At 3009 I tried to explain why I consider this statement a tautology.
Eckard
More realistic fundamentals: quantum theory from one premiss. by Gordon Watson
Dear Gordon Watson
Thanks for well studied comments on my essay
Your observations about truth do indicate that you are well educated and knowledged person... It is very nice that you work is based on experimental evidences from QM. Any study or work will be successful if it is based on experiments.
..............Your words....
From this recap, I trust you can see that I am in agreement with this (from you) --- "I use everyday physics as achievable by engineering" --- me happily recalling that many famous physicists were said to be, firstly, engineers.
............... Thank you for the supporting comments...
..............Your words....
Alas, as such an engineer, focussed on fundamental foundations, I'm in no position to comment on the grand sweep of schemes like your Dynamic Universe Model.
But from the above it follows that you need have no concern as to what I might mind (or what might be my opinion) about you and your work. I wholeheartedly encourage anyone that seeks to make sense of reality to proceed at their own pace and in their own way; and (as we agree) always with facts and evidence in mind!
In this regard, here are three commonsense mantras that I suspect we share: (1) Reality makes sense and we can understand it. (2) Correlated tests on correlated things produce correlated results without mystery. (3) Only the impossible is impossible.
So for me it is a bonus to see that you are NOT following a branch of main-stream physics that endorses naive-realism: with its consequent quantum-mysteries and nonlocality!
Also: I very much appreciated the question-and-answer-style of your essay; especially the emphasis on experimental results. Though I am more cautious re this conclusion: "No imaginary or negative time axis." Sure that I understand your meaning, I suggest the reference to "an axis" is unnecessary. For me it possible to reason "backward-in-time" from later evidence; like how it was that the Titanic sank so quickly.
With my thanks again for your comments, and wishing you every success; Gordon
PS: As requested, I will post this on your FQXi essay-site.
.............. thank you for nice blessings and Good opinions expressed on my essay.
You have written a nice essay and I am giving a high score ...
Best Regards
=snp
Dear Gordon,
This response is my reply to the comment you posted on my essay "A Fundamental Misunderstanding". I have also posted this response on my essay thread too.
In answer to your question "what happened to classical energy conservation in each and every interaction?":
Every particle detect or non-detect obeys normal, Classical Physics. Energy conservation is obeyed - why would it not be?
If a particle isn't detected is may be simply absorbed by a molecule in the apparatus or elsewhere.
(Questions: 1, 2, 2a) The reason for the Classical prediction being the blue line is this:
Classically each detector has a semicircle of directions where an incident photon will give a + result, and the other semi-circle (of the whole circle)
where an incident photon will give a - result.
When both detectors A and B point in the same direction (or exacly opposite), the semi-circles overlap perfectly giving a correlation of +1 or -1.
As detectors A and B are rotated, the semi-circles' overlap decreases linearly to a minimum (90 degrees between A and b, giving a 0 correlation) and then increases to a maximum again (i.e. now giving a correlation -1 or +1 respectively). So the amount of correlation expected is a straight line from +1, through 0 and then to -1.
(3) Yes of course different experiment have differing detection efficiency, and different papers have different correlation results too, but there are no experiments with 100% efficiency; indeed the best efficiencies are still quite low, allowing for a significant non-detect count.
(4) What is GHZ? are you referring to a particular experiment/paper?
A single particle event doesn't prove anything. The correlation is built up from numerous events. To discount non-detects one would have to have very good (approaching 100%) efficiency, which no experiment yet has come close to.
(5) I am aware that the detection loophole has been used to explain the BT result for a long time, and I used to talk to Caroline Thompson about Physics in the past.
My paper is mainly about showing that the detection loophole is still a viable explanation as the so called 'loophole free' experiments using a Steering Inequality do not close the detection loophole as claimed. My model shows a clear violation of the Steering Inequality using Classical Physics via the detection loophole.
The two computer challenge is exactly the same as my model. The two functions for determining the results from A and B could easily be run on different computers
in different rooms - or even different Galaxies if you like. It will still give the QM correlation using a Classical model based on non-detects.
I don't have time at the moment to analyse and undertand your paper fully, but I did pick up on this excerpt:
"For us, EPRB entanglements arise from the pairwise conservation of angular momentum; as in (3). (ii) A logical necessity therefore follows: if the a-component of О»i is known (say, via Ai = 1), then (if tested), the a-component of Ојi will certainly deliver Bi = в€'1."
