Digital Quantum Reality

(Cover image from: A.G. Manning, R.I. Khakimov, R.G. Dall, and A.G. Truscott, "Wheeler’s delayed-choice gedanken experiment with a single atom", Nature Physics, vol. 11, July 2015, DOI: 10.1038/NPHYS3343) In previous posts, we have discussed several quantum mechanics scenarios (for example here , here , here , etc.) and seen how they are perfectly reproduced by our local-realistic model , both theoretically and numerically. In this post we shall describe a further test for our model, that is reproducing the non-classical behavior of interferometers. We shall consider in particular  atom interferometers , and leave those operating with photons to when we shall treat quantum electrodynamics. A rather general interferometer scheme, shown in the figure below, consists of: (i) a source S where a beam in a particular state is prepared, (b) a first splitting of the beam into two paths, BS1, with different momentum states and phases (iii) a recombination M of the two paths (...

In all previous posts we have considered a local-realistic model for quantum mechanics working in a one-dimensional scenario, where motion is only along dimension x. However, ordinary space is made of three dimensions, thus the lattice geometry should reflect this fact. The extension of the model to the 3D case is not completely trivial and will be described here. A first element has been already introduced in this post , where the source preparation and the attribution of a source momentum to particles have been described. The key notion is the limiting condition that we recall here as Simple equations of motion are trivially extended to three dimensions. Basically, in the absence of quantum forces, each dimension is independent from the others, except for the limiting condition above. Similarly, no special treatment is required for external forces, which are intended to work separately on each dimension. Motion rules in the presence of quantum forces introduce a few new q...

Although we have denoted as " quantum forces " the interactions between a particle and the previous instances in an ensemble (interactions mediated by the lattice ) that are ultimately rensponsible of quantum behavior, in the previous posts we have considered free particles that do not interact with the external world and are not subject to external "true" forces. However, the local-realistic model of quantum mechanics that we promote in this blog describes external forces as well. The principle is similar to that governing quantum forces: during their walk on the fundamental lattice, particles m ay capture external bosons , which mediate external forces, and incorporate their momentum. The event of encountering and capturing an external boson is denoted as " External Reset (ER)", in analogy to the Quantum Reset (QR) discussed in this post . Figure by Borb, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3816716 A force field is t...

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 evaluat...

In our quest for a local-realistic model for Quantum Mechanics, we have discussed in the last post how the lattice - that mediates locally the interactions between single instances of a same ensemble of particles - is progressively " trained " as subsequent particles are emitted. With the lattice already trained, the Matlab code discussed in this post can be strongly simplified as shown below. %%% Simulate an ensemble of Np particles emitted at intervals Nti  %%% from either of Ns distinct sources xs(1,...,Ns) having  %%% probability Ps(1,...,Ns).  Evaluate the frequency of arrivals at %%% a 'screen' after Nt  iterations. %%% %%% Parameters: Np,Ns,Nt,Nti,xs,Ps. %%% %%% Evaluate the number of possible bosons for this scenario. B = Ns*(Ns-1)/2; %%% Evaluate a priori the probability of each Quantum Reset iB = 0; for i = 1:Ns-1     for j = i+1:Ns         iB = iB+1;         Pb(iB) = 2*Ps(i)*Ps(j); ...

In this blog I am presenting a new model for Quantum Mechanics based on local-realistic rules for ensemble of particles. A first version of the model has been published in this journal ; an extended version in this preprint . In a previous post , I have shown that the direct simulation of the rules of motion, even for a relatively simple quantum scenario such as a two-slit experiment, can take an unpractically long computing time. In fact, the dynamics of the lattice and particle bosons involved may take a large number of iterations before they converge to the values from which the stanbdard QM behavior emerges. This post discusses a first method to accelerate the simulations . This method consists in assuming that all lattice boson momenta have already converged to their steady-state values. This normally happens only after a large number of particle emissions of the same ensemble has been simulated, so that many particles have visited each lattice node. Here we assume that th...

In a previous post , I have introduced the mechanism with which the proposed model treats the states superposition and ultimately represents intereference. The key roles are played by the footprints that a particle leaves on each lattice node visited, and the exchange of " bosons " between the particle and the footprints. These bosons possess a momentum, that is summed up to the particle-carried momentum to form the total momentum propensity (in the absence of external forces, which will be introduced in a future post). It is now time to describe in detail the rules concerning the formation and the evolution of such bosons. We have seen that each particle carries on a counter, called span , which sums up its position jumps since the emission. At a certain iteration, the span, ℓ, is thus equal to the distance covered so far, x - x 0 . The span is left as a footprint to the nodes visited. At a certain iteration, each node ( x,t ) thus possesses a trace λ xt . An exemple ...