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
Declan, re the correlation graph that you sent me: please post the graph as an attachment on my essay-thread. I would like to reply in detail with reference to that context. Thanks; Gordon
Declan, this is from my essay thread, in reply to the graph that you emailed me. GW ...............
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 Watson More realistic fundamentals: quantum theory from one premiss.
Declan, I've replied below, showing how Malus does give the correct result: and sure that you will spot your simple mistake when you see my equations. Cheers; Gordon
Hello Declan,
Pasting in from a thread with Peter Jackson in the comments of essay by Michaele Suisse and myself. Want to wade thru comments on your essay, then come back to offer more:
Peter,
Looked again a couple times at Traill's essay. Perhaps starting to get the connection Terry Bollinger was trying to point out.
From perspective of the geometric wavefunction interaction (GWI) model Michaele and I are working with two essential points relevant to Declan's essay seem to stand out.
1. There exist two different varieties of quantized impedances - scale invariant and scale dependent. Forces associated with invariant impedances can do no work, cannot share energy/information. Resulting motion is perpendicular to direction of applied force. These are the conduits of non-locality. They communicate only the quantum phase of entanglement, not a single measurement observable. Here the GWI approach appears to be in harmony with what Declan shows.
2. What distinguishes quantum from classical is quantum phase. Once one accounts for the fact that phase is not a single measurement observable, from the perspective of our synthesis of geometric wavefunction interactions with quantized impedance networks QM appears 'classical', again in agreement with Declan's conclusion.
Having arrived at this, now feel ready to take a look at Watson, and then yours again. Tho we're not math folks here, Poincare sphere is only slightly familiar to me from Penrose's road to reality.
Dear Declan Andrew Traill,
The tables on page 10 and 12 are similar.
The page 10 table has been arrived at using 7 squares as below:
No. Fig. Angle Area
1 15c 00 100
2 14c 15 093
3 13c 30 075
4 12c 45 050
5 11c 60 025
6 10c 75 007
7 09c 90 000
The table on page 12 has been arrived at using 9 squares and the precision is to the first decimal place.
Kamal Rajpal
Dear Declan Andrew Traill,
2D space can be filled up with squares but not with circles. See figures 1, 2, 3 and 4 on pages 4, 5 and 6. You are calculating the area inside the circle only. I am doing it inside the square. This was the mistake made in 1935. See paragraph 1 on page 11.
The tables on page 10 and 12 are similar.
The page 10 table has been arrived at using 7 squares as below:
No. Fig. Angle Area
1 15c 00 100
2 14c 15 093
3 13c 30 075
4 12c 45 050
5 11c 60 025
6 10c 75 007
7 09c 90 000
The table on page 12 has been arrived at using 9 squares and the precision is to the first decimal place.
Kamal Rajpal
Declan,
Does your code completely fit the mechanism in Peter Jacksons essay? It took me some time to familiarise myself with it as it includes a number of fresh views and elements, all rather better evidenced and more logical than the original. I hope we're in for that revolution and hope to see you keep working together! I suspect only a strong collaboration will penetrate established views.
I'm giving you top marks for yours as, like Peter's, it's so fundamentally important. I wish I could help as it looks like there's some detailed mathematical or algorithmic back up still needed, unfortunately not my specialism.
Very best of luck in the judging, though from what I've seen in the past it's a bit of an 'old pals' or community benefit excercise, rather opposite to the point of fqXi!
Very well done anyway.
Rich
Declan, Richard
I explained the fit to Richard. It's been interesting how few have or have bothered to follow the mechanism. I set out a way ahead on my blog in answer to Gordon. Hope you two can reach agreement.
Andrew Beckwith complains he's been multi 1 bombed as I know you have so do read & support his if you haven't yet.
Very best
P
Hi,
Have you tried to put it on a Bloch sphere? The slope is important. Is it intermediate?
Ulla Mattfolk
Also, how is the QM line computed? uncertainties? entanglements????
Declan,
I've discovered that if you make a lot of FQXi comments for a lot of essays, figuring out whether someone has replied can be... tricky, even if you sign up notifications. The notifications do not tell you who added a comment! So my apologies, I only just now found your reply above, even though I looked for one (apparently in the wrong place) a couple of times.
Yes, you are exactly right that a ball is how your space should be described, not a cube. I don't recall why for sure, but I think I said "cube" only to emphasize that you model was using a nicely visualizable 3D space.
Bummer that more folks didn't get your model, though at the same time my own near-dismissal helps me understand why. Yours is a model that you have to dig into pretty deeply before you can start seeing how the transforms work out.
Likely I'll have more to say on this issue later, but for now I'm just playing catch up. I absolutely love that there are no ratings now, just comments! That makes it so much easier for folks just to talk about ideas, if they want to.
And apparently there is no deadline whatsoever for making comments, which is strange. But I looked, and the comments I made a few days ago on an essay thread you created 5 years ago is still there. Wow!
Cheers,
Terry
Declan Traill
If you read this you may be interested in my last blog at:
Regards from John-Erik Persson
