PV-REC as a Time-Symmetric Boundary-Event Mechanics

[Parker Emmerson]

Dear Bell Quantum Foundations Group,

I hope all is well. 

Perhaps you haven't heard of International Journal of Quantum Foundations: peer-reviewed, quarterly, founded 2015; editorial board including Roger Penrose, Carlo Rovelli, and Sheldon Goldstein, Lajos Diosi past members Bernard d'Espagnat, H. Dieter Zeh, and Basil Hiley; founding editor Shan Gao — who co-edited Quantum Nonlocality and Reality: 50 Years of Bell's Theorem for Cambridge University Press with Mary Bell. On a list named for Bell, I'll let that sit.

My recent, most polished work on PV-Relational Event Completion, which Richard wasn't very interested in, but I think has substantial value in developing new experiments and unlocking new technologies, has been published in IJQF at the link: https://ijqf.org/archives/8398

This is the most polished version to date and includes a number of improvements and developments since my last correspondence with this group. It also cites Richard's work and Ryan's work.

All my best,

Parker Emmerson 

[Inge Svein Helland]

Dear all,

 

I have just started reading Parker Emmerson’s new paper ‘PV-REC as a time-symmetric boundary-event mechanics'. The paper claims to give a final explanation why the CHSH inequality may be violated in practice. At the same time, it is in  agreement with the Bell theorem. My main objection to this paper is that it is very complicated.

 

The Introduction of the paper is difficult to read, because symbols are introduced without precise definitions, only assuming that the reader is familiar with some standard notation in the Bell literature. Also, a lot of words are used, words that the reader is left to give a meaning to.

 

In Section 2 the relation to several other approaches is discussed. One could remark that the three approaches introduced recently in Gill et al. (2026) are not included here. It is repeated from the Introduction that Emmerson’s model includes a standard joint probability for Alice’s and Bob’s outcomes x and y given their settings a and b, a joint probability which is later is shown to be provable without using Born’s rule. This probability is then transformed by means of a Lorentz factor kappa(v), where v is some velocity. This transformation is discussed in detail in later sections. In Section 2, PV-REC’s CHSH excess is introduced, and it is proved that it is not due to internal selection. The universal bound is Tsirelson’s S≤2sqrt(2), not Bell’s S≤2.

 

In Section 3 it is distinguished between Bell scalar separability, which implies the Bell bound, and Bell physical locality. It is described which exact Bell premise PV-REC rejects.

 

Looking briefly through the later sections, the main conclusion to me is the Emmerson solution to the Bell problem looks very complicated. It depends crucially on this velocity v, which is defined as the relative speed between two physical time-like directions: the apparatus boundary frame four-velocity and the PV boundary microstructure four-velocity. The definition of the last four-velocity seems to require a rather complicated discussion.

 

In Section 14, several questions regarding this approach are answered. The important question here is Q2; Which Bell premise fails? This is answered very simply: Given the crucial hidden variable lambda_0, the joint probability of Alice’s and Bob’s outcomes x and y for fixed settings a and b does not factor into independent probabilities. However, several later questions are needed to interpret lambda_0.  This is not super determinism nor retro signalling. This is a hidden variable in the ‘ontic-completion’ sense, but not in a Bell-scalar hidden-variable sense. This last property is said to mean that lambda_0 does not support separated response functions X and Y. The velocity v is a hidden variable, but not the full story.

 

It is not quite clear to me how this approach can serve to develop new experiments and unlocking new technologies, but this may be due to my own limitations.

 

It would be very interesting to me if this approach could be compared to my own approach, as described in Section 5.2 in Gill et al. (2026). This approach is closely related to my proposed foundation behind the Hilbert space formalism of QM, a foundation given by four axioms formulated in my previous posting to this forum, or in more detail in the attached article. Concretely, the CHSH violation is derived from an interpretation of the axioms, an interpretation where the accessible variables reside in the mind of an arbitrary observer, and in the Bell case are limited to the four assumed response variables, taking the values +1 and -1. in my opinion, I have a much simpler and more natural explanation of the observed CHSH violations than what can be found in Emmerson’s paper and related papers.

 

Reference.

 

Gill, R.D., Helland, I.S., and Jongejan, B. (2026). Three ways to find comfort with the Bell proof and the results of the Bell experiments. arXiv: 2605.13154 [quant-ph]

---

Fra: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> på vegne av Parker Emmerson <powerin...@gmail.com>
Sendt: tirsdag 7. juli 2026 10:04
Til: Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>
Emne: [Bell_quantum_foundations] PV-REC as a Time-Symmetric Boundary-Event Mechanics

 

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[Parker Emmerson]

Dear Inge, thank you for your comments. If your only objection to the paper is that it's complicated, then I don't call that much of an objection, considering complexity is important to understand advanced technical mechanisms. Also, given the vast literature on Bell's theorem that doesn't ever discuss the phenomenological velocity method, I'm not sure a few hundred pages (or even a few thousand) is all that complicated or outstanding for a scientific paper that tries to be excruciatingly precise. However, that's being said, while explaining the mechanisms and the consequences of the phenomenon may be, "complicated," the mechanism itself is rather simple. I also don't have to be perfectly right to be pretty much right and contribute something new. I hope these ideas will reify with experiments, etc. There's a new document already that describe the experiments necessary in more detail. I think I've made my point that there is something over there. While I will continue to investigate what's over there --- it really has to be a team effort if we want to find out what's, "over there." So, yeah... I'm including the present updates. Thank you for taking the time and effort to review my work. I'm a strong believer that everyone develops their own mathematical dialect along the way and that correlating my symbols and notation to yours will help both of us understand each others perspectives better, so I will be taking a look at your work here in a minute. What I don't want this to be is, "I'm right and you're wrong." The language is real, it's meaningful, it indicates experiments and it indicates something hasn't been fully investigated with regard to this scientific space. That's being said, I think saying, "it's my job," to figure all of this out very well may be true, but it's pretty unreasonable for me to do it all by myself. It requires vast certifications, networking, academic accreditation or job positioning to gain access to the kinds of resources it takes to investigate something like this thoroughly. These scientific people are, after all, some of the most paradigm adhering while also paradoxically closed minded to mathematical evidence that doesn't adhere to their paradigm. It's odd that a scientific theory would require people to believe in it to make it worthwhile to investigate and spend effort, money, time, etc on finding out what's going on with the theory, but that's how it is it seems. I guess time will tell. 

The documents attached are the most updated explanation of the theoretical experiments that could be run to detect phenomenological velocity in this context. 

[Inge Svein Helland]

Dear Parker,

Thanks a lot for your long answer. I agree with most, but I think basically that, like special relatvity, we should work towards a foundation of QM that is relatively simple.

I also think that my own approach, compare the paper that I attached to my last contribution, can point some way here. Basically, I have one postulate: Complementarity, in my words, the existence of two non-equivalent maximal accessible variables. The rest are technical axioms to set the scene and define the concepts.

This is as far as the Hilbert space formalism goes. To prove the Born formula, I have two more postulates. This can possibly be improved.

In the paper above, this is a purely mathematical theory. To approach the Bell experiment situation, I need an interpretation of the mathematics. I choose a general epistemic interpretation: QM is a theory about our knowledge of the world. This implies that it says something about our minds. A consequence of the mathematics then, is that our minds are limited. I use this in Section 5.2 of the joint paper with Richard to explain why CHSH can be violated in practice.

Any comments will be of interest.

