Tuesday, 29 May 2012

Pilot Waves for and against Part 1

Well the debate has been going on the science and physics OU Fora about the meaning or not of quantum physics as all such debates we do seem to going around in circles those of my fellow OU students reading this blog may find part 1 of the discussion here

and part 2 here


You will see that I have come close to losing my temper some times with a certain person, Still I'm not the only one who finds his attitude slightly infuriating which is reassuring.

Any way as promised here is a brief summary of the Pilot wave approach. This was intially thought of by De-Broglie and the basic idea is that each particle is accompanied by a Pilot wave. (Not that a particle is a wave or vice-versa), this Pilot wave guides the particles in situations such as the two slit experiment giving rise to the characteristic interference pattern on the screen, but a particle only passes through one slit at time. It was proposed at a conference at Solvay in 1927 but wasn't really taken up as most physicists were more impressed with the views of Bohr/Heisenberg and Schrodinger. The rest is history as they say, physicists got on with the business of using quantum physics to calculate the properties of molecules, atoms and solids etc and the pilot wave theory got quietly dropped.

That was until David Bohm rediscovered it and published two papers in the early 1950's these weren't taken seriously most notoriously because David Bohm claimed that the theory required the use of hidden variables to explain things like paticle states. So it was ignored until Bell came on the scene, as is well known he devised an experimental test which could distinguish between hidden variables and the standard predictions of quantum mechanics, it was shown that the predictions of quantum were vindicated and hidden variables were ruled out. You might have thought that would be the end of the story physicists could get on with the real business of developing the applciations of quantum mechanics to ever more and more complex problems. However there was a get out clause (there always is) In deriving his contradiction Bell made two assumptions

i)  There were no hidden variables dictating spin components
ii) There were no non local interactions affecting the measurement of 1 particle a long distance away from another one.

As both were required it was perfectly possible for Bohmians to reject ii) and keep i). Most physicists were until quite recently prepared to accept i) and reject ii). However i) has its own problems if taken literally it implies that properties are created by an act of measurement against our notions of common sense.

Of course all that is a bit of an exaggeration, if on the statistical interpretation the wave function is simply a means to generate probabilities then measuring something does not create a property of a particle. All that happens as say when one throws a dice is that one of the possiblities is realised. But then that means that quantum mechanics is no more than an algorithm for correlating the mathematics of quantum mechanics with probabilities and doesn't really explain anything. Well I think I still hold that view, but nevertheless I'm slowly being persuaded, that there is more to the De-Broglie Pilot wave theory than I first would expect.

There has been quite an industry actually using the De-Broglie Bohm theory to perform calculations. Most impressive is it's explanation of the two slit experiment, It shows how the two slit experiment can be explained with each particle taking a definite trajectory and passing through a single slit, there is none of the usual problems associated with believing that an electron splits in two then magically reforms when it is detected.  Neither is there any notion of wave packet collapse occuring as a result of measurement.

A really good introduction to the De-Broglie Bohm pilot wave theory is given here by these lectures by Mike Towler.


Best to start with the popular lecture


I still think there are major problems with it which I will expound on in another post. Anyway I;ll leave you to enjoy the lectures and make your own minds up. The fact that something has moved from being a speculative tool to one where real calculations can be made has to be something.

On another note to do with real waves I was slightly disappointed with the results of my last TMA from MS324 in the low 80's. I missed a key point in one of the questions about the boundary conditions and in my favourite question number 2 I dropped a few marks because I missed out the first term in the series still a reasonable score but not as high as I hoped.

Bye for now

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