Fact and Fiction

Thoughts about a funny old world, and what is real, and what is not. Comments are welcome, but please keep them on topic.

Saturday, October 22, 2005

State vector collapse?

This is a story of setbacks and revelations along my route to understanding quantum mechanics properly. The lesson that I have learnt along this route (and elsewhere) is never to accept what people tell you without first checking it all for yourself. If you don't have the resources to do these checks, then you must "label" the information as being potentially unsound.

Why did my undergraduate physics teachers insist that QM states collapse when you observe them? They did it because that's what they were taught themselves. They then went on to describe "paradoxes" in QM, with whimsical names like Schrödinger's Cat, Wigner's Friend, etc. Of course, as an innocent physics undergraduate I ignored the "paradoxes" and concentrated on doing QM calculations so that I could get the answers to come out right. As Richard Feynman said "Shut up and calculate" (or maybe it wasn't Feynman - see here), so that's what I did, and it worked pretty well for me.

The trouble came later when I had more time to think about QM. By then I had forgotten about the "paradoxes", but nevertheless on deep reflection I realised that something was not quite right about QM. I turned it over in my head for most of the time that I was doing my PhD on quantum chromodynamics, and eventually came to the conclusion that some of what my QM teachers had been teaching me was rubbish. What they had taught me was an "effective theory" (i.e. something that works, but which you shouldn't look at too closely) and not a "fundamental theory" of QM, yet they had given me (and everyone else, including themselves) the impression that they were teaching a fundamental theory of QM.

If you are told that something is fundamental then you tend to attribute to it an exalted status, where you are supposed to be able to derive everything from it. It takes on the role that axioms have for mathematicians; fundamental and immutable (actually, nothing is immutable in science). Unfortunately, just as you can write down contradictory axioms, you can also write down contradictory QM. What is the evidence for this? The above mentioned QM "paradoxes", of course!

How do we fix this problem of the QM "paradoxes"? In my musings during my PhD I rebuilt my understanding of what QM was about (this took a long time with many false starts), and the one part that didn't fit naturally was the so-called state vector collapse, where observing a physical system caused its state to collapse from a linear combination of alternatives into a single one of the alternative physically permitted possibilities. The QM equations simply didn't specify how this collapse occurred (or even that it occurred at all), so why were we taught that it did occur? I came to the conclusion that it was mainly for calculational convenience (i.e. an effective theory), and that it simply did not happen that way in practice. In fact, I found out later on that the interpretation of QM that I had derived for myself was already well-known as the Everett interpretation of QM (see the The Everett FAQ), but because I had been conducting my QM musings in secret (at the physics laboratory where I did my PhD it was thought to be distinctly unsound to be questioning the foundations of QM) I knew nothing of this prior work. Later on, as I mused deeper and deeper about QM, I refined my viewpoint further, but it still has a distinctly Everett-like flavour. The details are too technical to be repeated here.

It took a long time for me to flush out the errors that my QM teachers had taught me. All attempts at discussion about this with other physicists met with blank stares and uneasy behaviour. The implication was that they thought that I was a crackpot, which didn't form a good basis for building confidence in the correctness of my ideas. Anyway, over the following years it gradually became clear that I had been right all along. For instance, I took instantly to quantum computation, which was so self-evident to me (given my Everett-like view of QM) that I wondered what all the fuss was about. A very good exponent of these quantum computation ideas is David Deutsch, who has written an excellent book on the subject called The Fabric of Reality.

Of course, I can't say that state vectors do not collapse, but just that it is not necessary to assume that they do, and there is nothing at all in the QM equations of motion that says anything about collapse. If there is ever any experimental evidence for collapse, I would be interested to see how the underlying dynamics of collapse is then added into the QM equations of motion.

Unfortunately, QM still appears to be taught in the same way that I was taught it, producing hordes of people who "shut up and calculate". There will be a few of them who will go through the same rediscovery process that I went through. I hope it is easier for them than it was for me.

State vector collapse? No way!

4 Comments:

At 25 October 2005 at 23:37, Blogger A Future Metaphysician said...

I've been trying to explain this concept to people for some time... and find a great deal of psychological resistance to the idea. I can now sympathize with Galileo when he tried to sell the notion of a moving Earth to his Catholic friends.

Deutsch's multiverse (I call it an "omniverse," since he argues that every possible timeline actually exists) has many remarkable implications, including some ethical implications. If you know that you will experience every possible outcome, you face your choices differently. Every day becomes your last, in one sense, yet you can face every trial with joy, since you know there are timelines where you triumph over the adversity.

Deutsch is very interested in the science, but the folks at the "Fabric of Reality" yahoo group were uninterested in the ethical and practical implications of the theory. I hope to address some of this at http://futuremetaphysics.blogspot.com

 
At 26 October 2005 at 19:55, Blogger Steve said...

I guess the psychological resistance is coming from people who wrongly assume that their standard intuition is enough to handle everything, including situations that they have not encountered with their standard senses. QM is exactly the sort of thing that standard intuition is not set up to handle.

I follow David Deutsch's work with interest. I wouldn't go so far as to assert that reality is exactly as described by QM, and thus all possible timelines actually exist. All we can really say is that there is no experimental evidence to the contrary (as far as I know). What we need to do are experiments that specifically set out to detect state vector collapse when QM says it shouldn't be occurring, and then revise QM accordingly.

 
At 4 May 2007 at 09:25, Anonymous Anonymous said...

As a complete layman I prefer Cramer's Transactional Interpretation to the Multiverse one.

 
At 4 May 2007 at 19:20, Blogger Steve said...

The transactional interpretation is a more sophisticated version of the Copenhagen interpretation, where the wave function collapses over an extended overlap region between "offer" and "confirmation" waves. As such, it makes use of wave function dynamics that is not actually specified by QM itself, and this is the reason that I don't like this interpretation.

 

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