JB:?You know the present paradigm well; so you have raised so many questions that it requires a book.Go to my website.?
Don?t insult me, will you. While I am open to new descriptions of superconductivity without cooperons, the internet is clogged with websites like yours where people claim to have discovered things that will revolutionize physics, philosophy and you name it and prove that whatever knowledge has been developed up to date is entirely wrong.
I will assume that at least you know the author of the book, if you are not him. So a few pieces of advice. I believe that you are aware of the fact that such a book can never have the general audience as a marketing target. In which case, the lack of a list of publications on the topic, as well as reviews by people working in solid state physics don?t exactly qualify the book as more than a hoax. The author should be aware of that, given his academic pedigree. So as I said before, I will wait for the published papers.
JB:?Nonetheless, if you have linearly independent coordinates you cannot differentiate them relative to each other. If time is one of the coordinates it means that nothing can change within the remaining 3 coordinates. This is where mathematics predicts unequivocably what will happen in such a 4 dimensional (Euclidean)space. So I will leave it there for you to ponder.?
You can leave anyplace until it gets rotten. Mathematics does not unequivocally predict such a nonsense (at least that is what comes out from what you say). And until you clear this up in a more cogent manner, I wil treat it as a nonsense, and I will send you back to learn calculus, differential geometry and theoretical mechanics.
JB:?The statistcal interpretation of the wave function is accredited to Born; not Bohr. In fact Born was belatedly given the Nobel Prize for it in 1954. It is based on Heisenberg's Uncertainty Relationship, which, according to Born implies that one cannot know the position and momentum of an electron at the same time.?
You are right, my bad. I apologize. It was Born who stumbled upon the ideea that the square of the amplitude is the localization probability distribution.
JB:?If this is true, then all the calculations to design electron microscopes and electron accelerators MUST be wrong.?
Eppur si muove?
JB:?The fact is that even if one could make perfect measurements Heisenberg's Uncertainty Relationship should still hold. Thus let us apply Born's interpretaion by using "perfect" measurements.?
Then let?s.
JB: ?This means that when measuring the position of an electron with momentum p, one will get a position but the momentum will become indeterminate. When now again measuring the momentum of the electron you get another value which can be larger than the original value p. This implies that the electron's energy has increased even though one has made perfect measurements. This not possible.?
I agree it isn?t possible, but there is an error in your nicht gut gedankt experiment screaming at me. If you measure the position precisely, say you get x1, the measurement error for the momentum is indeterminately large, via Heisenberg uncertainty relations. This means that the momentum can be anything, and you don?t know what it is, since you didn?t measure it. Let?s say it was p1.
If you then measure the momentum precisely, you get a value, say p2. But since you don?t know what p1 is, from the first measurement, you cannot actually say that p2 can be larger than p1. You?ve introduced this assumption ad hoc, and of course that if you consider it valid, you get a violation of energy conservation. The problem is that you cannot introduce it as you please, unless you have some very heavy observational evidence for it. Which you don?t have such evidence. Au contraire.
JB:?You might want to argue that perfect measurements are not possible and walk away. This is correct in all cases (also clasically), but this does NOT remove the fact that the Born interpretation of the Heisenberg's Uncertainty Relationship has NOTHING to do with acuracy of measurement. Thus the Born interpretation has to be wrong because it violates the conservation of energy.?
I won?t argue that perfect measurements do not exist in fact. For the time being it isn?t necessary for the example you gave to figure out where and how experimental/instrumental errors come into play. Not even principialy.
And while I am open to arguments about Born being wrong in its interpretation, yourr example hardly qualifies as that. For the time being, it qualifies only as a not so well thought experiment. But then I am sure you won?t agree with my conclusion.
