Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

pjackson

Richard,

The EPR experiment is now ready for all to repeat. I'll describe what Alice & Bob do and find. As our 'discrete field' model is of nature we do also need 90-180^o, but just treat 112.5^o as equivalent to 67.5^o etc. I identify detector field electron behaviour found after QM's formulation. An important role for it emerges along with a logic for QAM 'superposition'.

1. Alice opens your envelope and turns her dial (the top 180^o of a 'ring' with one slot) to the chosen EM field setting angle. An instant after the angle is set the random 'singlet state' particle arrives and 'interacts' with it; It's also a (half) disc, which just sits behind, either the Head or Tails side faces the dial. Bob does the same far away with the opposite state particle (so no short range phase-lock etc.)

2. The particle orbiting charges +1 (green) and -1 (red) are represented by colours on the disc with a sequential Red to Green spectrum. Head & Tails sides are 'opposite', so non mirror-symmetric, as OAM (red is behind green). One student at a time represents the photo-multipliers, so watches the 'slot' in the filter dial.

3. When a colour appears in the slot the choice must be made; Is the colour 'closer' to Green? or to Red? ('up' or 'down'). The limited setting angles you specified correspond to; 0^o= green, 22.5= lime, 45= yellow, 67.5= gold, 90= sand, 112.5 = buff, 135= peach, 157.5= orange, and 180^o= red. A box is ticked with the binary decision; Up/Down (Green/Red), and the setting angle recorded beside the tick.

4. Alice works the dial and one student makes a subjective R/G choice each time. Most choices are fair, and the results are intuitive; Red or Green (180/0^o)? both get ~100%. Orange or Lime (22.5^o)? still very easy for most ~97%. Peach or Yellow (45^o)? rather more uncertainty ~88%. Buff or Gold (67.5^o)? clearly trickier as less than 30%. At around the pale 'Sand' colour (near 90^o) certainty 'bottoms out' with ~50:50 decisions. 5 observers had min 10 goes each, at min 20 relative setting angles (so avoiding 'familiarity bias'.)

5. For analysis of each 'local' result set; single particle experiments have find violation of the Bell inequalities (that in itself problematic for QM's assumptions). So do we. Now note that 'numbers' representing energy of charge, between +1 and -1 can be substituted for colours for simplicity and precision. (Malus' Law re-emerges; Intensity related to cos^2 theta). That bit couldn't be simpler!

6. We have violations at local 'absolute' angles for A and B but we now need the RELATIVE angle correlation violations. Here we employ the 'particle' spectrum. Take any one angle and simply 'superposed' the A,B data there on the circumference. All identical settings then have perfect correlation. 180^ 'opposite' findings have the least correlation (i.e. Red v Green). We are simply setting a new relative datum at each angle selected. There is no conspiracy, and no more detector influence than in Bells set up, also that single particle findings have already confirmed, and most importantly; the exact influence found in nature (see below).

7. For the 90^o=50% correlation let's use 45^o (Yellow). 90^o away from 45^o is 135^o (Peach). So we ask the question; Does Peach correlate/anti-correlate with Yellow? (is Peach closer to Yellow than it's spectral opposite?). Uncertainty is maximised as peach is 90^o away! But at over ~120^o (Orange) 'anti-correlate' has ~77% certainty. Whatever the angle (colour) chosen, the 90^o relationship remains, i.e. Correlating A,B,=90^o (Sand) we find full A,B, result correlation, but deciding if red/sand 'correlates' (relative 90^o) is as hard as; sand/red, so also 50:50. 30^o Lime/Yellow = >95%. as locally, and as you might expect.

So we seriously violate the Bell Inequalities and no state reduction is required. None is needed classically as we've invoked nature. As angular momentum is not mirror symmetric. Here's the big shock; In the DFM, ALL spin 1/2 particles really ARE a superposition of both states in the same way that Earth is a 'superposition' of clockwise and anticlockwise rotation. It's observer dependent (from which pole!), so 'vector' dependent. Particle spin is conserved with propagation axis ('rifled'), but detector field electron orientation IS NOT conserved. Electron QAM 'flips' at 90^o. (i.e. http://arxiv.org/pdf/1312.4881.pdf). (CSHS and Hardy are then both invalid). QAM internal momentum is 'conserved' on rotation in 3 axes, but direction on 'exchange' varies. Other 'directions' can't be combined with a single 'operator' but have discrete 2nd order distributions which binary statistical analysis is 'blind' to.

As momentum transfer ('detection') is relative, all particles may then be found in either state by A or B at any setting. That insight is what gave the discrete field model prediction of the 99.999% anomalous findings in Aspects experiment (discarded for lack of a theory to fit them) also found (and not analysed!) in Weihs et al) electronic version; so rotation variant with voltage. The DFM is then also falsifiable by further precise time resolved pair experiments.

As I've discussed in my last 3 essays the model suggests a route for convergence of QM and Relativity, as Bell predicted. His inequality limit remains valid, but the theorem needs a caveat as he inherited a hidden flawed assumption underlying QM. We can now 'say' more than we could back then about particles.

I hope you can make sense of that. Give it a test run and it simplifies.

Best wishes

Peter

Akinbo Ojo

What is the use of repeating the EPR experiment and trying to prove and disprove Bell's theorem when fundamental definitions are ambiguous and starting assumptions are not well defined?

For example, "local length 1 is identical to global length 1" and "...an acceptance of the sense of continuum at all points, being of a same single thing, just at a different place"

Questions:

Can a single thing that is claimed to be of zero dimension occupy a place in any sense of the word 'place' or can it itself be occupied in physical reality? Or what is the meaning of at a different place? Can something without extension be at a place?

Is local not subsumed within what is global? And if so, how can the local length be identical to and contain the same Euclidean set of points as a global length?

But when one demands answers to these questions from those who will have us overlook them, they get irritated and rather than answer they tell you to go and read books on continuous geometry when we all know the answers are not even in those books. If the answers were already there the FQXi community will not still be debating whether reality was analog or digital.

