This might be a good time for me to respond to one of your earlier comments.
I was under the impression that it’s a big mystery what complex numbers are doing (i.e., what is their physical function, what do they mean) in QM. I was under the impression that this is a matter of much speculative debate. Yet when I said that, I was downvoted a lot, and you implicitly alleged that I was obviously ignorant or misinformed in some way, and that we have a perfectly good understanding of what complex numbers are doing in the Dirac equation. Could you or someone please give me some background info, so that I can better understand the current state of understanding of the role of complex numbers in QM?
Note that complex numbers can be replaced with 2x2 real matrices, such as i=(0,-1;1,0), since multiplication by i is basically rotation by 90 degrees in the complex plane. Given that the Dirac equation is already full of matrices, does it make you feel better about it?
Could you or someone please give me some background info, so that I can better understand the current state of understanding of the role of complex numbers
I did (on the physical usefulness and non-mysteriousness of complex numbers, not quantum mechanics specifically).
And thanks for that, but I’m interested in their role in QM specifically. I don’t have an objection to complex numbers, I just want to know what they’re doing, if you see what I mean.
This might be a good time for me to respond to one of your earlier comments.
I was under the impression that it’s a big mystery what complex numbers are doing (i.e., what is their physical function, what do they mean) in QM. I was under the impression that this is a matter of much speculative debate. Yet when I said that, I was downvoted a lot, and you implicitly alleged that I was obviously ignorant or misinformed in some way, and that we have a perfectly good understanding of what complex numbers are doing in the Dirac equation. Could you or someone please give me some background info, so that I can better understand the current state of understanding of the role of complex numbers in QM?
Note that complex numbers can be replaced with 2x2 real matrices, such as i=(0,-1;1,0), since multiplication by i is basically rotation by 90 degrees in the complex plane. Given that the Dirac equation is already full of matrices, does it make you feel better about it?
Error
I did (on the physical usefulness and non-mysteriousness of complex numbers, not quantum mechanics specifically).
And thanks for that, but I’m interested in their role in QM specifically. I don’t have an objection to complex numbers, I just want to know what they’re doing, if you see what I mean.