What is phenomenological velocity?
Richard Gill
Parker Emmerson
Dear Richard,
Thank you for opening a separate thread.
I am somewhat dismayed by the question “what is phenomenological velocity?” because that is precisely what the papers are about. Still, I will try to answer briefly and concretely.
Phenomenological velocity is not introduced as an ordinary Bell hidden variable. It is not a particle trajectory, not a pilot wave, and not a new scalar (\lambda) to be inserted into Bell’s original formula. It is an algebraic and phenomenological event-formation structure arising from a cancellation-sensitive construction: an expression equivalent to unity can cancel in the scalar shadow while still carrying branch, fiber, and exceptional-locus structure in the lifted architecture. In that sense, PV is “hidden” structurally, not hidden as a pre-written Boolean outcome.
The basic algebraic idea is this. In the original PV construction, a Lorentz-type coefficient is injected into a height-function architecture in a form that algebraically cancels:
[
h=l\sin\beta\frac{
\sqrt{(l\alpha+x\gamma-r\theta)\sqrt{1-v^2/c^2}}
\sqrt{(l\alpha-x\gamma+r\theta)/\sqrt{1-v^2/c^2}}
}{\alpha}.
]A purely scalar reduction cancels the Lorentz factor and returns the ordinary expression. I do not deny that cancellation. But the point of PV is that the inserted unity has an internal architecture. One can write the relevant reduced compatibility expression as
[
-l^2\alpha^2+x^2\gamma^2-2rx\gamma\theta+r^2\theta^2+l^2\alpha^2\sin^2\beta=0,
]and then introduce the (c)-scaled form of the same expression. This gives the formal ratio by which an expression of one is made to carry an implicit (v)-structure. That is why I describe the method as a modus ponens manipulation of oneness, or as a push-out operation in algebraic form. The expression can cancel, but the cancellation does not exhaust the architecture by which the unity was established.
This is also where the undefined aspect enters. Mathematica will typically return the two formal (v)-solutions associated with the square-root ratio, but there is also the overlooked third case: on the exact compatibility locus, the ratio becomes (0/0). Thus (v) is not merely an ordinary scalar solution. It is tied to a branch-sensitive and exceptional-locus structure. The solution method brackets the immediate conclusion “undefined” long enough to expose the formal architecture of unity, and then acknowledges that undefinedness as part of the event horizon of the construction. This is why “phenomenological velocity” is the appropriate term: it is not just a velocity in the ordinary mechanical sense, but a velocity-structure disclosed by algebraic reduction, branch behavior, and formal expressibility.
This is also why I distinguish Bell-compliance from Richard-compliance.
Your two-program challenge is Richard-compliant: it asks for two scalar programs,
[
x=A(a,\lambda), \qquad y=B(b,\lambda),
]on one common Kolmogorov probability space, with unconditional binary outputs. In that class, CHSH follows. I do not dispute that. In fact, my papers explicitly say that no algebraic reformulation of PV can violate Bell–CHSH while remaining inside that single-ensemble Kolmogorov model.
But PV is not meant to be a Richard-compliant two-program scalar model. The point is that the physical/event structure may have to be represented before Booleanization, using branch structure, noninjective fibers, holomorphic functions, sweeping nets, saddle maps, or microcausal noncommutative linear algebra. In such a representation, the final (+/-1) report is the Boolean projection of a richer event-formation process, not the primitive object.
The adaptation to Bell theory proceeds in stages. First, if PV is forced into the ordinary Bell-local Kolmogorov form, Bell wins. That is accepted. Second, if PV enters as exceptional-locus or defined-only semantics, then it can change the effective reported ensemble, which is why the setting-dependent selection paper analyzes accepted laws (\nu_{ab}) and total-variation dispersion. Third, if PV is lifted into noncommutative microcausal structure, then the event algebra is no longer a global Boolean valuation table. In that setting, one can represent the singlet law through local noncommuting alternatives and cross-wing commuting algebras, yielding
[
P(x,y\mid a,b)=\frac14(1-xy\cos(a-b)),
]and hence
[
E(a,b)=-\cos(a-b).
