Mr. Bollinger

I beg your pardon sir, I don't want to be disrespectful but you confused me in the end of your comment where you say "... my biggest problem,and it's one that affects many of the large number of submissions this year: You did not answer the question FQXi asked which was to explain what makes a theory "more fundamental" " The confusion arises when the actual title of the contest is read "what is fundamental?". It does not ask anything else besides "what is fundamental?". No theory of something "more fundamental" is required and the explanations of different interpretations are freely chosen by each participant. In this regard it seems that Mr. Shirazi's essay is a personal approach for the question asked by the name of this contest ,"what is fundamental?". Why is that a problem if the content of his way of viewing things is relevant for what we call to be "real"?

So, either all the essay's that you sustain having the same problem (which will be "other interpretation than yours of something that lets you interpret whatever you want") are wrong in interpretation, and then maybe the contest question is wrongly asked, Or you're on the wrong track of thinking that everybody should think like you in interpreting an open question.

...or some third option?

Respectfully, Silviu

Silviu,

To see an outstanding example of an essay that stays razor-sharp in answering the question as asked by FQXi, please look at essay 3034 by Karen Crowther.

This issue is not complicated. I realize a lot of essayists decided this year to reinterpret the actual question posed by FQXi as an opening for presenting personal physics theories. However, I have not been able to see any interpretation of what FQXi actually asked that supports such a reinterpretation. I have done two special issues of a technical magazine myself, and from that first-hand experience I can assure you first hand that submissions that specifically address the theme as stated are both hugely appreciated and make life a lot easier for the reviewers.

That said, I enjoyed reading your essay, and in particular your idea that massive versus massless could be reinterpreted as a change in dimensionality. Intriguing!

Cheers,

Terry

Dear Terry (if I may),

There seems to be a slight mix-up in that you replied to Silviu's response to your comment by name, yet indicated something in your last paragraph which suggests that you may have thought that you were addressing me. Indeed, I am coming a little late to this conversation, but let me thank you right away for taking the time to read my essay and making some thoughtful comments. Also, I am flattered by your appellation, but I am not a professor, just a researcher. I would like to respond to some of your comments in detail.

First, your essay contestant pledge. What a wonderful idea! I have participated in this essay contest every single time except the last, and I have expressed my distaste for the author rating system both to the moderators and even to Max Tegmark himself. I understand why he does it, but unfortunately it comes at great costs, including that ratings are invariably bound to be influenced by factors other than the rater's best judgement of the essay's quality. With your permission, I would like to forward the pledge to Max, and suggest that either it or something similar be made a requirement for participation in future contests. It won't deter the determined colluders and cheaters, but it will help make the whole thing less farcical, I believe.

Second, some thoughts on your feedback on the essay itself:

"In terms of physics, I think your observation that there is a unbreakable dimensionality barrier between sub-light (massive) and light speed (massless) particles is a nice alternative way of saying massive versus massless."

It is actually more subtle than that, as I will try to show In the second part of the 2-part series of which my essay entry was the first part. The second part will, after developing an analogous reconceptualization of time dilation, apply these ideas to quantum mechanics and derive some novel distinctions, including one involving mass.

"I don't see a new invariant in this. I've read your dimensional abatement several times, and every time I get back to the same conclusion: This is still one-dimensional Lorentz contraction, just with more dimensions added."

I understand your point of view and agree that by itself, dimensional abatement does not contribute anything not already contained in Lorentz contraction.. However, in the second paper I will combine it with its analog for time dilation to derive certain insights that could not be derived using just the concepts of length contraction and time dilation and use these as a starting point exploring for my real target: quantum foundations.

"I don't immediately see the advantage of defining the photon as 2D, even though I find that an intriguing idea."

Thank you, at this stage I agree that the value is more philosophical, but I am glad that you are open-minded enough to consider that this really is an implication of special relativity which has gone unrecognized so far.

Photons are... odd, and complex, and can push the limits of quantum theory even now if you dig deep into them. (I have a great little book on that that I seem to have lost, hmm...I)

I agree and I would love to find out which book you have in mind, if you remember.

