• [deleted]

ahahaha the extradimensions are a pure joke , return at school Murphy and buy a better book of maths.

Learn what is the 3D distribution since the BB, learn what is the evolution and the polarity between mass and light on the entropical arrow of time before pondering ironical extradimensions.

Georgina ahaha what a work they do not understand even the quaternion and the PRIME numbers ahahah and they insist furthermore. Perhaps they want grants, isn't it ?

The irony at its paroxysm above the deterministic thoughts....

and the words shall not change this simple evidence.

  • [deleted]

Hi TexMurphy,

Source event, an interaction of material objects (separate from observer)----photon data transmission ----output event observed, (interaction of data with sensory system giving brain activity experienced as (output) image observed.) This is two different events not the same event occurring in two different places. The observer only sees a fabrication of the former event from the data received. This can not be occurring simultaneously because of the speed of light at which the data transmission occurs.

Re dark matter, it is supposed to have extra mass to account for galaxies holding together. An absence will not have any mass.

You ask "How long does it take for an idea to spread?" How long is a piece of string? It depends. If no one talks about it it may as well be a secret. Is it accessible to people who might tell others? Is it understood sufficiently to talk about it with others? Who thinks it is interesting or cares enough to tell someone else about it? Who thinks someone else might actually be interested or amused by it? Who thinks they won't be made to look stupid or be judged if they mention it? Is it reaching a target audience who could be interested in it? Celebrity or unknown originator? Media interest?......

Yes it exists in two space times the space-time fabricated by the speaker and the space-time fabricated by the listener. Which are different because they are in different positions obtaining different input from the environment. Which would be more obvious if facing each other rather than next to each other.

you said -"There must be many more dimensions than we thought". It depends upon what you are thinking about.

  • [deleted]

Greetings.

Given the topic of this article, I would be seriously remiss were I not to put in a plug for my recent essay, 'Toward a Helpful Paradigm for the Nature of Time,' which will be found here.

As Georgina Parry noted in an earlier post, there is an informal group of FQXi bloggers whom I fondly think of and refer to as the FQXi 'time mafia,' to which I confess being an occasional collaborator and fellow traveler. It might not be too far fetched to say that we are, to varying degrees, more or less obsessed with the quest for what David Deutsch would call a "good explanation" for the nature of time. Our comments on the topic are spread out over numerous FQXi blogs, and thus not easily accessible in total. Many, but certainly not all, of our comments will be found under the various essays which were submitted as part of the FQXi essay competition on the nature of time in 2008.

I am optimistic that slow progress actually is being made toward some sort of agreement or consensus among at least some who thing about these things. I am further encouraged by well-founded rumors that highly regarded authorities on the topic such as Lee Smolin are even now nearing completion of new books on the topic. As I suggest in my latest essay, this topic need not forever remain an impenetrable mystery. It would be exciting to see it well resolved during our lifetimes.

Best,

jcns

  • [deleted]

Dear Steve,

you sound happier.3 laughs in one post! Yes a grant would be very nice but very unlikely I expect. Its not just a thing of mathematical beauty that may or may not be realistic but something with the power to unify and answer questions. Not just one but many. Which can incorporate different kinds of mathematics because it is different parts, with different forms, functioning differently, and best described differently. Though they might all be unified under one mathematical formalism.

Dear TexMurphy,

I did reply but its accidentally in the wrong place, separate from this.

  • [deleted]

The D-brane in n dimensions fixes the endpoints of strings in Dirichlet boundary conditions. If we let σ be the parameterization of an open string, the Dirichlet boundar condition is for the string X(σ = 0) = X(σ = 2π) = 0. Here the string length is parameterized for σ \in [0, 2π]. This turns out to be dual to the Neumann boundary condition, where the momentum is held fixed. The Neumann boundary conditions are ∂X(0)/∂σ = ∂X(2π)/∂σ = 0. The brane may be wrapped around a compactified space, say for a D-8 brane 4 of these dimensions might be wrapped around a Calabi-Yau (CY) manifold. A string on the brane will then respect this and effectively the string is also wrapped around the CY. If we let the string have length X then n/r = dy/dτ

