calculated, not measured, that being 2 × 10^−23 metres = 20 ym, the effective cross-section radius of 1 MeV neutrinos as measured by Clyde Cowan and Frederick Reines. correct?

Sorry, I'm feeling particularly geeky today.

I referred earlier to Dyson quote for examination of a forward looking examination of such spaces, to have it concluded as easily so.

It is not just an willy-nilly proposal that extra dimensions serve to help us look at the depth of the world around us, or that some construct methodological process of Flat land exists as an geometrical expression of the way we see the world leading topological dissertation of expression?

On the Hypotheses which lie at the Bases of Geometry.Bernhard RiemannTranslated by William Kingdon Clifford

[Nature, Vol. VIII. Nos. 183, 184, pp. 14--17, 36, 37.]

It is known that geometry assumes, as things given, both the notion of space and the first principles of constructions in space. She gives definitions of them which are merely nominal, while the true determinations appear in the form of axioms. The relation of these assumptions remains consequently in darkness; we neither perceive whether and how far their connection is necessary, nor a priori, whether it is possible.

From Euclid to Legendre (to name the most famous of modern reforming geometers) this darkness was cleared up neither by mathematicians nor by such philosophers as concerned themselves with it. The reason of this is doubtless that the general notion of multiply extended magnitudes (in which space-magnitudes are included) remained entirely unworked. I have in the first place, therefore, set myself the task of constructing the notion of a multiply extended magnitude out of general notions of magnitude. It will follow from this that a multiply extended magnitude is capable of different measure-relations, and consequently that space is only a particular case of a triply extended magnitude. But hence flows as a necessary consequence that the propositions of geometry cannot be derived from general notions of magnitude, but that the properties which distinguish space from other conceivable triply extended magnitudes are only to be deduced from experience. Thus arises the problem, to discover the simplest matters of fact from which the measure-relations of space may be determined; a problem which from the nature of the case is not completely determinate, since there may be several systems of matters of fact which suffice to determine the measure-relations of space - the most important system for our present purpose being that which Euclid has laid down as a foundation. These matters of fact are - like all matters of fact - not necessary, but only of empirical certainty; they are hypotheses. We may therefore investigate their probability, which within the limits of observation is of course very great, and inquire about the justice of their extension beyond the limits of observation, on the side both of the infinitely great and of the infinitely small.

Best,

Steven,

The basis of the arms of LIGO have a equatorial calculation to demonstrate measure? It's size. Kip Thorne demonstrated that.

Best,

Steven,

Projective Geometry of what?:)

Best,

Bee you have to build a framework that is consistent with the ideas of model apprehension of dimensional understandings in order for any model to appear.

"Without this foundational basis" how are you to work backward from a complex issue, to arrive at any simplicity?

Einstein:I attach special importance to the view of geometry which I have just set forth, because without it I should have been unable to formulate the theory of relativity. ... In a system of reference rotating relatively to an inert system, the laws of disposition of rigid bodies do not correspond to the rules of Euclidean geometry on account of the Lorentz contraction; thus if we admit non-inert systems we must abandon Euclidean geometry. ... If we deny the relation between the body of axiomatic Euclidean geometry and the practically-rigid body of reality, we readily arrive at the following view, which was entertained by that acute and profound thinker, H. Poincare:--Euclidean geometry is distinguished above all other imaginable axiomatic geometries by its simplicity. Now since axiomatic geometry by itself contains no assertions as to the reality which can be experienced, but can do so only in combination with physical laws, it should be possible and reasonable ... to retain Euclidean geometry. For if contradictions between theory and experience manifest themselves, we should rather decide to change physical laws than to change axiomatic Euclidean geometry. If we deny the relation between the practically-rigid body and geometry, we shall indeed not easily free ourselves from the convention that Euclidean geometry is to be retained as the simplest. (33-4)http://www.bun.kyoto-u.ac.jp/~suchii/EonGeometry.html

Interesting comment Eric.

The choice has always been:

Freedom and integrity versus status and compromise.

Occasionally a rare person like Einstein, through quirks of fate, gets to have freedom, integrity and the appreciation of the scientific community.

The optimistic bottom line is that a realy good idea always rises to the top when given enough time. Mendel's discoveries in genetics were ignored for 135 years, then suddenly got discovered. Bach's music was nearly lost to the world, only to be rediscovered and cherished.

