Not doing this as a direct reply dialog as this does not overcome a bar of preponderance of being more guiding than misguiding. By writing somebody with buy in can come mitigate the what-woudl-have-been-misguidings.
Like, very roughly speaking, when you start trying to make quantum mechanics play nice with relativity, the laws of physics glance at the idea that you might need to specify an origin point, scoff, and then ask you to to also specify a continuous function from spacetime to the unit circle. As a warm-up. (It’s the U(1) part of the SU(3) × SU(2) × U(1) symmetry, if I understand correctly.)
Corresponding idea would be to map each point in U(1) to a spacetime
You don’t need QFT here, gauge invariance is a thing for quantum Newtonian charged particles moving in a background electromagnetic field. The gauge group consists of (sufficiently regular) functions g:R3→U(1). The transformation law of the n-particle wavefunction is:
ψ′(x1…xn)=n∏i=1g(xi)qiψ(x1…xn)
Here, qi is the electric charge of the i-th particle, in units of positron charge.
This stuff is designed for multple electrons in spatially different places. The extension would be to say that you have a superposition of where a single electron could be and each of the “possibility slices” gets to act out the role of a separate electron. So for discrete cases (such as slit right and slit left) not being able to do a continuum is not that big of a problem. Mathematically it could be educational how to differentiate two electrons being simultaneously present vs one electron being in a superposition of both of the locations. My brain can’t intuit that thing and my hand is too shaky to have reliable symbolic answer for that.
In quantum computing the complex phases do not seem especially photonic. Photons are bends in the U(1) that correspond to electromagnetism. The “convergence forces” being relied would probably take on a similar form because they are based in the same things. This kind of “possibleton” would have the aspect of travelling from one possibility to another. Wait, does that mean that electron in superposition in two locations would electronmagnetically interact with the other position (I do not think this is how it goes in vanilla theory)? How does “self-energy” factor into this?
There is such a theory of “dark photons” but they add an additional U(1) to do the dark things in. It was motivate to explain gravitational effects which sources would not be seen.
Not doing this as a direct reply dialog as this does not overcome a bar of preponderance of being more guiding than misguiding. By writing somebody with buy in can come mitigate the what-woudl-have-been-misguidings.
Building up things in my mind as reading other content
Corresponding idea would be to map each point in U(1) to a spacetime
comment there
ψ′(x1…xn)=n∏i=1g(xi)qiψ(x1…xn)This stuff is designed for multple electrons in spatially different places. The extension would be to say that you have a superposition of where a single electron could be and each of the “possibility slices” gets to act out the role of a separate electron. So for discrete cases (such as slit right and slit left) not being able to do a continuum is not that big of a problem. Mathematically it could be educational how to differentiate two electrons being simultaneously present vs one electron being in a superposition of both of the locations. My brain can’t intuit that thing and my hand is too shaky to have reliable symbolic answer for that.
In quantum computing the complex phases do not seem especially photonic. Photons are bends in the U(1) that correspond to electromagnetism. The “convergence forces” being relied would probably take on a similar form because they are based in the same things. This kind of “possibleton” would have the aspect of travelling from one possibility to another. Wait, does that mean that electron in superposition in two locations would electronmagnetically interact with the other position (I do not think this is how it goes in vanilla theory)? How does “self-energy” factor into this?
There is such a theory of “dark photons” but they add an additional U(1) to do the dark things in. It was motivate to explain gravitational effects which sources would not be seen.