Some familiarity with linear algebra and the notion of quantum states as objects in Hilbert spaces is necessary if you want to follow the logic as it's presented. That's a question of obtaining competence with a mathematical toolkit, which isn't going to be everyone's cup of tea, but it's available to anyone who takes it on.
It's easier, of course, to keep it mysterious by not fully taking that step, and there's nothing wrong with that. But keep a beady eye out for those who assert that quantum mechanics is fundamentally mystical or paradoxical or incoherent, and perhaps aren't sufficiently imaginative to recognise that there are subjects for which far more clarity exists than they may experience themselves. Especially those who make a living by doing so.
There are a lot of them about.
So here we have a public lecture on quantum mechanics by Sidney Coleman of Harvard University, given in 1994. In it, he explains how quantum mechanics is not at all reliant on:
- anything special about the measurement process
- the collapse of the wavefunction
- indeterminacy
- anything inherently probabilistic or random
- non-locality or spooky action at a distance
It's fashionable to go all out to get people excited about the weirdness of quantum mechanics. And that's great... to start with. Hopefully the people who are truly excited by it will, at some stage, want to know what's going on, rather than just holding on to the idea of it being weird.
Bursting the mystical bubble of something doesn't make the wonder of it go away. It opens it right up, and opens up new worlds with it. As Feynman put it, "It only adds. I can't understand how it subtracts."
If you prefer to get your insights from the greats while watching the wonders of nature and listening to music rather than attending lectures, then I don't blame you. Watch this video instead. It's nice :)
Tip of the hat to Matt Strassler.
4 comments:
QM is inherently random. Taking an example from Bohm in 'Causality and Chance in Modern Physics', consider the nucleus of a uranium atom. We could now perform this experiment for real. Place a single atom of U on a calorimeter and wait for its decay. QM asserts that there are no microscopic parameters that control the decay of that nucleus. That this observable phenomenon has only a probabilistic cause. In short that there is nothing that causes it to decay at the particular time at which it decays.
Hi Anonymous,
The observations you describe are correct, of course. I don't know if you watched the lecture, but Coleman explains why the results of any quantum trial will necessarily agree with the experimenter's definition of randomness, even without there being any inherent randomness in the theory.
He compares it to the self-evident observation that the Sun goes around the Earth. Those very same observations are consistent with a different view (for example that the Earth goes around the Sun), which requires a little more effort and abstraction on our part, but on deeper inspection turns out to be a simpler, more powerful and less paradoxical approach.
None of it denies the fact that the Sun moves across the sky; and none of it denies that the model of the Sun going around the Earth has a great practical value for the majority of people.
Whether that's a fair comparison or a provocation is perhaps a matter for debate! Perhaps it's a matter of taste. The point is that, while it might have practical value, a randomness postulate is simply not necessary.
But can we know "what's going on", even with detailed study?
Feynman often gets quoted (an misquoted) on this topic along the lines that "no one understands quantum mechanics".
I'm no specialist, but from what I do know this still appears to be correct.
QM is spooky, it is weird, no one understands "what's going on" at an underlying level (and maybe they never will, maybe it is truly incomprehensible). At the same time QM is rigerously testable, predictable, and quantifiable, which is why its so powerful. This last part is typically left out when the spookiness of QM is applied to explain as an explanation in some new domain.
We can know what's going on to some extent. Some very significant extent.
Often what people mean by "knowing what's going on" is having a heartfelt, intuitive, concrete grasp of it. Like we know that there's ground beneath our feet when we walk. I very much doubt quantum mechanics can be like that, because we are human beings who have evolved intuitions to cope with the things around us and have lived our lives in contact with things from a fraction of a millimetre to a number of kilometres in size, none of which, to our direct perception, do what quantum mechanics tells us things do. So it would be too much to ask to have that kind of a grasp of it.
I think that is why quantum mechanics seems "spooky" to us. That is why it seems incomprehensible.
Surely it's the solidity of the ground we should question? When we do, quantum mechanics can explain that just fine. It's our intuitions that get it backwards.
Having read and heard a lot of Feynman, I'm confident that this is the point he was making when he said that nobody understands it.
We certainly have a theory that can be expressed exceptionally clearly, at least at an operational level (and also by a variety of coherent philosophical realist approaches). We certainly have a theory that is astonishingly accurate, that we can use to determine the properties of physical systems with enormous precision and more predictive power than we know what to do with.
It also appears to apply to everything in the physical universe. (Gravitation is a notable theoretical exception, of course; but as we have no experience of anything observable or measurable for which quantum effects of gravity would have any effect, that issue remains purely academic.)
What's amazing is that nature seems to work by these crazy rules, and we seem to have found them. We can grasp them precisely using mathematics even if we can't grasp them with our common sense. And while they're crazy, they're really not so crazy that we should allow them to be abused by those with mystical prejudices.
Many thousands of people use quantum mechanics every day. In many ways, it's just normal for them. Some peer more deeply into the philosophy than others, some peer more deeply into the more perverse abstract technicalities than others. None could honestly say they really know what's going on.
But then, do you really know what's going on with the closest person in your life? (Do you really know what's going on with yourself, for that matter?)
In those terms, we can't really fully understand anything of significance. QM may be remarkably strange part of our incomplete understanding of this fascinating universe, but with regard to that incompleteness, I guess I don't really see it as much of an exception.
I think some people just get a kick out of telling people how freaky it is. I prefer people who just go ahead and explain how it works :)
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