December 3rd, 2007


Relative Problems

Relativity. Special Relativity.

We're giving the PHYS-1150 second semester students a taste of Modern Physics these last ten days of class. And it is great fun to introduce concepts which might cause chunks of brains to come popping out of one's head -- or at least a good aneurysm or two. (grin) Einstein's two simple little postulates really raise havoc with things, and two decades of living on Earth tends to make my students believe strongly that one observer has to be preferred, though Einstein says no.

Still, I mentioned the pole vaulter problem today: A farmer with a 10-foot long barn bets a pole vaulter with a 12-foot pole that he (the farmer) can lock the pole vaulter and the pole in his barn lengthwise. The pole vaulter knows a 12-foot pole can't fit in a 10-foot barn, at least not without an angle, agrees to the wager. Then the farmer says, okay, run into the barn at 90% the speed of light. Who wins the bet? And I was pleased that one of my better students immediately suggested no one, because while the farmer sees a short pole easily fit in his barn, the pole vaulter sees his regular length pole easily poke all the way through an even shorter barn. Both are right, both are wrong... (grin) It turns out they cannot even agree at to the order of events as to whether both ends of the pole can ever be simultaneously inside the barn -- there is no simultaneity anymore.

To the students, this seems like so much science fiction. In the middle of discussion on Friday, a student asked, "Does this really happen?" Now this sort of question doesn't annoy me -- it tells me the student is really thinking about it and they are bothered that their foundations of reason are being shaken at a fundamental level.

Or do they think I'll 'fess up and say, "Oh no, this doesn't happen. I just invented these equations last week in order to jerk your chains and mess with you."?

The Second Reason

Of course there is a secondary problem. The further once delves into Modern Physics, the more one talks about things like particle pair creation or how increasing red shifts towards the ends of the Universe strongly suggests if one "plays the movie backwards" that everything rushes towards a common spot -- the Big Bang. Creation and the Big Bang, cosmology in general, are going to step on some people's toes in West Michigan. Or at the very least make them uncomfortable.

Where Do We Go From Here?

Speaking of relativistic calculations, John Scalzi's blog this month is having guest columns. The one on Sunday was from British SF writer Charlie Stross, writing about colonizing and traveling space -- planetary and interstellar. Charlie neatly sidesteps the worst nasties of relativity (grin), but his comments pretty much help explain why lots of SF authors, including moi, are willing to circumvent currently known physics to advance their stories.

In The Last Of The Very Small, h-bar Is King

Tomorrow we'll talk about Quantum Mechanics and models of the atom. All models of the atom are fundamentally wrong at some level -- we cannot easily grok a probability density cloud in 3-D, so we describe differing aspects of the quantum theory with varying metaphors.

Alas, we don't have the time to do much with only a few days left and only algebra skills in PHYS-1150, so we'll miss "the good stuff." But for the last few weeks I have been vastly entertained by a graduate Quantum Mechanics course being taught in the Bradley Commons conference room next to, and within earshot, of my office. What a difference a generation makes. Today all the grad students are sitting in lecture with their laptops humming, and as the professor talks about singlet and doublet states, they are setting up problems with Slater Type Orbitals and doing computational physics calculations on potassium and calcium atoms.

Hartree-Fock calculations, of course, was what I was doing in graduate school at Michigan Tech 1984-1989. My doctoral work took three years to generate some 155 data points, at approximately 24 hours per data point on a relatively fast Celerity C-1230/C-1260D UNIX box. Ten years later, I had a shiny new 166MHz Pentium Micron Millenia PC and a Windows 95/NT FORTRAN compiler. I converted my programming codes and set up one of my old nitromethane data points to run as a test. I'd planned to let it run as long as it took, but even before I was ready for bed, the prompt had come back in the MS-DOS box after only forty-five minutes. Sighing, I sat down to read the error reports to see where it bombed -- except it hadn't. It was done. 24 hours to 45 minutes in ten years. $100,000 versus $2000 computer. Moore's Law in action. Yikes.

Ten years later, I bench tested one of those runs on a dual-Athlon processor computer server someone in the department had built, and we had the time down to 3 minutes. Eep.

Yeah, graduate classes in Quantum Mechanics sure would be fun now.

Dr. Phil
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