references updated

Author: rcoreilly

citedrefs.json

@@ -2,7 +2,7 @@
 bibfile = "mechphys.json"
 +++
 
-The widely discussed  distinction between **contextual** vs. "real" variables is a source of considerable confusion within the QM world ([[@Shimony84]]; [[@Gudder70]]; [[@Khrenniko0]]; [[@Rovelli96]]. A contextual variable is effectively something that cannot be discretely localized and quantified --- its value depends in some necessary way on the surrounding _context_, which is usually taken to mean the state of the measurement apparatus. In the standard Copenhagen interpretation, _everything_ could be described as being contextual, given that _nothing_ is thought to exist in any localized, definite way prior to the measurement process.
+The widely discussed  distinction between **contextual** vs. "real" variables is a source of considerable confusion within the QM world ([[@Shimony84]]; [[@Gudder70]]; [[@Khrennikov01]]; [[@Rovelli96]]. A contextual variable is effectively something that cannot be discretely localized and quantified --- its value depends in some necessary way on the surrounding _context_, which is usually taken to mean the state of the measurement apparatus. In the standard Copenhagen interpretation, _everything_ could be described as being contextual, given that _nothing_ is thought to exist in any localized, definite way prior to the measurement process.
 
 However, in the pilot-wave framework, the positions of the particles (and _only_ these variables) are given a privileged status as being _real_, non-contextual variables, and _everything else_ about the quantum state is relegated to the usual _contextual_ status. Another way of stating this is that everything that must be computed from the wave function itself is contextual, and only the position values are excluded from this status.
 

content/contextual.md

@@ -0,0 +1,24 @@
++++
+bibfile = "mechphys.json"
++++
+
+To compute the vector gradient in our discrete space-time cellular automaton, we need to introduce a new fundamental computation over the neighbors (all the previous equations have all just involved a single neighborhood computation for the Laplacian $\nabla^2$). This is one sense in which the model starts getting a bit more complex (it turns out that this computation will also be needed later for coupling with the electromagnetic field as well). First, in a single spatial dimension for state variable $s$, we saw before (equation~\ref{eq.diff_avg}) that the differential can be approximated as:
+
+- $\frac{\partial {s}}{\partial {x}} \approx \frac{1}{2 \epsilon} (s\_{i+1} - s\_{i-1}) $
+
+{id="figure_gradient" style="height:20em"}
+![Computation of the spatial gradient using all 18 neighbors that have a non-zero projection along a given axis (in this case, looking at the x axis). The two face points ({{< math >}}+,-{{< /math >}} along the axis) have a full projection along the axis, and thus enter with a weight of 1. The 8 edge points each have a {{< math>}}\frac{1}{\sqrt{2}}{{< /math >}} projection of their overall distance along the axis, and thus contribute with that overall weighting.  Similarly, the 8 corners have a {{< math >}}\frac{1}{\sqrt{3}}{{< /math >}} projection weighting. In computing the weighted average, the sum of all neighbor differences is divided by the sum of the weighting terms.](media/fig_gradient.png)
+
+<!--- TODO: fig.space_cubes_grad_noleg.id -->
+
+In three dimensions, the computation can be made more accurate and robust by including more of the neighbors, just as we did for the computation of $\nabla^2$. The most relevant neighbors are the 18 that have some projection along an axis, as illustrated in [[#figure_gradient]]. These can be organized into 9 rays that project through the central point, so that the above approximation can be extended to:
+
+- $\frac{1}{(2 + \frac{8}{\sqrt{2}} + \frac{8}{\sqrt{3}})} \sum\_{j \in N\_{9}} k_j (\varphi\_{j+} - \varphi\_{j-}) $
+
+Where the neighborhood $N\_{9}$ contains pairs of points $j+$ and $j-$ that are opposite ends of the 9 rays through the central point, and the distance weighting factors $k_j$ are:
+
+- **faces:** $k_j = \pm 1 $
+- **edges:** $k_j = \pm \frac{1}{\sqrt{2}} $
+- **corners:** $k_j = \pm \frac{1}{\sqrt{3}} $</text>
+
+

content/discrete-gradient.md

@@ -17,7 +17,7 @@ The [[pilot-wave]] framework of de Broglie and Bohm provides the most natural, i
 {id="figure_double-slit-deb" style="height:20em"}
 ![Trajectories for particles in the double-slit experiment computed according to the de Broglie-Bohm pilot-wave model. The interference effects can be seen as relatively localized bumps in the trajectories, corresponding to steep gradients in the Schrodinger wave equation. Critically, the underlying trajectories are considered to exist at all points even if you don't happen to observe them.](media/fig_double_slit_debroglie_bohm.png)
 