Curiously, mediocre ideas like string theory, extra dimensions, Boltzmann brains, anthropic reasoning, it from bit, etc., find easy access to the limelight. Untestability may be their great secret.

RLO

RLO: "The optimistic bottom line is that a realy good idea always rises to the top when given enough time."

Unfortunately, our dataset suffers from selection bias: we only know about the cases that were successful. We remain blissfully ignorant of the good ideas that were lost, or that we never realised

weregood ideas, because, by definition, we either don't know about them or never realised their true significance.So yes, we see what

appearsto be a 100% success rate for good ideas in science "in the end" ... but we'd expect to see an apparent 100% success rate even if the true success rate was really bloody awful. The 100% figure doesn't necessarily signify that we're doing well, because we'd still end up awarding ourselves a mark of 100% if we were appallingly bad! :)become important only at scales that we have not yet testedNo massed sector symmetry observations exist. Massless photons are convenient and chemistry is derivable.violations of Loren[t]z invariance are extremely tightly constrained alreadyEuclidean triangles do not constrain elliptic or hyperbolic triangles. Circles are squared by quadratrix curves, but not within Greek rules. Physics can fail where it will not look (streetlight fallacy). Perhaps an "extra" dimension is massed sector curl.Standard Model/SUSY/SUGRA and quantum gravitations are "universally true" postulates plus rigorous deduction yielding dogma. 1956 physical theory was defective for calling Yang and Lee futile. It received manually inserted chiral symmetry breakings.

Isotropic vacuum plus Noether's theorems demand conservation of angular momentum. Empirical validations of both are exhaustive at all scales. Gravitation and quantum field theory demand both. A vacuum left foot active upon atomic mass configuration at atomic dimensions contradicts no observation. It ignores photons, achiral socks, left shoes, and right shoes sized too large to tightly fit. No observation forbids it.

If the vacuum is demonstrably albeit selectively

notmirror symmetric, fundamental derivation is falsified. 90 days in an Eotvos balance or 24 hours in paired DSCs outweigh hectares of fantastical Phys. Rev. D. Somebody should look. Teleparallel gravitation is compatible theory. The worst it can do is succeed, exposing chiral symmetry breaking as a Big Bang given.Hello ErkDemon,

I am not a big fan of probability arguments since they can badly mislead as well as inform.

In the modern era, say, since 1900, science has been a bubbling cauldron and ideas keep rising to the top and descending. My guess is that few ideas have never reached to public domain, although it may be just one book or article and then obscurity for a long time.

Hierarchical models of nature keep rising to the top and then descending into obscurity - only to rise again like the phoenix.

I seriously doubt that a really good general idea ever goes extinct. Specific proponents may shuffle off this mortal coil, but the ideas go on as long as there are recorded records and researchers who RE-search.

In the long view there is every reason for optimism.

RLO

Hi Steven,

I didn't have in mind precision, but resolution of structures. 1/1000 fm is approx the inverse of 10 TeV (or so) and thus what the LHC is able to probe. Curious coincidence it's also the precision of LIGO, I actually wasn't aware of that. Best,

B.

Hi Plato,

Yes, if spacetime is fundamental instead, that rules out some models, namely those in which it isn't. However, the question is typically not one of "is" or "isn't" but which model makes what prediction and how does it compare to data. Best,

B.

Hi Bee,

what exactly is a 'brane' ?

Best, Kay

Hi Kay,

Roughly speaking, it's a submanifold of a certain dimension. In string theory it has a more destinct meaning in that open strings end on it. Best,

B.

Hi Bee,

in that open strings end on itWhat does branes physically imply ?

Best, Kay

Bee:Yes, if spacetime is fundamental instead, that rules out some models, namely those in which it isn't.Was I correct then to see that you had eliminated "that model fundamentally based" on the idea of evolving dimenions that you felt "it was not a fundamental part of the model apprehension based on the phenomenological process "as you see it," and not as it so far remains?

Remember there is still a conformal field theory approach on the surface, as description of the interior of the blackhole?

That result has not changed.

Best,

Bee, this may be a good point to ask (sort of again): I thought that strings

neededlots of extra short-scale extra dimensions to operate, so is this new low-d concept compatible at all with string theory, or would ST at least need to be modified?Hi Kay,

In the model with extra-dimensions it means that particles with SM charges are bound to it. Best,

B.

