Sunday, September 10, 2006

Hawking's Views on the Possibility of a TOE

It turns out that Stephen Hawking has expressed a view recently on the possibility of a theory of everything (TOE) that is somewhat compatible with what I wrote in my previous post. In "A Brief History of Time," published a couple decades ago, he wrote that he thought that a theory of everything would eventually be discovered, but he has changed his views in the last few years.

It seems that he has explained this in a recent article:

Based on the following article it appears that his change of mind goes back to at least 2004:

I consider it a happy coincidence he now thinks a TOE is impossible, since the title for my blog was partly motivated by a line from "A Brief History of Time."

Of course it is problematic to try to address these types of subjects on a non-technical basis, but I am going to go ahead anyway and make a few distinctions between what Hawking wrote about and what I am talking about.

First of all, it seems to me that a TOE is not really the same thing as a theory combining the basic known forces (including gravity) since a unified theory of the four forces could eventually be found and there could still be physical phenomena not explained by it. For this reason it seemed a bit superfluous for Hawking to mix things like "quantum gravity" and "M theory" into the discussion. Put another way, if this discussion had taken place 50 years ago before the Standard Model was worked out, one could have said that the problem of unifying the electromagnetic force with the strong and weak forces was tied up in some physical equivalent of Gödel's theorem, but in hindsight this would have seemed sort of ridiculous. Why should things be any different for quantum gravity?

Next, I was a little troubled to see that Hawking didn't make the distinction between mathematics and an automatic system for doing mathematics. I think Gödel was talking about the latter. I don't think that Gödel's theorem says that there are particular mathematical results that are neither provable nor disprovable. Rather, it says that given any automatic system (i.e. a set of instructions a computer could carry out) for determining whether statements are true or false there will always be statements for which the automatic system will not work.

Finally, my view is that it has to be a matter of belief to say that there will never be a theory of everything in physics. Hawking seems to be saying that there could eventually be a definitive result analogous to Gödel's theorem. Perhaps he is onto something, but I am more inclined to think that this is the sort of thing that more and more physicists will accept over time, but that there will never be a definitive result that will end all arguments.