Bismillah. Received from Sabbir Rahman:
I just came across this superb YouTube video which beautifully demonstrates Dirac’s ‘visual metaphor’ for the spin of the electron (note that being a spin-half particle, the electron has to rotate through 720 degrees before it returns to its original position):
Some of you may recall that in my own model, electrons are described as rapidly rotating (Kerr) black holes, the singularity of which, when ‘blown up’, has the topology of a “double torus” (where ‘torus’=surface of a doughnut). In particular, the electron is formed from the rotating gravitational collapse of neutrinos, which become trapped in bounded orbits wrapping around the toroidal singularity.
Now these orbits wrap around the torus once in each rotation, but the curious thing is that each time an orbit crosses the inside of the ring (which occurs once in each revolution), the direction of time for the neutrino flips sign (from the perspective of an external observer, that is – the neutrino itself would be blissfully unaware of this). Thus, after completing two orbits of the electron’s ring singularity, each bounded neutrino returns to its original position both in space _and_ time, having spent half of the time travelling forwards in time and half of the time travelling backwards in time!
If you watch from 1:13 minutes into the YouTube video, where the dancer is rotating a cube in her hand, you can see a very precise analogy of what this neutrino motion looks like – imagine that every time the dancer’s arm is above her elbow that time is passing in the forward direction, and every time her arm is below the elbow that time us passing in the negative direction. I would even recommend that you try doing this yourself, to get a good feel for how this works – and perhaps get an idea of why, if indeed elementary particles like electrons, quarks and neutrinos, are indeed topological objects, they must be spinorial. If they had integer spin, then spacetime would get into a horribly tangle mess every time once of these elementary particles rotated.
From 2:02 minutes into the video, you can see how this works – although the electron seems to tangle up space horifically after the first 360 degree rotation, it miraculously untangles space again after a further 360 degree rotation – both mind-boggling and beautiful, I hope you will agree!