Schrödinger’s cat

I usually read novels in bed, as my brain tends to be too tired to take in any more information for the day.  So the fact that this is the third post I am starting with a reference to a popular science book makes me think that perhaps I have not been working hard enough…

The book in question is The Emperor’s New Mind, by Roger Penrose.  The main thesis of this wonderful book is, apparently (and in a very small nutshell), that the mind does not work like a computer*.  However, I am currently about 3/4 of the way through it, and this has not yet been touched upon!  Rather, over 400 pages or so, Penrose has valiantly attempted to explain Turing machines, classical mechanics, relativity, quantum theory and cosmology to the interested (and, one must assume, quite dedicated) layperson.  I can only assume that all this is going to coalesce into a grand theory of Mind, but it does so far seem like quite an ambitious project.  Having tried to achieve this kind of comprehensive introduction to even the smallest of mathematical subjects myself in previous posts (you might have noticed that I have long since given up trying to do this), I have great respect for Penrose’s tenacity.  I find that the problem with this type of enterprise lies in trying to tread the line between being impenetrable to non-mathematicians, and boring for mathematicians.   While The Emperor’s New Mind is a great book, I think it is safe to say that it probably falls on the former side of this line; it is perhaps not entirely suitable for bedtime reading.

Anyway, I have just been reading Penrose’s take on the maltreated feline of this post’s title, and it got me thinking, so I thought I would discuss it.  The cat in question is a paradox which Erwin Schrödinger came up with in order to show the absurdity of trying to apply quantum theory at the classical physical level (that is, the everyday world with which we interact, as opposed to the exceedingly odd quantum level of subatomic particles).   This is, of course, a massive and complex subject, and I will only provide the merest of scrapes of its surface!  If you happen to be a pedantic physicist, then please do comment on any inaccuracies in what follows.

First of all, I will need to briefly explain Heisenberg’s Uncertainty Principle.  This says that it is not possible to measure both the momentum and the position of a subatomic particle (such as an electron) accurately at the same time.   The more accurately we know one of these, the more our measurements of the other becomes a matter of probability.  This may not sound so odd as it stands.  However, consider an extreme example.  If the momentum of a particle is specified precisely at some point in time, then its future momentum is entirely predictable, just as you might expect.  However, if we now choose to measure its position (ie. simply work out where it actually is) , then we will find that, because the momentum was precisely specified, the particle has equal probability of being at any one point in space as any other! **  On the other hand, if we chose to first measure its position, then any future measurement of momentum will be completely uncertain.

So far, so wacky.  But now consider what we actually mean by “measure”.  I don’t know much about experimental physics (or indeed physics in general, I should confess), and have absolutely no idea how one actually goes about measuring the momentum of a single subatomic particle.  But this is not too important.  A measurement here simply means an act of observation, and it necessarily involves a conscious mind.   To measure a particle’s momentum is simply to “become conscious”  of its momentum.  But the consequences of the act of observation in quantum mechanics is a great source of confusion and paradox.  To observe a particle is to dramatically – and discontinuously – alter its behaviour.  A particle’s behaviour is smooth and predictable (albeit in a rather unintuitive way) up to the moment in which an observation takes place, at which point it suddenly changes.  In more scientific terms, a particle has a rigorous mathematical description  – a wavefunction – describing all its possible states; once the particle is observed, this wavefunction “collapses” into one of these possible states, and which exact state it collapses into is a matter of probability, rather than determinism.

In summary, the very act of observing a particle changes its behaviour!  This is quite mind-blowing.  Personally I think that it could be construed as fairly strong evidence that reality is an illusion created by our collective consciousnesses.  But that might be a result of reading too many books like The Tao of Physics and The Holographic Universe in my youth.  Roger Penrose is quite strongly opposed to this “subjective reality” theory (in fact, up to where I have read he is strongly opposed to most attempts at explaining such crazy quantum behaviour, but I assume he will eventually come forth with a theory of his own).

Anyway, back to Schrödinger’s cat.  So imagine a sealed container, inside which we deposit a cat (preferably someone else’s cat), a vial of cyanide gas, and a device which, when triggered by some quantum event, smashes the vial and kills the cat.  Note that it is not too difficult to give an example of such a trigger: Schrödinger himself thought of an electron which may or may not be emitted by a decaying radioactive substance; Penrose uses the example of a single photon which may or may not be reflected by a half-silvered mirror.  In both cases, it would technically be possible to set up the experiment so that there is an equal probability of the event occurring as not in a given time period.

Now we let the experiment run for the allotted time, and then ask the question: Is the cat alive or dead?  At this point, the natural reaction is to say that, well, it is certainly one or the other, and exactly which is a matter of probability.   And indeed this would be the case, if you were in the box with the cat (presumably wearing a gas mask).  But, as explained above, without an observer, a particle exists in a superposition of various possible states.  It is only once observed that the wavefunction describing these possible states collapses into the one which we observe.  So, if we assume that quantum effects can be magnified to the classical level, and if there is no observer inside the container (I’m afraid we must also make the possibly dubious assumption that the cat has no consciousness!), the triggering particle has both been emitted AND not emitted (or reflected and not reflected, depending on which version we use), in which case, until we look inside the box, the cat is suspended in some mysterious limbo state between life and death.

Of course, this is ridiculous.  And it perfectly sums up the absurdity of assuming that quantum effects can apply right up to the observable, classical scale.  If that were the case, then a cat could be simultaneously both alive and dead (similarly, a tree falling in an unpopulated wood could make both a sound and no sound).  But how can we possibly explain this?  If quantum mechanics perfectly explains the behaviour of subatomic particles, and subatomic particles make up the world we experience, how can it be paradoxical for us to experience quantum effects?

Well, this question has naturally been the springboard for a whole slew of alternative quantum theories.  Take the “many-worlds interpretation,” for example.  This is one of the more widely-accepted interpretations (which goes some way to demonstrating how crazy these explanations can get).  Very briefly and crudely, it suggests that there are infinitely many parallel worlds: rather than simply causing a particle to collapse into one of its simultaneous states, an observation of a quantum effect actually causes our current world to veer off into one of many possible parallel worlds.  In Schrödinger’s experiment, this would mean that the cat is indeed both alive and dead, but that these two possibilities occur in different worlds; opening the box and observing the cat causes our world to branch off into one of these two alternatives.  This theory imagines the unfolding of reality as a many-branched tree, rather than a continuous line.

Many other theories have been postulated, none of which I really feel inclined (or qualified) to talk about.  Needless to say, this is a thorny philosophical question.  It seems clear that while quantum theory is an accurate way of modelling reality on a certain scale, it is just not consistent with the classical world without some kind of grand re-imagining of reality.

* Incidentally, I can’t help but agree with this view. And I think that the fact that various cultures have at different times used anything from electromagnetism to hydraulics as metaphors for the workings of the mind just shows that we have a tendency to assume that whatever the technological state of the art is, that must be how our brains work! However this is a whole can of worms which I won’t devote more than a mere footnote to.
** Of course, the probability of a particle ever being at any given point is technically always zero, but you know what I mean.

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