Then why were you telling me about "Lorentzian structure" and "Wick rotation" in the context of QM?That doesn't follow. The argument for complex numbers in SR is in principle completely seperate from the argument for complex numbers in QM.
Auto-Didact said:More importantly, I see that you are focussing alot on #158; I would like to paraphrase Bohr by saying "Every sentence I utter must be understood not as an affirmation, but as a question."
Sorry for taking your post seriously.
Auto-Didact said:This thread is about complex numbers in QM in general; I think therefore that the arguments I give in other posts in favor of the fundamental place of complex numbers in QT cannot be dismissed so lightly.
I read your post #158 and commented on it. As far as I remember, I did not read your earlier posts, so I could not have dismissed them, neither lightly nor heavily. I don't think I have to read the entire long thread to post anything.
OK, I got it. I have a bad habit to read texts exactly as they are written. You have explained that your post #158 means something different from what is written there. I give up.Auto-Didact said:It is obvious to me that we have very opposing views of how we basically regard what a physical theory is; the difference between our views are what historically was called the applied mathematics view versus the pure mathematics view of physics.
The derivation of spin from first principles by Dirac is to me clearly a result of the mathematical existence of spinors, whether that is/was acknowledged or not by physicists at the time or even today. The existence of spin as a mathematical object can be demonstrated to be a consequence of the existence of spinors, with the gamma matrices operators which act on spinors. In this sense, gamma matrices are non-commuting elements of the Clifford algebra, giving spinors more degrees of freedom than scalar wavefunctions. This is what my post in #158 was alluding to.
In contrast, from what I understand from your point of view, it seems you would claim that spin is just a physical quantity following from any mathematical model capable of describing aspects of the physics, whether or not these descriptions can on the face of it immediately be shown (through trivial efforts/arguments) to be equivalent to some other purely mathematical model of spin we already have; indeed, such a pragmatic view is referred to as an applied mathematics view of physics.