Conservation of Twist Energy

 I worked for a while with the 1/r^2 – 1/r^3 solution set and quickly discovered that this is just a lucky subset of the twist field solutions–every solved solution is unstable.  I can’t even find the solution that works in the ring case that appears stable, although I quit working on this because I realized that the twist field would yield a lot of cases that dont go into the 1/r^2 – 1/r^3 subset of solutions.

So, I went back to the generalized twist field, and  realized I had set up my simulations wrong.  The twist, as explained in a much earlier post (“Turning Bicycle Wheel”), has to be in-line with the direction of travel in order for the circular polarization degree of freedom of a photon to exist.  But even so, simulations show that the width, and hence the energy of the photon, has to be conserved but is not if the twist is not moving at the speed of light.  Even when moving at the speed of light, it was not clear why the width would be constant–but it has to be, else conservation of energy wont happen.  How can I make a simulation which observes both the quantization and conservation of energy of the twists in the vector field?

I thought for a while about this, and attempted to draw a Minkowski diagram (3D + T) representation of the twist.

Picture of field twist in Minkowski spacetime

This got really interesting really fast.  After a few mis-draws (my mind isn’t very well wired to view things in 4D), I realized that in Minkowski space, there is no twisting of the photon along the light cone path–in fact, in the one case of a twist moving at speed c, there is no acceleration at all–no forces needed to explain the twist structure!  Each light cone path has a twist angle that does not change over time, thus showing how twist width is conserved and thus how a photon holds its energy quantum without dissipation.  It’s hard to see, but I attempted a diagram–note that along the red light-cone paths, there is no change of the field angle.  A narrowing of the twist width either timewise or space wise would require a merging or deviation of angle paths not possible without some force source.

This should provide a basis for how to simulate the twists in a way that conserves energy.

Agemoz

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