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Old 08-13-2010, 11:45 AM
Marko Vojinovic
 
Default OTish :D Colors of Cases for Fedora was: Open Letter

On Friday, August 13, 2010 06:42:29 Don Quixote de la Mancha wrote:
> Interestingly, the physicist Planck derived that emission spectrum
> from purely classical considerations of systems of harmonic
> oscillators. I'm afraid I don't recall the derivation, but it has the
> curious property that it explains a fundamentally quantum mechanical
> phenomenon without the use of any quantum mechanics in the derivation.
> Purely classical!

It isn't purely classical. It has the assumption that energy is emitted in
"discrete amounts", ie. is quantized, rather than being emitted in a
continuous (arbitrary) amounts. That was the crucial ingredient in the
derivation.

Of course, at that time quantum mechanics was not yet formulated, so the
derivation was heuristic in nature (rather than being a straightforward
consequence of quantum mechanics). But it was definitely not purely classical.

> Planck's Constant h is found in the function that describes that
> spectrum, and can be calculated from that derivation.

By "calculated from that derivation" I guess you mean "its value determined
from that function and some experimental data". There is no theory that could
predict the value of h, nor should there be any such theory.

> Now here is where it gets really bizarre: h bar divided by two is the
> spin of the electron! That is, when we say that electrons are spin
> one-half particles, we mean that their angular momentum is h bar
> divided by two. Spin one particles like photons have an angular
> momentum of one h bar.

The presence of Planck's constant in the magnitude of angular momenta is
immaterial. It is purely a consequence of the fact that we are used to
measurement units of everyday life scales (meter, second, kilogram), which are
obviously not so well adapted to atomic and particle scales.

What is really bizarre is the fact that the spin of an electron is half-
integer. One needs to "rotate an electron" by full two circles (720 degrees,
or 4pi radians) to get it back to its "initial position". Of course, for an
elementary particle the idea of classical rotation doesn't make much sense.
But there is *no* classical body around us with such geometric properties,
which is why we are so adapted to think that 360 degree turn always brings us
back to initial position. And that is why electron spin is so bizarre. :-)

Best, :-)
Marko

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