stochastic particles cleaned up, integrated

Author: rcoreilly

citedrefs.json

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+bibfile = "mechphys.json"
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+**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.
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+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.
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+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.
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+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.
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+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.
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content/configuration-space.md

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-TODO: intro
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+bibfile = "mechphys.json"
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+<!--- TODO: intro, also [[@MallickChandrashekar16]] -->
 
 # Complex Klein-Gordon Waves: Charge!
 

content/dirac.md

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+bibfile = "mechphys.json"
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+The **electron** is the most basic version of a fermion (spin 1/2), and is the focus of the modeling work here. We attempt to model it using the principles of [[stochastic particles]], as it couples with the [[Maxwell]] EM field. 
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+There is a quote somewhere about how if one could just understand this one thing: the electron coupled to the EM feld, then one would understand all the essential mysteries of quantum physics.
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content/electron.md

@@ -20,7 +20,7 @@ In summary, this quote from E. T. Jaynes is 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).
 
-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.
+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.
 

content/epistemic-vs-ontic.md

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 bibfile = "mechphys.json"
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-By far the most widely-used calculational framework in standard QM is the algebraic **matrix mechanics** approach, pioneered by Heisbenberg, Dirac, Hilbert, von Neumann and others in the mid 1920s. It involves _state vector_ representations of the state of a system, encoded via complex-valued vectors representing _probability amplitudes_ (i.e., a **Hilbert space**). This state vector is a specific way of encoding the configuration space of the entire set of relevant variables, and is thus manifestly non-local, and represents the entire state a given point in time, in a way that is thus incompatible with the principles of relativity.
+By far the most widely-used calculational framework in standard QM is the algebraic **matrix mechanics** approach, pioneered by Heisbenberg, Dirac, Hilbert, von Neumann and others in the mid 1920s. It involves _state vector_ representations of the state of a system, encoded via complex-valued vectors representing _probability amplitudes_ (i.e., a **Hilbert space**). This state vector is a specific way of encoding the [[configuration space]] of the entire set of relevant variables, and is thus manifestly non-local, and represents the entire state a given point in time, in a way that is thus incompatible with the principles of relativity.
 
 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). 
 

content/hilbert-space.md

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 <img src="media/icon.png" style="width:128px;height:128px;align-self:center">
 
-This is a work-in-progress wiki-like collection of documentation in support of the development of a computational model of the phenomenology of quantum electrodynamics (QED), based on the coupled [[Dirac]]-[[Maxwell]] wave functions, along with discrete [[electron]] particles, consistent with the [[pilot-wave]] framework of Bohm and de Broglie. This computational model is based on the [[cellular-automaton]] framework, which is arguably the simplest way that physics could autonomously emerge in parallel, everywhere in the universe, all at once.
+Wave reality is dedicated to exploring the idea that the quantum wave function is _real_, and not just a description of our state of epistemological ignorance.
+
+Specifically, this is a work-in-progress wiki-like collection of documentation in support of the development of a computational model of the phenomenology of quantum electrodynamics ([[QED]]), based on the coupled [[Dirac]]-[[Maxwell]] wave functions, along with discrete [[electron]] [[stochastic-particles]], consistent with the [[pilot-wave]] framework of de Broglie and Bohm. This computational model is based on the [[cellular-automaton]] framework, which is arguably the simplest way that physics could autonomously emerge in parallel, everywhere in the universe, all at once.
 