"For example, if you imagine a photon as a 3D sphere (technically a 2-sphere for purists) with a point orbiting around its equator, you can model all possible polarizations, from linear through elliptical to circular, as nothing more than different orientations of the sphere that is then projected (made 2D) along the axis of propagation. The cohesive value in that model of treating the photon as a 3D sphere before making the final 3D to 2D projective reduction in its dimensionality says to me that one should not simply discard the 3D view as irrelevant even for a particle traveling at c."

I was unaware of this model and it sounds very interesting. As you know, while the photon is according to SR completely length contracted, it does have a wavelength and period in the direction of motion, and this can result in 3D-behavior associated with photons, of which certain polarization states like circular polarization are an excellent example. So I agree with you: My claim that photons are dimensionally reduced was not meant to make any 3D conceptualizations of photons irrelevant. Rather, it was meant to elucidate what I believe to be an overlooked implication of special relativity.

For example, if you imagine a photon as a 3D sphere (technically a 2-sphere for purists) with a point orbiting around its equator, you can model all possible polarizations, from linear through elliptical to circular, as nothing more than different orientations of the sphere that is then projected (made 2D) along the axis of propagation. The cohesive value in that model of treating the photon as a 3D sphere before making the final 3D to 2D projective reduction in its dimensionality says to me that one should not simply discard the 3D view as irrelevant even for a particle traveling at c.

"Here's my biggest problem, and it's one that affects many of the large number of submissions this year: You did not answer the question that FQXi asked, which was to explain what makes a theory "more fundamental". "

My answer to the essay question is at the top of page 2:

"And this gives us a clue for identifying the most fundamental things of a theory within any given paradigm: it has to be those things which point to, or at least hint at, the next paradigm."

I structured my essay so that the theory I presented was an illustration of that answer. Now, if you had criticized my answer by saying that I did not sufficiently elaborate on it, or that I shoe-horned my own theory into the paper, I might have agreed with you, but to me, it seems a little unfair to say that I did not answer it at all. Be it as it may, my objective in this essay contest is not to win but to reach physicists, mathematicians and philosophers of physics who have a strong interest in foundational physics with some ideas which I believe are going to lead us to the next paradigm.

Actually, from your comments on another essay I saw, it appears that you do have an interest in the foundations of quantum theory, and so you are exactly part of the core of the target audience I am trying to reach. My essay entry was just meant as an advertisement for the second paper, which uses the ideas of the essay entry and a multitude of novel ideas to provide an ontology for the textbook interpretation of quantum mechanics. My hope is that my essay entry intrigues people enough so that they are willing to invest spending time and thought on the second essay, which is conceptually far more challenging than the first.

Thank you again for your well-considered comments.

All the best,

Armin

Dear Dr Armin Nikkhah Shirazi

This is a nice discussion and interpretation of "Lorentz contraction" You have correctly devised the four points viz... (1) focuses attention on two fundamental principles overlooked under the current paradigm, (2) permits a more fundamental understanding of speed of light invariance in terms of dimensionally reduced frames, (3) facilitates the identification of magnetic fields as line integrals of dimensionally reduced versions of electric fields, and (4) leads to the identification of a mathematical reason for the observed absence of magnetic charges. Best wishes to your essay...

I hope you will not mind that I am not following main stream physics...

By the way...Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay ....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

    Armin,

    Our past agreement that better fundamental understanding of both QM and SR continues. I was fascinated by your original and well argued hypothesis, though I confess I had to read most twice. An excellent job, worth a high score. However I remain unconvinced, for one particular reason; that there seems an even simpler way to solve the problem, with Doppler shifts. Please comment on this;

    I'm an astronomer familiar with plasma, astrophysical shocks, ionospheres, measurement, near/far fields and the great problems of ecliptic plane transitions and stellar aberration.

    If we consider Maxwell's near/far field transition zone (TZ) as the dense turbulent 2-fluid plasmas we find in those positions in space, so electrons absorbing EM in one rest frame k then re-emitting through the zone to eventually re-emit at c in the local electron rest frame there k'. Then the LT is implemented with wavelength Doppler shifted (so 1 sec pulses then found at 1/y sec intervals). Studying the surface of a lense we find exactly the same free surface electrons at the refractive plane increasing in density with speed.