In any case, IF and the emphasis is on IF ... Just if space (points, lines, surfaces, bodies) is discrete what becomes of EPR, Joy's work, etc? That possibility should be contemplated and a plan B provided to us.

Akinbo

Richard Gill

Peter, I can make no sense of that.

I asked for a concrete clear description of who does what, when. I don't want to know about your ideas of the fundamental physics. You said this was a classroom experiment which can be easily done.

What does student Alice do in classroom A when she receives (a) an envelope or other package from stern Professor Gerlach containing some kind of representation of hidden variables coming from a source and (b) an envelope from Angus who, far away, tossed a coin and wrote "H" or "T" on a piece of paper in the envelope.

And similarly for student Bob in classroom B who gets a message or some other kind of package from Gerlach, and a secret message in an envelope from Barbara.

pjackson

Richard,

Alice turns her dial, as Weihs did, to the random setting.

When the random H or T side hits the dial she sees a spectral colour.

She decides if it's closest to Red or Green, and ticks either the R or G box.

The setting angle is noted beside the tick.

(also as Aspect and Weihs found, the 'colour' she sees changes with setting).

Repeat 500 times. (Bob does the same with the opposite side of the coin/disc).

Her own local findings show the Bell inequalities violated, as do Bob's.

When collated (dumped in a 'bin') for each setting angle, and compared with other RELATIVE setting angles, the local inequalities remain in the data.

The most fundamental assumption of QM is challenged; the 'pure' singlet state.

Peter

Richard Gill

Peter, you do not do what I ask you to do. One coherent and brief description of who does what when. What do I need to do to run the experiment myself? I am not interested in your description of what statistics I will observe.

pjackson

Richard,

I've just sent you an experimental kit to help, with some simple instructions. (available to all at no charge on request).

Print off 4 copies (just one A4 colour page).

Cut out one spectral coloured disc to stick on the back of the other (non mirror symmetrically, so red behind green).

Cut out the dial with a slot as shown, so it can be pinned and the slot rotated to any of the marked (22.5^o) angles. (also take some card cut out a 1/4 quadrant, with 3 = spaced notches in the arc side, that can also pivot).

Select an angle and set the dial.

When the tosser has done his bit and the (H/T) coloured disc arrives, slot the correct side in behind the dial (with 0^o facing 0^o).

A colour will show in the slot. Show it to one person nominated each time, who then decides if the colour is nearer to RED or GREEN, ticks the box (R/G) and notes the angle. Due to systematic limitations the more who make the choice the better, and they should only see the colour in the slot on their go, not the process or discs etc. (modelling reality), or any other rounds or decisions

Repeat ad infinitum. (Bob does the same with the other H/T side of the disc).

The collator first analyses each LOCAL set of findings for each setting, then sends them off for statistical A/B comparison.

The 1/4 quadrant is then set with one radial side on the setting angle being analysed. The relative angles are then shown by the notches using the setting as the 'datum' (the quadrant may be either 'side' of the datum).

To make initial precise plotting easy someone could play Occam and read off the cosines of the angles (but I suspect the colour judgement process should be run through anyway for the classical proof).

If you didn't get the direct mail and 'kit' do let me know.

I hope Joy and others may also wish to give the experiment a try.

Best of luck.

Peter

Thomas Ray

I don't really want to get involved in this, Peter, but fools rush in.

Richard already identified the error ("You didn't give me a choice") some time ago, and it is unfixable:

Because the color spectrum is continuous, and radians are discrete, you're ever only going to get the 2pi rotation result that Bell's theorem already accounts for. In other words, the betweeness of color transitions depends on measurement settings just as in Bell-Aspect. There will always be a transition between the transitions -- which can be adapted to a "quantum Randi challenge" but never to a truly falsifiable scientific theory of quantum correlations.

pjackson

Tom,

Crossed in cyberspace. There's no error. I've given Richard free choice and it still works.

In fact the violations are well beyond the Bell limits. I clearly haven't explained the experiment in simple enough terms as discreteness of radians is not a problem. There's no need for the 'precision' all are focussed on when using a discrete number of data points. The important thing is to significantly violate the Bell limit.

Natures own spectral sequence is smooth. That means using recursive gauges to describe mathematically. I'm describing logically and geometrically, which is why crossing the equator by bicycle is moot. It's a smooth transition between clockwise and anti clockwise spin that shows that the foundations of QM did not reach Poppers bedrock, but were indeed 'incomplete'.

Best wishes

Peter

Thomas Ray

Peter, the free choice you give Richard (or anyone) is only "free" if he is allowed to choose at any time in the process and not just at the source. In other words, after you have compiled your data and by some process I don't comprehend have managed to find that Bell's inequality is not violated (although I don't think you will get that result because I see no true hidden variables in your protocol), and then Richard chooses his detector settings and you run that input, you will inevitably find that the inequality is violated -- why? -- no matter where in the spectrum of continuous colors he makes his choice, the angle of betweeness is fixed by detector dependence and is not continuous with the spectrum.

Yes, if you buy into the "quantum Randi challenge" this may be another way to validate the rotation through 2pi radians that Bell-Aspect predicts; it does not, however, constitute experimental evidence that hidden variables either do or do not exist. It simply verifies its own assumption.

I think my example of squaring the circle with compass and straightedge is apt: it is impossible because it would require a physically impossible infinite number of steps. Of course, we now know that it is not an insoluble problem to calculate the limit for approximate square equivalents to a given circle; what Richard disdains as merely utilitarian. However:

One can square the circle in non-Euclidean space. Obviously, this obviates Euclidean angles for the 1-to-1 correspondence of square to circle that results. What it also does, though, is to obviate dependence on an arbitrarily bound choice function; what I mean by that, is that the extra degree of freedom required to make the choice function identical to the correlation function (Joy's C_a,b) is built into the measure space as the limit of S^n parallelization. That is the true hidden variable.

