String theory predicts nothing?

[Robine]

When Einstein was working his way through special and later general relativity, many of his contemporaries thought he was on the wrong track. He wondered himself at times. The fact that String Theory is neither proven nor disproven today doesn't mean its wrong. Many past theories were considered impossible to prove until somebody figured out a test, like Michaelson-Morley, double slit experiment, and so forth. When you start on a trip how do you know where you will end up: you can't be sure but you keep going.

 

[pavsic]

I c
I realize that your work on this is in your book and in the papers for which you have provided arxiv links. I have not read these and so cannot usefully comment.
Personally I would welcome a "thumbnail sketch" of your theory, I you post one, that gives a condensed overview and points to specific pages in your arxiv papers (in case anyone is curious and wants to read more).

Good idea and I will think about that. For the moment, one can find description of my research activity at my home page http://www-f1.ijs.si/~pavsic/

I c
I am curious about your book. It is expensive ($86 I think, yes?) so maybe it is not for general audience? But if it is for the general reader then it has formidable competition from American popularizer authors (Greene, Krauss, Susskind, Randall...).

The book is mostly technical and intended for physicists. There are also
chapters for general audience.

 

[Robine]

Slightly tangential to the question is the following from MKaku on this website:
"..At present, the most promising (and only) candidate for a “theory of everything”, including quantum gravity, is superstring theory or M-theory. It is the only theory in which quantum forces may be combined with gravity to yield finite results. No other theory can make this claim..."

 

[marcus]

Good idea and I will think about that. For the moment, one can find description of my research activity at my home page http://www-f1.ijs.si/~pavsic/



The book is mostly technical and intended for physicists. There are also
chapters for general audience.

If you decide you want to have a thead here at PF to discuss your work, and you would like someone else to start it, just send a Personal Message (PM) to whomever you want. I would be glad to do it, if you would like me to.

the disadvantage is that people can freely criticize----sometimes they may make inaccurate criticisms and then you or someone else can argue back at them.

As you say, your work is already published in book form (Springer Verlag) and is represented at your website. So maybe there is no need to also describe it here! That just makes extra trouble for you. But if you want, let us know.

"Tangential" to the topic, as they say, is something I just noticed at the popular blog COSMIC VARIANCE.

http://cosmicvariance.com/2006/01/27/return-to-the-fold/

Clifford, one of the most active bloggers, reports that his PhD advisor Tim Morris has co-written a 6-page string paper after a break of 14 years---last paper 1992.
http://arxiv.org/abs/hep-th/0601114
As Clifford says---I think he puts it very nicely---his advisor has returned to the fold.

Matej you are highly multilingual, by my standards, and seem to have an excellent grasp of English. Do you know where the expression "return to the fold" comes from?

 

[pavsic]

Last week I was skiing with my wife and two daughters in Slovenian mountains. Weather was fantastic all the time, with majestic view on the LANDSCAPE and the Adriatic coast. A unique experience, in spite of the fact that there are so many different landscapes possible in principle, and yet I was experiencing just that particular one! Now I am back at work for a couple of days and I have obtained some ideas that might be useful for this thread.

I will skip the linguistic problem which I am not familiar with and go directly to string theory. The latter theory is so elegant that it is unimaginable that it could have no merits for future development of theoretical physics. But I think the question is not of whether string theory, canonical quantum gravity (or a variant of it), loop quantum gravity, induced gravity or whatever other theoretical direction is correct, but of how all those different approaches could fit together into a coherent whole. I think that they all have to be taken into account. However, they all have to be suitably modified and adapted, and new ingredients, like the concept of Clifford space, have to be included into the game.

String theory requires extra dimensions for its consistency. Compactification of extra dimensions, which has been a big business in string theory, is unnecessary, if one takes into account the brane world scenario, namely that our world is just a 3-brane that sweeps a 4-dimensional surface in a multidimensional (e.g., 10) dimensional target space. This is one possible modification in string theory, namely, to forget about compactification of extra dimensions. The idea that our universe is a brane in a higher dimensional space is not new, and I contributed to it as well, starting with a paper published in Classical and Quantum Gravity 2 (1985) 869-889 ( see for instance http://www-f1.ijs.si/~pavsic/BraneWorld and http://www-f1.ijs.si/~pavsic/PavHomPage#Brane )
What is new is the particular Randall-Sundrum model.

Another possible modification is to employ the merits of geometric calculus based on Clifford algebra, and the concept of Clifford space (C-space) as described, e.g., in the papers to be found at the following links (with the information to published references):
http://arxiv.org/abs/hep-th/0011216
http://arxiv.org/abs/hep-th/0110079
http://arxiv.org/abs/gr-qc/0111092
http://arxiv.org/abs/gr-qc/0211085