    So we have an infinite sequence of inertial systems in local background frames, complying with SR's postulates and both Minkowski AND Einsteins descriptions (1905 and 1952) yet quire different from doctrinal interpretation. I confess I find that simpler, more satisfying and well evidenced. I can find no reason why it wouldn't produce the effects we find. The question is can you?

    The biggest problem with mainstream seems that once someone derives and publishes something they insist on remaining wedded to it. It's quite natural, and you'll want to defend your idea, but I know you can analyse in an unbiased way.

    The model resolves the big issue of astronomy (your version may to) but insights into QM arose from the TZ interaction process so a final 'test' was to produce a classic QM. It took 4 years but a full ontology doing so is in my essay! See also Declan Traill's for the code and plot. Please attack it at will! There seems little chance of acceptance by mainstream in this eon so there's no rush!

    Very well done for yours. Detailed agreement on content is not a scoring criteria and you hit all those well. I look forward to chatting more.

    Very best of luck in the contest

    Peter

      Hi Armin. I think you are on to something with a theoretical study of dimensional abatement, as you call it.

      There is an aspect of general relativity which might also be interpreted in terms of dimensions in the way you suggest. Bowler shows how length, time, mass, energy, etc. are supposed to vary with the gauge scale factor. Various experiments provide confirmation to first order.

      There is a table in the Endnotes of my essay showing radial and transverse dimensional variability due to a gravitational field. See Ref 7: Bowler M.G., Gravitation and Relativity. Pergamon Press, Oxford (1976).

      Cheers, Colin

        Dear Armin,

        I'm sorry that I'm not well-equipped to appreciate your main argument here, though it seems reasonable and well-argued. Your opening section certainly makes sense to me, and in fact I think your "intelligent alien culture" is onto something by treating distance, duration and mass as derived quantities. I was also intrigued by your treatment of "relative dimensionality" in terms of volume-boundary ratios, but it wasn't clear to me how much is gained by this. Part of my problem is that I don't have any intuitive notion of "dimensionality" as you present it... so while I don't doubt that your two principles are correct, I didn't get a sense of their importance. I'm guessing that you have some strong intuition that put you on this particular path, and I imagine that would be clearer to me if we had the second part of this essay.

        Nonetheless I'm glad you're participating again, and I saw (in your comment to Terry Bollinger) that you're planning on taping a presentation on the Default Specification Principle... I'd be very interested to see that. I think this principle expresses a basic shift in how we think about possibility vs actuality, an important step toward making QM really understandable. In fact, I think the second part of my current essay would have made more sense if I'd had the space to include some discussion of this. The basic assumption I make is that everything is possible, to begin with, and the problem of creating a universe is essentially one of defining meaningful constraints. This is the same as what happens with quantum measurement - all the possibilities are there, until there's some constraining context that can specify one of them. The existence of an adequate context is all that's needed for something to become actual.

        I could certainly relate to your Conclusion: "All of these facts are easy to understand, profound, and in retrospect, I believe, utterly obvious." I'm sure you're right that the great obstacle to working out "the next paradigm" is that the clues are so obvious they get taken for granted.

        Best wishes,

        Conrad

          Dear Nikkhah

          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

          Hello Peter,

          You wrote:

          "However I remain unconvinced, for one particular reason; that there seems an even simpler way to solve the problem, with Doppler shifts."

          You never specified what in my essay you were unconvinced about. Reading the paragraph after that, it seems that your objections are to the standard way of interpreting the LT's. Unless your approach turns out to either

          1) have measurable implications that are different from the those of the standard intepretation, or

          2) lead to novel insights which are unavailable under the current interpretation,

          I would say it is neither better nor worse than it.

          The reinterpretation of length contraction which I discussed in my essay falls under the second rubric, with an eye on not just understanding in a novel way a facet of special relativity, but the entire contemporary worldview. What is in my essay is by itself not sufficient to do that, but it is a stepping stone towards it.