-[[#figure_double-slit-deb]] shows what the underlying trajectories of particles under the pilot-wave framework look like in a double-slit experiment, and [[#figure_double-slit-kocsis]] shows some recent data from an experiment where _weak measurements_ that minimally disturb the system allow one to infer particle trajectories, which look remarkably similar to those predicted by the pilot-wave model ([[@KocsisEtAl11]]).
+[[#figure_double-slit-deb]] shows what the underlying trajectories of particles under the pilot-wave framework look like in a double-slit experiment, and [[#figure_double-slit-kocsis]] shows some recent data from an experiment where _weak measurements_ that minimally disturb the system allow one to infer particle trajectories, which look remarkably similar to those predicted by the pilot-wave model ([[@KocsisBravermanRavetsEtAl11]]).
 
 {id="figure_double-slit-kocsis" style="height:20em"}
 ![Reconstructed trajectories of photons in a double-slit experiment using a weak measurement technique that allows aggregate trajectory information to be reconstructed over many repeated samples that are post-sorted according to a weak additional modulation of the system --- these are not individual particle trajectories. There is a striking correspondence to the predictions of the de Broglie-Bohm model. Figure from Kocsis et al, 2011.](media/fig_double_slit_kocsis_et_al_11.png)

content/double-slit.md

@@ -6,3 +6,8 @@ The **electron** is the most basic version of a fermion (spin 1/2), and is the f
 
 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.
 
+
+## TODO
+
+* [[@Holland05c]] -- back-reaction
+

content/electron.md

@@ -62,7 +62,7 @@ However, in the 1950's, David Bohm reinvented the original _pilot-wave_ model of
 {id="figure_double-slit-deb" style="height:20em"}
 ![Trajectories for particles in the double-slit experiment computed according to the de Broglie-Bohm pilot-wave model. The interference effects can be seen as relatively localized bumps in the trajectories, corresponding to steep gradients in the Schrodinger wave equation. Critically, the underlying trajectories are considered to exist at all points even if you don't happen to observe them.](media/fig_double_slit_debroglie_bohm.png)
 
-[[#figure_double-slit-deb]] shows what the underlying trajectories of particles under the pilot-wave framework look like in a double-slit experiment, and [[#figure_double-slit-kocsis]] shows some recent data from an experiment where _weak measurements_ that minimally disturb the system allow one to infer particle trajectories, which look remarkably similar to those predicted by the pilot-wave model ([[@KocsisEtAl11]]).
+[[#figure_double-slit-deb]] shows what the underlying trajectories of particles under the pilot-wave framework look like in a double-slit experiment, and [[#figure_double-slit-kocsis]] shows some recent data from an experiment where _weak measurements_ that minimally disturb the system allow one to infer particle trajectories, which look remarkably similar to those predicted by the pilot-wave model ([[@KocsisBravermanRavetsEtAl11]]).
 
