A positive measure is a real number greater than equal to 0. You're asking if I agree that a function space L^∞ "of a positive measure" (i.e., a non-negative number) is a C*-algebra?
There is no "the algebra of operators on a Hilbert space". There are infinitely many possible algebras. The...
Excellent! Great point at which you can start your proof. Because those of us who actually use this mathematics and need to understand it and apply it here would use spectral theory to obtain PVMs from an operator. You're the only "genius" who somehow thinks that we need an algebra of...
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How about observables? This is, after all, where commutativity comes into play. In the standard formulation of QM, observables are what give us a connection between theory and experimental outcomes. They are akin to “random variables” and encode information about the...
You do, actually. This is fairly basic. Keep in mind that non-commuting operators are just the composition of maps. While you don't know much about the mathematics compared to what you regurgitate, you must have taken algebra or something.
But for the benefit of others, whom I don't want misled...
No, it isn't. It is clearly not. This is absolutely basic. But you know NOTHING about measure theory and nothing about QM. You just regurgitate stuff you clearly don't understand. Hence, again, this:
I gave you weeks. You're supposed to be an expert in measure theory. I guess that means you're...
If you are an expert in measure theory, then things become rather simple. You claim:
Prove it.
And let me be crystal clear, because you can clearly obfuscate and backtrack quite easily, as you already have. I don't want to see a bait and switch proof where you copy and paste steps from some...
They aren't. Because if instead of you doing an experiment in a box, that can and may later conflict with my result that has you entagled with the system your are experimenting with, you are in a lab with a vial of poison that is triggered by atomic decay, then I describe you as in a state of...
As I already explained, the non-commutativity of operators was von Neumann's attempt to formulate an empirical result that wove together existing quantum theory into one framework that even he became dissatisfied with.
Also, for somebody who has asserted the failure of measure theory in spaces...
Which brings us to your fundamental misunderstanding of Bell's inequality, Bell's theorem, and most of the rest of the nonsense you've stated about QM and probability theory.
I'm going to really dumb this down (not because I think you aren't capable of understanding, but because I honestly...
No, you are clearly capable of using words you don't understand. You are capable of such fundamental misunderstanding of basic, beginning graduate level mathematics that I seriously question whether you can do more than produce generic statements I've seen students quote mine from wikipedia and...
I don't believe you. This is really basic stuff, and you keep getting it wrong. Over and over again.
The bolded part is all that matters here. Yes, they are not usually regarded as function spaces, but likewise 2x2 complex matrices (all one needs for violations of Bell's theorems and a slew of...
FYI- In addition to misrepresenting the use of C*-algebras in QM and operator algebras more generally, you've confused and conflated to different approaches with different definitions of states that actually matter. So your "norm 1" is true, for example, in the standard case but doesn't make...
Are you aware that this is considered one of the most radical interpretations of QM? It is far beyond the sort of indeterminacy or instrumentalism even attributed to Bohr and Heisenberg (mostly incorrectly) let alone relational QM, Healey's pragmatism, operationalist QM, the statistical...
In the sense that, technically, anything involving integration or even summation trivially must. However, QM depends on measure theory. Anything with integrals does. Quantum measure theory is still measure theory. Non-commutative measure theory (basically the same thing) is measure theory. POVMs...
No kidding. You can stop back-peddling. The problem claim is not that measure theory isn't relevant, it is your claim that:
This is patently false, absurd nonsense. You have confused an application of measure theory, or a use of measure theory, with what you claim measure theory to be, an...
You're the one equating function spaces with L2 spaces, not me. A vector space is a function spaces- trivially, in exactly the same way any of your claims about non-commutative operator algebras being relevant would have to mean you are including trivial cases where the operators are matrices...
What would a possible contradiction be when you allow for anti-realism to hold and don't bother with how quantum theory predicts anything? Indeed, how are you allowing for a contradiction to be possible regardless of realism when you haven't discussed how quantum theory can yield outcomes using...
It is not, in general, at all easy to determine whether or not an experimental result is in contradiction with quantum theory. This is for several (not necessarily distinct) reasons:
1) Quantum mechanics makes no predictions. By this I do not mean that either QM or quantum theory more generally...
You also said that a Hilbert space, which is actually essentially a function space (it's perhaps the prime example of one), need not be what it is (namely, a function space).
Meanwhile, your description of operator theory made no mention of measures, measurable spaces, sigma-algebras, or...
Completely false. That's like saying integrals are, essentially, the limit of rectangles under a curve or that vector spaces are, essentially, triples of real numbers. You've listed an example of measures that isn't even particularly relevant for many (if not most) of the relevant uses. Measures...