Why would you abandon a model that understands well the thermodynamic properties?

Gary Horowitz, Philip Candelas and Andy Strominger Witten showed how string theory can lead to realistic descriptions by compactifying the theory on a higher dimensional manifold known as Calabi Yau manifolds"D-branes provide the fundamental quantum microstates of a black hole that underlie black hole thermodynamics"Spacetime in String Theory

While talk is pervasive according too, as the experimental results of LHC proceed in regard to developments of thoughts and theoretic around Super symmetry then how has this model changed with regard to Horowitz plates above?

Historically some things cannot be changed unless the calculations were wrong? Are they wrong?

Should one abandon what is calculable for the want of proving something that is kocher with, while we wait for the energies to do their thing?

Should one abandon theorists?

In 1919, Kaluza sent Albert Einstein a preprint --- later published in 1921 --- that considered the extension of general relativity to five dimensions. He assumed that the 5-dimensional field equations were simply the higher-dimensional version of the vacuum Einstein equation, and that all the metric components were independent of the fifth coordinate. The later assumption came to be known as the cylinder condition. This resulted in something remarkable: the fifteen higher-dimension field equations naturally broke into a set of ten formulae governing a tensor field representing gravity, four describing a vector field representing electromagnetism, and one wave equation for a scalar field. Furthermore, if the scalar field was constant, the vector field equations were just Maxwell's equations in vacuo, and the tensor field equations were the 4-dimensional Einstein field equations sourced by an EM field. In one fell swoop, Kaluza had written down a single covariant field theory in five dimensions that yielded the four dimensional theories of general relativity and electromagnetism. Naturally, Einstein was very interested in this preprint .Voila!:)Best,

Hi Plato,

I haven't eliminated anything. I've merely said that the thought that the space-time of Einstein's Special and General Relativity itself might not be fundamental is a common one that has inspired many research projects. That doesn't even necessarily mean that space-time itself isn't fundamental, but that it possibly just isn't 4-dimensional or is a mess on short distances or swhatever. And it certainly doesn't imply any judgement on the promise of following such thoughts. There isn't really any model for the evolving dimensions, so I have nothing to say about what remains in that case. Best,

B.

Hi Neil,

I don't know what you're asking actually. The evolving dimensions are not equal string theory in case that's the question, and for all I can see it's not even motivated by string theory. You can do string theory in an effectively lower-dimensional space-time if you want, just compactify some more dimensions, then you can presumably first shrink the number of dimensions when you go to higher energies a la evolving, and then eventually increase them again when you get to the Planck scale. Just that I totally don't see the point in doing that. Best,

B.

If you can relate to Kaluza in the approach to move forward(projective geometries,) while he was in contact with the developments of relativity, then should not one consider a Geometric analysis, as part of that journey?

Best,

Hi Steven,

I had read it. Did it actually say anything non-trivial? Best,

B.

Hi Bee,

thanks, good interpretation.

Best, Kay

Just wanted to say thanks for your patience Bee.

Juan Maldacena:The strings move in a five-dimensional curved space-time with a boundary. The boundary corresponds to the usual four dimensions, and the fifth dimension describes the motion away from this boundary into the interior of the curved space-time. In this five-dimensional space-time, there is a strong gravitational field pulling objects away from the boundary, and as a result time flows more slowly far away from the boundary than close to it. This also implies that an object that has a fixed proper size in the interior can appear to have a different size when viewed from the boundary (Fig. 1). Strings existing in the five-dimensional space-time can even look point-like when they are close to the boundary. Polchinski and Strassler1 show that when an energetic four-dimensional particle (such as an electron) is scattered from these strings (describing protons), the main contribution comes from a string that is close to the boundary and it is therefore seen as a point-like object. So a string-like interpretation of a proton is not at odds with the observation that there are point-like objects inside it.Hi Steven,I had read it. Did it actually say anything non-trivial?

Hmm, I suppose you're responding to my comment at your post "This and That" regarding Gleiser's take on Monday's neo-Solvay debate, Asimov 11?

If so, you're right, there is absolutely NOTHING non-trivial in what he said to an expert in the field such as yourself.

