Simulating Space, Time, and Probabilities

Michail A. Zak

Bryan Sircely

We extend the probability-time framework—defined as the information-geometric arc-length of irreversible trajectories in state space— to a two-qubit open-system setting and sharpen its interpretation using a cross-metric amplitude-damping simulation. Probability-time is defined as the accumulated information-geometric arc-length of the irreversible component of a trajectory in density-operator space. For a Bell-state initial condition evolved under local dephasing and local amplitude damping, the dephasing case shows approximate collapse of concurrence curves when expressed against probability-time, whereas amplitude damping does not. The latest simulation further shows that, for the same two-qubit amplitude-damping trajectory, both the Bures--Helstrom and Kubo--Mori constructions produce monotone probability-time while yielding different numerical parameterizations. This supports a more precise claim: the metric-independent content of probability-time is the induced irreversible ordering, while the numerical parameterization remains metric-dependent.

Simon W. Saunders

Huber Nieto–Chaupis

A theory consisting in quantum mechanics and theorem of Bayes, is presented. In essence, the Bayes probability has been built from two subspaces. While in one some quantum measurements are done, in the another it is seen that the probabilities acquire their highest values. Thus, the validity of a prior probability makes sense is there is a clear difference between the done measurement of probability amplitude. Thus, the principles of machine learning compacted in the criteria of Tom Mitchell have been employed. The simulations have shown that the size of space has direct impact on the prior probability that presumably would get low values of probability in a limited subspace. These values have turned out to be strongly correlated to the times in which measurements are done in a big space. Therefore, it is evident the prospective applicability of this novel approach in all those scenarios that require of a quantum measurement in separated times.

Antony J. Bourdillon

A carrier wave in a 5-dimensional wave group is examined for information on electromagnetic waves and on particle probability amplitudes. Simulations by Maxwell’s equations show that the phase and group velocities in electromagnetic waves are equal, both in vacuo and in dielectric media. By contrast, particle probability amplitudes in wave packet motion are more complicated. A dependence of rest mass on relative phase and group velocities is derived by consistency. Occurrences that are simultaneous and connected on wave fronts in the rest frame, appear separated when observed in moving frames. Uncertainties in space and time are linked by the probability amplitude wave group.

Ilya Prigogine