Pasti: 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.
I agree that there are numerous books published by individuals who claim they have solved the problems of physics which qualified scientists have not been able to do up to now. The latest one that I am aware of is "The Final Theory". It usually does not take long to determine the wrong premises that have led such an author astray. In the latter book it is clear that the author became stuck in the time before Galileo. He does not understand the role that relativity (Galilean and Einsteinian) plays when analysing dynamical systems. It is a pity that such books are published. They muddy the water so that people ignore other books which are truly adding to our knowledge. You should at least have been opnminded enough to read the prologue to the book on "superconduction without Cooper pairs". The reason why the author was forced to publish a book is explained in detail. The book is at present being reviewed by competent scientists and these reviews (posistive or negative) will be posted on that website as they become available. There are already some reviews. The author of that book also challenges the whole scientific community to prove him wrong (in writing). Furthermore on the website it is clearly argued why the BCS theory is not a theory at all, and what the actual mechanism for superconduction must be. So I challenge you to read that and point out the flaws.
Pasti: 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.
Consider a four-dimensional Euclidean space with coordinates x(1), x(2), x(3) and x(4). these coordinates are lineraly independent so that
dx(i)/dx(j)=0 for all i not equal to j. Thus if the fourth axis relates to time in any way nothing can change within three-dimensional space defined by the first three coordinates. What I speculated on is that this might be why space-time must be curved; i.e. neither special relativity or general relativity can be described by an Euclidean metric. I further speculated that a Euclidean space-time might thus be considered as "nothing" because if it exists nothing can change with time within the three space coordinates. I just thought it might be an interesting idea, and did not expect that I will be sent back to relearn calculus!
Pasti: 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.
No you misunderstood: you first measure p1, then the position x1 and then p2 using perfect measurements. Now Shroedinger's equation is a statement of the conservation of energy. Thus if you start of with a momentum p1, then measure x1, and then p2, one must have that p1=p2 or else you violate the conservation of energy. After all there was no potential energy term involved. Furthermore it is a perfect measurement which, owing to its perfectness does not inject energy when making the measurement. Thus if p1 and p1 are different where did the energy come from or go to? I hope I have expressed myself more cogently.
Pasti: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.
The mistake that Born and Heisenberg made was to equate the wave-function in k-space as relating to de Broglie's wavelength and thus to the momentum of the electron. Now accept for arguments sake that you can model a single stationary electron in space by a localised time-independent field that does not spread with time and that you are within the same inertial framework in which the electron is stationary. The localised field lives in position space as well as in k-space. How do you measure the De Broglie wavelength of the electron? You cannot, because the De Broglie wavelength is a relativistic paramter. You will measure different values for it when you move at different velocities relative to the time-independent stationary field representing the electron. Thus the De Broglie momentum-wavelength relationship has nothing to do with the uncertainty in k-space. The uncertainties in position an k are determined, as for any other wave, by the boundary conditions. It is for this reason that an electron can spread out and go through both slits when it encounters the boundary conditions set by the slits. It is also for this reason why it can again become a localised wave when it encounters the boundary conditions set by the detector. You will now probably ask what the boundary conditions are which localises the electron wave in "free space". This relates to the mass of the electron. There is not enough space to treat it further in this forum. I hope that my discussion above might now convince you. Thanks for your responses it helped me to think more clearly.
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