 The primary goal of this project is to better understand the basic physics of electrons interacting with the electromagnetic field, and to try to sort through some of the notorious paradoxes and conceptual challenges that lie at the heart of quantum mechanics (QM). There is an easy-to-use GUI-based simulation software package (note: currently under development) that allows one to interactively explore various physics models, providing a concrete and hands-on level of understanding. This provides a different and potentially valuable set of tools for someone trying to learn more about how quantum physics actually works, which may result in quicker and deeper understanding than staring at equations :)
 
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 Furthermore, the [[Pauli exclusion principle]] prevents there from being two of the same _fermions_ (spin 1/2 particles like electrons and quarks) in the same quantum state, which in the pilot-wave framework means being in the same place at the same time with the same spin. This suggests from our computational, [[cellular-automaton]] perspective that there is some kind of underlying constraint like "slots" in a lattice for holding at most one of each type of particle. This is both a welcome simplification for our models of these particles, and a tantalizing suggestion that this computational perspective might provide some unique insights into the underlying nature of the physical world.
 
-This computational perspective also provides an interesting motivation for the need for waves. If you just have a simple discrete point-like particle sitting in some kind of lattice-like grid, it is very difficult to implement realistic force-field interactions among such particles, especially when using other discrete particles like "photons" to mediate these interactions. The purely particle picture of an electron constantly spewing baseball-like photons out in all directions to hit other electrons is very difficult to sustain. How does such a scheme ever achieve any kind of smooth field-like coverage of space using discrete point-like entities?  How many balls per femtosecond does it have to spew?  How do they manage to spread out uniformly over space and time, while properly conveying the dynamic interactions among the magnetic and electric aspects of the wave functions?
+This computational perspective also provides an interesting motivation for the need for waves. If you just have a simple discrete point-like particle sitting in some kind of lattice-like grid, it is very difficult to implement realistic force-field interactions among such particles, especially when using other discrete particles like "photons" to mediate these interactions. The purely particle picture of an electron constantly spewing baseball-like photons out in all directions to hit other electrons is very difficult to sustain. How does such a scheme ever achieve any kind of smooth field-like coverage of space using discrete point-like entities?  How many balls per femtosecond does it have to spew? How do they manage to spread out uniformly over space and time, while properly conveying the dynamic interactions among the magnetic and electric aspects of the wave functions?
 
-Instead, it is far more straightforward to use [[maxwell|EM]] wave equations to model the force field interactions among electrons. However, the ability of a discrete localized electron to "sense" such a force field as a distributed wave remains problematic: EM waves that influence electrons are widely distributed things, and small discrete samples at one point of a wave would not provide the proper net influence that the physical laws require. Thus, it works much better for the electron to also have its own wave field that is directly coupled with the EM wave field. In effect, the electron's wave field acts like a kind of antenna that senses and responds to the EM forces, and then conveys the results to shape the unfolding trajectory of the discrete particle through space and time, as captured in the pilot-wave model.
+Instead, it is far more straightforward to use [[maxwell|EM]] wave equations to model the force field interactions among electrons. However, the ability of a discrete localized electron to "sense" such a force field as a distributed wave remains problematic: EM waves that influence electrons are widely distributed things, and small discrete samples at one point of a wave would not provide the proper net influence that the physical laws require. Thus, it works much better for the electron to also have its own wave field that is directly coupled with the EM wave field. In effect, the electron's wave field acts like a kind of antenna that senses and responds to the EM forces, and then conveys the results to shape the unfolding trajectory of the discrete particle through space and time, as captured in the pilot-wave model. See [[stochastic particles]] for more details.
 
 We will ultimately implement this 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. We call this **Wave Electrodynamics** or **WELD**, which attempts to explain the same phenomena as _quantum electrodynamics_ ([[QED]]).
 
 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, including John Von Neumann, Stanislaw Ulam, [[@^Zuse69]], [[@^FredkinToffoli82]], [[@^Fredkin90]], [[@^tHooft05]] (2015); [[@Wolfram97]]).
 
 One of the primary challenges of this CA framework is reconciling the local interactions among neighboring cells, which so naturally produces a relativistic speed-of-light limit (one time step update per lattice cell), with the now irrefutable evidence for some kind of non-locality in quantum physics. Recent work within the pilot-wave framework has helped to significantly clarify the nature of these non-local interactions, and the broader conflict that they actually pose for all of QM, despite many attempts to downplay these issues from within the standard QM frameworks ([[@DurrGoldsteinNorsenEtAl14]]).
 
