Monday, December 03, 2007

The State of Physics in 100 Years

First, I wanted to point out a good read on math/science achievement differences between the sexes which I found via the Freakonomics blog.

I took a poll in my class the other day asking the students to rate their "belief" in certain aspects of modern physics. To get them started and to normalize the 0..10 scale, I basically asked them the probability they felt described the chance that a given theory/idea would still be around in 100 years. I put up the following (roughly in order of how I would rank them):

  • Special Relativity (SR)
  • Quantum Mechanics (QM)
  • General Relativity (GR)
  • The Big Bang (BB)
  • Inflation

SR finds itself at the top because it's hard to see how any new theory wouldn't conform to it. Likewise w/ QM, but to perhaps a somewhat lesser extent with hidden variables, non-locality, and interpretations. GR, despite its success, will surely come up for some modification, if only to fit into quantum gravity. But of course, there could be higher order curvature terms, other couplings, etc. Even more far out, maybe gravity is emergent. As for BB, depending on how one limits the theory, will surely be around, but to what extent? How changed will it be? And then there's inflation, and to this, one could add the anthropic principle. I'm not sure how much I want to say here, but I suspect we're getting pretty controversial. Of course, I wisely left off any theories-which-must-not-be-named, I think I'd rather go off and name a Teddy bear "Mohamed," than open that can of worms.

5 comments:

CarlBrannen said...

You can add a preferred reference frame (without any dynamics depending on the reference frame) to SR and the result will give you all the same calculations as before. That would completely gut the heart of SR and do it in a manner that is compatible with all of SR's predictions. So all nature has to do to eliminate SR is have a hidden preferred reference frame. The new physics can be very arbitrary, so long as it stays hidden at the energies we can explore.

The central mathematical assumption of QM is Hilbert space. To gut QM, one might reject Hilbert space. Hilbert differs from the more general Banach space in possessing an inner product. There are branches of QM (density operator theory) that do not require an inner product and so can be done with a Banach space. In those theories, the inner product gets replaced by the trace.

If you begin with a Banach space, you can get a Hilbert space if the triangle rule is true: |x+y|^2 + |x-y|^2 = 2|x|^2 + 2|y|^2, if I recall correctly. This is a natural linear kind of thing.

To break the triangle rule, you could suppose that it is true at very small energies compared to the Planck mass, but is not in general true. Then you would have a Banach space for QM in general, but a Hilbert space for the QM we see.

But in that case, I think you could argue that QM survived the generalization while SR did not.

Angry said...

Hi Carl,

Ok, sure the Universe could be wrong :)
We could have a Newtonian/Galilean Universe with absolute time and no ultimate speed limit. But what are the chances at this point given all the evidence to the contrary.

Bottom line, would your ranking of these be different?

CarlBrannen said...

Bottom line, I'd rank QM as more stable than SR simply because there are far more tests of QM than SR, and QM has a lot more fall back positions than SR.

Re: "evidence to the contrary". There is no evidence against preferred reference frames, only evidence that such cannot be detected in a given experiment. Absence of evidence is not evidence of absence.

I think that the best evidence for perfect Lorentz invariance was that it was such a shock when it was discovered that experiments were compatible with it. But those experiments were pre QM theory.

Lorentz invariance isn't so much of a surprise in a low energy quantum theory. Tommaso Dorigo kindly invited me to write a guest post on his blog and I chose this subject. In short, Newton's 3-d elastic equation for waves in an infinite media breaks into two branches (translational and longitudinal) each of which are, considered by themselves, Lorentz invariant. The 38 comments address the usual objections.

island said...

I think that inflation is already in desparate trouble despite all attempts to rationalize and deny it.

island said...

GR, despite its success, will surely come up for some modification, if only to fit into quantum gravity. But of course, there could be higher order curvature terms, other couplings, etc. Even more far out, maybe gravity is emergent. As for BB, depending on how one limits the theory, will surely be around, but to what extent? How changed will it be? And then there's inflation, and to this, one could add the anthropic principle.

I can't pass-up the opportunity to say that addresses all of the above.

I am waiting for the day when the LHC forces enough desparation onto the cutting-edge that they actually become willing to take a serious look at what they cannot dispute, as they should do anyway, without all of the drama.

It isn't GR that needs to be modified to fit QM. It's the other way round, and the fact that the referred physics roughly defines a complete theory, explains where my confidence comes from.

The vacuum state, per the current misinterpretation of Dirac's negative energy solutions, is the *real* problem.

Extraordinarily rapid inflation is crap!... remember that.