This Week’s Science News from SWTG

We Might Be In A Black Hole & We Might Have Got The CMB Wrong

Gamechange: Theories Of Everything Can’t Exist, Physicists Show.

Credit: NASA

A group of physicists just proved that a “theory of everything” doesn’t exist. They say it’s mathematically impossible. If they’re right, then a lot of physicists will have to rethink the purpose of their existence.

In this recent paper which I believe to be formally correct, the authors – including Lawrence Krauss – look at the prospects of a theory of everything that is also a final theory. I swear it's a coincidence that I talked about this in a recent video just a day after the paper appeared. Then again, I don’t believe in coincidence, so maybe the universe is trying to tell us something.

Be that as it may, in the paper they look at a theory of everything that combines all the known fundamental forces and explains all phenomena, at least in principle. Notably, such a theory must tell us how to consistently combine the quantum field theories of the standard model with Einstein’s General Relativity, which is not a quantum theory. It should explain dark matter and dark energy. And besides this, physicists also think that this theory would be the complete ultimate description of nature, with nothing more to be found. As Steven Weinberg put it, it’d be the “final theory”.

The authors of the new paper have three arguments for why such a final theory is unachievable. The first is Gödel’s first incompleteness theorem. This tells us that if the axiomatic system of the theory is consistent, there will always be true statements that cannot be proved true. This means that a theory of everything couldn’t really answer all your questions about everything. Okay, this isn’t the most original argument, but I guess they had to say it.

The remaining argument in the paper is, for all I can tell, new. They use two other “impossibility theorems” from mathematics. Tarski’s indefinability theorem, which says that within such a putatively final theory it’d be impossible to generally define what you even mean by true. Does the wavefunction truly collapse? Who knows? So then is your theory really about everything?

And then they use Chaitin’s argument about algorithmic complexity, which says that this final theory would inevitably have a complexity threshold beyond which no further statements could be proved. That’s awkward if you have a hugely complex system like, the example they name is, the inside of a black hole. If that exceeds the complexity bound, then well, your theory of everything can’t tell you what’s going on, so it doesn’t explain everything.

What are we to make of this? Should physicists who work on a theory of everything take their hats and eat the chalk?