Essentially it seems to me that you are saying that the two photons in the experiment have opposite angular momenta, thus conserving angular momentum across the experiment.
Yes, there is no doubt of that - but this is not sufficient to assure that detectors A and B have correlated results at different angles, as each detector has a probability of detecting each photon as either + or -. What the EPR experiment reveals is that when the two detectors have nearly the same orientation they have a high degree of correlation despite not knowing
where the other detector is. So to build up a high correlation between A and B, each detector would have to register more + results (for photons incident on them from at the samse angle) when the other detector is in a certain location; then register more '-' results when the other detector is in a different location, despite not being able to know that other detector's location!
Regards,
Declan Traill
Dear Gordon
If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.
Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?
My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.
Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?
For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.
My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.
By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.
To steal a phrase from my essay "A world product of evolved optimization".
Best of luck for the conclusion of the contest
Kind regards
Steven Andresen
Darwinian Universal Fundamental Origin
Thanks Declan, your prompt reply is appreciated. It's also good to see that we have some agreements; but I won't dwell on them for now. Instead I want to discuss what looks like (in my opinion) a serious point of disagreement.
Please note that I have no wish to discourage you -- quite the contrary -- because I think you have guts and brains; and perhaps it is me that errs. However:
Imho, what you call "Classical" or "Classical Physics" is not classical at all.
Thus your "reason for the Classical prediction being the blue line is this: Classically each detector has a semicircle of directions where an incident photon will give a + result, and the other semi-circle (of the whole circle) where an incident photon will give a - result."
May I take it that this "classicality" is part of your own theory? Or do you have a source? And can you be more specific, please, and consider your "detector" to be built from a polarizer followed by an analyzer?
For it's true that Bell 1964:(4) uses a similar approach, but only by way of illustration: for I'm not aware of any classical textbook advancing such a theory. What's more I do not see how your idea works for the usual classical demonstrations that are conducted with three 'sandwiched' polarizers: where brightness measurements show good accord with classical theory without allowances for "non-detects"?
You should be able to do the classical textbook calculation and see that it yields an expectation of one-half the QM value; which is NOT the blue line: instead it will be one-half the green line.
Then, regarding this next point of yours [with my emphasis]:
"Essentially it seems to me [DT] that you [GW] are saying that the two photons in the experiment have opposite angular momenta, thus conserving angular momentum across the experiment. Yes, there is no doubt of that - but this is not sufficient to assure that detectors A and B have correlated results at different angles, as each detector has a probability of detecting each photon as either + or -. What the EPR experiment reveals is that when the two detectors have nearly the same orientation they have a high degree of correlation despite not knowing where the other detector is. So to build up a high correlation between A and B, each detector would have to register more + results (for photons incident on them from at the same angle) when the other detector is in a certain location; then register more '-' results when the other detector is in a different location, despite not being able to know that other detector's location!"
In reply, with Einstein-locality ensuring that no detector has any 'knowledge' about the other: in EPRB (eg, using Aspect's experiments) the probability of +1/-1 from each detector is 50/50, for all (a, b); so there is no "knowing" required. And the related correlation is twice the classical correlation because pairwise "entangled" photons (ie, in the singlet state) are more highly correlated than pairwise correlated photons (in beams) correlated by linear-polarization only.*
Re the latter, I recommend that you do the classical calculation; re the former I would encourage you to study my essay and ask questions. For I am keen to see where we might disagree and where things might be improved; me noting that the only change I make to modern physics is to take Bohr's "disturbance dictum" seriously.*
* My own dictum: Correlated tests on correlated things produce correlated results without mystery; and correlated tests on more correlated things produce more correlated results without mystery.
PS: The GHZ I mentioned is [14] in my References; you'll see the 4-particle GHSZ variant of EPRB in [13].
HTH, with best regards; Gordon
Hi Gordon,
The disturbance interpretation is very appealing, since it maintains our realistic view of beables. I will come back to that below on how I see it, in light of the interpretation I gave in my essay. First one note on your essay.