-Without having any definitive results at this point, the approach taken here is to push the current WELD framework along as far as possible, addressing the many significant outstanding problems, and use the resulting computational models to further understand the nature of these non-local interactions. Given that electron particles are strongly interacting with distributed wave functions in this framework, it is not inconceivable that the necessary non-local interactions may emerge from these distributed wave interactions in a way that remains compatible with observed data. For example, it is already clear that the time step needed for updating the wave function computations is actually at least twice the speed-of-light rate in a simple CA, raising the possibility of supra-luminal interactions at the lattice level, while still maintaining fully relativistic dynamics in the EM wave function propagation.
+Without having any definitive results at this point, the approach taken here is to push the current WELD framework along as far as possible, addressing the many significant outstanding problems, and use the resulting computational models to further understand the nature of these non-local interactions. Given that electron particles are strongly interacting with distributed wave functions in this framework, it is not inconceivable that the necessary non-local interactions may emerge from these distributed wave interactions in a way that remains compatible with observed data.
+
+For example, it is already clear that the time step needed for updating the wave function computations is actually at least twice the speed-of-light rate in a simple CA, raising the possibility of supra-luminal interactions at the lattice level, while still maintaining fully relativistic dynamics in the EM wave function propagation.
 
 In summary, the WELD approach represents an exploratory computational-modeling approach that could afford important insights into the otherwise puzzling nature of the quantum world. We can already see from the above intuitive arguments that the central wave-particle duality of the quantum world actually makes good sense from the lens of trying to implement these systems in a computational model. One advantage of the computational modeling approach is that it allows one to explore more complex, nonlinear interactions that can be difficult to analyze mathematically. 
 
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 * [[Tools vs models]] identifies a critical distinction between calculational tools versus physical models, that are intended to provide a "mechanistic", autonomous model of how physics might _actually_ operate. There are typically many different ways to calculate a prediction, but presumably physics is not strategically selecting different calculational tools based on different configurations of elements --- it must be just doing one consistent thing across all of space and time. That thing is what we seek to understand here.
 
-* The contrast between the [[Hilbert space]] formalism vs. [[pilot-wave]] models provides a nice example of this difference between an efficient calculational tool vs. a physical model (respectively). Critically the pilot wave framework requires that the mysterious wave functions of quantum physics _actually exist_ as a real physical thing, which is a central pillar of the current approach.
+* The contrast between the [[Hilbert space]] formalism vs. [[pilot-wave]] models provides a nice example of this difference between an efficient calculational tool vs. a physical model (respectively). Critically the pilot wave framework requires that the mysterious wave functions of quantum physics _actually exist_ as a real physical thing, which is a central pillar of the current approach. The issue of the [[configuration space]] representation used in standard QM is particularly important.
 
 * [[Epistemic vs ontic]] uncertainty discusses a critical distinction between sources of uncertainty that are due to limits on our knowledge of the exact state of an underlying physical system, versus _true_ stochasticity that reflects a fundamental underlying physical process that is _inherently_ stochastic. The present framework requires this latter form of _ontic_ (also known as _aleatoric_) stochasticity to produce physically-accurate behavior of discrete particles like an electron within the CA framework.
 
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 * The [[Dirac]]] wave function builds on the KG equation to capture the phenomenon of _spin_, and provides a physically complete description of the quantum dynamics of a particle like the electron. This is what drives all the amazing predictive accuracy of the [[QED]] framework within the standard model of physics, and is what we hypothesize exists as a real physical wave.
 
-* Finally, the [[electron]] is modeled as a discrete particle that moves with _intrinsic_ (_ontic_) stochasticity under the influence of the Dirac wave function.
+* Finally, the [[electron]] is modeled as a discrete [[stochastic particles|stochastic particle]] that moves with _intrinsic_ (_ontic_) noise under the influence of the Dirac wave function.