Inge

---

Fra: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> på vegne av Parker Emmerson <powerin...@gmail.com>

Sendt: lørdag 11. juli 2026 20:08
Til: Inge Svein Helland <in...@math.uio.no>
Kopi: Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>
Emne: Re: [Bell_quantum_foundations] PV-REC as a Time-Symmetric Boundary-Event Mechanics

 

Dear Inge, thank you for your comments. If your only objection to the paper is that it's complicated, then I don't call that much of an objection, considering complexity is important to understand advanced technical mechanisms. Also, given the vast literature on Bell's theorem that doesn't ever discuss the phenomenological velocity method, I'm not sure a few hundred pages (or even a few thousand) is all that complicated or outstanding for a scientific paper that tries to be excruciatingly precise. However, that's being said, while explaining the mechanisms and the consequences of the phenomenon may be, "complicated," the mechanism itself is rather simple. I also don't have to be perfectly right to be pretty much right and contribute something new. I hope these ideas will reify with experiments, etc. There's a new document already that describe the experiments necessary in more detail. I think I've made my point that there is something over there. While I will continue to investigate what's over there --- it really has to be a team effort if we want to find out what's, "over there." So, yeah... I'm including the present updates. Thank you for taking the time and effort to review my work. I'm a strong believer that everyone develops their own mathematical dialect along the way and that correlating my symbols and notation to yours will help both of us understand each others perspectives better, so I will be taking a look at your work here in a minute. What I don't want this to be is, "I'm right and you're wrong." The language is real, it's meaningful, it indicates experiments and it indicates something hasn't been fully investigated with regard to this scientific space. That's being said, I think saying, "it's my job," to figure all of this out very well may be true, but it's pretty unreasonable for me to do it all by myself. It requires vast certifications, networking, academic accreditation or job positioning to gain access to the kinds of resources it takes to investigate something like this thoroughly. These scientific people are, after all, some of the most paradigm adhering while also paradoxically closed minded to mathematical evidence that doesn't adhere to their paradigm. It's odd that a scientific theory would require people to believe in it to make it worthwhile to investigate and spend effort, money, time, etc on finding out what's going on with the theory, but that's how it is it seems. I guess time will tell. 

The documents attached are the most updated explanation of the theoretical experiments that could be run to detect phenomenological velocity in this context. 

--

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[Richard Gill]

Dear all

Please note that Inge, Bart and I prepared one paper explaining what we agreed on and what we disagreed on! If you read the paper you’ll find that I don’t find Inge’s explanation helpful. It is mathematically interesting. I’d like to see the maths separated from the philosophical explanation. I know Inge is very attached to his interpretation. Just like I’m attached to mine. Bart has his own ideas. I am somewhat mystified and puzzled by them. I think he’s found a weakness in common expositions of Bell’s theorem which focus on factorization of probability densities. I think it should be expressed in terms of conditional probability distributions. Unfortunately many physicists are not at home with present day measure theoretic probability. It’s clear to me that Bell (1964) used informal physicist’s language because he knew they didn’t know 20th century mathematical probability theory (Kolmogorov, built in measure theory and using the Radon Nikodym theorem to give a solid basis to statistical conditioning)

Richard


Sent from my iPhone

[Parker Emmerson]

Dear Mark,

Can you please explain the motivation behind your comment? Are you suggesting that there is some contradiction in phenomenological velocity’s predictions on the non-Born sector and it’s not requiring the Hilbert space of quantum mechanics? For the record, I have never much adhered to the probability interpretation of reality - i.e. that, for instance electrons are actually a probability cloud. I’m more of the, “does not play dice,” camp.

All my best,

Parker  

On Sunday, July 12, 2026, Mark Hadley <sunshine...@googlemail.com> wrote:

Parker,

The born rule is the only way to put probabilities on a context dependent state. It's the only way to put probabilities on spaces and subspaces of a Hilbert spaces.

Mark

On Sat, 11 Jul 2026, 20:17 Inge Svein Helland, <in...@math.uio.no> wrote:

Dear Parker,

Thanks a lot for your long answer. I agree with most, but I think basically that, like special relatvity, we should work towards a foundation of QM that is relatively simple.

I also think that my own approach, compare the paper that I attached to my last contribution, can point some way here. Basically, I have one postulate: Complementarity, in my words, the existence of two non-equivalent maximal accessible variables. The rest are technical axioms to set the scene and define the concepts.

This is as far as the Hilbert space formalism goes. To prove the Born formula, I have two more postulates. This can possibly be improved.

In the paper above, this is a purely mathematical theory. To approach the Bell experiment situation, I need an interpretation of the mathematics. I choose a general epistemic interpretation: QM is a theory about our knowledge of the world. This implies that it says something about our minds. A consequence of the mathematics then, is that our minds are limited. I use this in Section 5.2 of the joint paper with Richard to explain why CHSH can be violated in practice.

Any comments will be of interest.

Inge

---

Fra: bell_quantum_foundations@googlegroups.com <bell_quantum_foundations@googlegroups.com> på vegne av Parker Emmerson <powerin...@gmail.com>

Sendt: lørdag 11. juli 2026 20:08
Til: Inge Svein Helland <in...@math.uio.no>

Kopi: Bell inequalities and quantum foundations <bell_quantum_foundations@googlegroups.com>

Emne: Re: [Bell_quantum_foundations] PV-REC as a Time-Symmetric Boundary-Event Mechanics

Dear Inge, thank you for your comments. If your only objection to the paper is that it's complicated, then I don't call that much of an objection, considering complexity is important to understand advanced technical mechanisms. Also, given the vast literature on Bell's theorem that doesn't ever discuss the phenomenological velocity method, I'm not sure a few hundred pages (or even a few thousand) is all that complicated or outstanding for a scientific paper that tries to be excruciatingly precise. However, that's being said, while explaining the mechanisms and the consequences of the phenomenon may be, "complicated," the mechanism itself is rather simple. I also don't have to be perfectly right to be pretty much right and contribute something new. I hope these ideas will reify with experiments, etc. There's a new document already that describe the experiments necessary in more detail. I think I've made my point that there is something over there. While I will continue to investigate what's over there --- it really has to be a team effort if we want to find out what's, "over there." So, yeah... I'm including the present updates. Thank you for taking the time and effort to review my work. I'm a strong believer that everyone develops their own mathematical dialect along the way and that correlating my symbols and notation to yours will help both of us understand each others perspectives better, so I will be taking a look at your work here in a minute. What I don't want this to be is, "I'm right and you're wrong." The language is real, it's meaningful, it indicates experiments and it indicates something hasn't been fully investigated with regard to this scientific space. That's being said, I think saying, "it's my job," to figure all of this out very well may be true, but it's pretty unreasonable for me to do it all by myself. It requires vast certifications, networking, academic accreditation or job positioning to gain access to the kinds of resources it takes to investigate something like this thoroughly. These scientific people are, after all, some of the most paradigm adhering while also paradoxically closed minded to mathematical evidence that doesn't adhere to their paradigm. It's odd that a scientific theory would require people to believe in it to make it worthwhile to investigate and spend effort, money, time, etc on finding out what's going on with the theory, but that's how it is it seems. I guess time will tell. 

The documents attached are the most updated explanation of the theoretical experiments that could be run to detect phenomenological velocity in this context. 

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[Parker Emmerson]

Dear Inge, 

Thank you for your reply. It seems your work is a reconstruction: from undefined primitives (theoretical variables, accessibility) plus symmetry assumptions where you derive the Hilbert formalism as the terminus. The Hilbert space is the output, and standard QM is recovered exactly. On the other side, PV-REC is a construction: it builds an event mechanics in the positive cone that never needs the Hilbert space at all, and standard QM appears only as the κ = 1 equilibrium sector of a one-parameter family. So Inge, your endpoint is PV-REC's special case. That asymmetry drives the following:

Mark --- I think you are pointing out the right place of contention between the two theories --- the potential point of disagreement with Inge's theory and PV-REC would be his probability postulate even though PV-REC does not explicitly have a problem with probability in general.

Another note: The fate of the inaccessible phi.

Inge's headline result is that the assumption of a universal inaccessible variable phi — one variable such that every accessible variable is a function of it — can be dropped from his basis. PV-REC arrives at a closely related conclusion from the opposite direction. PV-REC splits Assumption 1 into two halves:

1. The source-side half: all accessible preparation records are functions of one intervention-independent record lambda_0 = (v, epsilon, J, Xi). PV-REC keeps this. P(lambda_0 | do(a), do(b)) = P(lambda_0), no conspiracy.
2. The joint-counterfactual half: outcomes across all counterfactual setting contexts are functions of one setting-independent phi. This is precisely the Bell screening premise, and PV-REC's replay theorem shows the native mechanism violates it: at fixed Bob setting and fixed lambda_0 (including the seeds!), Bob's outcome can differ under a counterfactual change of Alice's setting.

