Hi Peter,

Thanks for your kind comments. It seems that many others, myself included, have exploited the detection loophole to violate Bell's inequality, but I have seen only one that converges to the sinusoidal correlation expected from QM. Richard Gill's analysis of Philip Pearle's work on quaternions resulted in this procedure, which converges nicely. I also posted the procedure with Declan's essay.

The method requires three(!) random numbers R1,R2,R3 generated uniformly over the interval 0-1 for each trial. Gill stores a large set of transformed random numbers, z,x,s, to be reused in trials for any combination of settings by Alice and Bob.

The first two random numbers are transformed to cover a spherical shell, and then projected onto a plane running through the center, forming a disc. Points on the plane are taken as 2d vectors (z,x), so the distribution of their magnitude is biased towards the edge of the disc, where it is most dense.

The third random number sets the threshold, s, for detection, with another carefully crafted distribution.

z = 2 R1 - 1

x = sqrt(1 - z^2) cos(2 pi R2)

s = [ 2 / sqrt(3 R3 1) ] - 1

A unit vector (az,ax) in the z-x plane sets Alice's angle, with (bz,bx) for Bob. Projections are calculated as follows

pa = (z,x) . (az,ax) = z az x ax

pb = (z,x) . (bz,bx) = z bz x bx

A detection occurs when the absolute value of both pa and pb is greater than s. The correlation for a detected event is given by the product of the signs of their projections

C = sign(pa) sign(pb)

The average correlation for this Gill-Pearle method converges to the cosine expectation as the number of trials is increased.

I tried implementing Declan Traill's algorithm in C without success so far. The procedures are similar, and the javascript code for noise generation and decision-making is easy to follow, but I have made some error in calculation, and will have to spend more time looking for it, or start over.

Cheers,

Colin

Hi Colin,

Your essay is well written, with a clear, fluid style.

I get that one of the "relativities" is Galilean, but I cannot say that the second or third ones ever clearly registered. Perhaps this is due to my resistance to "relativity" theories in general. The absoluteness of rotational motion and the rest frame corresponding to an isotropic cosmic background radiation suggest to me that all motion is ultimately absolute, however difficult it may be to ascertain the state of motion of a particular reference frame.

You appeal to the "river" model of black holes and write of "the speed of space moving inward to a gravitating object." As with others who have contemplated flowing space models, you've implicitly stopped the exploration at the outer surface of the source. I'd guess that the most interesting part of a gravitational field (whatever that is) is from the surface inward. This regime is nearly always left sadly unexplored.

In the present case, if "gravitational potential" is somehow correlated with flowing space, the flow should have no net direction at the center. If the flow is somehow responsible for the slowing of clocks due to gravity, the effect should go to zero at the center. A clock there would have a maximum rate. But if that's true, then not only the general relativistic, but also the Newtonian prediction for an object falling into a hole through the center would seem to be wrong: A test object would not oscillate along the length of an antipodal hole.

This highlights the importance of empirical evidence. It invites performing an experiment to find out what happens at the center (not of a planet like Earth, of course, but in a laboratory or satellite-sized massive sphere). What does your model predict for such an experiment? Does it make any other predictions that would facilitate deciding whether Nature is more accurately conceived according to your model, or that of the status quo?

Cheers,

Richard Benish

    Edwin Eugene Klingman expressed a similar uneasiness about the river model, and I responded with the following two paragraphs.

    The name 'river model' is rather fanciful. I also have great difficulty visualizing space moving into matter - it flows in but not out? A better explanation might be that it is some sort of wave motion that propagates through space. I am thinking of something like the moving pattern on a cuttlefish that sweeps over it in waves. The surface of the cuttlefish is not moving, but the pattern gives an illusion of motion. For waves of force, instead of lines of force, there would have to be some coupling between matter and waves, but also between waves to promote coherence.

