lots of possible ideas about spin, weak force, neutrinos etc in mediating the "internal" state of something like the electron. very interesting.

Author: rcoreilly

content/configuration-space.md

@@ -4,12 +4,12 @@ bibfile = "mechphys.json"
 
 **Configuration space** is a critical but perhaps generally underappreciated element of standard quantum mechanics, in most of its various formulations (e.g., in the [[Hilbert space]] formulation). It is the space defined by the **multiparticle** configuration of all the elements of relevance to a given experimental setup being analyzed.
 
-Because it describes the _configuration_ of these elements, it is **exponential** in size, with a different space corresponding to each combination of such elements, and manifestly [[non-local]]. Thus, it is an entirely implausible, highly problematic element of standard quantum mechanical approaches.
+Because it describes the _configuration_ of these elements, it is **exponential** in size, with a different space corresponding to each combination of such elements, and manifestly [[non-local]]. Thus, it is an entirely implausible, highly problematic element of standard quantum mechanical approaches, including the existing [[pilot-wave]] models.
 
-The need for configuration space at a mathematically deep level arises because the equations being used are _linear_, so they cannot represent any kind of actual interaction among different particles. Without configuration space, every particle would fully superpose on every other particle --- they would just slip on past each other. This is in fact how _bosons_ (e.g., _photons_) behave, but not how _fermions_ like [[electrons]] behave.
+The need for configuration space at a mathematically deep level arises because the equations being used are _linear_, so they cannot represent any kind of actual interaction among different particles. Without configuration space, every particle would fully superpose on every other particle --- they would just slip on past each other. This is in fact how _bosons_ (e.g., [[photons]]) behave, but not how _fermions_ like [[electrons]] behave.
 
-The [[pilot-wave]] approach has been (perhaps unfairly) criticized for using configuration space, because it posits that the wave function is actually a "real" thing, thus exposing the implausibility of this otherwise purely [[tools vs models|calculational tool]]. See [[@NorsenMarianOriols15]] for an analysis of the contributions of configuration space to the pilot-wave results.
+The [[pilot-wave]] approach has been (perhaps unfairly) criticized for using configuration space, because it posits that the wave function is actually a "real" thing, thus exposing the implausibility of this otherwise purely [[tools vs models|calculational tool]]. See [[@NorsenMarianOriols15]] for an analysis of the contributions of configuration space to the pilot-wave results. They concluded that indeed the configuration space contains a large amount of "redundant" information, and that even the simplest approximation for the inter-particle interaction terms does a reasonable (yet imperfect) job of capturing the behavior of the full configuration-space model. Exploration of higher-order terms in this approximation are ongoing ([[@Norsen22]]).
 
-However, if the underlying dynamics of the system are _nonlinear_, and in particular involve interactions between [[stochastic particles]] and wave functions, then it is possible that these nonlinear interactions end up producing all of the relevant dynamics that are otherwise captured via the configuration space calculational tool. This is the approach taken here.
+If the underlying dynamics of the system are _nonlinear_, and in particular involve interactions between [[stochastic particles]] and wave functions, then it is possible that these nonlinear interactions end up producing all of the relevant dynamics that are otherwise captured via the configuration space calculational tool. This is the approach taken here.
 
 

content/epistemic-vs-ontic.md

@@ -18,17 +18,11 @@ The Heisenberg [[uncertainty principle]] dictates that there is a fundamental li
 
 The incorrect incorporation of epistemic uncertainty in the standard Schrodinger pilot-wave framework is also evident in the inevitable spreading out of the wave function over time. In the epistemic case, this spread represents a very sensible increase in uncertainty about where something might be located, given more time since the last time its position was known. But given that the pilot-wave model maintains exact locations of each particle over time, it really doesn't seem to make sense for the wave function to spread out in this manner, at least for variables associated with particle positions.
 