 {id="figure_double-slit-kocsis" style="height:20em"}
 ![Reconstructed trajectories of photons in a double-slit experiment using a weak measurement technique that allows aggregate trajectory information to be reconstructed over many repeated samples that are post-sorted according to a weak additional modulation of the system --- these are not individual particle trajectories. There is a striking correspondence to the predictions of the de Broglie-Bohm model. Figure from Kocsis et al, 2011.](media/fig_double_slit_kocsis_et_al_11.png)

content/history.md

@@ -6,7 +6,7 @@ bibfile = "mechphys.json"
 
 <img src="media/icon.png" style="width:128px;height:128px;align-self:center">
 
-**Wave reality** is dedicated to exploring the idea that the quantum wave function is _real_, and not just a description of our state of [[epistemic vs ontic|epistemological]] ignorance. The reality of the wave function is strongly indicated by the classic [[double-slit]] experiment results, where some kind of spatially-distributed wave-like interference phenomenon seems to be influencing the trajectories of discrete particles. The [[pilot-wave]] framework of de Broglie and Bohm ([[@BohmVigier54]]; [[@Norsen22a]]), which posits a real quantum wave function guiding a discrete particle around, very naturally and intuitively explains all of the otherwise strange phenomena in these and many other classic quantum physics experiments.
+**Wave reality** is dedicated to exploring the idea that the quantum wave function is _real_, and not just a description of our state of [[epistemic vs ontic|epistemological]] ignorance. The reality of the wave function is strongly indicated by the classic [[double-slit]] experiment results, where some kind of spatially-distributed wave-like interference phenomenon seems to be influencing the trajectories of discrete particles. The [[pilot-wave]] framework of de Broglie and Bohm ([[@Bohm52]]; [[@Norsen22a]]), which posits a real quantum wave function guiding a discrete particle around, very naturally and intuitively explains all of the otherwise strange phenomena in these and many other classic quantum physics experiments.
 
 This website contains 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]]), starting with the coupled [[Dirac]]-[[Maxwell]] wave functions, along with discrete [[electron]] [[stochastic particles]], consistent with the [[pilot-wave]] framework. 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.
 
@@ -56,7 +56,7 @@ In this context, a recent paper showed that superliminal _causal_ mechanisms sho
 
 Second, the existing QM formalisms are _all_ based on the use of a [[configuration space]] representation of the physical world, which is manifestly non-local, and thus builds in the non-locality from the start. There is a glaring double-standard where the [[pilot-wave]] framework is dismissed for its reliance on this configuration space representation, while all other standard approaches likewise use precisely the same representation (e.g., in the [[Copenhagen]] interpretation and the [[Hilbert space]] matrix mechanics).
 
-The [[Copenhagen]] interpretation of QM, developed by Niels Bohr and Werner Heisenberg in the 1920's (see [[@history]]), is the source of most of the apparent paradoxes and conundrums associated with quantum physics. And yet, it remains the most popular interpretation according to informal surveys of working physicists ([[@Tegmark98]]; [[@SchlosshauerKoflerZeilinger13]]). In the face of the obviously non-physical aspects of this framework, the standard answer is to "shut up and calculate". This is the hallmark of a calculational tool, and as such, it seems prudent to consider this framework as such, and we will not spend any further effort here probing its fundamental strangeness.
+The [[Copenhagen]] interpretation of QM, developed by Niels Bohr and Werner Heisenberg in the 1920's (see [[history]]), is the source of most of the apparent paradoxes and conundrums associated with quantum physics. And yet, it remains the most popular interpretation according to informal surveys of working physicists ([[@Tegmark98]]; [[@SchlosshauerKoflerZeilinger13]]). In the face of the obviously non-physical aspects of this framework, the standard answer is to "shut up and calculate". This is the hallmark of a calculational tool, and as such, it seems prudent to consider this framework as such, and we will not spend any further effort here probing its fundamental strangeness.
 
 The next-most popular interpretation after Copenhagen according those surveys is the _many-worlds_ interpretation originated by [[@^Everett57]], which postulates that the entire universe splits at each measurement event. This nominally avoids the need for wave function collapse, but at what cost? An infinite accumulation of new universes spawning everywhere? This is so completely physically implausible that it just defies belief that so many people could even contemplate such a theory, just because it simplifies the math.
 

content/home.md

@@ -21,3 +21,6 @@ In contrast, the rest of physics likes Schrodinger's equation because it is more
 
 Thus, the overall difference is one of "mechanism" vs. "analysis," where standard physics is strongly weighted toward analysis (as in [[tools vs models]]).
 
+
+TODO: [[@DemiralpRabitz97]] -- dispersion-free wave packets!
+