Chance moves in mysterious ways.

That's not unique to QM. Any second order linear partial system has the same operation. Think of energy considerations.What do you mean by a "higher" norm? And what evidence do you have that other norms are physically trivial? That sounds confused.The linear operations on the space are derived using the Schrodinger equation. It doesn't. It says, apart from QM, there are other structurally rich systems that can be modelled in complex space. I have not said randomness doesn't exist. However, PaulK's abortive logic may have led to that conclusion somewhere.

Huh? What theory besides QM uses a 2-norm? How does it relate to energy? They are? How so? That certainly isn't what happened historically. The Schrodinger equation alone only gives unitary evolution. If you only had that, you'd think you were dealing with a standard physical PDE describing wave evolution. It's Born's 2-norm probability that then gives meanings to linear operators and their eigenvalues. It would make the post too turgid to go into. Any questions have their answer here:
http://www.scottaaronson.com/papers/island.pdf Yes, I understand that. Other things use complex numbers, why does it matter though? What are you saying? Fair enough. However if randomness has experimental tests such as the Aspect experiments which can directly falsify it then part of your original claim isn't true. The reason I'm bringing up this point about the mathematical structure in QM is because I'm trying to demonstrate that the random component has:
(a) Experimental support and the existence of experiments capable of falsifying it.
(b) We have found out properties of this randomness. Such as it having the 2-norm I describe above. This is a major insight. The existence of statistics other than the 1-norm humans had used up to then.This indicates that randomness is a feature of the world with properties scientists can study. This is a world away from

The length of a vector is a "2-norm". I'll leave the rest to you. The linear self adjoint Hamiltonian operator is derived from the time independent Schrodinger equation. That is where the eigenfunctions come from. He's basically saying, in very flowery language, that length is preserved under rotation. That's not special to the QM model. Ignore. It's an answer to an earlier question of yours, not a new point.I think it is getting circular. I believe you have mentioned a few mathematical terms without really understanding the mathematical detail. As we have each stated our perspective and are unlikely to reconcile them, I think we should leave interpretation to the insight of the reader.

Yes, and this reader has quickly come to the conclusion that you really know very little about QM, although perhaps a tad more than your cosmology. There are some gems above that will leave SG speachless Anyway, just a couple of points for both of you. It is quite possible that determinism will be restored in a deeper theory to QM, and this has been worked on for some time, both with decoherence and more recent work. Don't forget that all the Apsect experiments demonstrate is that there are no hidden CLASSICAL variables. It is all about statistics, and statistics do not in themselevs imply indeterminism.

What about the last part of my post about the existence of a falsification test for randomness, which you claim does not exist? The fact that it does exist is a direct refutation of your position. Obviously there exist cases where one gets the length of things with a binary operation. The point is, the fact that QM uses 2-norm probability is something new and interesting. It was never seen before in standard statistics and gives rise to new physical effects. This is an important point, because you calim that "randomness did it" is as good as "God did it", which obviously can't be the case unless "God did it" somehow implies which normed statistics you should use.Eigenfunctions of energy. That's one single operator. And it doesn't even mean anything until you have the square modulus (2-norm) Born rule. Sure why weren't Hilbert Spaces used before in physics? You cannot be serious. That's like saying "All relativity says is that different things see different stuff, big deal".

Okay, this makes me feel better. I will take it as a possibility when you say this to me, but when you are now saying this to Son Goku I know you're a nut.

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"The guilty one is not he who commits the sin, but the one who causes the darkness."
Clearly, he had his own strange way of judging things. I suspect that he acquired it from the Gospels. -- Victor Hugo

Um, how much of it did you actually understand?

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"The guilty one is not he who commits the sin, but the one who causes the darkness."
Clearly, he had his own strange way of judging things. I suspect that he acquired it from the Gospels. -- Victor Hugo

Yes, to be fair work on this stuff does exist. There could be a deeper deterministic theory underneath QM*. I'm trying to show that QM's randomness isn't scientifically worthless.Think of it as being like somebody defending Newton's action-at-distance theories two hundred years ago. Some people might claim that the action happening at a distance is like saying "God magically did it instantly". You'd defend it by describing everything it has done, perhaps unfairly ignoring the work of "propagation" theorists who could turn out to have the right answer.*As a side note do you know of a deterministic model which can replicate QFT. Every deterministic model I've ever seen only matches QM's predictions not QFTs. For example Bohmian Mechanics.

What would this "quite possible" restoration of determinism mean for the uncertainty principle? I take it that it could NO LONGER be a principle.