The formalism you use is not so transparent. However I think I got the idea. Where I see a problem is the link between formula (8) and (9). This needs more clarification. The source information (beta) disappeared. I can imagine, that this is because of the perfect correlation of the angular momentum (ref. 15.12). However from the observed polarization vector (ref. 15.10) the total information of the angular momentum (ref. 15.11) cannot be inferred completely. Hence the source (beta) should not disappear in the derivation of the conditional probability.
I will come back to the disturbance interpretation - how I see it - another time. Only so much: causes and effects are not as unambiguous as they seem and the condition for the possibility to make inferences from a measurement might depend on conditions not included in the description of the experiment (for instance the environment, which must be separable from the system).
Best regards,
Luca
Hi Luca, and many thanks! [nb: below, the superscript-function does not work with ±. I use "bold" to identify the start of my comments; not for emphasis.]
I agree: "The disturbance interpretation is very appealing, since it maintains our realistic view of beables."
I acknowledge that many agree with you: "The formalism [I] use is not so transparent."
But this next from you gives me hope for the formalism: "However I think I got the idea." nb: the formalism is meant to be physically significant in that a beable is represented by the same physically significant symbol: objectively/ontologically in spacetime and abstractly/epistemically in the mathematics.
I thank you for this: "Where I see a problem is the link between formula (8) and (9). This needs more clarification. The source information (beta) disappeared. I can imagine, that this is because of the perfect correlation of the angular momentum (ref. 15.12). However from the observed polarization vector (ref. 15.10) the total information of the angular momentum (ref. 15.11) cannot be inferred completely. Hence the source (beta) should not disappear in the derivation of the conditional probability." Please note: I do NOT infer to the total information of the angular momentum; for (as you rightly say) such cannot be inferred completely under β. However, I can carefully infer to the equivalence relations: and here I use a weaker, more general equivalence relation than that used by EPR and many others (about which we seem to agree; which is good).
In addition, note that β in (8) specifies the conditions under which the related (immediately-preceding) argument must be interpreted. So β drops out when we interpret (8) correctly and arrive at (9). This is explained in ¶6.2-6.3; but let me add for greater clarity:
The physical significance of the argument in (8) is this. Under condition β (and thus using the equivalence-relations established under β, etc) we are asked to evaluate the (possibly-disturbing) interaction between a polarizer δb± and a polarized particle q(a-). And we need the probability that q(b+) is the outcome. But, via our equivalence relations, this interaction/probability is just that covered (already classically) by Malus' Law.
So we use Malus' Law, to write (9) immediately. And we write QED because our result is that confirmed by QT under β. HTH?
In reply to this: "I will come back to the disturbance interpretation - how I see it - another time. Only so much: causes and effects are not as unambiguous as they seem and the condition for the possibility to make inferences from a measurement might depend on conditions not included in the description of the experiment (for instance the environment, which must be separable from the system)."
Agreeing with EPR, every relevant beable must be included in our analysis. So if you follow the suggestion in ¶4.1 to Watson (2017d:§2) you will see that my (1)-(2) includes the beable of spacetime, here reduced to 3-space since time and gravity are not essential beables under β.
With my thanks again, I look forward to your further comments on my disturbance interpretation: and any other concerns, critiques, suggestions, etc. I cannot be offended and learn much from such.
Gordon
Eckard, from me, via your essay-thread: GW. -------
Dear Eckard: above you wrote:
"Gordon Watson wrote: -- "Reality makes sense and we can understand it." --
In my understanding, this is a tautology because I am merely distinguishing between mysticism and conjectured reality of anything including the also comprehensive notion of the physical universe."
My use of that phrase is an affirmation that links to your statements: "There is only one reality;" and "Causality [see my use of -- "interactions" --] is most fundamental to reality." Thus, as in my essay, my efforts to understand begin with the premiss of true local realism (TLR)* in spacetime.
"Not curiosity, not vanity, not the consideration of expediency, not duty and conscientiousness, but an unquenchable, unhappy thirst that brooks no compromise leads us to truth." G. W. F. Hegel.
* TLR: true local realism is the union of true locality and true realism. True locality insists that no influence propagates superluminally, after Einstein. True realism insists that some existents may change interactively, after Bohr.
All the best; Gordon
By GW, from Declan Traill's essay-thread:
.........
Declan, referring to my earlier suggestion, and seeking to continue our discussion efficiently, it would help me if you could post your responses on my essay-thread so that I get an alert!
