Sunday, June 22, 2008

Things I don’t understand: The ‘Collapse’ of the Wavefunction

(NB: Let it not be supposed that the long delay since I last wrote something headed ‘Things I don’t understand’ means that there are not many, many, many, many other things that I don’t understand.)

In chemistry, the results of quantum mechanics that we are interested in are spectra. Whether these are lines in the ultraviolet/visible region corresponding to transitions between electronic states, or lines in the infrared region corresponding to transitions between vibrational states, or lines in the microwave region corresponding to transitions between rotational states, they are all transitions between energy states which are quite nicely defined.

We cannot ‘observe’ a chemical system in a particular state. We do not make a ‘measurement’ to see what state it is in. What we observe, what we measure, is its transition from one state to another. It seems entirely useless, as well as nonsensical, to say that a particular molecule was not in its first excited vibrational state until we hit it with a photon to give an anti-Stokes Raman peak.

In fact I am really quite vague about what sort of experiment you would do, in the traditional orthodox quantum mechanical sense, to measure the state of a system in such a way that its wavefunction ‘collapses’.

I don’t like the ugly discontinuity that the ‘collapse’ of a wavefunction introduces to quantum theory.

I don’t like the appearance of a privileged status for an ‘observer’ it introduces.

I especially don’t like the whole elaborate mass of New Age piffle that has been erected on this privileged status, a mass which has infected and compromised the otherwise splendid ouevre of Greg Egan, for instance.

A while ago I first came across de Broglie’s pilot-wave theory, and was impressed in my naive chemist’s way by the straightforward way it cut through the paradoxicality of the two-slit experiment. I wanted to know how this model had been developed since de Broglie cast it aside, and how the ‘collapse of the wavefunction’ looked in the pilot wave model. I couldn’t find anything then, because I didn’t know enough to look for the ‘de Broglie-Bohm’ model.

Apparently the collapse of the wavefunction is not a problem in the de Broglie-Bohm model. So it is non-local. Big deal. Every 1s hydrogen orbital wavefunction we tell our first year students about has a non-zero value at every point in the universe (though Excel, bless its heart, says with 15 digit precision that it is zero more than about a nanometre away from the nucleus). Better non-locality than mystical Copenhagen interpretation waffle about an ‘observer’, or worse yet, the deeply dippy ‘Many Worlds’ interpretation.

But why the de Broglie-Bohm model doesn’t get into trouble with the wavefunction collapsing- that’s something I don’t yet understand.


Anonymous said...

Listening to physicists, I learned that the collapse of the wave function is a problem of Schrödinger's wave mechanics, it is not inherent in quantum physics as such: no problem with Heisenberg's matrix mechanics.


Chris Fellows said...

Hmm, I don't think that can be correct, as the difference between the two implementations of quantum physics is only one of formalism. The wikipedia article on matrix mechanics avers that "The act of measurement in matrix mechanics 'collapses' the state of the system."

See also this interview with Heisenberg.