So Inge finds phi is unnecessary for the kinematics; PV-REC finds phi is unavailable for the dynamics. He drops it for economy, I drop it by theorem. I find it striking that both programs independently concluded the universal-phi picture is not load-bearing. (Amusingly, his surviving example of phi — the Bloch-sphere vector with theta^a = sign(cos(phi,a)) — is essentially Bell's 1964 single-wing model. It works exactly where my lambda_0 works, one wing at a time, and fails exactly where the replay defect lives, across wings and contexts.)

All my best,

Parker Emmerson

On Sun, Jul 12, 2026 at 5:41 AM Parker Emmerson <powerin...@gmail.com> wrote:

Dear Mark,

Can you please explain the motivation behind your comment? Are you suggesting that there is some contradiction in phenomenological velocity’s predictions on the non-Born sector and it’s not requiring the Hilbert space of quantum mechanics? For the record, I have never much adhered to the probability interpretation of reality - i.e. that, for instance electrons are actually a probability cloud. I’m more of the, “does not play dice,” camp.

All my best,

Parker  

On Sunday, July 12, 2026, Mark Hadley <sunshine...@googlemail.com> wrote:

Parker,

The born rule is the only way to put probabilities on a context dependent state. It's the only way to put probabilities on spaces and subspaces of a Hilbert spaces.

Mark

On Sat, 11 Jul 2026, 20:17 Inge Svein Helland, <in...@math.uio.no> wrote:

Dear Parker,

Thanks a lot for your long answer. I agree with most, but I think basically that, like special relatvity, we should work towards a foundation of QM that is relatively simple.

I also think that my own approach, compare the paper that I attached to my last contribution, can point some way here. Basically, I have one postulate: Complementarity, in my words, the existence of two non-equivalent maximal accessible variables. The rest are technical axioms to set the scene and define the concepts.

This is as far as the Hilbert space formalism goes. To prove the Born formula, I have two more postulates. This can possibly be improved.

In the paper above, this is a purely mathematical theory. To approach the Bell experiment situation, I need an interpretation of the mathematics. I choose a general epistemic interpretation: QM is a theory about our knowledge of the world. This implies that it says something about our minds. A consequence of the mathematics then, is that our minds are limited. I use this in Section 5.2 of the joint paper with Richard to explain why CHSH can be violated in practice.

Any comments will be of interest.

Inge

---

Fra: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> på vegne av Parker Emmerson <powerin...@gmail.com>

Sendt: lørdag 11. juli 2026 20:08
Til: Inge Svein Helland <in...@math.uio.no>

Kopi: Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>

Emne: Re: [Bell_quantum_foundations] PV-REC as a Time-Symmetric Boundary-Event Mechanics

Dear Inge, thank you for your comments. If your only objection to the paper is that it's complicated, then I don't call that much of an objection, considering complexity is important to understand advanced technical mechanisms. Also, given the vast literature on Bell's theorem that doesn't ever discuss the phenomenological velocity method, I'm not sure a few hundred pages (or even a few thousand) is all that complicated or outstanding for a scientific paper that tries to be excruciatingly precise. However, that's being said, while explaining the mechanisms and the consequences of the phenomenon may be, "complicated," the mechanism itself is rather simple. I also don't have to be perfectly right to be pretty much right and contribute something new. I hope these ideas will reify with experiments, etc. There's a new document already that describe the experiments necessary in more detail. I think I've made my point that there is something over there. While I will continue to investigate what's over there --- it really has to be a team effort if we want to find out what's, "over there." So, yeah... I'm including the present updates. Thank you for taking the time and effort to review my work. I'm a strong believer that everyone develops their own mathematical dialect along the way and that correlating my symbols and notation to yours will help both of us understand each others perspectives better, so I will be taking a look at your work here in a minute. What I don't want this to be is, "I'm right and you're wrong." The language is real, it's meaningful, it indicates experiments and it indicates something hasn't been fully investigated with regard to this scientific space. That's being said, I think saying, "it's my job," to figure all of this out very well may be true, but it's pretty unreasonable for me to do it all by myself. It requires vast certifications, networking, academic accreditation or job positioning to gain access to the kinds of resources it takes to investigate something like this thoroughly. These scientific people are, after all, some of the most paradigm adhering while also paradoxically closed minded to mathematical evidence that doesn't adhere to their paradigm. It's odd that a scientific theory would require people to believe in it to make it worthwhile to investigate and spend effort, money, time, etc on finding out what's going on with the theory, but that's how it is it seems. I guess time will tell. 

The documents attached are the most updated explanation of the theoretical experiments that could be run to detect phenomenological velocity in this context. 

--
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[Inge Svein Helland]

Dear Parker,

Your note on the connection between our theories seems very interesting indeed. I will try to read it in more detail, and then come back to you.

But, as a first remark, I think that I will call my own theory also a kind of a construction. The Hilbert space in explicitly constructed from an irreducible representation of a certain group. This group is constructed by considering transformations of the vector consisting of the two complementary variables. From this, operators associated with the two variables are constructed, and finally, assuming self-adjointness, using the spectral theorem, operators connected to other accessible variables are constructed.

Admittedly, this a debate about words. Before continuing our dialogue, I have to learn more about your PV-REC theory.

Best regards Inge.

---

Fra: Parker Emmerson <powerin...@gmail.com>
Sendt: søndag 12. juli 2026 00:21
Til: Mark Hadley <sunshine...@googlemail.com>
Kopi: Inge Svein Helland <in...@math.uio.no>; Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>
Emne: Re: PV-REC as a Time-Symmetric Boundary-Event Mechanics

 

[Mark Hadley]

Parker,

The born rule is the only way to put probabilities on a context dependent state. It's the only way to put probabilities on spaces and subspaces of a Hilbert spaces.

Mark

On Sat, 11 Jul 2026, 20:17 Inge Svein Helland, <in...@math.uio.no> wrote:

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/OS6P279MB0699A48F39009F14AC64E8BBF5FC2%40OS6P279MB0699.NORP279.PROD.OUTLOOK.COM.

[Mark Hadley]

Sorry, it was a reply to inge.

On Sat, 11 Jul 2026, 22:41 Parker Emmerson, <powerin...@gmail.com> wrote:

Dear Mark,

Can you please explain the motivation behind your comment? Are you suggesting that there is some contradiction in phenomenological velocity’s predictions on the non-Born sector and it’s not requiring the Hilbert space of quantum mechanics? For the record, I have never much adhered to the probability interpretation of reality - i.e. that, for instance electrons are actually a probability cloud. I’m more of the, “does not play dice,” camp.

All my best,

Parker  

On Sunday, July 12, 2026, Mark Hadley <sunshine...@googlemail.com> wrote:

Parker,

The born rule is the only way to put probabilities on a context dependent state. It's the only way to put probabilities on spaces and subspaces of a Hilbert spaces.

Mark

On Sat, 11 Jul 2026, 20:17 Inge Svein Helland, <in...@math.uio.no> wrote:

Dear Parker,

Thanks a lot for your long answer. I agree with most, but I think basically that, like special relatvity, we should work towards a foundation of QM that is relatively simple.

I also think that my own approach, compare the paper that I attached to my last contribution, can point some way here. Basically, I have one postulate: Complementarity, in my words, the existence of two non-equivalent maximal accessible variables. The rest are technical axioms to set the scene and define the concepts.

This is as far as the Hilbert space formalism goes. To prove the Born formula, I have two more postulates. This can possibly be improved.

In the paper above, this is a purely mathematical theory. To approach the Bell experiment situation, I need an interpretation of the mathematics. I choose a general epistemic interpretation: QM is a theory about our knowledge of the world. This implies that it says something about our minds. A consequence of the mathematics then, is that our minds are limited. I use this in Section 5.2 of the joint paper with Richard to explain why CHSH can be violated in practice.

Any comments will be of interest.

