Paradigm

• Particles move through space-time via the discrete Bernoulli Process, stepping to the left or the right at the speed of light w/ probability.

\begin{align}\beta = \frac{v/c + 1}{2} \notag\end{align}

• Consideration of the variance (on equal footing as the mean) of the space-time location of a particle yields new physics.

• The particle will step at the speed of light in all 3 + 1 orthogonal dimensions in the direction determined by binary random events.

• Like zitterbewegung where the particle moves back and forth a distance dx every dt time step.

• Only after a large number of steps will the Weak Law of Large Number kick in and the location and velocity will approach its average.

• Any investor knows that risk (variance) is just as important as return (mean).

• Application of measuring the mean in units of the standard deviation (which we use in the simple derivation) is known in finance as the Sharp Ratio.

• Consideration of variance in location of a particle moving via the discrete Bernoulli Process shows a unique reference frame where the jitter is minimized, which is a contradiction to the assumptions of special relativity.

• Our experiment was able to measure this unique reference frame.

• The theories of SR and quantum mechanics are so accurate in their respective spheres that we may comfortably assume a more general theory must match the predictions of these theories in their respective domains of application.

• By exploring the consequences of matching the mean of the Bernoulli Process to SR, we are led to an addition source of variance in both proper time and spatial dimensions, described explicitly by the Bernoulli process, that we classify as diffusive noise.