    My visualization of standing waves comes from experiencing them too close for comfort. I was fishing in a canoe with a friend at the [northwest] corner of the Lions Gate bridge in Vancouver. The tide was strong, a line got caught in the electric motor, and we were swept through rapids to the east side of the bridge. Having survived the rapids, we were being carried toward a field of standing waves being reflected off the shoreline looking like rows of jaws. I was surprised and terrified by the sight, and have wondered ever since whether the waves might act as trap. It is a long way to gravity from there, but the physical analogy of waves seems better than a river.

    I share Galileo's intuition about oscillation of a cannonball in a hole through the Earth, but intuition is a resource of last resort used in the absence of knowledge. Your point about empirical evidence is well taken. A space-borne test called LATOR was proposed which could measure deflection of a laser beam to second order, or about 1 part in 10^12 accuracy. I think LATOR and LISA (space based version of LIGO) would use similar technology. LISA is still another 15 years away, and LATOR seems dormant.

    Prof Colin Walker

    Your wonderful thinking about the fundamental aspects of gravitation, quantum mechanics and cosmology are identified, as well as departures from modern premises..... are very nice.... I hope you will have a look at this essay also....

    Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay and hope for reciprocity ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

    Some of the Main foundational points of Dynamic Universe Model :

    -No Isotropy

    -No Homogeneity

    -No Space-time continuum

    -Non-uniform density of matter, universe is lumpy

    -No singularities

    -No collisions between bodies

    -No blackholes

    -No warm holes

    -No Bigbang

    -No repulsion between distant Galaxies

    -Non-empty Universe

    -No imaginary or negative time axis

    -No imaginary X, Y, Z axes

    -No differential and Integral Equations mathematically

    -No General Relativity and Model does not reduce to GR on any condition

    -No Creation of matter like Bigbang or steady-state models

    -No many mini Bigbangs

    -No Missing Mass / Dark matter

    -No Dark energy

    -No Bigbang generated CMB detected

    -No Multi-verses

    Here:

    -Accelerating Expanding universe with 33% Blue shifted Galaxies

    -Newton's Gravitation law works everywhere in the same way

    -All bodies dynamically moving

    -All bodies move in dynamic Equilibrium

    -Closed universe model no light or bodies will go away from universe

    -Single Universe no baby universes

    -Time is linear as observed on earth, moving forward only

    -Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

    -UGF (Universal Gravitational Force) calculated on every point-mass

    -Tensors (Linear) used for giving UNIQUE solutions for each time step

    -Uses everyday physics as achievable by engineering

    -21000 linear equations are used in an Excel sheet

    -Computerized calculations uses 16 decimal digit accuracy

    -Data mining and data warehousing techniques are used for data extraction from large amounts of data.

    - Many predictions of Dynamic Universe Model came true....Have a look at

    http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

    I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

    Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

    In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

    I request you to please post your reply in my essay also, so that I can get an intimation that you replied

    Best

    =snp

    15 days later

    Dear Colin,

    Here we are again all together.

    With great interest I read your essay, which of course is worthy of the highest praise.

    I agree with you

    «recognizing the galactic redshift of light in the context of Planck's hypothesis dispenses with the big bang, inflation and dark energy». Great!

    I hope that my modest achievements can be information for reflection for you.

    Vladimir Fedorov

    https://fqxi.org/community/forum/topic/3080

    Dear Colin

    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

    Hi Colin,

    I just looked at your essay.

    To quote you: "In quantum mechanics, Planck's hypothesis about quantization of energy levels is essential, while the notion that quantum mechanics belongs in the domain of the small is questionable."

    I agree, and believe my work will "rocket" quantum mechanics into the furthest reaches of the universe.....really:)

    1. Big bang ....Maybe.

    2. Inflation... probably not.

    3. Dark Energy....I believe it is the stuff of space-time.

    Take a look at my essay, and let me know if it meshes with yours in some ways.

    Thanks for your essay,

    Don Limuti

    Colin,

    Re; above; The easy way to start is to follow through the actual mechanism using the brains visualisation skills computing power and logic. As Wheeler said, get the answer before doing the maths! I see you haven't read/commented on my essay yet (I always try to assess & score they who do!) The Process;

    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!

    If the numbers match CHSH>2 and steering inequality >1 you've got them right.