Much of my own research is devoted to proving that the structure of S^3 topology obviates the axiom of choice for all real continuous functions. In other words, proving that the measure space is complete.

Best,

Tom

pjackson

Tom,

"..by some process I don't comprehend have managed to find that Bell's inequality is not violated.."

We actually find the Bells Inequalities ARE violated, but I think that's what you meant. I've better explained the 'hidden variable' below I hope; it's the reversability of detector field orientation ('spin flip') at 90^o, which means that, due to non-mirror symmetry, angular momentum transfer will be the 'other' way subject to setting angle (the 'other' photomultiplier will click').

This false assumption identified by the 'discrete field' model is as fundamental as any could be. There is no requirement for Bob to find 'up' if Alice finds 'down'. HE TOO CAN FIND 'UP'!

You then correctly and perceptively identify that; "the angle of betweeness is fixed by detector dependence and is not continuous with the spectrum." which is the exact effect of the above discovery, and in no way 'disqualifies' it as the rational solution.

The experiment is classical and reproduces the QM predictions with no valid 'rule violations'. I also think many also misunderstand the real point of Occams razor; which is that the SIMPLEST solution is not only the right one but is also often far simpler than anybody has previously conceived.

The toroidal spin/orbit relation, where the 'charge' is spinning in its (helical) orbital path also explains the 720 degree 'return' characteristic of a spin 1/2 particle. That does 2 things; opens the way to fermionic QG, and, I suspect may provides some form of topological connection to something like Joy's 'parellelised 3 sphere'. But exactly how is beyond me.

There is one good way to falsify the DFM hypothesis; to find anything spinning or orbiting with any type of angular momentum that does not implicitly have BOTH spin directions subject to orientation. Do throw any you can think of at it.

Best wishes

Peter

Thomas Ray

Peter, there's no profit in verifying that Bell's inequality is violated. That's what quantum mechanical theory predicts. What we're looking for is that the inequality is violated without entanglement or nonlocality. That requires a degree of freedom that your model lacks.

"There is one good way to falsify the DFM hypothesis; to find anything spinning or orbiting with any type of angular momentum that does not implicitly have BOTH spin directions subject to orientation."

Spin and orbit direction are orientable by definition, with choice of initial condition. Your hypothesis is not falsifiable, because -- as in the "spinning dancer" illusion, and in Bell-Aspect experiments -- we can only extract information on one orientation for each observation.

The orientability of Joy Christian's framework is a topological artifact caused by compactification of R^3 on S^3 by a point at infinity. In other words, natural orientability is itself a topological property not realized in plane (either Euclidean or complex) domains and the numerical implementation of measurements in those domains. In my reading of objections to Joy's framework, this is the very hardest thing for detractors to grasp though it follows from elementary topology.

Even the extended complex plane C^ (Riemann sphere) with its point at infinity that compactifies the plane is insufficient unless there is a means of analytic continuation on the manifold S^2 X S^2 that doesn't send every result to infinity. Because S^2 X S^2 is identical to S^3, it is factorizable over the manifold at the limit of S^7 parallelizability -- which means that Joy's measure domain is continuous, flat, and of infinite range on parallelized S^3. All correlated results go to 1 or - 1 without boundary, without arbitrary coordinates, without any more than classical (coin toss) probability:

The only results possible on the equator of S^3 are 1, - 1, and the imaginary number i. In a complete (4pi) rotation, i disappears, though topological torsion does not. Both orientations remain anti-correlated, so that extra degree of freedom is built into the topological structure.

I wish I could make this simpler and shorter. I can't.

Best,

Tom

John Cox

Why does a slinky know its at the bottom of the steps? What percentage of times does it not know?

John Cox

Tom,

"the same thing as saying that local length 1 is identical to global length 1"

Yes, I see that. I don't see where anyone has a problem with constructing an infinite length of line as a mathematical object and designating a point as '0' to model -1 and +1 co-ordinates. Perhaps it helps to have an acceptance of the sense of continuum at all points, being of a same single thing, just at a different place.

"S^0 is the least element, not the first element, of S^n"

I see the distinction and was actually thinking that, but lacking the nomenclature I stated it as assuming there was something to begin construction.

Also my Christmas light analogy could be better stated as the -a.b result being found as a operation in parallel on the hypersphere surface between the nodes of the axes of the several spheres. The parallels of latitude sphere could be rotated on its y axis towards +1, the meridian sphere could be rotated on its x axis towards -1, and the hypermeridian sphere could be expanded on its z axis towards +1 and if a putty strip on a meridian of the initial (coincident axes) hypersphere was backlit and cast a semi-circular shadow on the 4D screen, that continuous rotations in parallel would cast a shadow like the putty strip was on the surface of a glass egg... the curve of an inequality by continuous rotation from a curve of an equality.

Still, that same rotation in a Newtonian matrix would require a series of operations on separate sides of the matrix. So it is not inconceivable that a spatial projection of co-ordinates in Newtonian space would have the serial result of a superluminal solution, where the parallel result would be relativistic.

What I need is a writer in mathematics like physics had in Assimov. If I could find how Hamilton went from tetrahedral slices off polyhedrons, to the orthogonal, I could probably comprehend the algebra. Wikilinks are great for reference about what you already know, but what you might need is usualy Pay Per View. Wikipedia's page on Michael Atiyah had a wonderful quote where he said that

algebra was the Devil's bargain with mathematicians, all you have to do is give up geometry. That made me feel better.

Incidentally, my spiel on gravitational recurve on a tetrahedron.. there would be 6 loops not 4. I lost a couple in my scibbles. Years ago I made a little magnetic octahedron that held itself together, it was fragile and weakest at the antipodal points but it would sit on the table til it was jolted.

Thanks, Tutor, jrc

pjackson

Akinbo,

The 'use' is to correct the starting assumptions by exposing the false ones.

