Noncausal solution, Lorentz Geometry, and trying a LaGrangian solution to deriving inertia

Happy New Year with wishes for peace and prosperity to all!

I had worked out the group wave concept for explaining non-causal quantum interactions, and realized how logical it seems–we are so used to thinking about the speed of light limit causing causal behavior that it makes the non-causal quantum interactions seem mysterious.  But when thinking of a universe that spontaneously developed from nothing, non-causal (infinite speed) interactions should be the default, what is weird is why particles and fields are restricted to the speed of light.  That’s why I came up with the group wave construct for entities–a Fourier composition of infinite speed waves explains instant quantum interference, but to get an entity such as a particle to move, there is a restriction on how fast the wave can change phase.  Where does that limitation come from?  Don’t know at this point, but with that limitation, the non-causal paradox is resolved.

Another unrelated realization occurred to me when I saw some derivation work that made the common unit setting of c to 1.  This is legal, and simplifies viewing derivations since relativistic interactions now do not have c carried around everywhere.  For example, beta in the Lorentz transforms now becomes Sqrt(1 – v^2) rather than Sqrt(1 – (v^2/c^2)).  As long as the units match, there’s no harm in doing this from a derivation standpoint, you’ll still get right answers–but I realized that doing so will hide the geometry of Lorentz transforms.  Any loop undergoing a relativistic transform to another frame of reference will transform by Sqrt(1 – (v^2/c^2)) by geometry, but a researcher would maybe miss this if they saw the transform as Sqrt(1 – v^2).   You can see the geometry if you assume an electron is a ring with orientation of the ring axis in the direction of travel.  The ring becomes a cylindrical spiral–unroll one cycle of the spiral and the pythagorean relation Sqrt(1 – v^2/c^2)) will appear.  I was able to show this is true for any orientation, and hand-waved my way to generalizing to any closed loop other than a ring.  The Lorentz transforms have a geometrical basis if (and that’s a big if that forms the basis of my unitary twist field theory) particles have a loop structure.

Then I started in on trying to derive general relativity.  Ha Ha, you are all laughing–hey, The Impossible Dream is my theme song!  But anyway, here’s what I am doing–if particles can be represented by loops, then there should be an explanation for the inertial behavior of such loops (totally ignoring the Higgs particle and the Standard Model for right now).  I see a way to derive the inertial behavior of a particle where a potential field has been applied.  A loop will have a path through the potential field that will get distorted.  The energy of the distortion will induce a corrective effect that is likely to be proportional to the momentum of the particle.  If  I can show this to be true, then I will have derived the inertial behavior of the particle from the main principle of the unitary twist field theory.

My first approach was to attempt a Lagrangian mechanics solution.  Lagrange’s equation takes the difference of the kinetic energy from the potential energy and creates a time and space dependent differential equation that can be solved for the time dependent motion of the particle.  It works for single body problems quickly and easily, but this is a multiple body problem with electrostatic and magnetic forces.  My limited computation skills rapidly showed an unworkable equation for solution.  Now I’m chewing on what simplifications could be done that would allow determining the acceleration of the particle from the applied potential.



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