Digital Quantum Reality

In our quest for a local and realistic model of quantum mechanics, we have discussed spin in recent posts. We introduce now an additional quantity and mechanism, which will play a fundamental role in spin entanglement. In my earlier 2020 arXiv paper , this "spin-flip mechanism" has been introduced and described as reproduced below. The following figure help explaining the spin-flip probabilities mentioned above. Remember that spin is defined as where s 0 is the source spin and M is the spin propensity. As shown in the figure 1d above, jumps of spin propensity occurring across an external reset cannot induce spin flips. Therefore, there is no spin-flip energy associated to an ER.  How is this spin-flip energy manifested? Naturally, into momentum. This momentum transfer can be described as   where V denotes here the momentum propensity. We can also represent this transfer as a " force ". Indeed, for small values of spin-flip energy, we...

In our quest for a local and realistic description of quantum mechanics we have developed a full concrete model incorporating many aspects of quantum behavior (quantization, uncertainty principle, wave-particle duality, Born rule, momentum entanglement, etc.), which we have been presenting in previous posts. However, a further class of genuine quantum processes requires a description of an additional particle property, which is intrinsic  spin . I have recently added spin in my model, as reported in my most recent ArXiv publication . With this post, we are going to discuss how spin can emerge from a more fundamental local-realistic mechanism. In addition to source momentum, particles have an intrinsic property that is a rational number comprised between -1 and +1, which we shall call " source spin " and denote as s 0 . In addition to momentum polarization , they also have another vector quantity, that is, three rational numbers {μ 0d } such that We shall call th...

Keeping on our quest for a local-realistic model for quantum mechanics (QM), we have recently discussed a set of rules for motion in three dimensions that yields the correct probability density functions as those predicted by QM. These rules include both quantum and external forces. We shall now discuss how potential barriers  (that have been introduced  here  for 1D motion) are described in the proposed model. Potential barriers are represented as sets of nodes where external bosons reside (when they are captured, they immediately reform) whose momentum is a function of the particle's momentum propensity V. Each of these nodes is characterized by a parameter a = {a d }, such that Each time a particle hits the barrier, it gains an external-boson momentum The meaning of the a's is now clear: they act like direction cosines of the normal vector to the barrier. For instance, for a 1D potential barrier, like those discussed in a previous post , we...

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...

In standard Quantum Mechanics, wave packets  (where the represented variable is a probability amplitude) are an essential tool to describe particles in many scenarios. In the local-realistic model that we present in this blog, we have discussed in earlier posts how to describe ensembles of particles emitted from a discrete set of posssible sources. Particles emitted from different sources will generally have a different span when they reach the same lattice node at the same lifetime, which results in quantum forces . Yet another piece of iformation is missing so far, to describe phase that plays such a big role, notably, in wave packets. The model assumes that, at sources, particles are attributed a further quantity, denoted as phase source ε, that is generally a rational number, together with the momentum propensity v 0 . We will see in a future post that the list of source-attributed quantites is not over! The phase source plays a role in the boson dynamics. In parti...

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...

After having described in the previous posts the motion of an ensemble of particles emitted at the same, perfectly localized in space, source, it is time to turn our attention to the emergence of quantum forces , which ultimately leads to the description of phenomena such as quantum superposition and the related interference. In this post, we shall discuss about the famous double-slit experiment and see how it is treated in the proposed model . In future posts, we will generalize the concepts introduced here. Consider a simplified, 1D version of a double-slit apparatus. where similar particles are emitted at a certain rate from either of two sources placed at positions x 0 = ±δ. Emitted particles have a constant speed along the perpendicular y direction, but a random initial speed along the x direction. At a certain distance from the sources along the y axis, a backstop is placed and particle arrivals are detected. Given the constancy of the y -axis velocity, will assume th...

In this blog I am presenting a local and realistic model that simulates ensembles of similarly-prepared particles evolving on a discrete spacetime, with the aim of retrieving the results of Quantum Mechanics. With the basic rules of motion described in this post  and the source preparation in terms of momentum described  in this post , we can already simulate an ensemble of particles for a very basic scenario. We assume that there are no external forces (including potential barriers), nor " quantum forces " acting. What the latter condition means, will be clarified in future posts. For the moment, it might be regarded as the scenario where there is only one location (one lattice node) possible as the source of the emitted particles. In this scenario, a simple pseudocode implementing the 1D model can be written as follows: %%% Simulate an ensemble of Np particles for i = 1 to Np    %%% Attribute a random source momentum    v0 = rand[-1,1] ...

In an earlier post , we have seen that two of the building blocks of a local and realistic model of Quantum Mechanics are the assumption of a discrete spacetime (the size of Compton wavelenght) and a three-valued momentum as a random variable, whose probability distribution is completely determined by its expected value, or momentum propensity . At a given iteration, quantum propensity V is the sum of two contributions, where v Q is the momentum contribution of quantum forces, and v F that of standard, "external" forces. Quantum momentum The quantum momentum is a quantity carried by the particle, which is first assigned at a certain value during the particle's preparation and may subsequently vary as a function of quantum forces. When a particle is prepared at a source,  v Q  is initialized to a value that we denote as  v 0  , the  source momentum . This quantity is itself a random variable: it can take rational values and is uniformly distribu...