I agree a 'point' particle is false, but it's the resultant discrete particle dynamic that's the key.

"Is local not subsumed within what is global?" No. They are equivalent, but discrete, so simply hierarchical, as Truth Functional Logic.

"what becomes of EPR, Joy's work, etc? That possibility should be contemplated and a plan B provided to us."

That's fair. It's all in the paper (preprint imminent) but to precee;

1. EP&R are proved correct, but with a reduced (recursive) quantum uncertainty as shown by Godel and Bill McHarris's essay on chaos theory.

2. Bell is proved correct with both his limit on random inequalities and his belief of 'no boundary' between QM and SR, which converge. But his theorem is false, so no FTL or weirdness is needed.

3. Bohr was correct in defining 'what we could say' about particles 90 years ago, but we now know far more. We just need to apply it. 'Superposition of spin directions' is what planet Earth has. It's 'observer dependent', and, as we well know, the observers field electron direction 'flips' at 90^o.

4. Points and line don't exist except as representations. Simple Cartesian systems can't faithfully model the dynamic evolution of interaction we call 'motion'.

5. I'm still pretty sure Joy's work has validity as a reasonable mathematical/ topological representation or 'approximation' of the real physical process. I know Joy still can't see that, but he's a mathematician so it's unsurprising. I equally can't penetrate his maths!

6. Cosmologically, a cyclic model emerges, resolving quite a string of anomalies, including CP violation (paper on that under revision but passed review and imminent).

You're already familiar with the fundamentals. If you can see any flaws in the last 3 essays do point them out for me. Many thanks.

Best wishes,

Peter

[deleted]

Peter,

Nice experimental proposal from you. Let's see whether the challenge is taken up.

On your reply, I agree with some but let me restrict myself to the aspect I feel is crucial to Joy's work and the forum topic...

In response to "Is local not subsumed within what is global?", you answer, "No. They are equivalent, but discrete, so simply hierarchical, as Truth Functional Logic". If local and global are equivalent, then why not do say with global and concentrate on the local which is more accessible and from there you can infer the global? If you say, hierarchical, what is on top and what is under?

You talk of representations and approximations of real physical processes. If the real physical processes themselves are amenable to study, why leave them and dissipate relatively more energy on the approximations and representations? If I can legally study and dissect your anatomy as a human being, why studying your photograph?

Joy's foundational statement on which all his work (or almost all) rests is that a line and a surface of which the line may well be a part contain the same number of points, do you agree? Then when you divide that surface into two unequal halves with one containing the line under consideration, both halves contain the same number of points as the original. When you bring them together again the sum of the points remains unchanged. Does this not signify that there is an unreal assumption in the representation?

This is the basis of the Banach-Tarski and Zeno paradoxes which in my opinion remains to be unanimously resolved.

I agree with Joy's quote of Einstein, that physics should represent a reality in time and space, free from spookiness, 'approximations', etc. But when you request that he clarifies what is meant by "Although lines and planes contain the same number of points,..." (see his Fig.1.1), Joy puts up a brick wall and Tom his partner instead tells you this is elementary mathematics too rudimentary for them to discuss at their exalted level, notwithstanding the innumerable unsolved paradoxes in their belief...Hmmm. Who is fooling who?

My reply getting long here. You may restrict yourself to answering whether you agree or disagree (with reason provided) whether a line and a surface of which that line may well be a part contain the same number of points?

Akinbo

[deleted]

"But when you request that he clarifies what is meant by "Although lines and planes contain the same number of points,..." (see his Fig.1.1), Joy puts up a brick wall and Tom his partner instead tells you this is elementary mathematics too rudimentary for them to discuss at their exalted level, notwithstanding the innumerable unsolved paradoxes in their belief...Hmmm. Who is fooling who?"

No one is trying to fool you or stonewall you, Akinbo. The duality principle in projective geometry is well understood from the work of Jean-Victor Poncelet in the 19th century.

Perhaps this collection of images will give you a more intuitive feeling for the geometry.

The paradoxes that you think are associated with these facts are not controversial. The Banach-Tarski construction is not actually a paradox, though it is often characerized as such (and has nothing to do with Joy's framework in any case). The Zeno arrow paradox and tortoise-hare paradox (which are also unrelated to Joy's research) are resolved by application of the calculus to physical systems in which space and time vectors converge on a limit.

pjackson

Akinbo,

The experiment's been repeated. All can do it, it's not just a 'proposal'. The kit is just an A4 piece of paper which I'll Email. You'll need some scissors, pritstik, tape, a drawing pin, a coin, a tosser and ideally a few friends or students.

You ask why not; "concentrate on the local which is more accessible and from there you can infer the global?

I agree, but it works both ways. The first way I've used in my (accepted- imminent) tokamak/galaxy evolution paper which also infers cyclic cosmology. From the other end; consider whether globes or binary OAM systems spin clockwise or anti clockwise, then consider what that may mean in 'spin 1/2 particle' terms. The answer exposes something that QM's hidden assumptions missed.

What's "above and below"? More Russian Doll's, or 'turtles all the way down' it seems. Somewhere eventually the gamma wavelength limit kicks in, (Optical breakdown mode) but 'up' is unknowable.

Joy certainly looses me with his 'points and lines' bit. I consider both as unreal abstraction of nature anyway so nonsense easily emerges. I'm sure it's mathematically precise, but nature isn't. That may indeed by Joy's point. The DFM suggests that if you want a (Hardy axiom 5) continuous transition between spins then ride a bicycle across the equator. You'll find no 'step' between spin 'up' and 'down'. In those terms Hardy's axioms are perfectly reasonable for DFM dynamics.

If you give me somewhere to post the kit to you can be one of the first to do it yourself.

Best wishes

peter

Akinbo Ojo

Thanks Tom and Peter for throwing some light.

