Clearly quantum mechanics involves very complex, subtle and difficult to understand ideas. It's a complicated story and, for that reason, I think it is important, if you want to have any hope of
any understanding of the plot (mine is certainly nowhere near complete, and the earlier parts are getting rusty. A bit like the Forth Bridge.), that you read it from as close to the start of the book as possible and try not to skip too much. The video gives half a dozen or so of the more exciting and sensational sentences from some of the later chapters. That is why I said in my previous post:
It turns out that as soon as you increase the wavelength to a size such that it is sufficiently docile not to disturb the electron too much, it becomes too long to tell which slit it went through. And that is the start of the interesting part.
In my view, the route in, for an unfamiliar audience, is the mechanism for the uncertainty in this particular case - the electron being disturbed by the light that is used to observe it. The general principle of the uncertainty, including the relatively extremely abstract mathematical concept of a "wave funtion", comes in later chapters and is, ideally, built on lots and lots of prior experience. When I was studying this at University it was the culmination of at least two years of mathematical foundations (on top of high school), including, for one thing, learning vector calculus and then how to re-frame the subject of classical Newtonian mechanics into a thing called Hamiltonian and Lagrangian mechanics, as preparation for the mathematical "shape" of the Schrodinger wave equation.
As I said, the part at the end of my post is where the interesting stuff is just beginning. And that interesting stuff starts with the curious fact that nature
appears to be conspiring to stop us from simulataneously measuring the position and the momentum of the electron
through the mechanism of the light that illuminates it:
As I said, what you find when you do this is that, as you increase the wavelength, and therefore decrease the energy of the photons of light,
just as you get to the point when the light is un-energetic enough not to disturb the movement (momentum) of the electron too much, you find that the wavelength is too long to measure its position accurately enough to tell which slit it went through. So this is the mechanism for the uncertainty principle
in this particular case.
Just as, in more conventional familiar situations, you find all sorts of different and apparently unconnected physical mechanisms which express other general principles, like, say, conservation of energy.
My point is this: to understand and believe what you are being told you have to start from the solid, individual physical situations, and only then move on to abstract general principles. Talking about the uncertainty principle and the wave function without first discussing examples of mechanisms for these principles is like asking somebody to believe in the principle of universal gravitation when they have never seen an object fall to the ground! It's too abstract. This, I think, is at the heart of the objections which are exemplified by the understandable disbelief of the sceptics who cry: "It's all just an abstract mathematical fairy tale!"
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Quotidian:
Bearing in mind what I said above: I don't deny the interesting mysteries of Quantum Mechanics. I just think it is important not to dive right into the middle of those mysteries and just be completely directionlessly bemused by them. I think it's best to see how the mystery evolved, in a continuous unbroken process, from ordinary-ness. Apart from anything else, I think that is the only way to fully appreciate what a mystery it really is.
I'm reading a book on String theory by Brian Greene now, and I'm sure he's a hugely greater authority on the detailed plot of this entire story than me, with my half remembered wine-softened physics degree. But, dare I say it, I disagree with his wording in the passage you have quoted.
It is absolutely true that uncertainty appears to be a deep, fundamental principle of nature, like the conservation of energy (or, in later chapters of the book, mass/energy) but it is important to understand the individual mechanisms by which this principle is established.