But consider: not all of your readers, myself included, have your expertise. My point was that he says nothing categorically wrong or in the "hype" category, and furthermore what he says is very compact and concise and wonderfully so in a very clear expository fashion, and we would all be better off reading gleiser's article such that we/your commenter's would have a clearer idea between that which is known, and not (therefore speculation), and be better commenters, thereby.

Hi Steven,I had read it. Did it actually say anything non-trivial?

Hmm, I suppose you're responding to my comment at your post "This and That" regarding Gleiser's take on Monday's neo-Solvay debate, Asimov 11?

If so, you're right, there is absolutely NOTHING non-trivial in what he said to an expert in the field such as yourself.

But consider: not all of your readers, myself included, have your expertise. My point was that he says nothing categorically wrong or in the "hype" category, and furthermore what he says is very compact and concise and wonderfully so in a very clear expository fashion, and we would all be better off reading Gleiser's article such that we/your commenters would have a clearer idea between that which is known, and not (therefore speculation), and be better commenters, thereby, which I do believe is something you and Stefan deserve moreso than you get at times.

Whether there are more or less dimensions at smaller scale will depend on being able to “see” into the perfect liquid.

http://www.int.washington.edu/PROGRAMS/10-2a/

At present, the conclusion that the medium generated at RHIC is a strongly coupled, near-inviscid, color-opaque fluid, with large initial energy density, should be considered to be qualitative, based on dynamical models with in some cases poorly constrained assumptions or approximations.

Just want to add ... you got nice looking twins.

jal

Hi Steven,

Yes, you're of course right. Gleiser says it well. I suppose I'm just a little tired of reading the same things over and over again but as you say there's always people for who it's the first time. Best,

B.

Hi Steven,

After reading Gleiser’s article I would say he has his own axe to grind, just as the others he alludes to as having. Somehow I think he confuses the recipe for making a (specific) cake with the possibilities of all recipes. That is just because there are many options to consider doesn’t demand more than one of them ultimately being significant.

That’s to say that no one has ever been able to demonstrate empirically there being more than one way to have a reality. So although I would agree the nature of reality presents as being very special I wouldn’t agree that’s the same as to finding it arbitrary. That is from my own perspective I find Gleiser’s metaphysical position not simply defeatist, yet verging on being unscientific.

"The Heisenberg-Bohr tranquilizing philosophy--or religion?--is delicately contrived that, for the time being, it provides a gentle pillow for the true believer from which he cannot very easily be aroused. So let him lie there."-Albert Einstein, letter to Erwin Schroedinger (May 31, 1938)

Best,

Phil

Phil, I address Gleiser's point (that he made in an earlier article) in my blog post "Marcelo Gleiser Has a Point.". My argument, basically, is that we can't have an a priori logical/mathematical argument for "a universe" (presumptive special-status "material world" that we apparently live in, as opposed to a literal mathematical model in the Platonic mindscape) being a certain way and not otherwise. That is, no strictly logical way to pick out some "possible worlds" from others. So the "correct equations" just will not fall out of any legitimate, strictly logical process, sorry.

Oh, that doesn't mean there cannot be any process or reason (larger sense, of "cause")

at allwhy the world exists or is like this, it just can't be "strictly logical." So the proper search is for finding the scheme that does indeed best describe it, guided if you want by your choice of intuitions (beauty, simplicity, harmony, creative expression of "the necessary Being", that life should have a home, etc.) BTW that sadly goes for parsimony as well. Really, has anyone shownwhywe should believe that things are basically simple, or that Nature (not to be confused with procedural convenience) really tries to follow Occam's Razor?Good points, Phil and Neil.

At this point Neil, I'll settle for Occam's spent dull razor, or maybe his Short Sword. Perhaps I'm being defeatist as well, but I'm not sure beings with IQ's under 300 are capable of figuring out the Universe.

Have a nice day. :-)

No, but wait! There's more!

I will never, never understand, and I have never gotten a clean answer, as to why we worry about TOE at all presently. How can you find a TOE when you haven't a theory of quantum qravity.

And how can you have a theory of quantum gravity with

outa grand unified theory of the subatomic forces, the electroweak and the strong?In other words, shouldn't it be GUT, or bust?

Hi Neil,

“Oh, that doesn't mean there cannot be any process or reason (larger sense, of "cause") at all why the world exists or is like this, it just can't be "strictly logical."”

