ok on a scale from one to ten exactly how likely is it for M-theorie to be true?
Right now it's a mess with the 'landscape' fiasco. There is, however, hope. Some of the more gifted string people, like Lubos, are trying to sort it out.
One. At this point the situation with M-theory is that one doesn't know what it is and whether it exists, but if it exists at all it is completely unpredictive. The last remaining hope, that somehow one could get predictions by a statistical analysis of the landscape, had just collapsed. All other hopes people put forward (e.g. that cosmology will save the situation), are pure wishful thinking, with nothing at all to back them up.
I'd give it a 5 or 6. I think it needs something additional to be able to get ino its non-perturbative area. The fact that it hasn't matured more than it has in the years since it was discovered is due primarily to the fact that its perturbative sector is more or less just pre-existing superstring theory, plus the mirror symmetries. In other words it's hard to get anything more than same old same old by treating M-theory perturbatively, but currently you might as well whistle for non-perturbative ones.
for more on the new paper by Shamit Kachru et al
M-theory, as a nonperturbative theory, does not yet exist. The best string theorists have done is to propose matrix quantum mechanics as a nonperturbative definition of M-theory. There have been matrix models that reproduce dynamics of the various string theories, but the matrix definition is still a conjecture. From a global view, all matrix models are just formulations of string theory using noncommutative geometry.
Noncommutative geometry, however, has surfaced implicitly in other approaches to quantum gravity, such as loop quantum gravity and dynamical triangulations. Thus, if these other branches happen to find a powerful noncommutative theory before the string theorists, they may not call the theory "M-theory", even though the theory may reproduce stringy effects.
So if we wish to say M-theory is the theory of quantum gravity that eventually works, I'll say a 10. But if the finders of the working quantum gravity theory do not wish to pay homage to Witten's "M-theory", you'll have a 1.
I would hope that we can distinguish between commenting on the apparent collapse of the string theory enterprise (it has been crashing and burning since January 2003 and looks worse month by month) and being cheerful about major progress and hopeful developments in Quantum Gravity.
Both kinds of discussion are, I believe, reasonable and legitimate. And we should have room at Physicsforums for both, since open discussion can help people make rational decisions about what studies to pursue (whether in or out of school, professionally or for fun).
However the present string debacle and advances in Quantum Gravity are going on in different arenas and the failing String enterprise's most articulate critics are not even the same people as those interested in QG.
QG and String/M are not rivals in the sense of competing to achieve the same ends. QG aims at a quantum theory of what spacetime is and how its geometry works, and a QG theory can only be considered a success if it reproduces Gen Rel at large scale. At present it looks like the QG people are getting ready for a battle royale among themselves as to which is better: Loop Quantum Gravity or Causal Dynamical Triangulations (LQG vs. CDT). They are mostly too busy with their own business to comment on the state of affairs in string theory.
One can speculate that once QG researchers have arrived at a useful quantum theory of spacetime and its geometry, (if they do, and to me right now CDT looks like the most promising approach), then a new theory of the particle fields and forces of matter can be constructed over it. the idea is to get the underpinnings right and then do the overlay.
In CDT the dimension of the continuum can vary with scale----the spectral dimensionality can be 4D at large scale and get down around 2 at small scale---which may get rid of some renormalization difficulties. This is very new. I have some links in my signature.
Anyway there is a great deal of squabbling and rivalry in store among different research lines in QG, having nothing to do with the troubled state of affairs in Stringland. As well as some remarkable signs of progress, like the Freidel/Starodubtsev paper (Quantum Gravity in Terms of Topological Observables hep-th/0501191). We should try to cover both stories without mistaking one for the other!
On what page, in what CDT paper?
In searching for a theory of quantum gravity, we cannot assume that fields and matter are independent of the construction of spacetime. In the Matrix formulation of string theory, the picture has emerged of spacetime being built from D0-branes and fundamental strings. This is tantamount to saying that dynamical triangulations are built from D0-branes (vertices) and fundamental strings (edges). In CDT, the precise form of a triangulation is not derived, but is rather defined. Thus, using insights from Matrix theory, we can understand CDT at a deeper level, and even have fluctuating dynamical triangulations. Even more, through noncommutative geometry, the dynamical triangulations would be fuzzy, and we would have a natural UV cut-off.
If this was in the CDT papers, it would be explicit. Just notice that spectral techniques are what NCG is all about. Triangulations from spectra is natural in NCG, and NCG can tell you exactly how to make the triangulation fuzzy. So it's possible to have a discrete space, that at the same time has a nice quantum mechanical uncertainty.
I believe you may have confused two things which are different mathematically, because on a naive level they "look" the same to you.
Strings live in a differentiable manifold. Mathematically they are different objects from edges in a piecewise flat continuum.
The space of CDT does not live in a smooth manifold---it is not embedded in anything with a differentiable structure.
Indeed the space of CDT IS NOT PIECEWISE FLAT AND IT IS NOT MADE OF SIMPLEXES! This is very important to understand. the space of CDT is the limit of (an ensemble of) piecewise flat continua.
for an analogy, thing of the nowhere differentiable paths in a Feynman path integral.
CDT gets rid of the smooth continuum altogether
so the theories are built on different mathematical foundations.
I have to go, will try to explain this a little more later on.
Three (assuming that ten is high and one is low).
Marcus, the confusion lies with you. In Matrix theory, the spectral space is a zero-dimensional manifold M. The strings emerge as elements of C(M). You are making reference to perturbative string theory, where a background manifold is specified. In Matrix theory, there is no pre-existing spacetime background; it must be generated. The most basic ingredient is an algebra, and the algebra used will determine the properties of the D-brane arising from the spectral construction such as dimensionality, gauge symmetry, etc.