Inge

---

Fra: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> på vegne av Parker Emmerson <powerin...@gmail.com>

Sendt: lørdag 11. juli 2026 20:08
Til: Inge Svein Helland <in...@math.uio.no>

Kopi: Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>

Emne: Re: [Bell_quantum_foundations] PV-REC as a Time-Symmetric Boundary-Event Mechanics

Dear Inge, thank you for your comments. If your only objection to the paper is that it's complicated, then I don't call that much of an objection, considering complexity is important to understand advanced technical mechanisms. Also, given the vast literature on Bell's theorem that doesn't ever discuss the phenomenological velocity method, I'm not sure a few hundred pages (or even a few thousand) is all that complicated or outstanding for a scientific paper that tries to be excruciatingly precise. However, that's being said, while explaining the mechanisms and the consequences of the phenomenon may be, "complicated," the mechanism itself is rather simple. I also don't have to be perfectly right to be pretty much right and contribute something new. I hope these ideas will reify with experiments, etc. There's a new document already that describe the experiments necessary in more detail. I think I've made my point that there is something over there. While I will continue to investigate what's over there --- it really has to be a team effort if we want to find out what's, "over there." So, yeah... I'm including the present updates. Thank you for taking the time and effort to review my work. I'm a strong believer that everyone develops their own mathematical dialect along the way and that correlating my symbols and notation to yours will help both of us understand each others perspectives better, so I will be taking a look at your work here in a minute. What I don't want this to be is, "I'm right and you're wrong." The language is real, it's meaningful, it indicates experiments and it indicates something hasn't been fully investigated with regard to this scientific space. That's being said, I think saying, "it's my job," to figure all of this out very well may be true, but it's pretty unreasonable for me to do it all by myself. It requires vast certifications, networking, academic accreditation or job positioning to gain access to the kinds of resources it takes to investigate something like this thoroughly. These scientific people are, after all, some of the most paradigm adhering while also paradoxically closed minded to mathematical evidence that doesn't adhere to their paradigm. It's odd that a scientific theory would require people to believe in it to make it worthwhile to investigate and spend effort, money, time, etc on finding out what's going on with the theory, but that's how it is it seems. I guess time will tell. 

The documents attached are the most updated explanation of the theoretical experiments that could be run to detect phenomenological velocity in this context. 

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[Richard Gill]

Inge does not only construct a Hilbert space. He also puts probabilities on it. I understand from his works that he is using a version of Gleason’s theorem.

Since the Hilbert space is in the mind of the observers, the probabilities are too. They are subjective probabilities arrived at from a theory of mind. 

The mathematics is impressive but the content is not physics. 

Sent from my iPad

On 16 Jul 2026, at 19:48, Inge Svein Helland <in...@math.uio.no> wrote:



To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/OS6P279MB069967BF35F5EE36EB35A08DF5FB2%40OS6P279MB0699.NORP279.PROD.OUTLOOK.COM.

[Bryan Sanctuary]

Dear all.

Richard said

"It’s clear to me that Bell (1964) used informal physicist’s language because he knew they didn’t know 20th century mathematical probability theory  (Kolmogorov, built in measure theory and using the Radon Nikodym theorem to give a solid basis to statistical conditioning)  "  

Richard is rewriting history to support his idol.  Many physicists are well aware of probability theory. Bell did not mention Kolmogorov in any of his papers until after 1982 when Fine pointed it out (18 years).  I do not think Richard's is right that Bell pussy footed around physicists, and I think Bell had NO idea tha joint definability is the Achilles heel of his inequalities.  If so, please find a statement by Bell that proves your statement.

This is another example of Richard making comments off the top of your head with NO basis..

Bryan

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[Richard Gill]

Dear Bryan, dear all

You continue to ignore the elephant in the room: your theory is incomplete. You introduce axioms out of thin air which give probabilities of measurement outcomes, but no “single shot" description of the generation of particular outcomes. You do not have a complete model, whether deterministic of stochastic, for the emission and detection including the particular measurement outcomes of one pair of particles.

This problem with QM is usually called the measurement problem. Bryan’s quaternion spin problem is afflicted by the same problem. 

He has his own analogue to the Born rule. He hasn’t got around to *deriving it*. In a very real sense he does not have a hidden variables model, in the sense of a model which explains the *apparent randomness* of measurement outcomes through an underlying deterministic process.

I came across a quite brilliant paper on this problem (in ordinary QM) by Donadi and Hossenfelder (2022)

https://arxiv.org/abs/2010.01327

Phys. Rev. A 106, 022212 – Published 19 August, 2022

DOI: https://doi.org/10.1103/PhysRevA.106.022212

The model reproduces QM and of necessity (ie, by Bell’s theorem) violates the statistical independence assumption.

Richard

[Bryan Sanctuary]

Hi Richard, and all.

I do only ONE THING. ONE THING.  I take Dirac's gamma^2 and multiply it by "i".   NOTHING ELSE

That makes i\gamma^2 a bivector. Richard, what is wrong with that???  Cl(1,3) to Cl(2,2).  Algebra only! But you do not answer specifics.

Then I just follow the logic.  No new axioms of Nature, as mathematically complete as Dirac; I have Boolean outcomes (shots),  it is real, it uses GA, it resolves the measurement problem, AND NO SPOOKINESS on the horizon, no QUANTUM WEIRDNESS

 and it scares the hell out of Richard because he realizes that maybe, just maybe, I have resolved the quantum problem with a classical spin. The Gospel of Bell will not survive, culminating in a forced apostasy that will cripple the revelation required to accept Bell's Boolean Bits.

If you had multiplied gamma by "i", then you would be in my position.

Bryan

[Richard Gill]

Bryan, I have no objection at all to your innovations regarding spin, bivector, and algebra.

You have not resolved the measurement problem. You are blind to it.

You go from your bivector stuff, rotors, and all that to probabilities. The jump from two (post interaction) spins to marginal and joint probabilities is an axiom which you have blindly positted. You do not go to measurement outcomes.

Sent from my iPad

On 17 Jul 2026, at 13:28, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Bryan Sanctuary]

Mark

No, the Born rule is NOT the only way.  Take the scalar grade of a multivector, and that gives the probability

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAN%3D2%2Bo2%2BRK_UCG5R8fY7BNdzRVfqzFV0LiegCb_vLdDZju1WSA%40mail.gmail.com.

[Bryan Sanctuary]

Mark,

What is not a Lorentz invariant, so be specific?

Bryan

On Fri, Jul 17, 2026 at 8:48 AM Mark Hadley <drmark...@gmail.com> wrote:

The fact that it's not Lorentz invariant is fundamental.

And that fact that he can write a paper with equations that are not Lorentz invariant without in anyway explaining it means the paper should not be taken seriously.

Mark

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[Bryan Sanctuary]

Richard

The Measurement Problem you say I am blind to is a major part of my bivector.  Recall instantiation.  That is measurement theory.

I have no wave function collapse, and that is the sum total of the measurement problem.  

[Richard Gill]

I know it gets you a probability.

I keep saying: you have rules to go from quaternions to probabilities. But no rule to take you to outcomes. +/- 1. Or clicks.

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On 17 Jul 2026, at 15:24, Bryan Sanctuary <bryancs...@gmail.com> wrote:



To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YyBttZAaZSioeySVzXxZbAWkhZ%3D3j5gqmQMMTsL8Jo8GQ%40mail.gmail.com.

[Richard Gill]

No Bryan, that is not the sum total of the measurement problem.

Sent from my iPad

On 17 Jul 2026, at 15:28, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Bryan Sanctuary]

Richard

Of course I have rules.I gave you Malus's law for coincidences

P_even = cos^2(a-b)/2. 

P_odd = sin^2{a-b}/2.

Have you seen that before?

so you are totally out in left field in almost everything you guess about my work

Bryan

[Richard Gill]

Bryan, you keep repeating yourself. I know you have rules. They enable you to reproduce the QM probabilities.

You do not have a locally causal mechanism leading to *outcomes* at the level of a single shot, such that the QM probabilities then emerge by averaging over possible configurations of any “hidden” variables.

In fact, if you think that Bell’s theorem is a true theorem, you should realise that it is impossible to find such a mechanism.