Suppose a closed string (loop) is then on the CY manifold, but there is no wrapping so the string may dynamically evolve much as a particle does. The CY manifold has periodic structure (similar to a cylinder or torus) and has zero net Ricci curvature. The reason for R_{ij} = 0 is somewhat technical, but strings on a surface with Ricci curvature expand themselves in a divergent manner. The string then orbits a region of the CY, say along the x_i coordinate direction with radius r with a momentum p = nħ/r. I will from now on make ħ = 1. If we let the string have length X then n/r = dX/dτ, and the momentum is then p = dX/dτ. Again we have the string length parameterized for σ \in [0, 2π]. This can be compared to a string that is wrapped around that coordinate direction of the CY manifold. This is like a rubber band slipped on a tube of radius r, and if I double the band winding the tension increases as does the string length 2πσ and so the length along the string is given by X = rσ. Hence the force (tension) increases as does the length; the energy spectrum also increases. The string has a tension T, which is a force which is the gradient of a potential with respect to the string parameter. The energy and force of the string obeys a Hooke's law and the force is E = Tr. The winding number is then a quantization of the energy spectrum of the string so E ~ wr = Tr. The winding number is then w = (1/r)dX/dσ. The one thing which is clear is that if I exchange R = 1/r the spectrum of the string with n quantum modes orbiting the string and the string with winding number w are simply exchanged. This is T-duality and it tells us

dX/dσ = dX/dτ --- under r --- > 1/r interchange

The string orbiting around the radius of compactification is equivalent to the string wound around that direction.

This then connects to open strings on the brane wrapped on a CY space. The closed string wrapped on a CY manifold may split into an open string with endpoints attached to the brane. The above condition for closed strings is for open strings a statement of duality between strings with Dirichlet boundary conditions and those with Neumann boundary conditions. This T-duality means that a charge associated with a string with Dirichlet BC is dual to the charge with Neumann BC. This is a way of getting a duality between say the electric charge and its magnetic monopole dual.

Let the coordinates y_i correspond to those on the wrapped brane. The motion of the string X with respect to these coordinates is governed by dX/dτ which is expanded as

dX/dτ = sum_i (∂X/∂y_i)(∂y_i/∂τ).

We may write this as

dX/dτ = ∇_yX•v,

where v, for v_i = ∂y_i/∂τ, is a tangent vector on the brane. We physically have the interchange r --- > 1/r for the T-duality. Appealing to the notion of reciprocal space in solid state physics and other areas, this is then expanded according to the momentum representation on the brane

dX/dσ = ∇_pX•u

where u, for u_i = ∂p_i/∂σ, is a tangent vector on the momentum representation of the brane. The D-brane is a large object with many modes, indicated below, so this representation involves for now the phase space representation (y_i, p_i) for i = 1, 2, ..., dim. Now appeal to quantum mechanics where we know that p_{op} = -i∇_y and the position operator x_{op) = -i∇_p, and the motion of the string is quantized.

A D-brane is built up from strings, and we may then consider the dynamics of the brane. Consider the unitary operators U and V corresponding to an N-dimensional Hilbert space so

UV = e^{2πi/N}VU,

with U^N = 1, V^N = 1. If we set U = e^{ip} and V = e^{ix} then

e^{ip + ix} = e^{ip)e^{ix}e^{-[p, x]/2}

and so

e^{ip + ix} e^{-[p, x]/2} = e^{2πi/N}e^{ip + ix} e^{-[x, p]/2}

or

e^{ip + ix} = e^{2πi/N}e^{ip + ix} e^{-[x, p]/2}

and so [x, p] = 2πi/N. For the x and p in a one dimensional subspace of the Hilbert space N = 1 and we clearly have quantum mechanics.

We now consider something additional. The brane or CY manifold is Ricci flat, but may have additional curvature for dim > 3. We then multiply

e^{i∇_i}e^{i∇_j} = e^{∇_i +∇_j + R_{ijkl}y^iy^k}.

The Riemann curvature is the Weyl curvature for Ricci flatness, R_{ijkl} = C_{ijkl}. In addition the curvature here is in O(ħ^2) and is then a quantized effect. We then make a similar argument again for the U and V operator with a commutation given by UV = e^{2πi/N}VU and find the Weyl curvature is then in units of ħ.

The braney dynamics in string theory then necessitates noncommutative coordinates. Here it was worked with momentum, where we have [p_i, p_j] =/= 0. This can just as easily be worked in position coordinates as well.

Cheers LC

  • [deleted]

Does anyone understand CIGTheory?

www.CIGTheory.com

Its claims are preposterous and I am wondering if it is explained simply enough, too simply, incomprehensible, too complex, or something else altogether?

