The Admiral of the String Theory Wars (2015)
nautil.us
nautil.us
String theory is a fairly well-developed mathematical theory. We don't understand everything about it, of course, but we really do know quite a bit. The situation is comparable to that of quantum electrodynamics in the 1960s; we've got enough of a theory that we can do reliable computations, but we're still missing some important concepts.
The octonion theory isn't a theory at all yet. Assuming that it will eventually become a theory, what we have now is more like Bohr's early quantum mechanical models or de Broglie's wave-particle duality. We've got some heuristics and some numerical coincidence and some toy models that suggest there might be something there. But no one has actually found a mathematical model that extends or explains the Standard Model of particle physics.
https://motls.blogspot.com/2016/02/the-utter-insanity-of-woi...
I did find this video[1], where a professor explains why he at least believes there is something to it. Tl;dr - they weren't looking for strings. They sort of 'popped out' of the equations.
(The maths behind it is awful complex btw, I only have some second-hand knowledge thanks to my SO being a differential geometry geek and reading a bit of Yau's book The Shape of Inner Space)
It's important to note that the equations of string theory (both when it was one theory and when it was 5 theories were beyond our ability to solve exactly. We could only approximate them, originally with things called "perturbation methods".
Perturbation methods involve solving something for the big influences, then adding in corrections to deal with smaller influences. For example, suppose you wanted to calculate the orbit of a small moon in a close orbit around a large planet. You could first calculate what the orbit would be in a universe that just has that planet and moon--we can do that exactly. Then you could add in the small differences that would be caused by their sun and other planets in their system--the perturbations caused by the sun and other planets.
If, however, you had a planet with two large moons, you might not be able to solve it for just the planet and one moon, then make small corrections for the other moon and the sun, because the influences of the other moon is not small. The exact solution for one planet and moon is just too far off from the final solution for the former to be tweakable into the later.
There's a thing called the "string coupling constant". Perturbation methods can only be used in the 5 string theories when the coupling constant is less than 1. Eventually they found out how to solve some problems in each of the theories even with coupling constants larger than 1, and to the surprise of most they found that the 5 theories could be split into 3 groups.
One group contained two of the 5 theories. A universe following one of those theories with a coupling constant of, say 0.5, would be identical to a universe following the other theory with a coupling constant of 2.0. The two theories are said to be duals of each other.
Another group contained just one theory. That theory was dual of itself. That is, a universe following that theory with a coupling constant of 0.5 would be identical to a universe following that theory with a constant of 2.0.
The final group contained the remaining two of the 5 theories. I'm having trouble remembering how those were connected.
Anyway, somewhere along figuring out that last group, it was found that low energy point-particle approximations of some of the string theories gave some of the 10-dimenensional supergravity theories that had been worked on before string theory to try to unify gravity and QM.
Then in 1995 Witten showed that if you took some of the string theories and go from low to high coupling constant, the physic you get has a low energy approximation that matches 11-dimensional supergravity.
Anyway, where they got to from there was that the 5 string theories had come out 10-dimensional due to the fact that they could only approximately solve the equations, and that string theory actually was an 11-dimensional theory, and the 5 string 10-dimensional theories (and 11-dimenensional supergravity) are just different perspectives on the one 11-dimensional theory that you get when you make certain approximations or take it to certain limits.
(I may have botched an arbitrarily large amount of the above, so caution is called for)
[1] https://www.amazon.com/Elegant-Universe-Superstrings-Dimensi...
Essentially, string theory was inspired by Fynmann diagrams, via considering the 1-D particle "world-lines" in those diagrams as 2-D "areas".
The rest of the _very_ complex theory comes logically after. A lot of physicists point towards the "natural" nature of string theory as a favourable aspect of it, in stark contrast to QM which has _always_ been unnatural. The statistical nature of QM - "probabilities and uncertainties", has a "hidden-variable/phenomenon" about it, very much like how the random motion of a particle on the surface of water was seen (by Einstein no less) to actually be brownian motion - in this case water particles hitting the surface particle. QM often screams "I don't know but maybe X is Y and Y is Z with Q% chance", meanwhile string theory says "what if X is Y, and therefore A, B, C, D, ...", which is how classical physics and GR (Einstein) was done. The latter way is seen as a much "stronger" and "insightful" way of physics, and string theory walks more towards that nice line than QM ever did.
As a physicist myself, QM has always stank. Everybody knows it. It "works" like HTML/CSS/JS "works". I've always thought that QM has an identity crisis. It tries to stretch itself in two very distinct directions, towards "Quantum Physics" (randomness, uncertainty, strange things like entanglement), and yet relies on vague classical things like "mass". With the Higgs Boson, it relies less on classical things and _indeed_ the Higgs Boson was very sought after (hence the huge celebration for it's discovery) because it pulled QM away from classical physics. But still, QM has a few "smelly" parts. When you see that Schrodinger equation and see that mass variable, doesn't that make you...uncomfortable? Kind of like downloading a "login-form" javascript UI library and using it, and having no idea what it's about or what's going on or how it works.
What do you find lacking in Greene's description or explanation? I found "The Elegant Universe" pretty good.
I feel I have a decent, yet layman grasp of the standard model, yet know nothing of string theory. There is a real lack of solid information in this regard (string theory for the layman), and a lot of hand waviness.
For example, the difference between working in Haskell and knowing the Monad abstraction, versus using the descendants of that work such as async/await in a language like JS, C#, or Python and no longer needing to know/worry about the Monad abstraction because that's now a compiler/interpreter concern. (An interesting edge to that analogy too is that reminder that Haskell's use of the abstraction provides more opportunity, as do-notation works with all Monads, but for now async/await is specialized to just one Monad. This is useful to the string theory/M-Theory question as well, as some users of string theory/M-Theory seems interested in mathematically exploring all possible worlds under the theory, not just necessarily the practical ones that align with the world we live in, in case the overall abstraction or do-notation equivalent is useful in other situations.)
Not sure those go together.