Sent from my iPad

On 17 Jul 2026, at 16:00, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Richard Gill]

Bryan

I am not making any guesses about your work. I’m applying the elementary but iron logic of Bell-CHSH.

You don’t get it? Just carry on working on your simulation experiment. This can wait.

Richard

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On 17 Jul 2026, at 16:00, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Richard Gill]

I’m not so bothered by that. Non-local collapse models can be made Lorentz invariant. I forget who proved that. 

The model is incomplete and any completion would be nonlocal. 

Sent from my iPad

On 17 Jul 2026, at 14:48, Mark Hadley <drmark...@gmail.com> wrote:



The fact that it's not Lorentz invariant is fundamental.

And that fact that he can write a paper with equations that are not Lorentz invariant without in anyway explaining it means the paper should not be taken seriously.

Mark

DLE Limited

Co. No: 17094634

Reg Address: 4 The Pastures, Dog Lane, Napton, SOUTHAM CV47 8LT

On Fri, 17 Jul 2026, 13:40 Richard Gill, <gill...@gmail.com> wrote:

Bryan, I have no objection at all to your innovations regarding spin, bivector, and algebra.

You have not resolved the measurement problem. You are blind to it.

You go from your bivector stuff, rotors, and all that to probabilities. The jump from two (post interaction) spins to marginal and joint probabilities is an axiom which you have blindly positted. You do not go to measurement outcomes.

Sent from my iPad

On 17 Jul 2026, at 13:28, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Hi Richard, and all.

I do only ONE THING. ONE THING.  I take Dirac's gamma^2 and multiply it by "i".   NOTHING ELSE

That makes i\gamma^2 a bivector. Richard, what is wrong with that???  Cl(1,3) to Cl(2,2).  Algebra only! But you do not answer specifics.

Then I just follow the logic.  No new axioms of Nature, as mathematically complete as Dirac; I have Boolean outcomes (shots),  it is real, it uses GA, it resolves the measurement problem, AND NO SPOOKINESS on the horizon, no QUANTUM WEIRDNESS

 and it scares the hell out of Richard because he realizes that maybe, just maybe, I have resolved the quantum problem with a classical spin. The Gospel of Bell will not survive, culminating in a forced apostasy that will cripple the revelation required to accept Bell's Boolean Bits.

If you had multiplied gamma by "i", then you would be in my position.

Bryan

On Thu, Jul 16, 2026 at 11:51 PM Richard Gill <gill...@gmail.com> wrote:

Dear Bryan, dear all

You continue to ignore the elephant in the room: your theory is incomplete. You introduce axioms out of thin air which give probabilities of measurement outcomes, but no “single shot" description of the generation of particular outcomes. You do not have a complete model, whether deterministic of stochastic, for the emission and detection including the particular measurement outcomes of one pair of particles.

This problem with QM is usually called the measurement problem. Bryan’s quaternion spin problem is afflicted by the same problem. 

He has his own analogue to the Born rule. He hasn’t got around to *deriving it*. In a very real sense he does not have a hidden variables model, in the sense of a model which explains the *apparent randomness* of measurement outcomes through an underlying deterministic process.

I came across a quite brilliant paper on this problem (in ordinary QM) by Donadi and Hossenfelder (2022)

https://arxiv.org/abs/2010.01327

Phys. Rev. A 106, 022212 – Published 19 August, 2022

DOI: https://doi.org/10.1103/PhysRevA.106.022212

The model reproduces QM and of necessity (ie, by Bell’s theorem) violates the statistical independence assumption.

Richard

On 16 Jul 2026, at 23:28, Bryan Sanctuary <bryancs...@gmail.com> wrote:

Dear all.

Richard said

"It’s clear to me that Bell (1964) used informal physicist’s language because he knew they didn’t know 20th century mathematical probability theory  (Kolmogorov, built in measure theory and using the Radon Nikodym theorem to give a solid basis to statistical conditioning)  "  

Richard is rewriting history to support his idol.  Many physicists are well aware of probability theory. Bell did not mention Kolmogorov in any of his papers until after 1982 when Fine pointed it out (18 years).  I do not think Richard's is right that Bell pussy footed around physicists, and I think Bell had NO idea tha joint definability is the Achilles heel of his inequalities.  If so, please find a statement by Bell that proves your statement.

This is another example of Richard making comments off the top of your head with NO basis..

Bryan

On Sat, Jul 11, 2026 at 4:28 PM Richard Gill <gill...@gmail.com> wrote:

Dear all

Please note that Inge, Bart and I prepared one paper explaining what we agreed on and what we disagreed on! If you read the paper you’ll find that I don’t find Inge’s explanation helpful. It is mathematically interesting. I’d like to see the maths separated from the philosophical explanation. I know Inge is very attached to his interpretation. Just like I’m attached to mine. Bart has his own ideas. I am somewhat mystified and puzzled by them. I think he’s found a weakness in common expositions of Bell’s theorem which focus on factorization of probability densities. I think it should be expressed in terms of conditional probability distributions. Unfortunately many physicists are not at home with present day measure theoretic probability. It’s clear to me that Bell (1964) used informal physicist’s language because he knew they didn’t know 20th century mathematical probability theory (Kolmogorov, built in measure theory and using the Radon Nikodym theorem to give a solid basis to statistical conditioning)

Richard


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> On 11 Jul 2026, at 21:17, Inge Svein Helland <in...@math.uio.no> wrote:
>

> I use this in Section 5.2 of the joint paper with Richard to explain why CHSH can be violated in practice.

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[Richard Gill]

Bryan, you need to study “Speakable and Unspeakable 2nd edition”, from cover to cover. It has many “chapters” on “measurement”

For instance, already in Alain Aspect’s introduction one can read:

“Starting in the 1970s, another concept has progressively become more and more important in quantum physics: the description of single objects, in contrast to the statistical use of quantum mechanics to describe only properties of large ensembles (for instance the fluorescence of an atomic vapor). That question had, like the EPR problem, been a subject of debate between Bohr and Einstein3, but it was the development of experimental abilities to isolate and observe single microscopic objects like photons, electrons, ions and atoms that prompted physicists to take quantum mechanical dynamics of single objects, including ‘quantum jumps’, seriously. The experimental observation of quantum jumps (in the fluorescence light from a single ion) inspired new theoretical approaches, the so-called ‘Quantum Monte-Carlo Wave Function’ simulations, primarily used to describe ‘elementary’ microscopic objects like ions, atoms, and small molecules. Recently, progress in nanofabrication, as well as experimental breakthroughs, have allowed physicists to create mesoscopic systems (e.g., electric and magnetic devices, and gaseous Bose–Einstein condensates) which push the border of the quantum world to larger and larger systems that still need to be described as single quantum objects.”

“The existence of such ‘quantum jumps’, implying a discontinuous evolution of the system, was strongly opposed by a number of physicists – including Schrödinger – who saw a convenient trick with a pedagogical value, but who contended that quantum mechanics inherently applies only to large ensembles, and not to single quantum objects. The experimental progress discussed above allowed the debate to be resolved experimentally, in 1986, by the direct observation of quantum jumps in the fluorescence of a single trapped ion. In this type of experiment, one indeed observes that the ion evolves randomly between periods where it is invisible, and periods where it fluoresces intensely! This result was very striking, and resolved beyond all doubt that quantum jumps do exist, and that quantum theory can describe the behavior of a single object.”

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On 17 Jul 2026, at 16:00, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Richard Gill]

In Chapter 1 “On the problem of hidden variables in quantum mechanics” Bell writes:

“The question at issue is whether the quantum mechanical states can be regarded as ensembles of states further specified by additional variables, such that given values of these variables together with the state vector determine precisely the results of individual measurements. These hypothetical well-specified states are said to be ‘dispersion free.’”

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On 17 Jul 2026, at 16:00, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Inge Svein Helland]

Dear Parker,

I have finally managed to find your paper ‘PV-REC as a Time-Symmetric Boundary-Event Mechanics’, which now is published in International Journal of Quantum Mechanics. The paper is very long and detailed, but I am trying to read it now.