The idea here is that closed p-branes can be approximately described by the corresponding oriented (p+1)-areas. So with a closed string (1-brane) one can associate an oriented 2-dimensional area. Instead of describing p-branes ``exactly'' by means of their embedding functions, we can describe them approximately by means of the multivectors associated with oriented (p+1)-areas. The latter multivectors can be elegantly represented by wedge products (antisymmetrized Clifford products) of the generators of Clifford algebra. In general we can consider arbitrary linear superpositions of multivectors, called polyvectors or Clifford aggregates. Extended objects such as p-branes are thus modeled by Clifford numbers (for more details see http://arxiv.org/abs/gr-qc/0211085 and some other more recent papers of mine to be found on ArXive). A very lucid paper in a similar direction was written by A. Aurilia et al. (http://arxiv.org/abs/hep-th/0205028 ).
The continuous set of all possible Clifford numbers that model extended objects form a 16-dimensional manifold, called Clifford space (C-space). The components of such Clifford numbers (polyvectors) with respect to the basis Clifford numbers (which are a unit scalar, 1-vectors, 2-vectors, 3-vectors and a 4-vector), are generalized coordinates (polyvector coordinates) of extended objects. It is common to describe an extended object approximately by its center of mass coordinates x^\mu (components of a position vector). But such description is very rough, because it assigns to the object a point (the center of mass), and says nothing about the object's extension. More information about the objects is provided, if its bivector, trivector and fourvector coordinates are given. Those coordinates generalize the concept of center of mass coordinates http://arxiv.org/abs/gr-qc/0211085 .

So we have that extended objects are described by Clifford numbers. On the other hand, it is well known that the elements of minimal left or right ideals of Clifford algebra can represent spinors. So spinors are automatically present in the polyvector description of extended objects. This provides an alternative way of introducing spinors into description of strings and branes: instead of separately postulating spinorial coordinates, besides the usual bosonic coordinates, it turns out that they are incorporated in polyvectors.

A polyvector describes a point in 16-dimensional Clifford space (C-space). From the point of view of the underlying 4-dimensional spacetime M_4, this is just an extended object, or better an extended event. This is not yet a dynamical system. In order to obtain a dynamical system, one has to consider, not a point in C-space, but, e.g., a line in C-space, that is, the polyvector coordinates have to depend on a parameter, say \tau. From the point of view of M_4, we have a 1-parameter family of a extended objects. In the usual relativity, we have a 1-parameter family of point-like objects (point events), that is a world line. Now, since we involve into the game also higher grade coordinates, such as x^{\mu \nu}, the worldline acquires an extra structure: it is no longer a line in M_4, it is a sort of a thick line. This is an alternative description of the superparticle.

A next possible step is to consider a 2-parameter surface in C-space, a wordlsheet, described by the polyvector coordinates x^\mu (tau, sigma), x^{\mu \nu} (tau, sigma), etc.. From the point of view of M_4 we have a 2-parameter family of extended objects (or better extended events). In the usual theory, we have a 2-parameter family of point-like objects (events), i.e., a world sheet. Now we have a generalization of the concept of world sheet: the worldsheet is no longer infinitely thin, but is has certain finite structure, it is a thick world sheet. This is an alternative description of superstring. Such description automatically contains spinors (for the reasons given above), and it also involves more than four dimensions, namely sixteen dimensions of Clifford space. But those ``extra dimensions'' are not of the same nature as the usual extra dimensions of spacetime. The underlying spacetime is still 4-dimensional. The higher dimensional nature of C-space is analogous to the higher dimensional nature of, say, the 3N dimensional configuration space of a system of N-particles. All those particles still live in 4-dimensional spacetime. So it has turned out that there exists a consistent formulation of string theory in C-space. We do not need to postulate the existence of extra spacetime dimensions in order to have a consistent (quantized) superstring theory. Instead, we can generalize string theory to C-space, as indicated above, and it turns out that the quantum algebra of Virasoro generators closes [http://arxiv.org/abs/hep-th/0411053 , Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings, http://arxiv.org/abs/hep-th/0501222] . Such approach to string theory opens a number of new possibilities that, in my opinion, are worth of being further investigated.

There is also a connection with Kaluza-Klein theories, which can now be formulated in 16-dimensional curved C-space [Phys.Lett. B614 (2005) 85-95 http://arxiv.org/abs/hep-th/0412255, http://arxiv.org/abs/gr-qc/0511124] . The Dirac equation can be generalized to curved C-space, and here we have a contact with standard model (and beyond).

Finally, there is a possible connection with loop quantum gravity, spin networks, and spin foams, where an unsolved problem is of how to obtain a classical spacetime manifold as a low energy approximation. I think that this is a hopeless task, because what one could expect to obtain is not a 4-dimensional spacetime, but a spacetime with extra structure, which might be just that due to Clifford space. So what one can expect to obtain as a low energy approximation to a spin foam, is not merely a manifold of points, but a manifold of points, lines, surface, etc., that is, a Clifford space [http://arxiv.org/abs/gr-qc/0511124]

What about predictions? There is a lot of predictions in such a theory, also at low energies, but they have to be carefully worked out (after we succeed in formulating a version of the theory that will appear satisfactory from the theoretical point of view). This requires time and team (of researchers).

Matej Pavsic

 

[selfAdjoint]

Thank you for this exposition, Dr. Pavsic. I found it extremely interesting and especially liked the avoidance of spacetime points, which are the cause of so much trouble. The higher Clifford Algebra constructions are especially interesting too and I hope you will consider posting more about them.