Hi been having a heated discussion on the OU science fora about the meaning or not of quantum mechanics

Those who follow this blog will know that I tend to be quite sceptical about any attempts to go beyond the current formalism as

a) No new physics will come out of it (Or none that we can distinuguish between experimentally)

b) Any attempt to see the wavefunction as somehow real leads to all sorts of problems

i) The idea of superposition being something physical until observed seems to imply that we create reality

by an act of measurement

ii) In the two slit experiment the idea that an electron or large particle somehow splits in two and then magically reforms (if taken literally) at the detector seems totally incredible (where does the energy come from etc) why bother with CERN if we can split electrons in two simply by passing them through slits.

iii) If a particle really is a wave how come the pattern only emerges after several impacts on the screen rather than all at once. It is only after a statisitically significant number of events have occurred that anything like a pattern interpreable as a wave function can occur. So that the 'wave aspects' are esssentially statistical the usual fuss about the pattern still occurring even though there is only one particle in the intererometer being irrelevant (or just as relevant as the throw of a single dice).

For these reasons I prefer the statistical interpretation of quantum mechanics, which says that the 'wavefunction' is essentially a probability amplitude whose modulus squared gives the probability of certain events happening. This implies that the wave function is not a property of a single system but more a mathematical device for generating probabilities, it differs from that of classical probability in the sense that to account for the quantum mechanical viewpoint we have to use complex numbers. I then went on to show how you could account for the sinusoidal dependence of the probabilites on the phase factor for a two state system. Also how it was quite striking how classical probabilty could be recast in the language of quantum mechanics specifically the Dirac formalism. For a recap see these two posts

http://chrisfmathsphysicsmusic.blogspot.co.uk/2011/05/quantum-mechanics-of-two-state-systems.html

http://chrisfmathsphysicsmusic.blogspot.co.uk/2011/05/mathematics-of-two-state-systems-2.html

I also gave a reference to a paper by Marcella which gave an explanation of how the typical form of the two slit interference pattern can be interpreted as a single particle build up of many events, where the particle does pass through a single slit, which acts as a measuring device the uncertainty in the particles position being due to not being able to know precisely the position of the particle and being responsible for the wave like appearance.

http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

In all fairness I should point out that a subsequent paper has been written criticising the above paper

http://arxiv.org/abs/1009.2408

And this was presented as a falsification of the Marcella paper, by one of the contributers to the forum. I beg to differ, all it shows is that Marcella has hidden some of his assumptions and that the use of free particle eigenstates is equivalent to a classical wave theory. It would be possible to adapt the Marcella paper to make it more accurate eg by the use of a superposition of free particle eigenstates (often referred to as a Gaussian wavepacket) and removing the assumption that it was equally likely for the particle to emerge from one of the slits. All this would be a distraction from the main point, namely that it is possible to give a particle like interpretation of the two slit experiment using the formalism of quantum mechanics. Indeed as that is what physically happens namely particles really do appear individually and only eventually is a wave like pattern revealed it would seem bizzare to attribute wave like properties to individual electrons, neutrons or buckyballs. Obviously collectively the wave like properties are manifest so wave particle duality is simply when considered as a single entity quantons (for want of a better word) behave like particles but when considered collectively they behave like waves.

The statistical interpretation to my mind is the bottom line, it makes the least number of metaphysical interpretations, one can avoid all the usual problems, real wave collapse, and so forth. It by definition is consistent with the formalism so physicists can get on with the real job, namely developing and applying the formalism to predict and understand the properties of solids, stars, quantum fluids, elementary particles, lasers etc. Or in a word physicists can 'shut up and calculate' and leave the 'interpretational stuff' to other people.

For more information on the statistical interpretation this web site gives a good introduction and overview

http://statintquant.net/siq/siq.html

However as a consequence of the dialogue on the OU science forum, I have become a bit more interested in the so called Pilot wave theory initiated by De-Broglie and subsequently developed by David Bohm. I'll discuss more about it in another blog, giving my reasons as to why out of all the myriad interpretations of quantum mechanics which seek to go beyond the statistics, this is the one I consider most promising. One of the striking things is that the motivations behind the pilot wave theory, seem very similar to the motivations behind the statistical ensemble theory. I will point out the comparisons between the two in a later post. Also there has recently been an experiment showing that classical systems can show wave particle duality.Something that hitherto has never happened before. I'll leave you to ponder about the significance of this experiment for now.

http://phys.org/news78650511.html

Hmm, let's see if I can comment...

ReplyDeleteAh, I can!

ReplyDeletePerhaps you can explain something that I've never been able to understand: given that an electron can behave as a wave or particle, why do we assume that it must be either?

Why don't we treat it as something else entirely?

arb mate

nellie

Well the reason why I subscribe to the view that electrons are essentially particles and not waves is because

ReplyDeletei) They have properties that are essentially individualistic namely mass and charge and intrinsic spin

ii) When one actually looks at the interference pattern it is the cumulative build up of individual events whicn only after a significant number have built up is interprable as a wave pattern

iii) OK of course that implies the trajectories that an electron traverses is not a classical trajectory but then either the Bohm theory or Feynman's path integral approach would claim that was the case anyway.

So my bottom line is that 'quantons' behave individually as particles but collectively as waves. Given that an approach such as Marcella's spells that out in detail then thats good enough for me. All the usual talk of a particle splitting in two just does not make any sense. Of course that means one has to move away from seeing the 'wavefunction' of quantum mechanics being applicable to an individual particle or pairs of particles. Just as eg the Binomial probability distribution only applies to a number of events and not an individual event. Of course as I explained (or at least demonstrated) on my earlier posts about two state systems in order to account for quantum physics. one has to make the move from probabilities being real numbers to being the square root of probability amplitudes once that is done all the allegedly bizzare effects associated with quantum mechanics can be explained.

I love this post Chris. I'm going to bookmark and then review it once I have finished The Quantum World, next year. Hopefully be able to provide a more intelligent response then.

ReplyDeleteExcellent stuff though

Dan

Thanks for the thumbs up Beware I do stress the statisitcal aspects a lot more than most people would. So you are not getting the orthodox view.

ReplyDelete