I can see we are diametrically opposed on this one. I could make all sorts of argumentation other then what I’ve already offered; although I hardly find that as necessary, for as I’ve pointed out no one thus far has logically or physically demonstrated that reality could be any other than one way (that is with or without entities to perceive its existence). More so I find it more than a little naively arrogant to insist reality “can’t be strictly logical”, as that is a hypothesis which has neither a logically or physically confirmed underpinning.

I have always found it it strange that to declare someone as being a Platonist, as opposed to a positivist, is so often found as being enough to have such “logical” argumentation to be dismissed out of hand. So if the understanding of reality is found to be too difficult it doesn’t have it as necessarily logically irresolvable, as it could as likely mean we are thus far not up to the task. Never the less I won’t get myself in a knot about it, although I do wonder when that “gentle pillow” Einstein refers to will no longer be found as so comforting :-)

“The end and the means towards it may come about by chance. We say, for instance, that a stranger has come by chance, paid the ransom, and gone away, when he does so as if he had come for that purpose, though it was not for that that he came. This is incidental, for chance is an incidental cause, as I remarked before. But when an event takes place always or for the most part, it is not incidental or by chance. In natural products the sequence is invariable, if there is no Impediment.”-Aristotle, ”Physics” (aprox. 350 B.C.)

Best,

Phil

Hi Steven,

“How can you find a TOE when you haven't a theory of quantum gravity?”

The answer would be if both QM and GR were found as only consistent within a limited domain; which would require an explanation exceeding each of their individual perspectives. For me that would be like wondering how the orbit of Mercury could be possibly understood before we find Vulcan; as to presuppose that such a thing must necessarily exist as a prerequisite for its possible resolution.

That is for me for something to be considered science, it must act as the instrument which reflects reality and not one serving to reflect theory. Another way to express it, is even if one has the correct metaphysical direction, this could still bear little fruit without having it complimented with a completely logically and physically supported ontology.

The one thing I do find as curious, is today it’s so often suggested that verifiable predictions are seriously limited primarily by our ability to perceive, while they might be just as limited in having not having realized as to what might be readily perceived if things are correctly conceived. That is I find it curious that lately we have all these unexplained phenomena and not the existence of single one had been predicted beforehand by way of our foundational theories.

So in the end I would argue there is far too much emphasises placed on reading the tea leaves, confined to strictly ‘what’s thought’ being certain we know, rather than predicting the leaves that as of yet have gone unnoticed and to offer explanation as to why. So between the choices of ‘not even right’ and ‘not even wrong’, we must still leave room for the ‘not to have been conceived’.

Best,

Phil

Phil, I think you have the logical order reversed: it's not whether someone can demonstrate whether "reality" should be any

differentfrom it is now, because to do that they have to demonstrate why it should be any way, like this way, at all: that issue actuallysupportsmy original point. So they can't demonstrate either why it should be like this, or why it should be different. My argument is based on the most rigorous abstraction about the potential logical basis for worlds to exist or not, and what I consider the most astute "abstract minds" like those of David Lewis and Max Tegmark agree. I think their failure is to think that, therefore, there is no "reason why" in a broader sense. But math/logic has no toolsin principlewith which to bless and pick out some possible worlds and not others. It just doesn't, this is a logical shortcoming in vein of e.g. GĂ¶del's incompleteness theorems etc.As for arrogance: it might be arrogant to assume something about inscrutability of the universe, but then it would be arrogant to assume that we certainly can find out. Sauce for goose ... Note that I'm not saying we can't find an order, or that things aren't basically lawful, but that we can't say why that order and not another one, with pure reason.

Well, I noticed as do many that e.g. the fine structure constant has a logically ugly value of ~1/137 which is however very good for our being able to exist, and I think *that* is more to the point of the "why" of all this, FWIW.

Hi Neil,

Like I mentioned from the beginning, we are diametrically opposed on this issue. As for instance that somehow you find GĂ¶del’s conclusion(s) being to suggest there is a limit to logic, rather than what it is, being the limit of mathematics in of itself being able to having it represented in its completion. Such a conception in part is what I refer to as being resultant of naive arrogance.