Now, to be clear on a significant point of difference in our theorizing: ie, I point out that your theory is not classical.
In your essay you write that Figure-1 shows the "Classical prediction in Blue." From your comments above, I take it that you did not derive that line yourself? And that you have no such derivation?
Here's what I find when I check the two sources that you cite in comments above:
You write: "It's not just me saying that the Classical prediction is linear, it says so on the Wikipedia page on bells theorem: See the diagram in the overview section here:https://en.m.wikipedia.org/wiki/Bell%27s_theorem"
But, in reply, please note the Wikipedia wording:
"The best possible local realist imitation (red) for the quantum correlation of two spins in the singlet state (blue), insisting on perfect anti-correlation at zero degrees, perfect correlation at 180 degrees. Many other possibilities exist for the classical correlation subject to these side conditions, but all are characterized by sharp peaks (and valleys) at 0, 180, 360 degrees, ..."
The best possible local realist imitation: insisting that it be bound by two points!* Best possible? Imitation? And presumably a naive-realist (see next).
You also write: "Also see this presentation by Alain Aspect on the EPR experiment:
http://online.kitp.ucsb.edu/online/colloq/aspect1/pdf/Aspect1.pdf"
Please note that Aspect's slide is headed: "NAIVE example of LHVT."*
Thus, so far, nowhere do I see a classical calculation delivering your Blue line. (And my comments on the non-classicality of your attempt to MATCH the Green line remain.)
* PS: The benefit of classically deriving one-half the GREEN line, based on polarized particles is that you can see that the tighter correlation under the singlet state in EPRB will deliver an understandably different (but related) correlation, without mystery.
HTH; Gordon Watson More realistic fundamentals: quantum theory from one premiss.
Gordon,
I was happy to accept that the linear expectation was already derived by others, and on thinking about it could see how it was derived (as I explained earlier with the hemispheres) so I saw no need to re-derive it in my paper as it is in the Wikipedia page anyhow.
Incidentally Alain Aspects presentation does show how it was calculated on page 13, with the sign() formula for A and B.
Regards,
Declan
Background to Wholistic Mechanics (WM)
Whereas QM emerged from the UV-catastrophe ca1905, WM emerges from the locality-catastrophe typified by John Bell's dilemma ca1965: ie, seriously ambivalent about AAD, Bell adamantly rejected locality. He later surmised that maybe he and his followers were being rather silly -- correctly; as we show -- for WM is the local theory that resolves Bell's dilemma [there is no AAD] and proves the Bellian silliness.
So WM begins by bringing just one change to modern physics: rejecting naive-realism, true realism insists that some beables change interactively, after Bohr's disturbance-dictum. Thus recognising the minimum-action associated with Planck's constant, WM then recognises the maximum speed associated with light: for true locality insists that no influence propagates superluminally, after Einstein.
The union of these two classical principles -- the foundation of WM -- is true local realism (TLR). Under TLR, EPR's naive criterion for "an element of physical reality" is corrected, then the Laws of Malus and Bayes are validated in the quantum world. Then, via the R-F theorem ca1915, Born's Law is seen to derive from elementary Fourier theory. This in turn allows us to understand the physical significance of Dirac's notation; etc. Thus, beginning with these elementary natural principles, WM's universe-of-discourse focuses on beables in spacetime: with mathematics taken to be our best logic.
NB: Formulated in 1989 in response to a challenging article by David Mermin (1988), many leading Bellian physicists and philosophers have committed to review the foundations of WM and its early results. Since no such review has ever been delivered, I am not yet aware of any defect in the theory. Further, WM provides many ways to refute Bell's theorem (BT): one such is provided on p.8 of my essay.
PS: To those who dismiss my essay due to an alleged typo in the heading, I follow C. S. Peirce (absent his severity): "It is entirely contrary to good English usage to spell premiss, 'premise,' and this spelling ... simply betrays ignorance of the history of logic."
Assuring you that critical comments are most welcome,
Gordon Watson More realistic fundamentals: quantum theory from one premiss.
Gordon,
As I already showed you in my email correspondence including the correlation graph and model code, modeling the EPR experiment using Malus's law does not give the correct correlation curve.
So whatever your maths shows, if you cannot model it and get the correct correlation curve then it is wrong.