Dr. Joanna Karczmerek may wish to consider CIG's offerings when writing her paper. Why not? It can't hurt. CIG Theory can always be discarded. We can always throw out CIG Theory, but we should at least make an attempt at its understanding. Is that too irrationale? I personally have stopped thinking these days. I QUIT! No movement, no time. Try www.CIGTheory.com please

  • [deleted]

No Georgina, they are just stealers !!! They have profitted of my english at the begining. They have utilized like strategy a pseudo mathematical superimposings mixed with an ocean of pseudo threads and discussions. They try in fact simply to steal my works with a kind of false mathematical superiority.In fact they are not able and skiling to ponder works like mine even in team and groups.So they try to imply a kind of confusions mixed with a kind of diffamations and calomnias about me. The real irony is that I know who are these persons and why they make that. The most impressing is their hates and their strategies. Furtyhermore their sciences are not really foundamentals and generals.In fact they are just motivated by their own frsutrations .They motivate themselves between them with politeness and false sciences. Like they are not really general and foundamental, so they repeat always the same with full of hate for me.An other parameter is the lack of recognizing and also the lack of funds at a time so improtant.In fact they simply fear and they are simply frustrated. They are also full of hates and full of envy. They like the vanity, the money and their team.They like the conferences and the pseudo celebrity. I eat their sciences at my breakfast. When I see Joy, Lubos, Th,and several others, I laugh simply in seeing their endeavour.If they were rational, I will admit ,but in fact this team is a team of incompetents.Their maths....a pure joke, their physics, a pure joke, their generality, wawww ohh my god.Their conclusions, an ocean of confusions.

In fact mister murphy shane watkins reeves tegmark florin cristi th joy lubos noldus aguire and selected friends .....me alone! I am persuaded that they like my courses of sciences.I give them courses all days in live, just for their vanity and their redemption of course.Mr Witten and Mr Lisi, you think really that you can arrive at this toe with me like strategy ? well , and what are the roads of these false mathematical superimposings. The M Theory Mr Witten and the spherical universl strings with the E8 and the 7 sphere of Joy???it is that the strategy of New york witht he help of several institutes with partners like you say. Me alone my friends and you in team .You have forgotten your universal foundamentals dear scientiosts or what ? Are too much occupied with the monney and the vanity. Have you forgotten what is a real searcher, a real scientist? Have you forgotten the aim of sciences.Or are you too much interested in the business? Frankly all this since that you knew my theory is a pure circus with sockpuppets and with an ocean of hate and incompetence. It is not the road of sciences and the responsabilities of institutes of researchs. For example Joy from the perimeter should focus more on rational sciences than these stupidities of parallelizations. Still a lot of monney lost for nothing.Th the same, he could work like a techical engineer if he accepts several foundamentals instead to loose his time with the publicity and the marketing, but pzerhaps it is his road the marketing after all.Lubos for example could learn the 3d instead of pondering also a publicity for the extradimensions with a vanitious frame of reference of nothing for nothing.In fact these persons are not able to ponder real innovations, so why several systems loose their money ??? Of course all understands that the human nature is the human nature but all this circus is became a real parody of sciences. The competences must be well utilized.

The formalism georgina you say , the universal axiomatizaion is not a play !!! The strategy is not a general universality.

  • [deleted]

www.CIGTheory.com

I have sent my theory off to at least one hundred reknown physicists, and some not so reknown, dozens of Publishers and Journals, Newspapers, Ripley's Believe it or Not!, and the Royal Society. How many comments have I received? Zero.

Does this mean my theory is right or wrong?

The theory explains where Space comes from, it explains Dark Matter, Dark Energy, Red Shift anomalies, Wave Paticle Duality, much more. Is this the way the community works?

Thanks A Lot Guys/Girls,

Mr. Doug

PS: My deepest apologies for venting on Dr. Joanna's article site. She's the best.

    • [deleted]

    Mr. Lipp,

    You wrote, "How many comments have I received? Zero. "

    Even that is no longer true about your theory; you are now receiving a comment.

    We here in the FQXi community generally attempt to treat one another with a basic level of respect, and we try to give one another the benefit of the doubt regarding motives and intentions, until proven otherwise. With this in mind, I went to your website and looked at your theory. Your Postulate II is: "1) If you believe it, it is true. 2) I believe it!"