Tom just on impulse without deeper thought... You mention the application of the calculus to physical systems and as you pointed out calculus in the way it was invented by Leibniz and Newton made use of the "limit". What does "limit" mean? This is suspicious as it suggests that despite all best efforts to make space and time continuous and infinitely divisible ad infinitum (without limit) mathematically, there has to be a "limit" physically and mathematically before calculus can be made to work to describe dynamics. The question is what will this infinitesimal value be, if there must be a limit? dx in dx/dt can certainly not work with a value zero.

Akinbo

John Cox

Tom,

Thanks for the pages, I moved to this thread because the other has gotten long in the tooth. That's not surprising when what I've been learning is that comments are coming from different kinds of maths with conflicting definitions, or rather definitions that are contrary to how the math at hand is presented.

The hell with Wikipedia, I went a got a Cliffsnotes pre-calculus and found a couple sites about 3D animation which are more helpful is demystifying the framework. After that, 'a'lice and 'b'ob can waltz around all they want. Back to the books for this kid. jrc

Akinbo Ojo

Tom, what is dx in Calculus? Is it the infinitesimal distance between one point and the next?

Akinbo

[deleted]

"...what is dx in Calculus? Is it the infinitesimal distance between one point and the next?"

It doesn't mean anything by itself, Akinbo. As you said earlier, what we mean to write is dx/dt, the derivative of x with respect to t. There is nonstandard analysis (Abraham Robinson) that deals mathematically with real infinitesimal objects; however, if we speak of physical applications which obey real (Lebesgue) measurement criteria, we come up against the primary reason that Einstein intended general relativity to be only an intermediate step to a complete theory of gravity.

As it is, general relativity is mathematically complete -- i.e., it is a set of closed logical judgments on a specified domain that predicts measurable phenomena that we have verified to be true. In other words, the independent mathematical model corresponds 1 - 1 with the physical measurement.

If the domain is of infinite range, we run into the problem of cosmology -- what is the derivative of x when t = 0? That's why physicists say the theory "blows up" near the singularity of creation. We can only "wind the clock back" to a short time interval after the theoretical big bang event, on the assumption of a point of infinitely dense mass-energy at the beginning of time (whatever that means).

Quantum cosmology has the advantage of probability calculations based on the assumption of fluctuations in energy values in 2 dimensions. A deterministic (classical) theory, however, begs pairwise correlation of particle events over an infinite range of the continuous 4 dimensional spacetime domain, which gets to your questions:

We already know that in 4 dimensions, if one asks "where did creation begin?" -- the answer is "at every arbitrarily chosen point of spacetime." Quantum theory allows -- on the assumptions of quantum entanglement and nonlocality -- that correlations measured in 3 dimensions describe all phenomena locally and the events not measured are assumed nonlocal. What does "nonlocal" mean? -- it implies that all phenomena are observer-created, and that every local measurement in 3 dimensions changes the configuration in 4 dimensions. ("God plays dice.") However:

The assumption of 2 primordial correlated points that prevents physics from blowing up at the singularity implies that all quantum correlations are primordial. So the question of how much distance exists between one point and another is moot -- the events are correlated at every distance of the 4 dimension domain, because the domain is continuous (and if Joy Christian is right, also simply connected), without the assumptions of entanglement and nonlocality.

Ordinary calculus, whether in ODEs or PDEs, is burdened with having to arbitrarily specify boundary conditions (dx/dt). It is obvious that we need a different mathematical method to have a classical theory of quantum correlations in which all measurements are real and local, independent of boundary conditions, probability measures and arbitrarily chosen coordinate systems.

Joy Christian's topology-based research supplies the framework that makes such a theory possible -- we can wind it back all the way to the singularity, where the non-zero torsion built into the topological model rescues us from the cosmological problem, and where we can see that the singularity exists (and is avoided) for every measurement function continuous from the initial condition.

Best,

Tom

Thomas Ray

Argh. Last was mine.

Akinbo Ojo

Thanks Tom. Quite a lot to digest. No further questions at the moment but I will revisit again. Have you read the Is the moon there when nobody looks paper I linked?

All the best

Akinbo

Thomas Ray

I know the article, Akinbo. What should I be looking for specifically?

Best,

Tom

Thomas Ray

Here's something to think about. The article concludes with the end of a poem by RP Feynman:

"I cannot define the real problem,

therefore I suspect there's no real problem,

but I'm not sure

there's no real problem."

Which is exactly the crux of Joy's breakthrough -- he has defined the problem, precisely as that of the chosen measure space -- which in Christian's framework is complete, continuous and simply connected -- versus the incomplete and multiply connected space of quantum mechanics. The really crucial difference is that QM predictions are not independent of experimental measurements; Joy Christian's mathematical framework is.

Thomas Ray

John R, I don't understand everything you're saying, but of what I do understand:

I hope that the distinction between least element and first element doesn't come off as pedantic. What I mean, is that 'least element' implies a well ordering of elements on the open interval [0, oo). The significance is that a well ordered measurement, independent of an arbitrarily chosen coordinate system and arbitrary boundary conditions, exists at every point of the S^3 manifold -- without relying on the axiom of choice. This is different from the measurement setting dependence claimed by Bell's theorem adherents, in which boundaries of choice are conditioned by prior probability.

"Perhaps it helps to have an acceptance of the sense of continuum at all points, being of a same single thing, just at a different place."

There is, however, no different place, if all physics is local. That is, if local and global length 1 are identical.

Thomas Ray

Maybe I can put it a little better: Bell's theorem adherents do not believe that a space of complete measurement functions exists, that is both local and real. They accept that all real measurements are local, and results of the experiment not done are nonlocal.

If all physics is local (local length 1 identical to global length 1), all measurements are both local and real; in other words, there is no prior probability for the experiment not done -- no quantum entanglement, no superposition of states. The space of complete measurement functions is well defined, while the measurment space of Bell's theorem is not.

Richard Gill

Tom, your notion of a "Bell theorem adherent" is totally obscure to me. What I call Bell's theorem has no "measurement space". According to wikipedia, Bell's theorem states "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."