    Let me know how you get on.

    Peter

    Dear Colin,

    I'm sure your explanation of the red shift is the best. Your work is very serious and deserves a good score. Two relativities are also one of the possible good approaches to explain the movements in the reality. Note that my essay describes the current state (without the analysis of the movement).

    Regards,

    Branko

    Hi Colin,

    Before this contest closes, I wanted to thank you again for the positive remarks you made on my blog. Of all the entrants you understand me the fullest. We do not agree on everything...so what. However, we both see QM as a phenomena that has been forced into the microscopic. When it explodes onto the dimensions of the universe physics will be changed.

    This essay contest will be noted by historians as having two entrants having a foresight into the future.

    Being understood is such a pleasure.

    Thank you,

    Don Limuti

      Thanks Don. It is good to feel appreciated, and back at you. For sure, our ideas resonate nicely.

      Colin

      Dear Colin,

      You wrote an interesting essay in which you compared and contrasted alternatives to the current paradigm on gravity. I will offer some comments which are meant to help you consider possible ways to present them in a way that your ideas will be more likely considered by the relativity community.

      1. On page 2 you write:"It turns out that the radial escape velocity required for general relativity is the same as Newtonian escape speed. This coincidence indicates that the foundation of general relativity is entrenched in the classical realm."

      I suspect orthodox relativists will dock you for this because, as I understand, the coincidence comes about because of a cancellation of two factors. Now, you might have meant that the fact that the cancellation which results in the same escape velocity is exact indicates that the foundation of GR is entrenched in the classical realm, but that requires an application of the principle of charity of which you may or may not be the beneficiary.

      2. I know that you have pursued the idea of multiplicative potential for some time now, and unfortunately I do not recall the answer to the following questions, so I ask now: Can you derive it from the Einstein Field Equations (EFE)? If not, is this because they require a modification? You gave an alternate potential formulation for the Schwarzschild solution. If the latter is not correct, do you mean that its derivation from the EFE is faulty or that you need modified EFE? Although I have only tangential contact with the relativity community, I think that they might be more receptive to an approach formulated in terms of field equations. Of course, that also means that any of the observed predictions of GR, most recently gravitational waves, also have be accounted by it.

      3. The cosmological implications seem intriguing but unfortunately my background is too little to be able to seriously evaluate them. Questioning Hubble recession seems like it might be a radical step for many cosmologists.

      I do hope that your ideas are seriously considered and compared to experimental data. It might be that GR still has some surprises in store for us.

      All the best,

      Armin

        I like this essay a lot!

        You certainly got me thinking Colin. I especially like the idea of applying the product integral to relativistic motion. Truly inspired! Your approach is not quite fully refined, but it has much to recommend it over the standard formulations. Well done! I have a lot to say, but I'll rate a few more essays first - while there is still time.

        All the Best,

        Jonathan

          Dear Colin,

          Thank you for your asking about CMB.... My Paper on CMB is available at

          http://viXra.org/abs/1606.0226

          CMB is nothing BUT star light, Galaxy-light and Light from Other inter stellar & Inter Galaxieal Objects in the Microwave region. CMB anisotropies and variations were were calculated and and discussed in the in the above paper given by the above link

          I request you please have a look at this paper and calculations..........

          Best Regards

          =snp

            Thanks snp. CMB is starlight. That is what I have been thinking. Just downloaded your paper.

            Cheers

            Colin

            Hi Jonathan

            I read your essay when it first came out. I wanted to work out an idea about a kind of circular symmetry before commenting, but then a bit of exhaustion set in which was quite debilitating, and made it easy to put things off . I did manage to rate your essay and several other nice ones the day before the deadline, and have recovered some energy after a good sleep and some exercise.

            Will post to your essay blog later today, hopefully before the old brain gets tired and fuzzy.

            Al the best to you,

            Colin

            Thank you Colin Walker,

            You please ask me any questions if you need. I will try to clear your confusions....

            Best regards

            =snp

            Dear Colin,

            It appears that your response was cut short by the cyberpoltergeists lurking around here, ha.

            Armin