But what strucks me first is that, according to this paper, PV-REC is a theory connected to the Bell scenario. In ‘Accessible Variables and Boundary Events’ you have a very interesting comparison of PV-REC with my general derivation of the Hilbert space formalism from weak conditions. As I read this last paper, PV-REC is here a more general theory.

Am I misunderstanding something basically here, or do you somewhere generalize your theory from the Bell scenario to a more general framework? In case, how can I understand the 'velocity' v for instance?

Best regards Inge.

---

Fra: Parker Emmerson <powerin...@gmail.com>
Sendt: søndag 12. juli 2026 00:21
Til: Mark Hadley <sunshine...@googlemail.com>

Kopi: Inge Svein Helland <in...@math.uio.no>; Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>
Emne: Re: PV-REC as a Time-Symmetric Boundary-Event Mechanics

 

[Parker Emmerson]

Yes, Thank you, Inge, it is very interesting indeed. The phenomenological velocity has taken on a kind of life of its own, and it helps us gauge where we are in our logical train of thought. I write about phenomenological velocity in my book, "phenomenological velocity," where I provide detailed algebraic step by step solutions of how to use modus ponens to embed the Lorentz coefficient within a height of right-cone function. Of course, folding a circle into one cone is a waste of time. Why make only one cone when you can fold two cones out of the same circle simultaneously? This is referred to as, "orbifold geometry." Learning concepts like subtrahend and minuend was also delightful. What started off as an algebraic trick using modus ponens became flexible conceptually and migrated into higher mathematics. Of course, I have always used computers for my mathematics, and now the calculators are more advanced and powerful than ever. You may find, "The Cone of Perception," to be introductory and interesting. I have actually outsourced the parameterization of the circle's folding into a cone so that now we have python code for it in 3D. We also have python code which I subsequently developed with AI for the folding of a circle into two right cones. You'll see a lot of coefficients from quantum mechanics in there related to colored quarks. The mystery was, "why should there be a solution to something that ought cancel out with itself?" - but because of the exceptional locus - there is... - (the Lorentz coefficient applied to the height of the cone in such a way that it ought cancel out) --- you can see this description in: 

https://ijqf.org/archives/8027 (This is my first paper I published with IJQF) - I also pack everything into the attached document

https://zenodo.org/records/14188472

https://zenodo.org/records/13959848

https://zenodo.org/records/8433050

I try to explain this to people -- that it matters, that it's relevant, but I'm not sure they are listening. You can see it for yourself - run the computer algebra system's solution. I contacted Mathematica about it multiple times, they laughed at me. Thanks for listening. What's interesting, and I think this might be what you are getting at - is that this technique, of solving for the Lorentz coefficient within the allegedly commuting radicals - 1) reveals non-commutation 2) has linguistically leap frogged into symbolic manipulation (I tried my best to exercise these kinds of notations in my book Limbertwig)

It's a complex topic. I hope this helps to point you some resources in understanding phenomenological velocity as I have coined the term.

[Richard Gill]

Dear Inge, 

I think you mean International Journal of Quantum Foundations (not of Quantum Mechanics)

https://ijqf.org/archives/8398

As I understand it, Parker’s theory allows information to travel faster than the speed of light, hence one can call it a theory based on retro-causality. Phenomenological velocity is a velocity exceeding the speed of light. 

Notice that it is time-symmetric! Standard QM with actual collapse is not time symmetric.

Your theory, Inge, is a theory of minds, not a theory of a physical reality independent of minds. 

What Inge and Parker have in common is a deep religious belief. This makes you both happy to believe in things which others would call supernatural.

Richard

On 29 Jul 2026, at 09:59, Inge Svein Helland <in...@math.uio.no> wrote:

Dear Parker,

I have finally managed to find your paper ‘PV-REC as a Time-Symmetric Boundary-Event Mechanics’, which now is published in International Journal of Quantum Mechanics. The paper is very long and detailed, but I am trying to read it now.

But what strucks me first is that, according to this paper, PV-REC is a theory connected to the Bell scenario. In ‘Accessible Variables and Boundary Events’ you have a very interesting comparison of PV-REC with my general derivation of the Hilbert space formalism from weak conditions. As I read this last paper, PV-REC is here a more general theory.

Am I misunderstanding something basically here, or do you somewhere generalize your theory from the Bell scenario to a more general framework? In case, how can I understand the 'velocity' v for instance?

Best regards Inge.

---

Fra: Parker Emmerson <powerin...@gmail.com>
Sendt: søndag 12. juli 2026 00:21
Til: Mark Hadley <sunshine...@googlemail.com>
Kopi: Inge Svein Helland <in...@math.uio.no>; Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>
Emne: Re: PV-REC as a Time-Symmetric Boundary-Event Mechanics

 

Dear Inge, 

Thank you for your reply. It seems your work is a reconstruction: from undefined primitives (theoretical variables, accessibility) plus symmetry assumptions where you derive the Hilbert formalism as the terminus. The Hilbert space is the output, and standard QM is recovered exactly. On the other side, PV-REC is a construction: it builds an event mechanics in the positive cone that never needs the Hilbert space at all, and standard QM appears only as the κ = 1 equilibrium sector of a one-parameter family. So Inge, your endpoint is PV-REC's special case. That asymmetry drives the following:

Mark --- I think you are pointing out the right place of contention between the two theories --- the potential point of disagreement with Inge's theory and PV-REC would be his probability postulate even though PV-REC does not explicitly have a problem with probability in general.

Another note: The fate of the inaccessible phi.

Inge's headline result is that the assumption of a universal inaccessible variable phi — one variable such that every accessible variable is a function of it — can bedropped from his basis. PV-REC arrives at a closely related conclusion from the opposite direction. PV-REC splits Assumption 1 into two halves:

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/OS6P279MB069938A1F426B1F3E6121CBDF5CA2%40OS6P279MB0699.NORP279.PROD.OUTLOOK.COM.

[Inge Svein Helland]

I am sorry, Parker; I do not have the time to read all your detailed papers. I understand that you are very preoccupied by the concept of phenomenological velocity, a concept that has no place in my own theory.

To begin with, I am satisfied with the kinematics of non-relativistic quantum mechanics. Links to relativity can be found; I refer here to the joint book with Harish Partasarathy, which I attach here. But as a basic point, I want to keep things simple.

The simplest possible setting is that of two r-dimensional maximal accessible variables, what Niels Bohr called two complementary variables. My main result is that this setting implies the existence of a Hilbert space, an r-dimensional complex vector space, such that all accessible variables have self-adjint operators (matrices) accociated with them, matrices such that the eigenvalues are the possible values of the actual variable.

I appreciate your observation that the accessible variables can be associated with a sigma-algebra. But otherwise, if your own theory is based upon the Bell-scenario, I think that one must look upon the latter as a very rich and deep theory, but in connection to the result sketched above, only a special case.

Best regards Inge.

---

Fra: Parker Emmerson <powerin...@gmail.com>
Sendt: onsdag 29. juli 2026 10:59

Til: Inge Svein Helland <in...@math.uio.no>
Kopi: Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>

Emne: Re: PV-REC as a Time-Symmetric Boundary-Event Mechanics

 

[Inge Svein Helland]

Yes, Richard, my notation for the journal was a misprint.

I repeat: My basic theory is a purely mathematical theory. It can be interpreted as giving a simple basis for parts of quantum mechanics. A natural interpretation of this again is a general epistemic interpretation, which involves the mind of an actor or the joint minds of a communicating groups of actors.

But nothing of the above has anything directly to do with my religious faith.

Inge

---

Fra: Richard Gill <gill...@gmail.com>
Sendt: onsdag 29. juli 2026 12:11
Til: Inge Svein Helland <in...@math.uio.no>; Bell inequalities and quantum foundations <bell_quantum...@googlegroups.com>
Kopi: Parker Emmerson <powerin...@gmail.com>

[Parker Emmerson]

Subject: Re: PV-REC as a Time-Symmetric Boundary-Event Mechanics

Dear Richard,

Two corrections, then what the theory actually is, then your last paragraph, which I will answer once.