As to those mysteries such as the fine structure constant in being approximately 1/137, I find this no less astounding or significant that 22/7 would in approximation be the proportion of the least perimeter to enclose the greatest area (that is if reality being what it has to be). I suppose the difference being I find no reason to abandon logic to dictate reason, while you think their being reason to. Although I don’t find this so much of a surprise, more as simply confusing, as I hold true reason being the manifestation of logic and fail to understand how only with its exclusion will have things to become better understood.

Best,

Phil

It's not 22/7, Phil. It's 4. Engineers round up.

Phil, as for GĂ¶del's Incompleteness Theorems, they do show a limitation on what we can know. However, it may well be that the GITs are not the best analogy, since I am saying not just that the picking out of our world from various possible math models is inscrutable to us but perhaps "there is still a matter of fact about it in logic that we just can't discover" (as is for some issues about infinite sets.) I am saying rather, there really is not a matter of fact about it in logic (the answer is not even Platonically real but unreachable to us, it is actually not there in the logical space.)

Your comparison of FSC to Ï€ is likely not apt. Pi is literally derived straight from pure math as a

definedinternal matter of relationship, whereas the FSC Î± is found empirically. If there is a mathematical representation of Î± as some combination of powers and special numbers etc. (and some wags have come rather close in trying, starting with the great Arthur Eddington - BTW whom I do not hold against him for trying) then even so, we could ask "why no some other mathematical combination to be *actualized* in a world? That is the question. As Tegmarket alrightly IMHO note, it is (put into my own metaphors) like looking at a vast array of conceptual forms that "could be worlds" if made flesh so to speak, and then seeing some special glow or transcendent smell that some of them have, that is not part of their description as models per se. But having such extra properties of manifestationality (I couldn't resist) is like "dualism." It just literally "does not compute" from the logical structure of things.In any case, it is no more "arrogant" etc. (and I know, you mean that as a conceptual critique) to think one appreciates that there can't be such a distinction, than it is to think there is such a distinction even though no one has come up with one

or even shown the way to how it could be done, or what sort of feature it might be. "Can't we all just get along?" So live and let live. I ask the indulgence of your sympathy, I'm smarting enough from loss of your esteem by inadequate appreciation of Bohm ;-|.I wonder if Bee could consider imposing a rule: nobody gets to post more than 3 responses in any given thread. Or perhaps no given individual can post more than 200 times per year.

Hi Neil,

I think we’ve taken evolving dimensions into becoming devolving dialogue. I’d actually prepared a response yet found it having me restating the same. As for the esteem I hold for your ideas and efforts, let me offer as a final thing for you to consider, which may also first appear as a contradiction; with that being I truly hope your submission to the FQXi essay contest does well.

Best,

Phil

There was an article yesterday in Physical Review Focus on the topic, see

Testing for Vanishing Dimensions

Wow, that's interesting, thank you Bee. From the article:

"Evidence of vanishing dimensions may already have been detected in cosmic ray showers in the Earth’s atmosphere. A 2005 reanalysis of cosmic ray data showed that the jets of particles produced by the most energetic cosmic rays were aligned closer to a plane than would be expected, which could signify dimension reduction [2]."Woosh, really? Wow.

0-dim = Black hole singularity; fundamental particles

1-dim = galactic filaments; gravity

2-dim = galaxies; strong force

3-dim = galactic clusters; electroweak force

4-dim = Universal expansion; dark energy

Just a quick thought, and it's probably wrong.

In an ana and keta world, we must

expandour thinking. D'oh! Sorry.Phil:

That is I find it curious that latelywe have all these unexplained phenomena,and not the existence of single one had been predicted beforehand by way of our foundational theories.Phil could you elaborate more as to unexplained phenomena?

To me anomalies that exist in nature have to comply as to satisfying more then one time as to it being unexplained?Is this a accurate statement in your view?

This has bee my difficulty and my lure to the the issues of quantum gravity and gravity alike.

I mean if we were to compile reasons why people are interested, what would be some of those reasons and are they suitable motivational factors that support any investigation and research into that matter at hand?

Best,

Thanks Bee for article.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

—

Nikolai LobachevskyThis part of the issue is to see relations with the real world in concert with the mathematics?

Hodge Conjecture

Is that abstract world totally on it's own, or, is it really describing the basis of reality as a schematic drawing of all that evolves around such conceptions? It's dimensional construct?