    You have thereby immediately lost all credibility with me, and I suspect with virtually anyone who would extend to you the respect and the benefit of the doubt which is customary here and who would begin to read what you have written. If I believe that the moon is made of green cheese, that is not true. Sorry.

    You obviously have devoted a great deal of effort to creating your website. Why would you do so, and then lead off with statements such as the one quoted above which are virtually guaranteed to alienate potential serious readers? You appear to be intent on wasting not only your own time, but the time of others as well. I can't help wondering why anyone would do so. Is this your labor-intensive way of trying to "punk" the scientific "establishment," or what? Just curious.

    jcns

    • [deleted]

    Dr. Smith,

    Respectfully, I disagree. We must rely on our beliefs, no matter how strange or bizzare, for only then can we build and trust, no matter how little, our fragile reality. Do you believe that you are existing in the Milky Way, spiraling through Space? How strange. If you believe that the moon is made of green cheese so be it. There are zillions of realities out there. It is what makes the multiverse possible. And it is only the majority that decides what is the correct view, though it would be a most interesting Many World's Universe where the minority decides reality.

    Besides, if you can't get past a little humor to read a thoroughly groundbreaking theory, that is your degree of freedom. I am still waiting for the community to respond to CIGTheory. But, many thanks for at least openng the website! More than I've gotten from anyone else!

    To satisfy your immediate curiosity, "Please Keep Reading" - at least try the Fourth Law of Motion - many years of effort. Or maybe the explanation of the reality behind the wave-particle duality Double Slit experiment. Or maybe the solution to Dark Matter. Or Red Shift Anomalies. Or Dark Energy. Or the Horizon Problem. Fact is, one theory, one view, satisfies each of the above problems simultaneously (the 4th Law is independent of the others).

    Hopefully, you will finish the theory and reply with great thought and after deep contemplation.

    Do you have any better ideas where and how Space manifests itself?

    Does any other theory combine the fundamentals? Or describe Black Holes and Space in one equation, and as manifestations of one another?

    And yet, there are so many things I don't want to believe in, like sickness and poverty, and that become part of my reality despite my tryng not to believe, that I do not feel I have any control over my beliefs whatsoever, for if I did, I would never believe in many of the things I see and hear.

    Please finish reading the theory, and then after you understand it, if you can understand it, if it is understandable, feel free to scientifically disprove it. It is welcome. It is what I want. I have written my discoveries as simply as I can, and with my limited knowledge in the field. Open your mind.

    thank you

    doug

      • [deleted]

      Mr. Lipp,

      I appreciate your honesty. You at least do not pretend to be anything other than what and who you are. That in itself is refreshing. That not withstanding, no, I'm afraid that I couldn't get past a little humor to read your groundbreaking theory. Sorry. Humor, in general, is a good thing, but science is not about humor. Science is about good explanations. If you have a good explanation, don't hide it behind humor, or behind anything. We all have only a limited amount of time to spend trying to figure out how the universe works. We need to focus much of that time on thinking about the work of people who have serious ideas to share with us.

      Please read some good books such as David Deutsch's recent book, 'The Beginning of Infinity.' You don't need to be a science or math whiz to enjoy reading it. Then think about your theory, and then re-write it to make it come across from the get-go as something more than mere humor. We need all the really good explanations we can get. If you have a good explanation, put it out there, in serious language. Trying to figure out how the universe works is hard work. None of us can do it alone. Fortunately, others have helped pave the way for us. Take a good look at what they've already done. And good luck to you.

      jcns

      12 days later

      Hi Steve. In our observation the universe is a sphere, so is everything indeed easily being describde as sphere, because a sphere has a center, the center you can see as a singulairity (a sphere with radius zero) and around this (non existing) singulairity there is space, this space in my opinion needs not to be in the form of a sphere but also can be a "blob" (constitution of several spheres ? , but then you introduce new centers and so new origins). But you are right for making calculations it is easier to accept spheres as blobs, only our universe in my opinion is not constituted of pure mathematical forms as we are aware of, chaos is also a form of order. Neither do I believe (it is like religion because there are no experiments untill now possible) in strings. I like them on the beach with beautiful women, but that is another reason that we all are experiencing what we call "reality" and have CONSCIOUSNESS.

      regards

      Wilhelmus

      2 months later
      • [deleted]

      Hi Joanna,

      Quoting your article: "Scarily, the work may also force us to rethink what time actually is: "If one could construct a theory where the entire spacetime including the time were emergent, then you would discover that time is an illusion and have a more fundamental understanding of why it is there," says Karczmarek. "But that's the holy grail of the field, and I wouldn't be surprised it if takes fifty years to make any progress on it.""