          If your preferred interpretation functions in a similar manner, then you should work out those consequences and add them to the arsenal of evidence in favor of your worldview.

          Best,

          Armin

          Dear Colin,

          Great to hear from you, and thank you so much for the reference to the table. I did not know about it, and it certainly looks intriguing. I will have to think some more about it to understand how it relates to my ideas. What I presented here is just, in a way, the tip of the iceberg, but regrettably presenting the rest is taking longer than I expected (also, I am currently traveling, and that does not help, ha).

          I will shortly attempt to comment on your essay as well.

          All the best,

          Armin

          Dear Conrad,

          thank you for your extended comments. I will reply to some of them below:

          "I was also intrigued by your treatment of "relative dimensionality" in terms of volume-boundary ratios, but it wasn't clear to me how much is gained by this."

          Each paradigm is based on certain fundamental ideas which serve as a foundation for everything else that follows. However, without what follows, the significance of those ideas is by no means clear. While I presented some novel things for which relative dimensionality is a conceptual starting point, I admit that there is far more that needs to be shown to appreciate what is to be gained from it. That was supposed to be shown mainly in the second paper. However, my 2012 FQxi paper also alluded to it indirectly (the schema in the appendix uses relative dimensionality within each box as a means of transitioning from the dimensionality of one box to the next).

          "Part of my problem is that I don't have any intuitive notion of "dimensionality" as you present it... so while I don't doubt that your two principles are correct, I didn't get a sense of their importance."

          There are two answers to this:

          1. Within the limited context of my essay, I think that bringing out the consideration of dimensionality elucidates the straightforward geometric relationship between electric and magnetic fields. I had hoped that this would be one of those things where once it is pointed out, people would ask themselves "Why did I not notice this before?". That does not seem to have happened, and I really think that I am bumping into an effect that Kuhn already recognized, which is that scientists operating under a paradigm cannot easily see relationships which require a network of concepts that fall under a different paradigm.

          2. Within a broader context, I think that not seeing the importance of it is not your fault. In part 2 I proposed to analogous principles which seem equally trivial. However, when the four principles are combined together, one arrives at a non-trivial consequence which can be used to rule out certain speculative ideas. I will simply state them here briefly, skipping over a bunch of definitions which are needed to really make the principles meaningful, and ask you to tell me whether this helps see the importance. The two analogous principles are:

          a. The actual existence in spacetime of an object is invariant under spacetime coordinate transformations.

          b. The dimensionality of a timelike hypersurface in spacetime is everywhere the same.

          It is not difficult to derive from these four principles, that physical existence is partitioned into equivalence classes of existence in given n+1 dimensional spacetimes. Thus, the only objects that can actually exist in 4-dimensional spacetime are 3 dimensional objects. Similarly, the only objects that can actually exist in, say, 11-dimensional spacetimes are 10-dimensional objects. Consequently, speculations which suppose that 4-dimensional objects could exist in 11-dimensional spacetimes either violate one or more of the trivial principles, or are wrong. That is one of the most immediate of the important consequences of these principles. The partition of physical existence was already implicitly assumed in the schema of my 2012 paper, but now I can derive it from a set of fundamental principles.

          " I saw (in your comment to Terry Bollinger) that you're planning on taping a presentation on the Default Specification Principle... I'd be very interested to see that."

          Thank you for your interest, I will notify you when it is uploaded.

          I will read your essay shortly and leave a commment.

          All the best,

          Armin

          Armin,

          Yes indeed. Already done. Identified across a wide range of sciences. Even cosmology, papers published and essays here scored top 10 inc. 1st & 2nd. I recall you made good connection with some.

          The problem is that even when an established theory leaves anomalies and paradoxes no better fit theory can replace it due to the way our minds work; We build mental models and compare input to those. It its a poor fit we reject it.

          That's the 'cognitive dissonance' I discussed last year. It's just the human condition and current state of our intellectual evolution. Indeed, (like you so far!), many don't bother to even look! Those who do, properly, are rewarded.

