Confused at a higher level

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And physics, too

Posted by Arjendu on January 15, 2008

Some of my research kicked back to life.

The first is my stymied project on parameter scaling in the difference between classical and quantum mechanics. A friend had asked why I didn’t ask a ‘competitor’ to comment, and thinking about it, I inverted the way in which I have recently gotten into collaborations. That is, recently, people have come to me with an idea to see what I thought of it, and my questions and comments have proved valuable enough that I got involved with the research. This time, I wrote to Nathan, a bright young grad student who I had run into at a conference and who has published some results related to mine, and asked if he would care to look at my paper and see if he could figure out a way past the road-block of neat results, but no clear physical intuition. He has some spare time at the moment, and no constraints on him to not start new collaborations, so he gave it a whirl.

He had a great question almost immediately. The focus of this paper is to show that a particular distance function to measure quantum-classical difference works marvelously in demonstrating parameter scaling. But there are factors of hbar (ok: hbar is Planck’s constant, and critical, crucial, in setting the scale for quantum mechanics) that make no sense, and if you can’t explain your results, how on earth can you trust it, let alone publish it? He thought that the issue was that we were looking at a quantum-classical distance function that was not appropriately dimensionless. Which immediately led us into the issue that everything in phase-space has weird dimensions (I know I’ve lost all the non-physicists but pretending you are reading along, phase-space is where you look at both the position and the momentum of a particle. Since you are in this hybrid space with distances in different directions having different meaning, it is intrinsically weird).

Anyway, it was good to be able to talk about a physics puzzle that was bothering me, and now Nathan’s going to take a longer and more detailed look at this issue of dimensions. As always, it is discussion that gets me going when I am stymied, and nowadays even more so with a lack of time to sit down and focus. I’m happy to have a new collaborator.

I also got back in touch with Arik — we’ve both been distracted, and unable to proceed on the response to our paper from Physical Review Letters. But there was a useful conversation this afternoon: We are still going back and forth on whether we have enough data already to answer the referee. Today’s discussion landed up on the issue of whether chaos induced by measurement counted as chaos due to quantum effects. I say, sure, measurement’s quantal, darn it. But I can see the referee’s point somewhat.

And another call, not really physics, but sort of — an alum, now in a newly cooked-up interdisciplinary bio-and-physics-and-chemistry program, wanted to talk about issues of feeling mathematically rusty, feeling not quite trained enough mathematically for what he wanted to do, etc. I tried to remind him that the problem always outranked the solution, and that elegant mathematical solutions were in general not available in biology — it is far too nonlinear, complex, and downright messy (from the theoretical physicist’s perspective) so feeling like he didn’t have enough math to do theoretical biology was, to my mind, a question of attitude rather than fact. Particularly for him — this kid took a ton of math here at Carleton. We’ll find out.

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3 Responses to “And physics, too”

  1. Hi Arjendu – Nice blog! (Thanks for your email; my apologies for not responding quickly – it’s been a crazy break+new semester.)

    The issue of dimensions is fun to teach. The whole idea of dimensional analysis and scaling, with the host of dimensionless parameters that come in (e.g., the Reynolds number) is very important and can lead to real physical insight, and yet it’s almost always skipped in a physics curriculum.

  2. agm said

    Hehe. I spent nearly an hour teaching dimensional analysis yesterday, hope a small part of it sticks. Soon they’ll get to quizzed to see how much they understood, when they get asked to make Reynolds number…

  3. Hey Arjendu, Doug, Aramis –

    It’s a small, small world when I can find a single webpage with comments from two of my favorite professors and my roommate.

    I’m glad to hear that Arik’s still involved with the quantum research at Carleton.

    Happy new year, all!

    Cheers,

    ~Mark

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