Line defects and String Theory

In summary, the appearance of threads such as Causes of loss of interest in the String program and Is string theory really science? are symptomatic of the frustration of modern physicists struggling to formulate in a predictive way the concept of elementary objects that are geometrically linear, rather than old-style points. This frustration is likely due to the lack of a geometrical framework that is suitable for describing the physics of high-energy objects. However, if there is no obvious reason why the only geometries useful for physics are exclusively either Euclidean or Riemannian, it might be worth taking the risk of revisiting Volterra's excursion into the defect geometry of a continuum.
  • #1
Paulibus
203
11
The appearance here of threads such as Causes of loss of interest in the String program and Is string theory really science? are for me a symptom of the frustration of modern physicists struggling to formulate in a predictive way the concept of elementary objects that are geometrically linear, rather than old-style points.

A century ago, when Einstein was engaged in his struggle to formulate his new concept: gravity as a distortion of simple Euclidian spacetime, his frustration became relieved by learning about tensors, a recent geometrical invention of the mathematicians Tullio Levi-Civita and Gregorio Ricci-Curbastro. Modern physics owes a great deal to these 19th Century Italians. Here I’d like to suggest that we might yet come to owe even more to like folk.

Einstein singled out one kind of distortion of Euclidian geometry; that described in the 19th century by Bernhard Riemann. I’m guessing here that this step opened the door, as it were, to other kinds geometrical distortions being used to help describe yet more fundamental stuff, as string theory seems to be struggling to do.

It’s not clear to me whether today’s string theorists are aware of another Italian
mathematician’s work and its extensive later 20th century ramifications, which have to do with the physics of crystals. Like Luigi Bianchi, Vito Volterra was a student of the 19th Century differential geometer and topologist Enrico Betti. Volterra described stringy topological defects in continuous elastic media –called distorsioni; later dislocations and disclinations. In the 20th Century these stringy line defects were applied to explain much of practical importance in real crystalline materials. There’s a huge literature about this; see for example F.R.N. Nabarro, Theory of Crystal Dislocations, OUP, 1967.

From my level of (great) ignorance I’d be interested to know whether Volterra’s work has had, or could have, any utility in string theory. Einstein is surely a good act to follow!
 
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  • #2
A friend who publishes esoteric stuff in GR has remarked to me that the sad reality is that everyone is so busy with their own work that there’s not much time for kind of cross-fertilisation of ideas I suggested above; fleshing out Volterra’s ideas might take a lot of work. I agree. But:

If there is no obvious reason why the only geometries useful for physics are exclusively either Euclidean or Riemannian, I’d like to add that, despite the press of work and the dread prospect of lots more, it might be worth taking the risk of revisiting Volterra’s excursion into the defect geometry of a continuum.

I remark further that quantitative geometry can be more useful than qualitative geometrical concepts. In Euclidean geometry, for example, Pythagoras’s theorem seems more practical than the qualitative concept of the congruence of shapes. And in Riemannian geometry the qualitative concept of space(-time) curvature is rendered practical for predictive purposes when it’s quantified using coordinates, in terms of the curvature tensor Perhaps predictive physics Beyond the Standard Model could use a successful struggle to quantify Volterra - style defect geometry in terms of coordinate geometry. Or maybe one is already available that I could be pointed at?
 
  • #3
I think I’ve discovered why this thread is barking up the wrong tree, as it were. The
idea that line defects may have any implication for physics ‘Beyond the Standard
Model’ seems to have been explored pretty thoroughly, but impotently, by one
Hagen Kleinert, starting as long ago as 1987 (more recently, see arXiv:gr-
qc/0307033v1). Like other current non-Baconian proposals, his scheme seems
quite remote from any verification/disproof by observation and experiment.

Kleinert’s scheme may also be tainted with his specious (for me, maybe for others
too) philosophy that
Kleinert and Zaanen said:
...God may have chosen a
completely different extension of present-day Lorentz invariant physics to
extremely high energies ...
.

Discussions of the present plethora of theoretical schemes designed to unite GR and QM seem now to me as futile as those of sports commentators about horse-racing prospects --- in a world with only imaginary horses. So I’ll close now.
 

1. What are line defects in physics?

Line defects, also known as dislocations, are imperfections or irregularities in the structure of a material or crystal lattice. They can occur due to stresses or lattice mismatch during crystal growth or deformation processes.

2. How do line defects affect material properties?

Line defects can significantly influence the mechanical, electrical, and optical properties of materials. They can act as barriers to dislocation motion, causing materials to be stronger and more resistant to deformation. They can also affect the material's electrical conductivity and thermal conductivity.

3. What is the significance of line defects in string theory?

In string theory, line defects are used to represent the fundamental building blocks of matter, known as strings. These defects, or strings, vibrate at different frequencies, giving rise to the different types of particles in the universe. They also play a crucial role in unifying the four fundamental forces of nature.

4. How does string theory explain the existence of line defects in the universe?

In string theory, the universe is made up of tiny, vibrating strings rather than particles. These strings can stretch and form loops, creating line defects in the fabric of space-time. These defects are thought to have formed during the early stages of the universe and may have led to the formation of galaxies and other large-scale structures.

5. Can line defects and string theory be tested experimentally?

While string theory is still a theoretical framework and has not yet been fully tested, experiments have been conducted to study the properties of line defects in materials. These experiments involve using specialized techniques, such as x-ray diffraction and transmission electron microscopy, to observe and measure the behavior of dislocations in crystals. This research provides insights into the fundamental principles of string theory and its potential applications in materials science.

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