Here is a recent pretty clear formal statement of the theorem: http://arxiv.org/abs/1402.1972

In order to convert a metaphysical claim into a mathematical theorem one has to make clear definitions of the concepts you want to mathematise and then relate to one another. One can always object to the definitions. They are of course subject of is ongoing debate.

Thomas Ray

Richard,

"What I call Bell's theorem has no "measurement space". According to wikipedia, Bell's theorem states 'No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.'"

Another good reason not to rely on Wikipedia. That is not what Bell's theorem states; that is what Bell's theorem concludes. And the problem with that conclusion, is that the predictions of quantum mechanics are entirely based on empirical evidence and probability measures -- an open, inductive system unrelated to scientifically closed judgments (e.g. special and general relativity) in which predictions of the mathematical model can be shown independent of experimental results.

"Here is a recent pretty clear formal statement of the theorem: http://arxiv.org/abs/1402.1972"

Thank you. The authors validate what I have been saying all long: "Our reformulation imposes determinism in what we see as the only consistent way, in which the `ontological state' initially determines both the settings and the outcome of the experiment." In other words, the theorem nonconstructively "proves" what it assumes a priori. To impose determinism on the initial condition automatically excludes a deterministic model free of arbitrary coordinates and boundary conditions demanded by a classical measurement schema.

"In order to convert a metaphysical claim into a mathematical theorem one has to make clear definitions of the concepts you want to mathematise and then relate to one another."

My definitions are precise.

"One can always object to the definitions. They are of course (subject to)ongoing debate."

Then debate the side of why you think it unnecessary to specify your Bell's theorem measure space, in order to validate its arithmetic prediction for strong quantum correlations.

Tom

Nick Mann

Here's an idea that fits in with crowd funding. Something's needed to raise the consciousness of both the scientific community and the general public.

So why not commission a flash mob in Vienna during the Bell fest for some action along the street in front of the venue? Vienna does flash mobs quite artfully. You could feature huge photo placards of Einstein, Podolsky, Rosen and Christian. And John Stewart Bell with an X painted across his visage. Colorful streamers, drums, bugles, outré costumes. Perhaps a processional statue of Isis to match the motif on Joy's website. Be sure to notify local media in advance and get plenty of footage of your own for posting on YouTube. There's still time! Just a thought.

Nick Mann

Alain Aspect is scheduled to give a public lecture at the Austrian Academy of Sciences (Großer Festsaal), Doktor-Ignaz-Seipel-Platz 2, at 8 PM on Friday 20 June 2014. This address is a large and stately neoclassical building right in the center of the city with a big crystal chandelier and polished marble columns inside the splendid hall itself (where Aspect and his listeners will bathe in the glow of one another's perfect certainty) ... I mean: is this opportunity to be allowed to go to waste?

One hopes Dr. Christian wouldn't let it pass on grounds of dignity and decorum. We live, after all, in the 21st century. And even in the one before this, when there was so much less information clutter to cut through, Einstein famously stuck out his tongue for the camera. A PR genius, he'd have loved flash mobs.

pjackson

Tom,

I've searched for dynamic 'duality' images but not found much. Your link was broken, could you re-post it for me. As far as I can see I may be suggesting an 'extension' to current descriptions of duality.

I hope you may let me send you the one page 'kit or parts' to try the simple experiment violating Bell's limit classically. I'm disappointed few have asked for it. I suspect you may find some insight into connections with Joy's work which seem beyond Joy and I. My thesis is founded on particles NOT having pure singlet states but dual states, with what's detected being dependent on detection conditions, where I invoke the electrons 'spin flip' at 90^o to reverse the angular momentum exchange.

Best wishes

Peter

Thomas Ray

Hi Peter,

If you google point-line duality, you'll find it.

https://www.google.com/#q=images+for+point+line+duality

pjackson

Tom,

Thanks, but it's not 'point/line' but any 'dynamic' duality I was after. I'm familiar with the former (your first link), it's the second that's dead. But if it's the same topic it's no help. I'm trying to find any prior examples of what I've derived, which is smooth 3D duality of motion.

I'll answer you other post below, but it does look like you're missing the key point the experiment is based on. QM when formulated assumed there could be such a thing as 'pure' quantum states, (spin up, spin down) purely on the basis that we only ever found one or the other.

Quantum 'spin' is no better defined than 'matter' itself, but it's recognised as (quantum) angular momentum (AM), because it's measured as an exchange of AM and everything self contained, so rotational or orbital, has AM.

It's also a fundamental truth of AM (that QM seems to have missed) that it always has two conditions subject to observer aspect (so which way you look at it/measure it);; both clockwise and anti clockwise spin.

Have you worked out which way Earth spins yet? It is of course BOTH directions at once. Just because you look from above the north pole and find 'clockwise' does NOT mean that the southern hemisphere spin state 'collapses!' Now that's true of ALL spin 1/2 particles, including the electrons of the detector EM field.

Those electrons 'flip' at 90 degrees detector dial angle. So the AM transfer is then found to be in the opposite direction!! A man of your intellect should not have to think about the implications of that fact for too long before the penny drops.

...like a 100 tons of rock through the muddy foundations of QM.

I propose that is a genuine 'physical' theory, with a rather significant variable 'hidden' right before our eyes.

Have you found the implication? - thus the prediction of the aberrations in Aspect and Weihs 'time resolved pair' experiments, which proved to be born out - in the 99.999% of data discarded for lack of a theory to fit it!

Best wishes

Peter

John Cox

Peter,

"I'm trying to find any prior examples of what I've derived, which is smooth 3D duality of motion.'

Try www.spaceandmotion.com it's a wave structure of matter site with linkable citations but I think the webpage is inactive at present. I've run across a few math and physics sites that deal with the ying and yang of relative motion.

