Playing Beethoven with Heisenberg

Yes, I did that last week at ‘band camp for adults’.  Along with an excellent violinist I’ve played with for years, the three of us read Beethoven’s second piano trio (Opus 1, #2) with Heisenberg’s son Jochem (who, interestingly enough, is a retired physics professor).  He is an excellent cellist who knows the literature cold.  The violinist and I later agreed that we have rarely played worse.  Oh well.

Later that evening, several of us had the pleasure of discussing quantum mechanics with him. He didn’t disagree with my idea that the node in the 2S orbital (where no electron is ever found) despite finding the electron on either side of the node, forces us to give up the idea of electron trajectory (aromatic ring currents be damned).   He pretty much seemed to agree with the Copenhagen interpretation — macroscopic concepts just don’t apply to the quantum world, and language trips us up.

A chemical physicist in the the discussion, for some reason went on an on about just how useless he found QM in his work.  It can’t be that bad if computational chemists can use it to predict electron density and shielding (and chemical shifts) of a given structure.  What a jerk. This is the same guy (but a first rate violinist) who tried to impress us all with how much money he had 2 years ago, by mentioning that the $2000 worth of wine he bought at one pop wouldn’t fit into his station wagon.  Once a cloaca, always a cloaca.

I didn’t get the assigned reading (see the last post) done at all.  Instead I plowed through the first 100 or so pages of “Representations and Characters of Groups” by James and Liebeck. Interestingly, one of the pros coaching the amateurs is using Lie groups and topology in his attempts (as a prof in a music department) to figure out how various keys and harmonics are related to each other.  Even though Lie groups are continuous, and nothing is more discrete than the notes of a scale, embedding the musical scale on the surface of a torus seems to give insight.  As is typical of the crew that goes to amateur chamber music festivals there was a mathematician around (former department chair) we could consult.  Apparently representation theory helps explain the deep structure of groups, which of course is related to symmetry, which is related to the spectra of symmetric molecules, and chapter #32 (the last in the book pp. 367 –> ) is titled “An application of representation theory to molecular vibration”.

It took all week to get the (mathematical) notation straight.  One irritating thing was that there were at least  3 functions of two operands used

l. (vector, group) –> vector

2. (group, group) –> group

3. (scalar, vector) –>  vector

But none of the functions were given names, so that when the operation was performed the operands were just juxtaposed, and you were supposed to figure out the what was being done just by context.   In addition, the entities were given very similar names  FG-Module, FG etc.  Sometimes the same name stood for two different things, FG could be the group vector space over F or it could be the group algebra of G over F.  Again the context was crucial.  A few different names would have been helpful. It shouldn’t have taken me all week to see what was going on. 

So the coach and I cried on the shoulder of the mathematician (a cellist), who said — read the definitions very carefully boys.  He’d been a physicist before becoming a mathematician and noted that physicists always used the same symbols for important entities — m is always mass, f is always force etc., etc.  Not so in mathematics, where the symbols for the same entity vary from paper to paper, book to book.   He thought that mathematicians had invented so many things that they’d run out of letters. 

Well, enough.  The stack of incompletely read journals measured 4.5 inches, and it’s time to see what the research community has been up to.

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Comments

  • Wavefunction  On August 24, 2010 at 8:26 am

    Interesting account! You would have enjoyed the Robert Burns Woodward memorial symposium at the ACS which I attended yesterday. Some provocative stuff which I will write about soon on my blog.

  • Wavefunction  On August 25, 2010 at 1:41 pm

    -He thought that mathematicians had invented so many things that they’d run out of letters

    Worth noting the mathematically virtually impregnable book “The Mathematical Theory of Black Holes” by the late Nobel laureate S. Chandrasekaran. Apparently there is so much math in the book that “Chandra” as he was called ran out of all known Greek and Roman symbols and had to invent some of his own.

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