If there are 10^500 solutions to $ Theory, doesn't that make it bunk?

[swampwiz]

(NOTE: "$" == "String")

https://getpocket.com/explore/item/dark-energy-may-be-incompatible-with-string-theory

The leading candidate for a “theory of everything” weaving the force of gravity together with quantum physics, string theory defines all matter and forces as vibrations of tiny strands of energy. The theory permits some 10⁵⁰⁰ different solutions: a vast, varied “landscape” of possible universes.

 

[MathematicalPhysicist]

If you ask me there are much more than 10^500 possible universes... but let them do their "calculations".

 

[Demystifier]

The mere fact that a theory has a lot of solutions is not a problem at all. For example, the Newton equation for a free particle in one dimension
$$\frac{d^2x(t)}{dt^2}=0$$
has an infinite number of solutions.

A more precise statement about string theory is that it has a lot of vacuum solutions. However, here "vacuum" does not mean what someone naively might thought. The "vacuum" means a solution which represents a local minimum of some potential energy. But our ordinary theories, like quantum electrodynamics, can also be thought of as theories with an infinite number of "vacua" in that sense. E.g. every type of crystal (ice, diamond, ...) can be thought of as another type of "vacuum".

Now someone might say that what counts is the number of true vacua. Quantum electrodynamics, for instance, has only one true vacuum, the state with zero number of photons, electrons and positrons. But the so called string vacua, when expressed in terms of fundamental degrees of freedom of string (or M) theory, are not true vacua. The string vacua for string theory are more like different types of crystals for quantum electrodynamics.

Finally, one may object that the true problem with a lot of string solutions is that, a priori, one cannot predict which of the solutions is realized in nature. But again, this is not much different from quantum electrodynamics. For instance, quantum electrodynamics has a solution in which intelligent beings have 12 hands and 2 heads, living on a planet with 2 suns. The theory cannot predict that we, the actual intelligent beings, have only 2 hands, 1 head and 1 sun.

 

[sysprog]

If there are $10^{500}$ solutions to $x=y$, that doesn't entail that $x\neq y$, right?

 

[ohwilleke]

Bunk is too strong a term. A better description would be incomplete. Maybe it is on the right track, maybe it isn't. But, we need a more complete theory to narrow it down.

And, what do you know, we kind of have one. The Swampland conjecture and the Weak Gravity Conjecture (more clearly explained in power point form here, at the beginning before it goes beyond the introduction of the concepts, with some references to underlying peer reviewed published journal article authorities) points out that almost all of the string vacua (and perhaps even all of them) can be categorically ruled out because they have one of a small handful of properties that are inconsistent with the observed universe. Specifically, "We refer to the space of quantum field theories which are incompatible with quantum gravity as the swampland. [Vafa, ’05]"

This flips the problem from being one of too many solutions ( $10^{500}$), to a case of serious doubt about whether we can find any solution that meets this addition criterion.