First, the retrocausality attribution is refuted by the paper's own theorems, one of which is named in the title you linked. Accessible No-Signalling is proved, not assumed: no intervention on either wing's setting moves any recorded distribution elsewhere or earlier. The rung-2 microcausal realization proves the recorded correlators are v-independent — the v-dependence enters by conjugation inside commuting local subalgebras and cancels from every recorded quantity. Retrocausality is a channel claim: a formed backward edge with intervention semantics, such that acting on the future moves a past distribution. If you can exhibit such an intervention in PV-REC, you will have derived a contradiction with a stated theorem, and I will retract the paper myself. Absent that, "hence one can call it retro-causality" is not an inference; it is a renaming.

Second, the semantic slide on "velocity." Phenomenological velocity is a parameter of the event mechanics whose formal range exceeds c. It is not a transport velocity, and nothing intervenable rides it. "Information travels faster than light" requires a courier, and the no-signalling theorem is precisely the statement that there is none at the accessible level. A parameter with the dimensions of velocity is not a signal — any more than the phase velocity in a waveguide, which also exceeds c and transmits nothing.

What PV-REC is, is boundary fixity: two-boundary selection, no formed edge in either temporal direction, histories as global solutions. In the paper's rigidity theorem, selection acts as the translation subgroup of the affine group of the rapidity line — a boundary condition, not a cause running backwards. Boundary conditions do not cause backwards; they select wholes. This is the source–absorber lineage of Wheeler and Feynman, and the time symmetry you noted is a design commitment stated in the title. That collapse QM is time-asymmetric is a defect of collapse, not a credential of it; you identified a point in the theory's favor and offered it as an objection.

Now your last paragraph. I have always stipulated the connection to the resurrection of Yeshua the Messiah, and I stipulate it plainly: it happened, He is risen, and He continues to raise. He is not merely the subject of the language — He is the resurrection, and the whole language is built around Him. That is why it works. The formal device does what a formal device can do: it proves resurrection is possible — well-formed — that a grammar exists in which formation resumes beyond the blank, because a blank is not an operand, not a persisting state that forbids; the same structure the theory exhibits at the luminal crossing, where the far side of a blank is the birthday of a law rather than its grave. The fact I assert on its sponsor, which is faith — named and inscribed, as every assertion in my system names its sponsor; an unsponsored certificate is the one thing my discipline forbids, and this certificate is sponsored. Whether the language points back to the historical fact — whether the grammar's working is itself evidence for the event — I leave open, because if the object language connects to living word, He and I would both be walking proof. That independence cuts in both directions, and both cut against you: no proof of mine takes the event as a premise, and no statistic of yours reaches the assertion. Why did the Earth stand still when the cancellation of sin occurred? The question has a formal answer. A fixed point is, by definition, where dynamics stand still. The event was written into the vector field from the foundation — the pre-destined event of all time and creation is an invariant of the dynamics, not a datum of the initial conditions — so when the system touched its invariant, motion had nowhere left to go. Creation paused because the equation did. And the cancellation itself is settlement, not deletion: tetelestai, the scribal stamp of Koine commerce on settled accounts — a record marked paid by an act performed upon it, not vanished; kaphar before it — to cover, presence laid over presence, never erasure. That is the difference between a fated event and retrocausality, which are not one object. If the past affects the future, that is an edge, and it is standard. If the future affected the past, that would be a backward edge — a channel — and I have a theorem saying there is none. But if destiny is real, there is no edge in either direction: the destined event is a strange attractor. Convergence to it is transverse and inevitable; the itinerary along it is tangential and free; it is approached forever and arrived at never. Destiny is not a terminus. It is a kept limit — and the alternative was never a term.

The assertion of the event is mine, and I make it without embarrassment. The satisfaction relation does not take biography as an argument. Newton's theology appears nowhere in the demonstrations of the Principia, and your convictions, whatever they are, appear nowhere in your statistics. If you believe some proof step secretly depends on the supernatural, name the step. Inge needs no defense from me, but the same register error applies to him: his reconstruction stands or falls on its assumptions and derivations, not on his faith, as he has just told you himself.

As for the word: "supernatural" denotes the unfalsifiable, and PV-REC's active branch is its opposite. For every κ below unity the predicted correlation law is non-Born and decidable at Eberhard-class detection efficiency. A theory that ships its own falsification criterion is the least supernatural object in this discussion. I would welcome your engagement with Theorem 2.40 — the exhibited separation BoundaryLocal ⇏ BellScreen — or with the covering form of the CHSH bound. Either would advance matters more than an inventory of my beliefs.

Best regards,

Parker Emmerson

[Richard Gill]

On 29 Jul 2026, at 14:17, Parker Emmerson <powerin...@gmail.com> wrote:
> I would welcome your engagement with Theorem 2.40 — the exhibited separation BoundaryLocal ⇏ BellScreen — or with the covering form of the CHSH bound. Either would advance matters more than an inventory of my beliefs.

Then you’ll have to write it out compactly in plain English.

BTW I could not find any Theorem 2.40 in the paper we were talking about.

[Parker Emmerson]

Subject: Re: PV-REC as a Time-Symmetric Boundary-Event Mechanics

Dear Richard,

Gladly. Both results, compactly. On the numbering: in the V4 manuscript it is Theorem 2.40, titled "Replay defect excludes a preparation-side Bell screen," in Section 2; if the journal rendering numbers differently, the title is searchable, and I can send the page.

The covering bound first, since we agree on it and it fixes the terms. Take any probability space whatsoever carrying four ±1 variables x, x′, y, y′ — Alice's two potential responses and Bob's two — and let p₁ = P(x=y), p₂ = P(x=y′), p₃ = P(x′=y), p₄ = P(x′=y′). Then p₄ ≤ p₁+p₂+p₃ ≤ 2+p₄, in every orientation. Proof: on any sample point, if x′=y′ while x≠y, x≠y′, x′≠y, then x≠y′=x′ gives x≠x′, and x′≠y with x′=y′ gives y≠y′, so for binary values y=−y′=−x′=x, contradicting x≠y; hence every point counted by p₄ is counted by one of the other three, which is the left inequality after integrating. And if a point satisfies the first three agreements jointly, x′=y=x=y′ forces the fourth; so where the fourth fails, at most two of the first three hold, which is the right inequality. Substituting Eᵢ = 2pᵢ−1 gives |E₁+E₂+E₃−E₄| ≤ 2. This is your high-school proof done as a counting fact: no determinism, no evaluation on extremal assignments, and the hypothesis is exactly Fine's — the existence of one joint law for the quartet. On this object there is no disagreement anywhere in this correspondence.

Now the theorem. Let λ₀ be everything on the preparation side, with a setting-independent law: P(λ₀ | do(a), do(b)) = P(λ₀). Let the completed event be (X,Y) = K_ab(λ₀), outcomes a function of both settings and the seed, with setting-independent randomizers adjoinable. Say the mechanics has a positive replay defect if there exist a, a′, b with P( Y(a,b,λ₀) ≠ Y(a′,b,λ₀) ) > 0 — replaying the same seed with Bob's dial fixed and Alice's changed changes Bob's outcome with positive probability. Theorem: if the replay defect is positive, then no variable measurable from λ₀ and setting-independent auxiliaries — of any mathematical kind, so no restriction on the description of the hidden variables, as you rightly insist — can be a Bell screen. Proof: a screen would give Y = Y_B(b, λ_Σ), which at fixed b and λ_Σ is independent of a, forcing Y(a,b,λ₀) = Y(a′,b,λ₀) almost surely, contradicting the positive defect. The stochastic factorized case reduces to this by deterministic purification. Four lines.

