a new proof for the truth of string theory

The proof presented in my previous blog post has meanwhile be examined by many commentators (two) and I have now enough confidence to use its structure in a slightly different context.

1) String theory is the possible 'theory of everything', underlying the physical reality of our world Wo.

2) We know that s.t. leads us to the concept of a multiverse M which contains our world, but many other possible worlds too: M = {Wo, W1, W2, W3 ...}.

3) It is possible that one of those worlds contains evidence for the truth of s.t. (e.g. the energy scales are such that it is easy for physicists to probe the Planck scale).

3b) Therefore M contains at least one world Wst where s.t. is evidently true.

4) But if s.t. is evidently true for one world Wst, then it must be true for all worlds in M.

5) Therefore s.t. is evidently true for our own world Wo.

6) You will notice that the above conclusions are independent of detailed assumptions about the (composition of) multiverse M.

I am aware that this is a physicist's proof and look forward to mathematicians formalizing it in the decades to come.

Also, I am sure that some string theorists already use this argument implicitly, but I still think there is some value in making it explicit.


Anonymous said...

How do you go from it is possible that one world contains proof, to therefore there is proof??

wolfgang said...

if s.t. is evidently true in one world Wst of the multiverse M= {Wo, W1, W2, ... Wst ...}
then it must be true in all other worlds

for the same reason that if it is possible for somebody to proof Fermat's last theorem in a US university, we know it is also true in Asia, the Andromeda galaxy and all other possible worlds.

Anonymous said...

That wasn't my question. You said it is "possible" that a world contains evidence, therefore it MUST be true for all worlds. That's like saying it might be raining, therefore it is.

wolfgang said...

i think it is easiest if you tell me which of the three steps 3) 3b) or 4) you think is wrong

Anonymous said...

It does not follow from "it is possible" that "it must be". No single one of your premises is wrong, but there is a flaw in the logic, called a non sequitur.

The only thing that would follow from 3 is

3b) Therefore it is possible that M contains at least one world Wst where s.t. is evidently true.

You could try to be trickier, like St. Anselm of Canterbury, but ultimately you can't logically argue things into existence.

If it was true, then you could say that in some world, Wst, there must be evidence that string theory exists, therefore it exists here as well. But that argument is circular (and really, you still couldn't claim that, because just because something is true, doesn't mean there is physical evidence for it.)

Anonymous said...

In my last paragraph the "it" in "If it was true" is meant for string theory. If string theory was true.... (I don't deny it is true, I just don't think you can prove it with logic).

wolfgang said...

>> No single one of your premises is wrong

the multiverse M contains all worlds possible in string theory.

We agree that Wst is possible.

stmt 3b: Therefore M must contain Wst.

I don't see the non sequitur.

>>It does not follow from "it is possible" that "it must be".
well, it seems that s.t. is able to overcome such old-fashioned prejudice 8-)

But I think we are going in circles here...

Anonymous said...

Heh, talk about circular. You say that s.t. includes the understanding that all possible worlds exist, and then use that premise to prove that s.t. is true?

You're going from "it is possible" to "it must be" apparently contains other premises, and troublesome premises, so I don't think there is any magic here.

Also, whether or not it is REALLY possible, is hard to say. I don't admit it's possible. I don't deny it's possible either, I don't know. My background is philosophy, not physics. I do know that it might not be possible for reasons we don't yet know.

If s.t. is true then it's possible, if it's not, then... well it might not be possible, and that's why it isn't. I would refer to Quine's "On What There Is" for a further illustration of why discussing what is 'possible' leads to silliness.

Interestingly, proving something is "true" is debatable in itself. Science can find good models that are good at predicting things, but whether it actually finds truths, depends on the definition of truth. S.t. is a great model, so maybe that means it is as true as any other?

Ponder Stibbons said...

Unlike mathematical theorems, physical theories are arguably not the kind of things that are true in all possible worlds. The truth of a physical theory is usually taken (in philosophy) to be a contingent fact.