Hawking multiverse implications for "all" histories

[trinko]

After reading Hawking's Grand Design I'm curious about what appears to be an inconsistency in his reasoning.

His basis for the multiverse is that every permutation of M-Theory corresponds to different physical laws and that every possible history is relevant for predicting the state of a system--such as the pattern produces in the familiar two slit experiment.

However it would seem that if in fact one has to sum over all states one would have to sum over all the states where the laws, or at least constants, of physics were different.

As I understand it Hawking is saying that each multiverse corresponds to a different set of laws based on a different M-Theory geometry. Yet if some sort of random selection occurs at the start of each universe it would seem that at all subsequent times in that universe the probability for a path based on all possible M-theory variants would be non-zero. Yet that's clearly not the case since if it were we'd be seeing results inconsistent with our calculations which are based on a single set of constants.

Another way to ask this question is to ask by what mechanism Hawking proposes to cut off all but one instantiation of M-theory--or at least one set of constant values--once a new universe is formed.

Am I missing something or is this something Hawking doesn't address.

Thanks for any help.

 

[secur]

I don't have the book but it's a popular account, breaks no new ground, so I believe I can guess the only possible meaning it could have re. your question.

You ask "if in fact one has to sum over all states one would have to sum over all the states where the laws, or at least constants, of physics were different."

When QED sums over paths, or histories, these are only in our "own universe", with the same physical laws. Each history, or "possible path", starts at the electron's emission, and ends at the detector (assuming a typical 2-slit experiment). Of course, summing over them gives the right answer, due to mutual cancellation of any paths which are far from the correct solution.

Looking at the same scenario with Multiple Worlds Interpretation, we pretend that each electron path causes the entire world to "split" into multiple copies, one for each path. (Speaking loosely here). They're capable of interfering as in QED. Except for the electron, all the rest of the "worlds" are identical so ignorable.

Now, the multiple permutations of M-Theory have some similarity to this, but involve the entire universe, with (possibly) different physical laws entirely. There's absolutely no way those could be involved in sum-over-histories QED! So probably they have nothing to do with this description, but it's confusing enough to make you think so. Maybe he's deliberately trying to tie them together as part of the "grand design", using similar terms, promoting confusion.

If he really were using M-Theory permutations ... you're right he would need a mechanism to limit the M-Theory worlds to those precisely similar to ours, with the same physical laws; which mechanism is not too hard to imagine, but wouldn't be spelled out in a book like this.

Regardless, it's really inconceivable that he's doing QED-type approach throwing in all M_Theory worlds with different physical laws. Of course I could be wrong.

If that doesn't help maybe someone else will answer your question, or tomorrow I could look through the book in the library. In that case, please give the page number.

 

[bhobba]

However it would seem that if in fact one has to sum over all states one would have to sum over all the states where the laws, or at least constants, of physics were different.

I can't follow what you are saying here. Can you elaborate?

In QM one doesn't sum over all states. In Feynman's sum over histories one sums over all possible paths:
https://en.wikipedia.org/wiki/Path_integral_formulation

But that doesn't really have anything to o with the multi-verse.

Thanks
Bill

 

[secur]

trinko, if you're still around,

I glanced at Hawking's book in the library, and saw that my post above seems correct. As one facet of his Grand Design, he's trying to make this equivalence:

experimental fact == QED sum-over-paths == MWI histories == M-Theory's all possible permutation Universes == speculation

Thus fact == speculation

Because this correspondence is a bit iffy the whole thing gets confusing. So if you read carefully, you'll get confused.
Recommendation: just skim it, then it makes more sense