For applicable correlation in real world events helps to solidify understanding of abstract things so it's important to me that while phenomenology sets it's sight on verification as to theoretical idea, the cost is great, but the end question about it's real world application is very real? Why enter such abstractions, if you do not want to enter the real world?

Best,:)

G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)

Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of natureHow is the "time line of the universe constructed?"

You have to realize that such emergence into the views of universal formulations, has to have some associative response from the quantum world to see that such relevance in the cosmological participation could have ever pointed to the motivation of these universes coming into being, that it would go through a phase transformation relevant to each particle description? Is this correct? This presented itself in a "way of seeing" that stretches the mind imaginations that I wonder if I had indeed gone off the deep end.( some of my private thoughts:)

Best,

Hi Plato,

Perhaps I should have rather said observations left as unexplained phenomena, i.e. dark matter and dark energy. That is the observations which prompted each to be labelled as such were not anticipated by way of either the currently established theories or ones proposed to supersede them. That is from this perspective it’s not completely fair to say there hasn’t been opportunities to make predictions which could have been subsequently confirmed; that is even if not proposing new science.

Best,

Phil

Plato wrote:

How is the "time line of the universe constructed?"Beats the shit out of me, my friend. How do YOU think it is constructed? Read any Sean Carroll lately? Any 2nd Law of Thermodynamics ... which ... I personally think should be the base law to build all the other Laws on, to come to (eventually) that one Law to rule them all and in the darkness bind them?

Plato also wrote:

G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)Interesting equation.

How about ...

Click here then go down to the diagram under "Modern Physics - Conventional Sequence of Theories" and ask yourself the following question:

For symmetry purposes alone, why can't the Electronuclear Force (GUT) be:

SU(4) Spin(6)

?

Why not? I have no idea if that's right, just throwing it out there.

Hi Steven,

Then we must not forget what flavour we are talking about as if it being a particle of pure flavour or one of mixed flavour, such as a boson when compared to a fermion. So we should also be asking how many dimensions are required for vanilla and how many for maple walnut? :-)

Best,

Phil

Or how many there are for Rocky Road, Phil? I can't count that high.

For the professionals: enumeration.

Phil, I hear you. My point was that if 3 quarks define a nucleus and they are treated as 0-dim "particles" in a phenomenally and phenomenologically way, then 3 points define a 2-D plane, is all I'm suggesting.

@ Steven, "time line of the universe" - regardless of specific motivation of poser, it is possible to construct a "cosmic time" in which clocks tick off proper time since their creation (in effect, "as if they could have") since the big bang. That corrects for the idea in special relativity that rates of time depend on relative motion, and allows a common universal time to describe events (but it is approximate, not precise due to difficulty of perfect operation esp. in literal terms.) It fits in with Robertson-Walker metric too as best I gather.

Cosmologists suppose that the same CBR temperature would be found at the same CT, and it would correlate with observed Hubble "constant" at that time, etc. Hence, a galaxy "receding from us at 0.6c" doesn't effectively have time running slower. (Think of it this way too: in order to be consistent, a galaxy receding from us and *falling* back in from combined net gravity couldn't be younger like the traveling twin in SRT, it was in "free fall" and no different from us. But in the classic twin scenario, the stay-at-homes are inertial observers versus the space traveler experiences acceleration.)

Physically, the effect can be interpreted as an object moving from the "false vacuum" (where = 0) to the more stable "true vacuum" (where = v). Gravitationally, it is similar to the more familiar case of moving from the hilltop to the valley. In the case of Higgs field, the transformation is accompanied with a "phase change", which endows mass to some of the particles.

The quoted text above as a "image map" is a process of formalization that some of the visionaries like Poincare understood from a perspective of hills and valleys.

G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)

This is a constructive phase and demonstration of a GUT as part of the recognition of that timeline.

Why Steven "a cosmic censorship" and you can be a part of the selection of those who would see the universe "as different" then the process of examination that is vital to understanding the evolution of dimensions?

I also had in mind our Surfer Dude when thinking abut this as an example of the mathematical approach given too, the first minutes/microseconds of the universe.

Best,

Rotation of the E8 root system in eight dimensions, with particle assignments corresponding to gravitational, electroweak, and strong charges.

Bee,

Why are posts being delayed? They were there and then gone, the next second.

