Working on meta-string theory December 18, 2006Posted by dorigo in humor, mathematics, physics, science.
A comment by Alejandro made me ponder over the need for a meta-string theory.
Sure, we were blessed with two best-selling books about the failures of string theory quite recently: so, asking 2006 to bring more to the just cause of allowing non-string theoretical work in particle physics to get their due share of attention in physical departments throughout the world seems a bit over the top.
However, think about it for a second. How do you kill a theory ? By showing it is internally flawed to an irreparable level, or by showing it is utterly inconsistent with the data. They tell me that both of these avenues appear impossible with string theory these days, because of the theory’s own shortcomings: the lack of a well-defined internal structure (say a lagrangian function or a usable symmetry group as its basis), and the lack of any prediction for experimentally measurable observables. [I know, I am getting flamed for this…]
However, one could conceive a meta-string theory even in the absence of a well-defined string theory. Whatever string theory is, we can formally give it a name: S. One can then imagine to work on S with suitable operators E which modify S, namely E[S] = S’. What E does is to provide S with an experimental input which influences the theory in such a way to make it change form. For instance, imagine we discover a fourth generation set of particles: it is quite likely that S will change into S’ in order to accommodate -or even post-dict- the set. Easy to do, since S was not hindered by a precise pre-defined structure.
We can also imagine new mathematical developments M: their action on S is formally the same: M[S]=S”. For instance, maybe if M provided an indication of which, among the zillions of vacua of the theory, is to be preferred for some specific reason, that could make S very different from what it is right now.
Of course, all E and M are by definition idempotent. That is, E[E[S]]=E[S]. They also should commute, E[M[S]]=M[E[S]], in order for the formal system to make sense: in other words, the theory one develops should not depend on the order by which theoretical and experimental input is used in its construction. Discussing other properties would take us too far.
Given this very basic formal system, one is direly looking for an example of a suitable operator N which, applied to string theory in its present form, produces the null element: no theory.
So what could such a N be ? Would N== no SUSY work ? No, not enough unfortunately, as far as I understand. SUSY is generally appreciated by string theorists as a step in the right direction, but no proof – and no SUSY is therefore not a show stopper. Maybe N is the combination of several experimental and theoretical inputs ? Unlikely.
The search for N is on. But let’s make a point here: having designed our formal system of operators acting on theories, we can well say we already are half-way through: we do not need to prove anything, just saying we hypothesize the existence of a N such that N[S]=0 should suffice. It is now up to string theorists to demonstrate that the set of N is null.