      I hope you won't mind if I share my aether theory with you. I think it will explain everything including time. If the aether is made out of waves, then everything makes sense. I call them aether medium waves.

      I got the idea from atomic clocks. There is an atomic clock that uses Caesium-133 which emits 9,192,631,770 cycles per second. The most accurate clocks in the world are atomic clocks, and they use EM frequency.

      Nature makes available to us an electromagnetic frequency spectrum with radio waves at the low end, and gamma rays at the high end. Nature gives us a frequency range that spans more than 24 orders of magnitude.

      I believe that the fundamental properties of the vacuum are: aether medium waves that span an unknown frequency range (a lot more than 24 orders of magnitude). AM waves are 3D and they move at the speed of light relative to their own existence.

      What do you call 9.1GHz? Answer: a very accurate clock.

      What do you call an EM frequency that spans more than 24 orders of magnitude? Answer: time itself.

      If we make AM waves, which behave like electromagnetic frequencies, the foundation of the vacuum, then quantum mechanics and QCD fall into our laps.

      How does nature define the existence of distance? Care to make a guess?

      4 months later
      a year later
      • [deleted]

      Baggott[Farewell to Reality: How Fairy-Tale Physics Has Betrayed The Search For Scientific Truth] and even more spot-on Unzicker-Jones[Bankrupting Physics: How Top Scientists Are Gambling Away Their Credibility] critiques shame physics' shameless rock-star media-hype P.R. spin-doctoring veracity-abandoning touting sci-fi "show-biz" trending viral exacerbated by online social networks veritable diarrhea via proliferation of uncritical "pop-sci" science-writers where all is spectacle versus little is truth. Lacking Kant-Popper skepticism and falsification, lemming-like stampedes infect not only "pop-sci" science-writers to the abandonment of reality, quantitatively and much worse qualitatively qualified by adverbs: might, could, should, may,... rather than a simple factual is. Scientific societies and universities and government agencies/laboratories, motivated by their mutually-interdependent but greedy financial needs/wants, are swept up in their very own hype, routinely touting by claiming that whatever is "the next big thing", "cutting-edge" bombast... ad infinitum, ad nauseum!!! Allogorically an Indian tribe where all members are chiefs, with multi-feathered bonnets versus few braves with single-feather bonnets each. The result? Lots of angry naked birds freezing in the bushes. The result turns serious physics into a mere carney sideshow, full of fury but signifying absolutely nothing(except the latest trendiness)!!! Witness recent GIGO claims that string-theory holographic-universe affects high-Tc superconductors Drude-Lorentz optical conductivity. Witness failed Anderson resonating valence-bond(RVB) high-Tc superconductivity theory, at the time denuding the Brazilian rainforest with gazillions of papers published on a mere ego-driven double Nobel prize fantasy, versus Keimer experimental discovery that all cuprates dominant intermediate-coupling-bosons are "paramagnons" aka Overhauser(RIP) spin-density waves. Witness recent Overbye NYTimes article on holographic universe (rediscovery of duality of Stokes-theorem) so full of jargonial-obfuscation to prompt many frustrated comments, including one from emeritus APS journals editor-in-chief, as to its jargonial-obfuscation unintelligibility, full of fury but signifying absolutely nothing INTELLIGIBLE! Witness Bak/BNL/DOE self-organized-criticality(SOC) "tad late" rediscovery of Newton's F = ma mere algorithmic-renaming of Barkhausen-Tatro-Siegel burst acoustic-emission! Witness 2007 physics Nobel-prize Fert-Gruenberg decade-later rediscovery without prior attribution of 1970-1977 Siegel[JMMM 7, 312(1978); https://www.flickr.com/search/?q=GIANT-MAGNETORESISTANCE] granular-GMR. Each was the trendy "latest big thing" modulo either lack of prior attribution or "inadvertent", aka out and out bombastic chicanery!!! Siegel caveat emptor "Buzzwordism, Bandwagonism Sloganeering for Fun Profit Survival and Ego" extant is classic John Bradshaw[Healing the Shame That Binds You, Hazelden(1980s)]-Brian Martin jargonial-obfuscation exacerbated sociological-dysfunctionality!!!Attachment #1: 3_FULL_PAPER_COMPLEX_QUANTUM-STATISTICS_IN_FRACTAL-DIMENSIONS.pdf

      10 months later

      Tom,

      Thanks, but I asked for bread but what you offered me is a stone! I have no dollars to get any info where you linked. I hope you don't mind my posting here...

