Training the particles
As shown in a recent post, the simulation of the local-realistic model that we are presenting in this blog can be accelerated by considering the lattice as being already trained after a large number of non-simulated instances (particle emissions) of the same "state" (ensemble of similarly-prepared particle emissions). In practice, lattice training means replacing the lattice boson momenta (LBM) with their steady-state values, instead of waiting the very long time that is necessary for convergence.
A similar "trick" can be used to further accelerate simulations, by considering also the particles as trained. Particle training is the process that leads particle boson momenta (PBM) to converge to their steady-state value during a particle 'flight'. This steady-state value can be evaluated from the rules of motion and the various source probabilities, as explained in my first publication:
As for the steady-state LBM, the barred ω, it has been evaluated in a previous post.
This analysis unveils the remarkable result that the sine functionality, which is so characteristic of the wave behavior of quantum mechannics, actually derives from the decay law of the PBM, which in turn can be expressed only with fractonal numbers.
We can observe particle training by analyzing the results of a simulation performed with this code for the double-slit scenario. Remember that this scenario implies the existence of only one type of particle bosons, that are created when particles emitted from source ('slit') 1 meet traces of particles emitted from source 2.
The figure below considers one particle out of the ensemble and compares the iteration-by-iteration value of the PBM (black dots), its running average (red), as well as the quasi-steady value predicted by equation (43) above. The convergence is clearly visible after a sufficiently large number of iterations.
A similar "trick" can be used to further accelerate simulations, by considering also the particles as trained. Particle training is the process that leads particle boson momenta (PBM) to converge to their steady-state value during a particle 'flight'. This steady-state value can be evaluated from the rules of motion and the various source probabilities, as explained in my first publication:
As for the steady-state LBM, the barred ω, it has been evaluated in a previous post.
This analysis unveils the remarkable result that the sine functionality, which is so characteristic of the wave behavior of quantum mechannics, actually derives from the decay law of the PBM, which in turn can be expressed only with fractonal numbers.
We can observe particle training by analyzing the results of a simulation performed with this code for the double-slit scenario. Remember that this scenario implies the existence of only one type of particle bosons, that are created when particles emitted from source ('slit') 1 meet traces of particles emitted from source 2.
The figure below considers one particle out of the ensemble and compares the iteration-by-iteration value of the PBM (black dots), its running average (red), as well as the quasi-steady value predicted by equation (43) above. The convergence is clearly visible after a sufficiently large number of iterations.
Comments
Post a Comment