all references now in place

Author: rcoreilly

citedrefs.json

@@ -8,7 +8,7 @@ However, in the pilot-wave framework, the positions of the particles (and _only_
 
 For example, [[@^Norsen14]] analyzed a pilot-wave model of _spin_, and showed very clearly that it is contextual in nature. There are no predefined, definite spin values for any particles (indeed this is mathematically impossible as discussed in a moment), and the interaction with a spin-detecting Stern-Gerlach magnetic field apparatus is responsible for _creating_ a definite spin value along a given axis, where none existed previously. The same logic applies to the momentum and energy of the particles, which also depend on the wave function, as elaborated in [[@^Norsen17]].
 
-Is there something fundamental within quantum theory that promotes position variables to this privileged status that they have in the pilot-wave framework?  In general, the answer appears to be "no", although there is ongoing philosophical debate on this topic ([[@Schoeren22]]; [[@Wallace20]]; [[@North12]]; [[@NeyAlbert13]]). In the standard matrix mechanics approaches, the quantum state is chosen to be whatever is most convenient, and this could be a momentum basis instead of position, for example. However, if it turns out that the position variables somehow do provide a uniquely useful basis for "real" variables, as in the pilot-wave model, that would be an intriguing result.
+Is there something fundamental within quantum theory that promotes position variables to this privileged status that they have in the pilot-wave framework?  In general, the answer appears to be "no", although there is ongoing philosophical debate on this topic ([[@Schroeren22]]; [[@Wallace20]]; [[@North12]]; [[@NeyAlbert13]]). In the standard matrix mechanics approaches, the quantum state is chosen to be whatever is most convenient, and this could be a momentum basis instead of position, for example. However, if it turns out that the position variables somehow do provide a uniquely useful basis for "real" variables, as in the pilot-wave model, that would be an intriguing result.
 
 There is a further quantum property that is critical to appreciate in the context of contextuality, which is whether different quantum variables _commute_ with each other or not. Mathematically, two variables $A$ and $B$ commute if their order of application (multiplication) doesn't affect the result:
 

content/contextual.md

@@ -6,7 +6,7 @@ By far the most widely-used calculational framework in standard QM is the algebr
 
 This state vector evolves under _unitary_ transformations (rotations in the complex vector space), which preserve the overall magnitudes of the vectors, even as they rotate around in the space. The unitary nature of the rotation transformations represents the behavior of the system when it is being governed by the [[Schrodinger]] wave dynamics under the Copenhagen dualistic framework, which perfectly preserves the overall underlying probability space as long as nobody "looks at it the wrong way" (i.e., makes a measurement). Then, at the end, a "measurement" is made by collapsing the probability space down to a single discrete outcome (i.e., along an eigenvector of the resulting state). 
 
-This matrix formalism is equivalent to a self-consistent form of probability theory, which can be derived from abstract axioms having nothing to do with quantum physics ([[@Gleason57]]; [[@Jaynes90]]; [[@CavesFuchsSchack02]]; [[@FuchsMerminSchack14]]; [[@Mermin18]]). Indeed, this framework is so general that its only real physical commitment is that quantum physics obeys strict conservation laws: if you start with X amount of spin distributed however uncertainly across some state variables, then you have to end up with the same total uncertainty in spin distribution at the end, prior to the final measurement step, when everything collapses. 
+This matrix formalism is equivalent to a self-consistent form of probability theory, which can be derived from abstract axioms having nothing to do with quantum physics ([[@Gleason75]]; [[@Jaynes90]]; [[@CavesFuchsSchack02]]; [[@FuchsMerminSchack14]]; [[@Mermin18]]). Indeed, this framework is so general that its only real physical commitment is that quantum physics obeys strict conservation laws: if you start with X amount of spin distributed however uncertainly across some state variables, then you have to end up with the same total uncertainty in spin distribution at the end, prior to the final measurement step, when everything collapses. 
 
 Thus, the claim that standard QM is such a successful framework must be understood within this context: yes, it is accurate in capturing this basic fact of conservation, but it really isn't going very far out on a limb here: nothing wagered, nothing lost; but also perhaps not so much gained.
 

content/hilbert-space.md

@@ -36,7 +36,7 @@ In effect, the electron's wave field acts like a kind of antenna that senses and
 
 One approach is to implement a wave-particle model through coupled [[Dirac]] wave functions for the electron and [[Maxwell]]'s equations for EM, with the Dirac wave providing the guiding [[pilot-wave]] for a discrete electron particle localized within a cubic lattice grid.
 
-The waves in this model are all implemented using the same cubic lattice grid that the discrete electron particles live on, where local neighborhood interactions among the lattice cells implement a highly spatially symmetric form of the _Laplacian_ spatial gradient function at the core of the wave function. In short, the entire model is essentially an elaborate form of [[cellular automaton]] (CA), which has many appealing properties as the simplest-possible framework for a physical system, as advocated by a number of theorists over the years (John Von Neumann; Stanislaw Ulam; [[@Zuse69]]; [[@FredkinToffoli82]]; [[@Fredkin90]]; [[@tHooft05]]; [[@tHooft15]]; [[@Wolfram97]]).
+The waves in this model are all implemented using the same cubic lattice grid that the discrete electron particles live on, where local neighborhood interactions among the lattice cells implement a highly spatially symmetric form of the _Laplacian_ spatial gradient function at the core of the wave function. In short, the entire model is essentially an elaborate form of [[cellular automaton]] (CA), which has many appealing properties as the simplest-possible framework for a physical system, as advocated by a number of theorists over the years (John Von Neumann; Stanislaw Ulam; [[@Zuse69]]; [[@FredkinToffoli82]]; [[@Fredkin90]]; [[@tHooft05]]; [[@tHooft16]]; [[@Wolfram97]]).
 
 ## Quantum non-locality and standard interpretations
 

content/home.md

@@ -4,7 +4,7 @@ bibfile = "mechphys.json"
 
 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 [[QED|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 ([[@AspectDalibardRoger82]]; [[@AspectGrangierRoger82]]; [[@TittelEtAl98]]). Furthermore, in many cases they make good physical sense, in reflecting the strict conservation of some property such as spin.
+We have also seen that standard QM calculational tools including [[configuration space]], [[Hilbert space]] matrix mechanics state vectors, and Fourier space [[QED|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 ([[@AspectDalibardRoger82]]; [[@AspectGrangierRoger82]]; [[@TittelBrendelGisinEtAl98]]). 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.