      Here is what some other sources say:

      "In mathematical physics, Minkowski space or Minkowski spacetime (named after the mathematician Hermann Minkowski) is the mathematical space setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime".

      "In special relativity, the Minkowski spacetime is a four-dimensional manifold, created by Hermann Minkowski. It has four dimensions: three dimensions of space (x, y, z) and one dimension of time. Minkowski spacetime has a metric signature of (-+++) and is always flat. The convention in this article is to call Minkowski spacetime simply spacetime. (It should be noted, however, that Minkowski spacetime is only applicable in special relativity; general relativity used the notion of curved spacetime to describe the effects of gravity and accelerated motion)".

      Other sources more or less say something similar. Are you comfortable with this definition? If you are kindly help resolve some of my headaches.

      Since Minkowski space applies only to Special relativity, I assume it is part of this world and not the hereafter. This space is said to 1). Apply only to Special relativity. 2). Is said to be always flat.

      My headache is that Minkowski space-time may not exist on Earth surface, since Earth surface is not flat space-time, even if only slightly curved by Earth's gravity. Even the moon's surface would be even flatter. The experiments used to support the postulates of Special relativity were done on same Earth surface, and same Minkowski space used to mathematically support the experimental findings, when it applies only to flat surfaces. How do you do the reconciliation?

      In my innocence, what does not apply somewhere cannot be used as the foundation for what is said to obtain in that same place.

      Thanks in advance for prescribing a right medicine for my headache.

      Regards,

      Akinbo

        Sorry, Akinbo, your thinking about physics and spacetime is so foreign to what I know that I can't help you.

        Dear Tom, that is why I asked you what you know about Minkowski spacetime and whether you agree with what I saw on the web about it. Is it too much to ask?

        Absolutely it's too much to ask, Akinbo. Internet quips and wikipedia do not a physics education make. There are fundamentals to get familiar with.

        Akinbo,

        Your point is a valid one, with no answer except in terms of the unsatisfactory 'domain limits' identified by Einstein. Tom's schema assumes Relativity as it's start point so can't really further address the issue.

        My co-author on a few papers is a Minkowski and we've looked at his antecedent's work in much detail. His view was mathematical, and his concepts are hardly truly reflected in the evolved 'interpretation' of Einstein's theory ("the postulates"). [Tom; You may prefer to stop reading here if 'locked in' as above].

        Some interesting quotes to give food for thought, including on "length contraction";

        Cologne 1908; "Then from here on, we would no longer have space in the world, but endlessly many spaces;" and "Not to leave a yawning void anywhere we will imagine that everywhere and everywhen there is something perceptible...I will use...the word "substance".

        (Axiom;) "The substance at any world-point may always, with the appropriate determination of space and time, be looked upon as at rest."

        "...we may define this magnitude... (c) as the ratio of the electromagnetic to the electrostatic unit..."

        "...cases with a velocity greater than that of light will henceforth play only some such part as that of figures with imaginary co-ordinates in geometry."

        That bit is entirely consistent with the DFM's 2ND ('apparent') case of 'speed'. Of LT's length contraction he wrote; "This hypothesis sounds extremely fantastical, for the contraction is not to be looked upon as a consequence of resistances in the ether...but simply as a gift from above,"

        Again I agree. There's little there that can't be interpreted as Einstein's 1952 descriptions, distancing his theory from the "interpretive embellishments" so may think IS the theory! Discrete Fields are consistent with his 1952 descriptions, as well as Minkowski's; "endlessly many spaces" which may be in relative motion but within them the substance' is always locally 'at rest'. That's just like 7 'atmospheres' at rest locally but moving at different relative velocities within the solar system.

        Back to your original question, the 'curvature' in deep space equivalent to de-Sitter is well described by the LT, precisely equivalent to from diffuse medium refraction (if not then where the refraction DOES emerge needs identifying!)

        Best wishes

        Peter