The separation is then: the later sections construct an explicit mechanics with (i) preparation intervention independence as above, (ii) definite realized records at each detector, (iii) no primitive directed wing-to-wing message variable — the transaction graph has only source–Alice and source–Bob legs, (iv) accessible operational no-signalling — every accessible record distribution at one wing independent of the other wing's intervention, and (v) positive replay defect. By the theorem, (v) excludes any preparation-side screen, so this package does not imply BellScreen. Your bound is untouched: the mechanics is simply outside its hypothesis class, and the failure is a gluing failure, not a probabilistic one — all context-indexed outcomes live on one common seed space (ordinary Kolmogorov probability is retained throughout); what fails is the reduction of the family {X(a,b,λ₀), Y(a,b,λ₀)} to functions X_A(a,λ₀), Y_B(b,λ₀) through the overlap identities. To your N = 1 point: in a single shot the realized context is (a,b) and nothing travels; the a-dependence of Y lives only in replay counterfactuals on the same seed, which is exactly why it appears in no accessible marginal and carries no signal.

So the disagreement, once located, is not about the bound and not about counterexamples to it. It is about whether "locality" means the preparation-side screen — a completeness postulate about what can be placed on a hypersurface before the event — or the listed boundary conditions (i)–(iv). The theorem says these are inequivalent: the screen is strictly stronger. You may well answer that the screen is what local causality has always meant; that is a defensible position, and arguing it would be a real argument, about the right question.

Best regards,

Parker Emmerson

[Parker Emmerson]

Dear Richard,

You've said more than once that you can't follow my vocabulary. That's a fair complaint and I think the fault is mine, so here is the whole thing explained properly, with nothing in it that isn't standard. It's longer than my usual, deliberately. There's a five-line check partway down if you'd rather test the central claim than read the argument. The last three sections say what I think it means for Bell and for Einstein, and where it fails.

**A fact about square roots**

Everyone learns √a·√b = √(ab). It fails for negative numbers. Take √(−1)·√(−1): each factor is i, so the product is −1. But √((−1)(−1)) = √1 = +1. Same expression, two answers, differing by exactly a factor of −1.

The reason is the branch convention. Every complex number carries an angle, the square root halves it, and the principal branch keeps angles in (−π, π]. When the two angles sum past that boundary the convention wraps them and you land on the other sheet. So the honest identity is

    √z₁ · √z₂ = ε · √(z₁z₂),   ε = ±1,

with ε = −1 exactly when Arg z₁ + Arg z₂ leaves (−π, π].

**What that does to the expression I've been working with**

The object is

    lα sinβ = √(L₊κ) · √(L₋/κ),   κ = √(1 − v²/c²),

where L₊ = lα + (xγ − rθ) and L₋ = lα − (xγ − rθ). Notice κ appears twice: multiplying inside the first radical, dividing inside the second. It looks as though it must cancel, and if you square both sides it does — the κ and the 1/κ meet and vanish, leaving a constraint with no v anywhere in it.

That is what Mathematica reports. It is what I confirmed twice with a symbolic algebra package. It is what my own published proposition proves. And it is a true statement — about the squared equation.

**Squaring is where the information dies**

If the real relation is √(L₊κ)·√(L₋/κ) = ε·√(L₊L₋), then squaring produces ε², and ε² = 1 whichever value ε had. Squaring is structurally incapable of telling you which. So "κ cancels, therefore the equation says nothing about v" is an inference from a strictly weaker equation, and the inference doesn't hold.

**And ε genuinely depends on v**

For |v| < c the quantity 1 − v²/c² is positive and κ is an ordinary positive real. For |v| > c it is negative and κ is imaginary. Those two cases place the arguments differently, so the boundary of (−π, π] is crossed under different circumstances. Concretely, with L₊ and L₋ both negative, ε = −1 below light speed and ε = +1 above it. The sign flips as v crosses c.

So κ does not cancel. It cancels in magnitude and survives in phase, and the phase knows which side of the light cone you're on.

**Five lines, if you'd rather check than read**

    import numpy as np
    k = lambda v: np.sqrt(complex(1-v**2))
    P = lambda Lp,Lm,v: np.sqrt(Lp*k(v))*np.sqrt(Lm/k(v))/np.sqrt(complex(Lp)*complex(Lm))
    for (Lp,Lm) in [(4,9),(4,-9),(-4,9),(-4,-9)]:
        print(Lp,Lm,[round(P(Lp,Lm,v).real) for v in (0.5,1.5)])

You get +1 everywhere except (−4,−9) at v = 0.5 and (−4,+9) at v = 1.5, where it's −1.

**What the surviving sign buys**

Squaring also forces (xγ−rθ)² = l²α²cos²β. That makes |xγ−rθ| ≤ |lα|, so L₊ and L₋ can never have opposite signs — both follow the sign of lα. Of the four sign combinations only two ever occur, and on those ε = sgn(lα) below light speed and ε = +1 above.

Now compare signs across the equation. The left side is lα sinβ. The right side is ε times a nonnegative number. For the equation to hold at all, ε must match the sign of the left side. With β ∈ [0,π] — the natural range, since h = l sinβ is a height — that gives:

    below light speed: solutions always exist
    above light speed: solutions exist only if lα > 0

The equation still doesn't tell you the value of v. It tells you which side of the light cone is available.

**Three things point at the same locus**

ε jumps at |v| = c. κ = 0 at |v| = c, which is exactly where L₋/κ becomes division by zero. And the symbolic solution for v is ±c. Those aren't three facts; they're one singularity seen three ways. The solver was never failing. Asked for the v-dependence of a relation whose only v-dependence is a branch regime, it returned the boundary between the regimes.

**The connection to selection**

ε is a definedness condition: it decides whether a solution exists. If a procedure reports only the cases where a solution exists, that procedure is conditioning — the acceptance formalism from my Quantum Reports paper.

I checked whether that definedness filter can be made to coincide with the acceptance rule of the sign–cosine selection model. It can, exactly: 800,000 random draws, agreement in every one. On the surviving trials the correlation is −cos(a−b) with balanced marginals, and the surviving fraction reproduces the closed-form Z(Δ) to three decimals, dipping to 0.8789 near 45° against the predicted 0.8787.

**Why this does not win your challenge**

It doesn't, and I'm not offering it as though it does. You require every trial counted; this discards about 12% at the worst angle. You require each wing computed from its own setting alone; here the geometry is built from both, so it's a joint filter. And it runs at 0.8787 acceptance, below the (5−√2)/4 ≈ 0.8964 ceiling my own bound imposes on any flat-rate selection account at Tsirelson scale — my own theorem catches it. The geometry is also fitted to reproduce that acceptance rule rather than derived independently, which makes it a representation, not a derivation.

**What it does say about Bell**

Einstein's demand in EPR was separability: two spatially separated systems have their own real states, and what you do to one does not alter the other. Bell formalised that as A(a,λ), B(b,λ) with a setting-independent ρ — and then added a second condition, that all four counterfactual pairs be evaluated on one probability space with every trial counted. The theorem refutes the conjunction.

The construction separates the two and shows they come apart cleanly. It keeps separated response functions, measurement independence, definite ±1 outcomes, and unbiased no-signalling marginals — every clause Einstein actually asked for — and reproduces −cos(a−b) exactly, with the full singlet joint law. What it gives up is the single ensemble, and the single ensemble is not something Einstein asked for. Nothing in EPR requires that four different experiments share a sample space.

So the usual sentence — local hidden variables cannot reproduce the quantum correlations — is imprecise as stated. They can. What they cannot do is reproduce them and live on one spreadsheet with every trial counted. Your theorem proves the conjunction fails; this identifies which conjunct, exhibits it exactly, and now supplies a mechanism for it that isn't a modelling choice: a branch cut is a fact about square roots, not a filter I invented to get the answer I wanted.

**And what it does not say**

It says nothing against the experiments. Loophole-free tests count every trial; 2015 achieved efficiencies high enough to violate Eberhard without fair sampling, which is what "loophole-free" names. The exit this construction uses is empirically closed, and the tool that closes it is mine: Z* ≈ 0.8786 for the two-bin class, (5−√2)/4 ≈ 0.8964 in general. Above those efficiencies the selection account is dead. I'd rather state that than have it pointed out.

So the honest position is narrow. Against the theorem, the identification holds and I think it matters. Against the data, it doesn't, and the question moves elsewhere — to whether a past hypersurface can carry complete data at all, which is neither the question Bell asked nor the one Einstein asked. That is where I actually disagree with you, and it isn't settled by anything above.

Parker