Regards,
Declan Traill
Dear Steve, thanks for dropping by and alerting me to your absorbing essay.
The fuller story: "As high seas crashed about you, a black bottle smashed aboard. Seeing the now-revealed message, you transcribed it here as your opening paragraph: not realising that you had discovered the long-lost introduction to Moby Dick."
Thus does your poetic bent go on to reveal your wide-ranging knowledge of important themes and buzzwords: inviting me to an exciting universe of discourse based on ideas, thoughts, poetry, etc. Alas, for me (an engineer), devoid of mathematics.
It's this last aspect that I seek to address in my essay -- mixing my poor poetry with simple math --- prompting another alas: it's nowhere near as popular as yours.
So please bring your poetry and your heavy-duty know-how to bear on my essay: for I will welcome such to trigger corrections and improvements. Hoping it will help to bring out the best in you, here's some background info.
Background to Wholistic Mechanics (WM)
Whereas QM emerged from the UV-catastrophe ca1905, WM emerges from the locality-catastrophe typified by John Bell's dilemma ca1965: ie, seriously ambivalent about AAD, Bell adamantly rejected locality. He later surmised that maybe he and his followers were being rather silly -- correctly; as we show -- for WM is the local theory that resolves Bell's dilemma [there is no AAD] and proves the Bellian silliness.
So WM begins by bringing just one change to modern physics: rejecting naive-realism, true realism insists that some beables change interactively, after Bohr's disturbance-dictum. Thus recognising the minimum-action associated with Planck's constant, WM then recognises the maximum speed associated with light: for true locality insists that no influence propagates superluminally, after Einstein.
The union of these two classical principles -- the foundation of WM -- is true local realism (TLR). Under TLR, EPR's naive criterion for "an element of physical reality" is corrected, then the Laws of Malus and Bayes are validated in the quantum world. Then, via the R-F theorem ca1915, Born's Law is seen to derive from elementary Fourier theory. This in turn allows us to understand the physical significance of Dirac's notation; etc. Thus, beginning with these elementary natural principles, WM's universe-of-discourse focuses on beables in spacetime: with mathematics taken to be our best logic.
NB: Formulated in 1989 in response to a challenging article by David Mermin (1988), many leading Bellian physicists and philosophers have committed to review the foundations of WM and its early results. Since no such review has ever been delivered, I am not yet aware of any defect in the theory. Further, WM provides many ways to refute Bell's theorem (BT): one such is provided on p.8 of my essay.
PS: To those who dismiss my essay due to an alleged typo in the heading, I follow C. S. Peirce (absent his severity): "It is entirely contrary to good English usage to spell premiss, 'premise,' and this spelling ... simply betrays ignorance of the history of logic."
Assuring you that critical comments are most welcome,
Gordon Watson More realistic fundamentals: quantum theory from one premiss.
Declan, re the correlation graph that you sent me: please post the graph as an attachment. I would like to reply in detail with reference to that context. Thanks; Gordon
Gordon,
Attached is the correlation curve, and here are the Alice and Bob functions modeling Malus's law that generated it:
function GenerateAliceOutputFromSharedRandomness(direction, sharedRandomness3DVector) {
var dot = Dot(direction, sharedRandomness3DVector);
var angle = Math.acos(dot);
var rand = Math.random();
if (dot > 0) {
if (rand < (Math.pow(Math.cos(angle),2))) return +1;
return -1;
}
else {
if (rand < (Math.pow(Math.cos(angle),2))) return -1;
return +1;
}
};
function GenerateBobOutputFromSharedRandomness(direction, sharedRandomness3DVector) {
var dot = Dot(direction, sharedRandomness3DVector);
var angle = Math.acos(dot);
var rand = Math.random();
if (dot > 0) {
if (rand < (Math.pow(Math.cos(angle),2))) return -1;
return +1;
}
else {
if (rand < (Math.pow(Math.cos(angle),2))) return +1;
return -1;
}
};
Regards,
Declan TraillAttachment #1: 9419AD67-D625-4CBF-880F-75AF534FD87C.png
Declan, thanks for attaching that strange (red-spotted) graph that you emailed to me. From your emails it appears you think it correct and that (somehow) my suggested remedy won't work. I'm hoping what follows (and further discussions, if necessary) may convince you otherwise.
