quantum mechanics - Could all strings be one single string which weaves the fabric of the universe?

This question popped out of another discussion, about if the photon needs a receiver to exist. Can a photon get emitted without a receiver? A universe containing only one electron was hypothetically suggested. And a similar theory was mentioned in Feynman’s nobel lecture in 1965:

As a by-product of this same view, I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, "Feynman, I know why all electrons have the same charge and the same mass" "Why?" "Because, they are all the same electron!" And, then he explained on the telephone, "suppose that the world lines which we were ordinarily considering before in time and space - instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world line, in the section in which it reversed itself and is coming back from the future we have the wrong sign to the proper time - to the proper four velocities - and that's equivalent to changing the sign of the charge, and, therefore, that part of a path would act like a positron." "But, Professor", I said, "there aren't as many positrons as electrons." "Well, maybe they are hidden in the protons or something", he said. I did not take the idea that all the electrons were the same one from him as seriously as I took the observation that positrons could simply be represented as electrons going from the future to the past in a back section of their world lines. That, I stole!

It was a very successful theft indeed, so let me try a theft too. Since Wheeler came up with this theory, we have come up with string theory that create electrons and other elementary particles by string vibrations. Could all strings also have equal properties or interactions, so they can create different particles with equal charge and mass? So if we merge Wheeler’s idea with string theory, we can formulate this into a hypothetical question: Could all strings be one single string which weaves the fabric of the universe? To simplify it even further we can say that a single particle drags the string along and tie the knots in the fabric of the universe together by interactions with itself. So then we get a single string or a single particle universe, which is the ultimate simplicity.

The speed of light can’t be a threshold for such a particle; because the particle itself must travel with infinite speed far beyond C and probably don't even have a velocity we can put any number on, but just call infinite speed. To go past the speed of light the particle must be without mass, and then it has no inertia and is free to go everywhere to interact with its own string which is woven into time, space, particles, mass, charge, magnetism, gravity, me, you and the universe itself.

Answer

Some of the responses to this question are sour because there are no equations, it speculates in a naive way, etc. However, it has an impressionistic resemblance to some important ideas which really may be part of the final picture in physics.

Specifically, I mean (1) the idea that all physical reality consists of vibrations in a single substance (2) the idea that the history of the universe is a knotted worldline.

(1) was the physical picture of 11-dimensional supergravity, the leading candidate for a theory of everything before string theory, and still an important limit of string theory. In d=11 SUGRA, everything is just excitations of supergeometry. In string theory and M theory, we have strings and branes, but it seems rather plausible that in the end these will turn out to be extended excitations of some "generalized geometry".

Regarding (2), the question talks about strings, but later it talks about a "single particle [that] drags the string along". So I take that to be a return to Wheeler's idea of a particle weaving back and forth in time, with the "string" being the world-line. Well, that doesn't sound like string theory, where strings describe two-dimensional histories, "worldsheets". However, before the people who know physics stop reading, hear me out...

What this reminds me of, first of all, is Witten's work on expectation values of knotted Wilson lines in three dimensions. Although it utilizes the apparatus of quantum field theory, that is usually conceived of as an exercise in mathematics only - a way to get knot invariants from a three-dimensional perspective. However, in his recent work on Khovanov homology, he managed to embed these calculations specifically into M-theory. And I think the work on the Jones polynomial originally derives from the first studies of topological string theory (and it continues to be developed in that context, e.g. see recent papers on the "refined topological string").

Now let us turn to gauge/gravity duality, in its AdS form and its far more problematic dS form. We now have many dualities in which string theory in AdS4 is equivalent to some d=3 theory of Chern-Simons plus matter fields. We also have one dS4 duality, proposed by Strominger et al, in which a Vasiliev gravity theory in dS4 is dual to a d=3 Euclidean field theory. And recall that Vasiliev theory may be a truncation of string theory.

So let's suppose, for the sake of discussion, that our asymptotically dS4 universe is dual to a Euclidean Chern-Simons+matter theory. I know this idea has problems, but perhaps it is a step towards something that really works, and not just a dead end... In any case, couldn't you form a loop basis for this dual theory? Similar to what the hated "loop quantum gravitists" do. But here you don't even need dynamics because time is going to be holographically emergent. The Hilbert space of the Euclidean theory is a superposition of knotted loop states, and everything about the dual dS4 theory should be obtained by applying the right operators to those states.

This may seem rather a long way from where we started. But still, the idea is that the universe is described by a string theory holographically emergent from a superposition of knots. Exactly how it would work is unclear to me, but this seems to define a rather weighty research program, rather than being a vaporous idea you can immediately refute. And yet ideas like this do emerge from vaporous musings like the one in the question! It's just that they have to be informed by logic and by physical and mathematical knowledge, in order to get anywhere.

So by all means, criticize people's vague musings. But be aware that sometimes, they have more potential than meets the eye...