As to the rationale of the line and plane having equal number of points, to make it dynamic ; drop the absolute, you can always cut the difference in half and still miss it. It's utilitarian; to graph anything you start from 0 but have two axes, hence 0=o,o so your line can extend along both axis(s), that means simply that an ordered set of points just like o,o exists that are silly because the set is less than zero. But that projects ordered pairs at any point along the line so that you can have a graph that encloses an area between the axes that actually has points in it. That's the same rationale as the imaginary number ( i ), a negative value on the number line is just -x, but sqrt -1 is also -1, so if you have a sqrt -1 you can also have a -1^2 which is an ordered set of points at the identical designated place along a line metric. As a matter of nuts and bolts utility it means that, yes a line is a set of ordered pairs (o,o ---> o sub n, o sub n) as might be projected across a plane of ordered points ( as distinct from ordered pairs of points) that are themselves projected as lone points from the ordered pair of points along each axis. The diagonal line that would project would still be an ordered pair set so that it can project a plane of lone points as the square of the hypotenuse. So yes, to evaluate vectors, the line at any designated value will have the same number of points as the plane.

0,0,0,0

We ain't takin' it to the Fair, as they say. It's close enough for gov'munt work. jrc

Thomas Ray

" ... smooth 3D duality of motion."

No such thing exists in any odd dimension set.

pjackson

Tom,

I can't see I'll need an 'odd dimension set'. Do you suggest so?

The smooth duality I invoke is of nature not mathematics. As the cycle is crossing the equator the Earth might be orbiting the sun to an observer in the Barycentric frame. That makes three. Mathematics a can on 'approximate' that with cardinalsations to metaphysical 'points'.

But is not all motion in sets of an infinite set? The cycle wheels turn smoothly as the sun orbits smoothly through the galaxy, etc. ad infinitum.

Best regards

Peter

Thomas Ray

Peter, here's what I mean:

In the quantum mechanical formalism, the 2-dimension complex plane imposes on an n-dimension Hilbert space -- meaning that a point is represented by a line, for the good reason that quantum mechanical space cannot be collapsed to a point. So we start out with 1 1 space (even) that when translated to a 2 1 space (odd) is missing the point at infinity of 3 1 space (even) in which we live. With that missing point, we sacrifice the degree of freedom that would allow a smoothly connected function ("...of nature, and mathematics ...")to accommodate the point-line duality of projective geometry, the orientability of a topological model, and to avoid infinities with a nonzero topological twist.

pjackson

Tom,

If we start with QM formalism, then that may inevitably be the case if we need to "accommodate the point-line duality of projective geometry" and accompanying constraints. I wrote somewhere above that that I always try to avoid metaphysical entities such as points and lines.

My derivation is far deeper foundationally, as far simpler, than the current geometrical assumptions, which are shown to be flawed. I've tried to avoid talking geometry as I don't wish to tread on Joys toes and think he's on the right track from the starting point he had to use, but it's his area not mine. But let me comment lightly, which I hope Joy will read and consider.

I agree that before this breakthrough can be confirmed as 'spectacular' I also have to physically explain the spin 1/2 '720 degree rotation' (which nobody yet has by the way). Wolff tried 10yrs ago via SU(2), unsatisfactorily. If you're not familiar with Wolff it was 'soliton' type concentric ring standing waves going in and outwards. He also inherited Dirac's incompletely defined distinction between 'reversal and 'inversion' of quantum spin.

The discrete field version is not 'concentric' rings, and not 'standing' waves. It is the spiral of a vortex, in both directions 'superposed', which is what creates the fast orbiting peaks of 'potential'. To keep it simple, now we can go to a sphere spinning on the x axis. We can rotate the axis in the y and z planes. We don't have to reverse the angular momentum! or 'time! (in CPT). However there IS a consequence. We're adding a NEW angular momentum (y,z planes) by doing so, which creates torsional asymmetry. The 360 degree internal symmetry is then violated, but one more turn and it's phase is recovered, as Dirac's brilliant original conception.

Misners 1973 'spherical rotation' property may then have a coherent physical analogue without 'ribbons'. I could also give you a recursive helical spin/orbit path description which is simpler for most and I've used in the paper to avoid going 'off topic', but it's incomplete.

Akinbo Ojo

Tom, Peter,

Let me first confess my ignorance of the finer mathematical details of the EPR/Bell's theorem/Joy arguments. But I intend to read the paper by David Mermin in more detail when I get the time as it seems well and simply written.

One of the ideas that has briefly crossed my mind is that in the experimental set-up with the two detectors and a source of particles between them, there is the assumption that between emission of particle from source and the two detectors, no other entity whatsoever is capable of interacting with the emitted particles. There is 'space' between emission and detection but going by the assumptions in the geometry considered by Joy and Tom it is merely 'relational' and it is hidden. Space is a nothing according to this view, although Newton disagrees. But is it? Can it be the 'hidden variable'? Can a space that can be curved and bent and 'varied' according to GR be an inert participant on the quantum scale? Note that Joy mentioned on Mar. 26, 2014 @ 11:13 GMT that space has 'spinorial' properties and he has linked a video for me to watch (which I will soon do).

Akinbo

pjackson

Akinbo,

Such variables are precisely what Bell ruled out. His logic is correct, and as simple as; "If +A and +B = +5, then B can't be more than +5." But that applies to his 'inequalities' (the random/stochastic variable limit). His written theorem was the INTERPRETATION of that proof - and all interpretation uses assumptions, hidden or not! Most are so familiar we forget them, i.e. that 5 = 5 (I've already shown that's false at a higher order too but I don't invoke that here).

Thousands of far greater minds than you and I have hit Bell's rock wall of logic. Richard correctly pointed out that it can't be 'disproved' per se, only 'circumvented'. The only way to circumvent is to start from a different place (starting assumptions). Now most claim Bell made NO assumptions. He did, he inherited QM's hidden assumptions, which included that 'quantum angular momentum' (QAM) does not have the properties of normal angular momentum (i.e as spin 1/2 takes 720^o NOT 360^o to 'return').