          Yes, it goes well beyond SR, i.e. replacing the 'Law of the Excluded Middle' to remove all paradox from logic, solves Stellar Aberration at last, etc. etc. All published & archived, some on arXiv, i.e. Resolution of Kantor and Babcock-Bergman Emission Theory Anomalies . and in videos. I decided if it was correct it should do the impossible; Unify SR and QM. That's what this years essay does. If you get to read it first see the 8 part sequence I've just put on my posts to familiarise yourself with an outline to fit the ontology to.

          It's an amazing discovery (in Bells words & as he anticipated) so I hope you get to study it.

          Very Best, and well done for yours, very good and agreeable apart from that one point. But 'agreement' isn't a scoring criteria of course (so I pencilled it in for well above its present level)

          Hope yours gets in the top group. Very best.

          Peter

          Armin, thanks for your response. To your point 1. - I agree. Within the current paradigm of course it's understood that there's a basic connection between electric and magnetic fields, and that makes it harder rather than easier to see the possibly more radical relationship you're pointing out.

          Likewise with your four principles... though I'm unclear about the concept of a "timelike hypersurface," otherwise my first reaction is, sure, why would this not be true? That makes it harder to see what's going on in your argument - as you say, 'this may even be alleged to be so obvious as to be trivial." For example, it does seem obvious that "the only objects that can actually exist in 4-dimensional spacetime are 3 dimensional objects." It's not until you take the next step and say an 11-dimensional spacetime can not contain 4-dimensional objects that it ceases to seem trivial.

          I'm not suggesting your arguments are trivial, only that the method of presentation may be backwards, for readers new to your approach. It might make sense to begin with the consequences that are clearly different from what we expect to be true, and show they're grounded in principles that seem clearly true.

          Now I know from experience that in working out fundamentally new ideas, one rarely has a lot of choice about presentation. I've done the best I can with my own FQXi essays, but I've never been able to stand back and say, I could have done this very differently... at least, not till after the contest was over - then (with help from friends and commenters) I gradually gain some clarity about my errors in strategy.

          And I face a problem that's maybe very similar to yours: for me, everything follows from the simple fact that things in our universe are observable and measurable. Hard to find anything more obvious and seemingly trivial than that! So maybe once this contest is over I'll be able to take my own advice about presentation.

          Thanks again - I look forward to seeing your further development of these thoughts.

          Conrad

          24 days later
          7 days later

          Dear Armin,

          I followed up your excellent tip about Brans-Dicke and found that Yilmaz's exponential metric is what I call the Machian metric.

          Dicke has said that Yilmaz's field equation is the local field equation needed for the exponential metric in isotropic coordinates. It has been shown to violate the equivalence principle. Although I expect the violation is beyond our current means of detection, this possibility can be set aside as less than ideal.

          I think that the problem with this sort of modification is that it does not address the basic issue, which is that a multiplicative process duplicating relativistic composition needs to be incorporated, instead of trying to add something as compensation. It looks like the field equations would need to be modified in a way that has not been proposed. And that is information gained!

          Regarding your dimensional theory and special relativity, if you look at the transverse variation due to gravity in my table of dimensional variability, you will notice that it exhibits the same sort of variation as the Lorentz factor, on substituting that for the gravitational scale factor. Perhaps it is less of a conceptual stretch to see GR as having two branches of dimensionality (radial and transverse), if SR is considered to be associated (somehow) with the transverse branch by virtue of their matching dimensional variability.

          Many thanks, and best wishes,

          Colin

          a year later

          For what it is worth, the updated (and nearly twice as long) essay on dimensionality and the essay on existence are online:

          Dimensionality in Physics (Version 2) can be found at:

          https://deepblue.lib.umich.edu/handle/2027.42/147435

          Existence in Physics (Version 2) can be found at:

          http://hdl.handle.net/2027.42/147436

          Finally, a short 2-page paper which summarizes the significance of the reconceptualizations of the Lorentz transformations can be found here:

          http://hdl.handle.net/2027.42/148314

          I believe that this is the beginning of the next paradigm shift in physics.

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