I'm also hoping that you will now quickly spot the source of "the twist" in your graph -- when corrected, it will mirror one-half the Green line -- so that you can then offer it as remedy to the many world-wide fallacies that attach to that misleading straight-line. Of course, as discussed, I would also encourage you to revert to formalism NOT modelism in this area: where the former is simpler (and far less misleading; see the equations below).
In a fairly obvious notation: α denotes Aspect's (2004) experiment (s = 1). β denotes EPRB (s = 1/2). Subscript c denotes a classical variant of the quantum experiments: ie, classically, the particle-pairs are correlated under linear-polarisation only. Thus, classically under c, and from my theory under "entanglement" -- see my essay -- we find:
[math]E(a,b|\alpha_c)=P(AB=1|\alpha_c)-P(AB=-1|\alpha_c)=\tfrac{1}{2}cos2(a,b).\;\;QED.\;\;(1)[/math]
[math]E(a,b|\alpha)=P(AB=1|\alpha)-P(AB=-1|\alpha)\;\;(2)[/math]
[math]=cos^{2}(a,b)-sin^{2}(a,b)=cos2(a,b).\;\;QED.\;\;(3)[/math]
[math]E(a,b|\beta_c)=P(AB=1|\beta_c)-P(AB=-1|\beta_c)=-\tfrac{1}{2}a.b.\;\;QED.\;\;(4)[/math]
[math]E(a,b|\beta)=P(AB=1|\beta)-P(AB=-1|\beta)\;\;(5)[/math]
[math]=sin^{2}\tfrac{1}{2}(a,b)-cos^{2}\tfrac{1}{2}(a,b)=-a.b.\;\;QED.\;\;(6)[/math]
The superiority of formalism over modelism then becomes clear. A physicist (thanks to Bohm), comparing (1) with (3) -- or (4) with (6) -- sees that the superior correlation of the quantum-source gives superior results, without mystery (compared to the weaker correlation provided by the "classical" source). In other words, pairwise correlation under linear-polarisation is weak compared to pairwise correlation under the conservation of total angular momentum.
It follows that the so-called "classical straight line" -- from all your sources -- is misleading: and the related flawed analyses do not support profound claims. Which is not to discourage you -- it is rather to redirect you from a popular dead-end to some real-physic; perhaps beginning with you challenging and correcting the hard-straight-liners; including Aspect.
To that end -- since my theory reflects the end that you (and many others) are seeking; with just one commonsense refinement to modern physics -- I look forward to discussing where I too might be on the wrong track.
With best regards; Gordon
Gordon,
Whilst the mathematical equations look nice, you cannot ignore it he modeling as that is the essential step to prove or disprove a theory. If you cannot generate the correlation curve using just Alice and Bob functions to determine detector results in a model of the experiment then you have nothing.
Regards,
Declan
Thanks Declan. Surely that 2-computer contest is still running ...
Trusting you've spotted the source of your erroneous twist; with best regards; Gordon
Yes but I think the contest doesn't allow for non-detect results, only and - results, making it impossible to do...
Gordon (Declan)
I'm leaving you two to sort that! We must of course explain the high non-detects, clearly near zero amplitude. And also both Aspect and Weighs' 'rotational invariance' - unexplained so the data dumped! Both computer codes and alorythmic sequence is needed as well as (apparently!) deriving the Hamiltonian!
I'm drawing a visual sequence, as that's how most brains best embed things. I've also posted this introductory aid memoir sequence in a few places to help; The Poincare Sphere was an important find (having already derived it from scratch last year!) Let me know if you think I've missed anything.
1. Start with Poincare sphere OAM with 2 orthogonal momenta pairs NOT 'singlets'.
2. Pairs have antiparalell axis (random shared y,z). (photon wavefront sim.)
3. Interact with identical (polariser electron) spheres rotatable by A,B.
4. Momentum exchange as actually proved, by Cos latitude at tan intersection.
5. Result 'SAME' or 'OPP' dir. Re-emit polarised with amplitude phase dependent.
6. Photomultiplier electrons give 2nd Cos distribution & 90o phase values.
7. The non detects are all below a threshold amplitude at either channel angle.
8. Statisticians then analyse using CORRECT assumptions about what's 'measured!
Peter