String theory and its many variations (most-recent reference within this website)
Within Wikipedia: String theory, M-theory, F-theory, Superstring theory
Leading theorists with whom there has been limited contact:
Ed Witten: Correspondence and reference to his research
Cumrun Vafa: Polchinski, No good idea (2021) and topological string theories
Juan Maldacena: Correspondence and reference to his research
Nathan Seiberg: Correspondence and reference to his research
Stefan Vandoren: Correspondence and reference to his research
Michael Duff: Correspondence and reference to his research
Gabriele Veneziano: Correspondence and reference to his research
Dean Rickles: Correspondence and reference to his research:
Hermann Nicolai: Correspondence and references
Robbert Dijkgraaf: Correspondence and references
There are many others, some old acquaintances like Kellogg Stelle and then other fine scholars such as: John Donoghue, Astrid Eichhorn, Dumitru Ghilencea, Jinn-Ouk Gong, Christopher T. Hill, Bob Holdom, Deog-Ki Hong, Sang Hui Im, D. R. Timothy Jones, Elias Kiritsis, Archil Kobakhidze, Manfred Lindner, Anupam Mazumdar, Philip Mannheim, Hermann Nicolai, Kin-ya Oda, Roberto Percacci, Eliezer Rabinovici, Graham Ross, Javier Rubio, Alberto Salvio, and Francesco Sannino.
There are so many resources to explore such as the 2016 conference (a Twitter reference!).
A little discussion: Strings were first assumed to be point-like particles of particle physics which became one-dimensional objects. We hypothesize that if there are such strings, they exist before Notation-1 back up on the bridge between the finite and the infinite. M-Theory does not do any better with its fundamentals. There is no clear consideration of infinity, π (pi), and spheres. There is a jump into levels of abstraction and no clear path to the working physics of our time. Within our grid, it appears that string and M-theory would engage from around Notation-10 to around Notations-30.
Although Dean Rickles is one of the most open scholars within these studies, every scholar is approachable. Our next step will be to confirm comments and incorporate some of these answers into this report.
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Key references to this page from the following:
JWST Carina Nebula: Ontological and Cosmological Conundrums, Quick Read – Different Analysis
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Research the origins:
“(Super) string theory has, to begin with, one dimensional constant, the string length. This is a measure of how long the closed strings are. If one is probing lengths far above this, then the closed string just looks like a point (i.e. a teeny tiny circle looks like a dot).”
“We currently have experiments indicating that an electron looks pointlike. I think (but would have to check for good sources) that one can say with a high level of confidence that an electron has a radius smaller than 10^{-20}m. So if an electron is a small string, then that small string had better be even smaller than this.”
“The Planck length is quite a bit smaller, sitting at around 10^{-35}m, so if strings are of this length (roughly, at least), then there are no contradictions with the experiments. More philosophically, the Planck length is seemingly a “fundamental length unit”, and if the strings are really fundamental building blocks, it would be neat if they had (roughly) the fundamental length. As per today, we do not know if strings exist and, if they do exist, what their length is. All we know is that it’s somewhere between bounds set by experiments (like the electron size mentioned above) and the Planck length. So to make a long answer short: If string theory is correct, the strings are somewhere between, as you write, the Planck scale and the CERN scale.”
Fourier transform.
“The Fourier transform is an interesting device. It makes sense directly on spacetime if you restrict your spacetime to have a certain structure (technically you want your spacetime to be a nice enough group). The main example is flat spacetime, where the Fourier transform is initially defined. One can also perform Fourier transforms on (co)tangent spaces instead, leading to the concept of Microlocal analysis. This is a subject which gets quite technical quite fast, but a main goal in that subject is to make sense of something like Fourier transforms when working on more general manifolds (i.e. in curved spacetime).
“Short answer: Do you want to Fourier transform your coordinates? Then you need restrictions on the spacetime. Do you want to Fourier transform spinors or scalar/vector fields or something like it? Then this you can probably do.”
Standard model constants.
Who said it? I am not sure. Before a page is opened to the public, it is collection zone by topic. Sometimes attributions are neglected. So what follows may well be from David Tong (String Theory, University of Cambridge, Part III, Mathematical Tripos, January 2009) or a dozen others. Ooops!
“I deliberately avoided the whole discussion of matching string theory to the standard model, since I was trying to write a thesis with a general relativist as target audience. If you “just” do super string theory in the “critical dimension” (meaning 9 spatial and 1 time dimension), you only have 1 free parameter to play with, namely the string length. This, however doesn’t reproduce our physics for several reasons, the most glaring being that we have only 3+1 dimensions. The by now standard solution to this is to postulate that the other 6 spatial dimensions are small and therefore not visible in normal circumstances. This is analogous to a small circle appearing like a point: a circle is 1-dimensional, but a small circle looks 0-dimensional. So far so good, but what are then these extra 6 dimensions? And this we do not know. Mathematically, one wants a 6-dimensional compact manifold. If one imposes certain super symmetry conditions (the condition being that we want some, but not too much, super symmetry in our 3+1 dimensions), then the extra 6 dimensions are forced to be a so-called Calabi-Yau manifold. The problem is, there are millions of such spaces. There might even be infinitely many (the jury is still out on that one, I think). If you think of the choice of compact 6 dimensions as a tunable parameter, then string theory gets extra parameters. These parameters are typically more subtle than the standard model ones, and not all lead to something like a standard model (e.g. one can end up with more than 3 generations of leptons -electron, muon, tau). In addition to choosing the compact 6 dimensions, one has to choose a bit more geometric date on this manifold, namely a so-called holomorphic vector bundle. You can think of this as more geometric choices for the extra compact dimensions. This abundance of potential compactifications (compactification meaning choice of compact 6 dimensions) leads to the so-called string theory landscape.”
“On a more fundamental level, one would like to know why 6 dimensions became compact (or why 3+1 “decompactified”) in our universe, and we would like a way of selecting the above geometric date in a way which doesn’t rely on fiddling with parameters until it matches the data. Whether this is realistic or not is not known.”
Worldviews limit perspective 