Set Theory

[astrotech]

Set theory provides foundations of mathematics in the sense that all the mathematical notions like numbers, functions, relations, structures are defined in the axiomatic set theory called ZFC. Quantum set theory naturally extends ZFC to quantum logic. Hence, we can expect that quantum set theory provides mathematics based on quantum logic. In this talk, I will show a useful application of quantum set theory to quantum mechanics based on the fact that the real numbers constructed in quantum set theory exactly corresponds to the quantum observables. The standard formulation of quantum mechanics answers the question as to in what state an observable A has the value in an interval I. However, the question is not answered as to in what state two observables A and B have the same value. The notion of equality between the values of observables will play many important roles in foundations of quantum mechanics. The notion of measurement of an observable relies on the condition that the observable to be measured and the meter after the measurement should have the same value. We can define the notion of quantum disturbance through the condition whether the values of the given observable before and after the process is the same. It is shown that all the observational propositions on a quantum system corresponds to some propositions in quantum set theory and the equality relation naturally provides the proposition that two observables have the same value. It has been broadly accepted that we cannot speak of the values of quantum observables without assuming a hidden variable theory. However, quantum set theory enables us to do so without assuming hidden variables but alternatively under the consist use of quantum logic, which is more or less considered as logic of the superposition principle.

Any thoughts?

[Samuel Nathan Richards]

I don't know that much about Set theory (well that in depth), but the general gist of it makes sense. Can you asume that the logic of the quantum can be directly proposed into the superposition principle? Are they not too dissimliar?
I had a look into the all of this, and it's still beyond what I know yet, so it goes on my list to look at when I go to Uni and have time to dulge around in this sort of stuff. I had a look at Quantum set theory, now that was a bit confusing...
I'm guessing you got this from somewhere, due to the fact that it states that it is a talk of some degree. Where is it from??

[astrotech]

I wrote this....and I was hoping you of all people would reply. Thanks Samuel. I am giving a talk at a local university an a weeks time. This is my subject matter.

[Samuel Nathan Richards]

Oh, WoW.... Well, you sure know your stuff. If you record it, or film it, send us a copy as I would like to hear the rest! Sounds great and would be useful for the future!