There is a clear pattern in the examples from tools vs models of the plausible physical models vs. calculational tools. All of the physical models are based on local propagation of signals according to simple laws, whereas the calculational tools tend to employ non-local equations. This difference is directly tied to the fundamental tradeoffs at work: the calculational tools need non-locality to enable simple single-step calculations, whereas the physical models use local dynamics to enable iterative, autonomous calculations to work in the general case. Indeed, it is difficult to imagine how an autonomous model could be strongly non-local: the amount of computation and communication required per step would become prohibitive.
We have also seen that standard QM calculational tools including configuration space, Hilbert space matrix mechanics state vectors, and Fourier space quantum field theory are all fully non-local state representations, and thus cannot help but to produce non-local results. Again, this is analogous to using Newton’s gravitational law or the Coulomb equations for EM: it is baked right into the model. Nevertheless, there are strong empirical results suggesting that at least some of these non-local effects are real (Aspect et al., 1982; Aspect et al., 1982; Tittel et al., 1998). Furthermore, in many cases they make good physical sense, in reflecting the strict conservation of some property such as spin.
Thus, the challenge here is to try to better understand how the underlying physical processes of quantum wave field interactions, unfolding over time through strictly local propagation mechanisms, can end up producing non-local effects consistent with the empirical data. An important available degree of freedom here is that while the speed of light is strictly obeyed by the Maxwell wave equations, it is unclear if such a constraint actually applies to the quantum wave fields. Furthermore, our initial implementations of coupled Dirac — Maxwell equations in the CA framework demonstrate that a faster rate of updating, with smaller incremental update steps, is needed for numerical stability, relative to the simple CA one-cell-per-unit-time speed of light value.
Thus, we are already necessarily in a “superluminal” space. For example, it seems logical that if the quantum wave fields updated at twice the speed of light (in the EM field), then they would always be able to “keep in touch” with each other, even for particles moving apart at near light speed, and this could mediate observed non-local effects. Again, we need to be flexible here and explore whatever mechanisms might actually work to capture the established empirical data. In my estimation, requiring 2x light speed quantum wave function propagation is far more reasonable than the completely non-local interaction assumed by the standard QM calculational models.
Entanglement and non-locality
The phenomenology of quantum non-locality is fascinating and confusing, and provides some insights into the relevant physical properties of the quantum realm. The primary line of investigation traces back to a paper that Einstein wrote with Podolsky and Rosen in 1935, known as the EPR paper, about the strange implications of quantum entanglement. In the standard formalisms, entanglement occurs whenever the aggregate quantum state of a system is not a simple product of its constituents: i.e., there is some kind of interdependency between the elements. This is closely related to the issue of contextual effects, and is particularly clear in the case of quantum spin, which is represented by state variables that do not commute with each other, meaning that their states are irrevocably intertwined with each other, and it is impossible to simultaneously specify all of them.
Furthermore, there is a conservation law associated with spin, so that the total spin of a system must remain conserved over time. Thus, if a spin zero particle splits into two spin 1⁄2 particles, these two particles must maintain opposite spin states (+1⁄2 and -1⁄2) to conserve overall spin, and this represents a strong form of entanglement. Thus, if you were to measure the spin state of one particle, you should be able to predict that the other’s spin state is the opposite. The extra challenge here is that, because spin is necessarily contextual, the measurement process actually creates a specific spin state in a particle.
Therefore, logically, it seems as though the measurement process operating on one particle must somehow “inform” a measurement process operating on the other particle, so that it produces the opposite result. In practice, these two measurements could be (and have been) performed on particles moving away from each other at or close to the speed of light, with sufficient space-like separation that it would be impossible for any actual light-speed communication between the measuring devices.
However, there is a no-signaling proof, based on the standard QM formalism, that shows that it would be impossible for the measurement process in one location to actually communicate information to the other process (Ballentine & Jarrett, 1987). Specifically, if “Alice” is conducting measurements in one location on particle A, and “Bob” is doing the same on B, there is no way for Alice to send some kind of message to Bob. In other words, there is no way for Bob to know, just by looking at the outcomes of his own measurement device, what Alice is doing.
Intuitively, this makes sense because neither knows the initial state of the particles, nor the state of the other’s measuring device, so they just record a bunch of seemingly-random spin measurements that would be indistinguishable from any other such experiment. It is only when Alice and Bob get together later and compare their results, that they can then discover the presence of correlations in the outcomes of their different measurements. It is these correlations that the famous “Bell’s inequalities” (Bell, 1964) are based on, which form the basis for the various empirical tests of quantum non-locality. Critically, these correlations are “preordained” in the laws of QM, and thus do not represent an additional degree of freedom that could be used to send new information. That is all that the no-signaling proof shows.
The above argument serves to satisfy many people that somehow standard QM formalisms are not violating the speed-of-light constraints of special relativity. But this really does not square with the original intuition that somehow the two “measurement contexts” of Alice and Bob must be doing something physical to establish these correlations, especially given the strong constraint that spin measurements are necessarily contextual (Norsen, 2011; Maudlin, 2011; Shimony, 1993). Furthermore, the pilot-wave framework unambiguously shows that entanglement phenomena directly require non-local interactions between the two particles (Norsen, 2014; Norsen et al., 2015).
Specifically, by replacing the standard configuration space formalism with separate wave functions for each particle, Norsen and colleagues can isolate the direct particle-particle interactions necessary to replicate the predictions that are otherwise obtained by the full configuration-space model. When the quantum state is not at all entangled, then no such particle interactions are necessary. However, with any amount of entanglement, these interactions are necessary, and, especially in the case of spin, would require some kind of effective non-local communication to replicate the observed results.
Thus, consistent with the original concerns of Einstein and colleagues, it really does seem as though quantum physics requires “spooky action-at-a-distance” in a way that is incompatible with simple local speed-of-light dynamics. The no-signaling proof does not actually eliminate this problem. Most people, adopting the standard QM formalisms that are inherently non-local, are not particularly bothered by this, and have already swallowed the “red pill” of physical ignorance anyway.
However, in our current attempt to provide a complete physical picture of how the quantum world operates, we must somehow account for these results, within a CA-like framework employing only local interactions among cells. Therefore, it seems as though some kind of superluminal quantum wave dynamics are likely to be required. Furthermore, it is critical to appreciate that the only localized elements of the quantum state are the positions of the particles, and everything else (momentum, energy, spin) is directly tied up with the wave interactions between the Dirac and Maxwell fields, which are widely physically distributed over space, and continuously mutually interacting with the fields generated by other particles.
It does not seem implausible that the necessary quantum correlations could emerge from such a system, and by simulating and analyzing this system in detail, and exploring different rates of wave function updating and ways in which the quantum fields from different particles interact, we should be able to better understand the otherwise mysterious nature of quantum non-locality.