What discrete field dynamics show is that the 720^o can be explained without having to abandon the more fundamental law that ALL angular momentum is of some 'volume/body', so implies that both clockwise and anticlockwise spin must exist subject to observer (detector) aspect. That gives a physical explanation of 'state superposition'.

It is that NEW fundamental assumption that circumvents Bells theorem (resolving the anomalies from experiments on the way) by combining it with normal electron 'spin flip' with changing detector field angle. It means that if Bob finds spin 'up', then Alice does NOT compelled to find the opposite 'state!

But to most quantum physicists suggesting no 'pure' states is like suggesting that Earth orbits the Sun not vice versa, it flies entirely in the face of 100 years precise well established physics so 'must be wrong'.

It's that 'wrong path' again. Does that better explain it?

Best wishes

Peter

Thomas Ray

" ... if we need to 'accommodate the point-line duality of projective geometry' and accompanying constraints."

In a theory of continuous functions, we do.

pjackson

Tom,

"In a theory of continuous functions, we do." I agree. Reducing descriptions of nature to 'functions' sets that constraint. My dynamic physical analysis avoids those convention limits - and I'm not entirely alone outside that box, i.e;

I've pointed out and demonstrated the inability of Cartesian co-ordinate systems to model motion (an 'evolution' of interaction) a number of times. You should but many won't, know this was also Einstein's view -from as far back as 1916! He never did find the way to consistently accommodate arbitrary transformations, but always preferred to talk in bodies and planes not points and lines, as did Minkowski right from 1908; "endlessly many planes exist in three dimensional space". And specifically Einstein;

SR & GR, 1916, section 24: "The method of Cartesian coordinates must then be discarded, and replaced by another which does not assume the validity of Euclidean geometry for rigid bodies."

Section 28; "non-rigid reference bodies are used, which are as a whole not only moving in any way whatsoever, but which also suffer alterations in form ad lib. during their motion. (more of GR).

We've established my viewpoint and methodology is unfamiliar to you Tom, (as to most!) but I'm sure you wouldn't claim that makes it invalid. It's about finding the 'new way of thinking' that Einstein, Bragg and a many others have recognised is needed.

Best wishes

Peter

Thomas Ray

"We've established my viewpoint and methodology is unfamiliar to you Tom, (as to most!) but I'm sure you wouldn't claim that makes it invalid."

That's true of course, and I don't.

If you think you've found a way to preserve physical laws under continuous and completely arbitrary transformations, I wish you well in communicating the details. You should remember, though, that planes are composed of points and lines.

Akinbo Ojo

Thanks Peter for simplifying. You certainly know more than I on this topic so let me not betray my ignorance. If what you say correctly depicts Bell's logic that "If +A and +B = +5, then B can't be more than +5." then I cant really quarrel with that. The question is does Joy agree with that depiction and is he quarreling with such a straight forward logic?

And thanks Tom for the link. It was interesting and I came away with the opinion that although "Einstein inferred from the special theory that physical reality must be described in terms of continuous functions in space", a little voice in him told him that God does not play dice and that is why before he died and rejoined his Maker, a period when one is usually remorseful, he told Abraham Pais that he "was not sure differential geometry was to be the framework for further progress", and later still, in 1954, just a year before his death, he wrote to his old friend Besso that he considered it quite possible that physics cannot be based on continuous structures. This dilemma was summed up at the conclusion of his Princeton lectures, where he said "One can give good reasons why reality cannot at all be represented by a continuous field..., and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory". A very honest man, don't you think? Why then are you ever ready to bet that reality is continuous.

When you have the time, you may also view attachment by Alba Papa-Grimaldi, "Why mathematical solutions of Zeno's paradoxes miss the point" where he discusses the 'infinitessimal' that strange (but I admit useful), unobservable and unverifiable mathematical quantity in which the process of change is hidden and on which continuous functions rest.

AkinboAttachment #1: zeno_maths_review_metaphysics_alba_papa_grimaldi.pdf

Thomas Ray

"Why then are you ever ready to bet that reality is continuous."

Because I believe in the same God that Einstein and Spinoza did, an impersonal nature of universally distributed goodness. No "Maker" who throws dice.

As complex as our physics is, we cannot explain how the world is comprehensible unless we allow that events manifesting as particle phenomena are self limiting, and if self limiting, pairwise correlated. These are elemental facts of both general relativity and quantum field theory.

Thomas Ray

Akinbo, Papa-Grimaldi concludes with a remark by Plato from the dialogue with Parmenides:

"...that queer thing, the instant. The word 'instant' appears to mean something such that from it a thing passes to one or other of the two conditions [sc. rest and motion] there is no transition from a state of rest so long as the thing is still at rest, nor from motion so long as it is still in motion, but this queer thing, the instant, is situated between the motion and the rest; it occupies no time at all, and the transition of the moving thing to the state of rest, or of the stationery thing to being in motion, takes place to and from the instant."

A few years ago, I asked a fellow conference participant after his presentation purporting to solve Zeno's arrow paradox by eliminating the very existence and idea of 'instant': "So, is motion possible?" The reaction I got was as if I have two heads. For all through the presentation, the presenter referred to things in dynamic motion all the way to the thermodynamic death and rebirth of the universe. He never once directly addressed Zeno's question from which the paradox derives: is motion possible?

One cannot escape the syllogism and its inverse; if motion is possible, instants (intervals of time) exist. That is, all motion is relative and therefore events are pairwise correlated (covariant).

One of the most difficult things to understand in general relativity is the lack of boundary between past, present and future. The model is perfectly well behaved, however -- and even more so in Joy Christian's modern version of relative becoming. It corresponds to a conjecture I made in a 2006 conference paper: "transitivity implies identity." That is, the self-limiting map of a function to itself is continuous. Empirical consequences of the idea are described by Christian's topological measurement framework -- the local interval of time is identical to the global interval.

Best,

Tom

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