My point is that a CDT is a derived concept. I've read through the CDT papers and have nowhere seen how to acquire a triangulation from more basic principles. When the authors eventually figure out how to do this, instead of presupposing the existence of a triangulation, they will realize they are doing noncommutative geometry.
this is what you said that interest me and I would like you to substantiate with some online article and page references.
It is fine with me if you reference a page from an article by Alain Connes on non-commutative geometry. I just want to see some connection established.
So far, all I can see is handwaving. And you have brought up the word "spectral" which occurs all over mathematics. Yes it occurs in the "spectral dimension" probed by diffusion processes. And it occurs in good old classical operator theory where the set of eigenvalues is the spectrum. the term must be on the order of 100 years old in mathematics if not more----50 years for sure. And yes the word "spectral" occurs in NonCommut. Geometry.
But what I need is text from you that shows a more substantial connection than the accidental use of the same word in different contexts.
BTW if you want more clarification about what is meant by "spectral dimension" in the context of diffusion processes and quantum gravity, try this:
The spectral dimension of the branched polymers phase of two-dimensional quantum gravity
Thordur Jonsson, John F. Wheater
29 pages 7 figures
Journal-ref: Nucl.Phys. B515 (1998) 549-574
they are talking about the SPECTRUM OF THE HEAT KERNEL in classical thermodynamics, or the associate Laplacian. This is the "spectral dimension" concept used in CDT. Plain old-fashioned random walks and diffusion process stuff. Nothing fancy.
I shall applaud you if you can find this concept of spectral dimension in an Alain Connes paper, and thus draw the connection you say is implicit.
Thank you, kneemo.
I was too polite to interrupt Marcus because I know how much he adores CDT. Marcus, listen carefully to what kneemo is trying to tell you (and what I have been trying to tell you for a long time).
what have you been trying to tell me about the relation of CDT and noncommutative geometry? I dont remember your ever talking about CDT, at all, Kea. but please make some clear points. I am interested as you can see, from my questions.
Here, I will quote the post i just wrote, and redirect the question to you Kea. maybe you will give me some definite online article and page reference
So let me redirect this to you Kea. I would be delighted if there could be demonstrated some real connection between CDT and NCG. But I want a real connection. Some object defined in common. So find me a page in some CDT article and a page of NCG that I can study and compare and see if they are talking about the same stuff. then I can evaluate for myself whether I think the connection is just vague handwaving or whether there is some substance to it.
Would you be willing to do that, Kea?
As far as I am aware, the words dynamical triangulations are not synonomous with CDT. In particular, in the paper
Construction of Non-critical String Field Theory by Transfer Matrix Formalism in Dynamical Triangulation
which is referenced by
On the relation between Euclidean and Lorentzian 2D quantum gravity
J. Ambjorn, J. Correia, C. Kristjansen, R. Loll
there is a background connection with the old Matrix theory. The point is that there is a long and complicated history to the CDT papers. Do you really want to ignore the evolution on the more mathematical side of things?
I admire the CDT papers, but they are not fundamental. At least, I don't see anything in them that is.
There seems to be a reluctance to accept that more abstract modern mathematics might have a simplicity sublime enough to do physics. Of course the mathematics looks complicated. Goodness knows I find it complicated. But who is the judge of what is simple? Posterity more than you or I. I've always felt I was much too stupid to understand anything that wasn't simple, and yet I find the combinatorics of Descent Theory to be essential to QG. Maybe I'm wrong.
I am sorry, Marcus, if I have been too lazy to investigate the connection between CDT and its related papers. I can see that it would be of interest.
hello Kea, I asked you to explain the connection of CDT and NCG. I am not asking about Watabiki's work (I know of him as a collaborator of Ambjorn and Loll). I am not asking about Ambjorn's work in string theory. When I checked over a year ago I saw he had done quite a bit in string.
what I want to be told about is the overlap between two interesting fields: causal dynamical triangulations and Noncommutative Geometry.
I want you to show me a mathematical object common to both.
you may be presuming in me more ignorance than is actually there
I have read fairly extensively in the the papers by Ambjorn and others in the 90s. And am not disinterested in the history.
yes I know (and was aware of Ambjorn doing string research and other crossover type stuff, and that the words "dynamical triangulation" can occur in other contexts besides CDT and have other meanings)
But that is sort of beside the point IMHO. I am not asking about string, I am asking about Noncommutative Geometry (which string is far from having a monopoly on!) and the NCG connection specifically to CDT. Please show me.
I would love to see it!
that sounds like asking someone "when did you stop beating your wife"?
Imagine if people (not me, I never would) were to be asking YOU such rhetorical questions. My training, as you probably know, is primarily in mathematics, and I love history. As someone who thinks primarily as a mathematician interested in physics, I pay close attention to the historical evolution. NO I do not want to be ignorant of the evolution of mathematical ideas. Do you?
AH HAH! HERE WE HAVE IT! You and I are two mathematicians, roughly at the same level of sophistication, i imagine, although we may know about different things. We both have looked at the CDT papers. YOU DO NOT SEE ANYTHING FUNDAMENTAL. And I do. I see a fundamentally new model of spacetime, and an historical breakthrough. I do not think CDT could have been or would have been derived from fashionable conventional math such as "M-theory".
If NCG was pregnant with CDT then I want to know rigorously and exactly how it was. If you dont happen to know, that's fine, just say
Let's follow up on this interesting difference of opinion. you see nothing fundamentally new in CDT, and i do. Let us talk it over. It might help clarify the ideas!
All right, Marcus. I will go away and look at the Reconstructing the Universe paper. It might take me a bit of time.
By the way, I'm more of a physicist than a mathematician. I don't understand the concept of a 'wavefunction for the universe'. Could you clarify this for us?
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