Re: Quantum Mechanics (Really)


Oh come on, Ogged.

The reason people are obsessed with QM (and I speak as a physicist here) tells us a whole lot about humanity and very little about physics. In particular it tells us that, as much as scientist want to deny it, sociology and psychology have an awfully large impact on the COURSE of science --- though in the end the "truth" wins out, the path there is messy.

QM was born at a time of social chaos in Europe, after the ancien regime was conclusively proved unfit for ruling through its handling of WW1, and naturally there was a feeling in the air of impotence, of meaninglessness, of nihilism. That's point 1. Point 2 is that it came about through various smart physicists trying one mathematical construct after another until they came across something that matched the experimental results. As each new piece of mathematics proved adequate, attempts were made to interpret what said mathematics "meant", but you have to remember that these interpretations were made under very limited circumstances, without at that point a full understanding of the entire experimental and theoretical manifestation of QM that we have today. Point 3 is that QM came about in the 20th century, by which point physics had become completely professionalized. The consequence of this is that it is very difficult to escape a certain orthodoxy regarding the interpretation of QM. There's simply no win in standing up and taking a whole lot of heat for saying "Yeah Bohr and Einstein were smart guys, but who gives a %*#@ what they said about what QM means --- they simply did not have all the facts at their disposal". And point 4 is natural human hagiography. Rather than understanding that Bohr, Einstein, and the newest member of the pantheon, Feynman (soon to be joined by Hawking and, if plays his cards right, Weinberg) were trying to understand nature and would welcome the obsolescence of their views for something better, we get presented with argument after argument that makes pretty much no sense, but is justified by "this is how Bohr/Einstein/Feynman" understood it.

So that's the negative. What's the positive?

First QM is not some religious faith-based voodoo. It is like any other part of science---to appreciate what is really going on, you have to let go of some pre-conceived notions of the structure of the world. The letting-go is more extreme in the case of QM than anything else, but there's the usual ramp-up of experimental evidence you get in a freshman physics text to justify it.

Next, and this is the part that is crucial and that is never explained adequately, you have to understand the way the world really is. I'm going to use some of the crappy and misleading standard terminology below in the interests of getting to the point fast, but be aware that the this terminology is part of the mess and I am not endorsing it. The state of the world is, put it technically, a complex vector in the free vector space over some underlying set of states; in the simplest cases, this underlying set corresponds to the states of everyday classical mechanics. So roughly what this means is that in the quantum analog of any classical system, any quantum state consists of an array of all the possible classical states, each with a complex number attached to them.

On top of this is a whole bunch of mathematical machinery to now tell you how states will evolve with time. The machinery is interested though, IMHO, frequently very misguided, not in the mathematics, but in how it is explained, but this is not the time to go into that.

However there are really only a few interesting problems with the above. The first is the question of why we do not perceive a shimmering multi-faceted world but just the classical simplification. This is not yet a solved problem, but the nicest answers invoke quantum GR and the idea that once a state, in all its multifacetedness, grows larger enough (by affecting more and more matter and energy), it results in different space-time curvatures for the different classical (more-specifically interpreted a spacial basis) manifestations, something "snaps", and the "wave function collapses". Note that this is the standard Schrodinger's cat thing, but doesn't require life or intelligence or anything else.

The second interesting problem is the issue of locality. This deals with the question of "what does it mean for an extended 'wave function' to collapse, in particular how can the collapse be 'instantaneous'?" The real world situation this problem applies to corresponds to something like some nuclear radioactivity gives rise to two photons in some mixed polarization state which propagate out in space, but at some point this EM field becomes entangled with a detector, the wave function collapse described above occurs and the entire SPATIALLY-EXTENDED EM state collapses into a classical EM state. Everything we know about relativity tells us there's something tricky about this scenario --- simultaneity is a property of a particular viewpoint, not something absolute. However the above sentence also shows us a way to deal with the problem. As long as there is some way we can define a canonical viewpoint (ie a canonical non-moving basis) based on the particular situation we are OK. So while it is an interesting problem to imagine what the recipe for constructing that canonical basis might be, there is no philosophical problem here.

A final interesting problem is the question of what "photon", "electon", etc mean. This is a tricky issue that I don't have time to go into. Suffice it to say that

(1) what is fundamental is a collection of fields. EM field, electron field, quark field etc.

(2) like any fields these have a spatial structure that can be described through the sum of some countable collection of canonical basis elements, eg sinusoids.

(3) each sinusoid can have variable amplitude --- BUT the amplitudes can only be integral.

(4) thus an elementary particle is a fragment of one of these fields with amplitude of one unit.

For the most part this is actually not too tricky in the case of bosons. For fermions things are very ugly first because of the fermion-ness (only amplitude 0 or 1) and second because of the spinor-ness (how the spatial direction associated with the underlying field changes as the field is rotated).

Two books that at least try to talk about QM as real science rather than as "gee whiz, how can we impress the peasants" are _Paradox Lost_ and _Shadows of the Mind_. WRT _Shadows of the Mind_ even if you don't believe, or are not interested in, the central subject of the book, namely whether computers can ever be intelligent like humans, it's worth reading for the chapters on QM and their impatience with the sort of "ooh, it's a mystery, no-one understands it and no-one ever will" nonsense you get in most books, even most textbooks.

One day I hope to write long essays on this material, where I'll have time to set up a clear terminology and to structure my arguments logically, but that's a while away. The result will, of course, be posted on the web.

Posted by: Maynard Handley | Link to this comment | 10-24-03 2:44 PM
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But I haven't even read the post I linked to yet! Not that I think it would help much. I confess, Maynard, this is pretty much over my head.

Posted by: ogged | Link to this comment | 10-25-03 10:23 AM
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