Post missing in relation to demo of Garrett's dimensional parameters as a example of model apprehension.

Best,

Hi Plato,

It’s all part of the Blogger seemingly arbitrary “I don’t like your HTML” algorithm. The only thing this really indicates is that A.I. is appropriately named:-)

Best,

Phil

Well in Bee's case, could the answer be ... Twins?!

But I must back up Phil, because blogspot really sucks of late.

For example, just recently they cut down on the number of recent feeds. That sucks, and although I can understand that from a business perspective if they don't have enough servers, that still sucks.

NOW if I am away from the puter for more than six hours, I'll miss some important feeds. Used to be 18-24 hours, sheesh.

Time to switch to Word Press or Scientific Blogging? Just a thought.

In parallel to his investigations of supersymmetric phenomenology, Ellis has also advocated phenomenological probes of quantum gravity and string theory. These probes include direct tests of quantum mechanics with the CPLEAR Collaboration and the derivation of Grand Unified Theories from string theory. In this vein, his work on tests of the constancy of the velocity of light and models of string cosmology received separate prizes from the Gravity Research Foundation.John Ellis (physicist)If you think one can be smarter then the "relevant correspondences to elaborations of model apprehensions," then, maybe John Ellis will test that for you too?:)[caveat:I do not speak for John Ellis]:p)

Best,

Hi Plato,

Sorry, I don't know what's up with Blogger. I've checked the spam queue where one of your comments was lingering, but that's it. Pls let me know should problems persist. Best,

B.

Hi Steven,

Yes, you find some details & references in the introduction to this paper. I didn't mention it because I didn't have time to look up the references. I would be cautious about this though. Extracting information from cosmic ray showers is very difficult. Best,

B.

Thank you Bee. I shall return the favor, I hope, by linking to this page, for you and your fine readers who have taught me much and to whom I am dearly indebted, which the FXQi page on the grant recipients of their $1,800,000 + "Time and Foundations" Large Grant Awards. Hopefully Julian Barbour won't feel the need to translate as many Russian papers, now. Unless of course he does it for pleasure as well, natch.

The theory also proposes that our current universe has four spatial dimensions, but we only experience a three-dimensional "slice" of it. The appearance of the fourth spatial dimension gave rise to extra energy, which generated a boost to the expansion of the universe, according to the theory.Testing for Vanishing DimensionsPart of the dimensional significance for me is the forward projection of Cerenkov reaching across barriers toward backdrops of measure.

This "linear assumption [collision point]" as a substrate structure scale is important in my view, and are attempts to model this as "undocumented relativistic measures as falling out of 4th dimensional views" through which muon detection scenarios have been formed. This has allowed us to seen objectively mass considerations and variations of.

I mean this has been difficult in my view as to correlate model appearance out of dynamical collision relations as to define particulate expression as energy valuation as a hierarchy of that zone.

Sound of pool ball billiards above the table.

What correlative functions of dimensional understanding for us to better picture the reality of that substrate of a space structure as to see "extra energy left with accounted particulates" as dimensional construct has been unaccounted for? It's how one sees at that collision point?

While we had moved this discussion to QGP idealizations this helps to form new views about that "objective collision point space" given as substrate views of the reality at hand.

Anomalies/ Phil's new factors for consideration of dark matter/energy as discriminating constituents as elements of dimensional significance are then avenues of concern as to "driving expansion," we know something is?

Always appreciative of corrections.

Best,

Thanks for the post and comments. Once again, it is very exciting to sense things so in flux at fundamental levels.

From my limited view, the Reconstructing the Universe paper is a conjuring trick akin to turning a silk scarf into a walking stick, mutable geometry into substantive projection. I wonder if, while working in such an abstract realm, does one wake up in the middle of the night in a panic, worried that one has made some subtle misstep, missed the firmer trail, taken leave of one’s senses? It seems strange that in fifty-two dense pages relating to quantum gravity the word “mass” was used only twice and both times as an adjective.

Are any dimensions simply qualitative or do they all emerge to give “elbow room” for some ranging dynamic, that is are all dimensions dynamically driven? Is there any general sense of a counterpoise to the dynamic, and active principle of constraint?

One can get the impression that, in nature’s grand origami, one of the early folds placed two active principals cross grained with respect to each other. Surely don’t know if this translates to anything like physics. Regards.

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