Still abge, at the end of the day I don't disagree that one can conceive of such a thing as mathematical contradictions in a physical theory. In some sense, the belief that such had been found (infinities) was what kept QFT on the ground for most of two decades before renormalization was figured out, and likewise, the Klein-Gordon equation was early discarded for similar reasons. So I can imagine somebody hoping to find that string theory gave absurd or contradictory predictions about something. I was just curious if that's what he meant.

Ah QFT. Very interesting stuff. Unfortunately I was unable to finish Susskind's The Cosmic Landscape in the 3 weeks I had it from the library so I need to get it back and read it again.

@semck

There are a number of places where QM could have contradicted itself. I don't have any books with me atm, but tomorrow in the lab, I'll list a few.

Similarly, some major breakthroughs were made in QM purely in a mathematical fashion. For instance, the Heisenberg Uncertainty Principle, is based solely on mathematics of QM and we have yet to disprove it experimentally.

@D33, I don't know the book or the equations (except by reputation), but I do agree that string theory is an exception to the usual pattern -- going on, what, 40-50 years and it's still much more a mathematical theory than a physical one. (Which, parenthetically, is just great for me, since I'm a mathematician and don't have to care, professionally anyway, about whether it's actually right. We've gotten some great math out of it!).

To your last question, yes, I'm familiar with a lot of that stuff, though no expert. While I have some concerns about string theory (just the usual ones), I do think the quest for quantum gravity is one of the most exciting areas in science today, especially now that LHC is up and running. Here's hoping it turns out to be awesome and exciting.

I heard a recent talk, incidentally -- and I'm struggling to remember who it was, or where I heard it, but anyway -- by somebody who suggested that everybody might be wrong in thinking it's GR that needs to be quantized. Maybe (he said) it's QM/QFT that needs to be geometrized.

By the "force particles" are you referring to virtual particles mediating forces, such as photons carrying the EM force, and hypothetically, gravitons carrying gravity?

For instance, the mathematics of Hilbert Spaces was developed just before QM experiments started taking place. This is in contrast to Classical Mechanics, in which some of the critical mathematics was being discovered at the same time as the experiments they were describing.

@abge,

Fair enough. I'll look forward to hearing them.

It's definitely true that in QM, as many times in the history of physics, experiments led to the creation of a mathematical theory, and then the math led to new predictions which were later verified. You mention the Heisenberg uncertainy principle. You could also mention the spectacular prediction by Dirac of antiparticles. Earlier, we have Maxwell's modification of Ampere's law, and (more spectacularly) his prediction of the existence of electromagnetic waves. Similarly, Einstein's predictions from SR and GR -- particle lifetime relativity, sunlight deflection, etc., etc.

Well, true, abge, but that's not to say that QM itself was developed mathematically apart from experimental thinking. The development of functional analysis by Hilbert, Banach and others was motivated by some deep questions in pure mathematics. They weren't thinking of expressing the behavior of particles with them.

Another example of this would be Riemann's invention of modern differential geometry, which would turn out to be key to Einstein's theory of general relativity fifty years later. Riemann, of course, did foresee that his theory might be used in some such way.

What area of math do you research?

Just a grad student now, but I'm interested in differential geometry, with a view toward theoretical physics.

"They weren't thinking of expressing the behavior of particles with them."

Agreed, but it is still different than a lot of earlier physics where the foundational math was being developed at the same time as the experiments.

Oh, for some reason I was under the impression you were significantly older than me. I'm a grad student myself, in Electrical Engineering.

"Agreed, but it is still different than a lot of earlier physics where the foundational math was being developed at the same time as the experiments."

Well, I think of Newton, where that's certainly true. After that, though, I think it's always been a lot of back and forth regarding who was ahead between math and physics. I mentioned Riemann, where math was 50 years ahead. Mostly it was real back and forth during the 18th and 19th centuries, but I'm not sure I would even say there was a lot of experimentation going on in classical mechanics, outside maybe astronomy. The big areas experimentally seem to me to have been thermodynamics and electrodynamics, and these were not that mathematically demanding, at least initially. (Vector analysis, of course, was invented well after Maxwell, so he expressed his stuff in undecipherable old-style analysis).

Perhaps I'm just more familiar with fields that happened that way. Engineers are notorious for being sloppy with math : )

"Perhaps I'm just more familiar with fields that happened that way. Engineers are notorious for being sloppy with math : )"

Ah, well, it's harder to be rigorous when you have to describe the actual real world and have stuff work. : ) You seem more knowledgable than plenty of engineers.

I do modeling of nanostructures, so I have to be more rigorous with my math than I might like.

Nice. So you're the reason we're all going to be killed by robots we can't see.

Yes, I was talking about the Photon, hypothetical graviton, gluon, etc.

If I prove the Searl effect, can I be a mod too?