]That is not a refutation of Bell’s algebra. It is a refusal to confuse Bell’s scalar shadow with the whole event-formation structure.
That is where Kochen–Specker and Fine matter. They warn us that global Boolean valuation structures should not be assumed for quantum-compatible event algebras. Your challenge asks for exactly such a global Booleanization at the outset. That is a fair test of Bell-local Kolmogorov programs, but not a neutral test of PV or of noncommutative event-formation models.
So my claim is not that Bell’s theorem is algebraically wrong. It is that Bell’s theorem rules out the local Kolmogorov bookkeeping representation. It does not automatically rule out the richer structure that may cast that final Boolean shadow.
As for “science politics,” I would put it differently. There is a semantic issue, yes, but it is not merely sociology. It matters whether words like “local,” “hidden,” and “real” are restricted to Bell’s specific formalization, or whether they can also describe mathematically local, structurally hidden, noncommutative or branch-sensitive event-formation. That is not ownership of language for its own sake. It is about whether the phenomenon has been flattened before it has been understood.
These structures are not ornamental. They may correspond to exploitable physical phenomena for different applications. PV predicts, or at least naturally motivates, a family of elementary-particle-like structures I have called alignons, cauchyons, Grammons, curvions, and Pontryagon pseudoscalars. Evidence for PV may therefore be sought not only in tabletop event-formation experiments, but also in existing CERN data, where branch, curvature, pseudoscalar, or fiber-structured anomalies may already be present.
I am one independent researcher, so I do not pretend to have the resources of an institution or a funded collaboration. Much of the work so far has been convincing people that phenomenological velocity even exists algebraically at all, then finding physical models that relate to it, Bell’s theorem among them, and then arguing that it is even worth taking seriously as physics. But if the algebraic structure is physically real, then it should have experimental consequences, and that is exactly why I think it deserves more than a Bell-template dismissal.
Searching CERN’s raw data is on my list of things to do. If you or anyone else is interested in seriously investigating the utility of physical phenomena revealed by phenomenological velocity experimental constructs, I am all ears. While I can help describe the physics experiments theoretically, it will take a team to put them into action if anyone actually wants to take this seriously. I have attached the proposed experiments.
A tabletop experiment may be feasible, as described in the attached document. Another route may be to look through already-existing CERN data for the particle or event-formation signatures predicted by PV. I have also thought about using IBM’s quantum cloud to run some of the circuit-level experiments. That is not typically where my skill set began, but my skill set has been widening. The interface and APIs may be a headache, but it is probably something I could learn to do. I simply have not had time to do all the research into those tools while also developing the theory largely alone.
The biggest criticism of phenomenological velocity may well turn out to be that, while it is demonstrable, it is demonstrable in a predominantly architectural kind of way. But that would still matter. Architecture yields technology, and it may also yield insight into event formation in nature. If PV gives a way to construct, detect, or exploit branch-sensitive, fibered, or exceptional-locus phenomena, then it is not merely language. It is a possible path to new experimental and technological structures.
I would not say I am an amateur researcher at this point. I have put years of effort into detailing the theory of phenomenological velocity without much practical help from others. It is a shame, really, that I remain almost the only expert on the topic. That is not because the idea lacks mathematical content. It is because convincing people that this “little algebraic trick” might be physically relevant has been a task in itself.
So the short answer is:
PV is an algebraic/event-formation framework in which a cancellation-sensitive expression of unity discloses an implicit velocity architecture, including branch, fiber, complex, and exceptional-locus structure. In the Bell context, the final Boolean outcome is a projection of that richer structure. Bell rules out the local Kolmogorov projection. It does not, by that fact alone, rule out the structure casting the projection.
All my best,
Parker
Bryan Sanctuary
"Why do people interested in Bell’s theorem and quantum foundations need to become expert in algebraic geometry?"
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Richard Gill
Richard Gill
<Phenomenological_Velocity_Experiment.pdf><Phenomenological_Velocity_Experiment_2.pdf>