-In summary, this quote from E. T. Jaynes is particularly apropos here:
+In summary, this quote from E. T. Jaynes ([[@Jaynes90]]) particularly apropos here:
 
-> "But our present QM formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature --- all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that the unscrambling is a prerequisite for any further advance in basic physical theory. For, if we cannot separate the subjective and objective aspects of the formalism, we cannot know what we are talking about; it is just that simple." (Jaynes, 1990).
+> "But our present QM formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature --- all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that the unscrambling is a prerequisite for any further advance in basic physical theory. For, if we cannot separate the subjective and objective aspects of the formalism, we cannot know what we are talking about; it is just that simple."
 
 From this perspective, one could make the following reasonable claim about the pilot-wave approach: it provides a very powerful _demonstration in principle_ that QM is compatible with a "realistic" underlying world where particles always have definite positions. Nevertheless the specific formulation in terms of the Schrodinger wave function operating in [[configuration space]] is very likely conflating epistemic and ontic uncertainty, and a more realistic wave function that only reflects whatever "real" aspect of the wave function remains after the epistemic part is subtracted away should be used instead.
 
-Furthermore, we should do away with the configuration space, and see what kinds of actual inter-particle interactions lead to the observed behavior that is otherwise being captured in the configuration space framework.
-
-Fortunately, important progress along this latter line has been undertaken by Norsen and colleagues, where they have used only separate realistic 3D spatial dimensions for each particle's wave function, and computed the remaining inter-particle interaction terms directly instead of through configuration space ([[@NorsenMarianOriols15]]). They concluded that indeed the configuration space contains a large amount of "redundant" information, and that even the simplest approximation for the inter-particle interaction terms does a reasonable (yet imperfect) job of capturing the behavior of the full configuration-space model. Exploration of higher-order terms in this approximation are ongoing ([[@Norsen22]]), but perhaps a more direct physically-based approach is necessary?
-
-As for the use of more physically realistic wave functions, some work has been done deriving pilot-wave models for the relativistic Dirac equation ([[@DurrGoldsteinNorsenEtAl14]]), but I am not aware of a more directed approach at factoring out the epistemic contributions. In this context, the motivation for the current WELD approach is precisely to develop a fully physically-realistic pilot-wave model using the coupled Dirac / Maxwell equations to mediate all inter-particle interactions, and compare this with real experimental data and the predictions of existing more standard pilot-wave models.
-
-Also, a recent paper has attempted to disentangle the epistemic vs. ontic contributions to the wave function using a novel analytical technique, and concluded that different quantum behavior can be associated with each of these contributions ([[@BudiyonoRohrlich17]]). Predictably, they reject the pilot-wave approach because of its incorrect use of an epistemic uncertainty wave to guide real particle trajectories.
+A recent paper has attempted to disentangle the epistemic vs. ontic contributions to the wave function using a novel analytical technique, and concluded that different quantum behavior can be associated with each of these contributions ([[@BudiyonoRohrlich17]]). However, their approach assumes that the [[uncertainty principle]] is purely epistemic, which is inconsistent with its fundamental basis in the basic properties of [[waves]]. As usual, any analysis is only as good as its assumptions. As a consequence, they reject the pilot-wave approach because of its "incorrect" use of a _purely epistemic_ uncertainty wave (under their assumptions) to guide real particle trajectories.
 

content/non-locality.md

@@ -12,17 +12,19 @@ Thus, we are already necessarily in a "superluminal" space. For example, it seem
 
 ### 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 _contextuality_ as discussed earlier, 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.
+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 spatial separation that it would be impossible for any actual light-speed communication between the measuring devices.
+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.
 
-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. 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.
+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 ([[@BallentineJarrett87]]). 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" ([[@Bell64]]) 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. Furthermore, the pilot-wave framework unambiguously shows that entanglement phenomena directly require non-local interactions between the two particles ([[@Norsen14]]; [[@NorsenMarianOriols15]]).
+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]] ([[@Norsen11]]; [[@Maudlin11]]; [[@Shimony93]]). Furthermore, the pilot-wave framework unambiguously shows that entanglement phenomena directly require non-local interactions between the two particles ([[@Norsen14]]; [[@NorsenMarianOriols15]]).
 
-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.
+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.