Even Rindler, whose name is attached to aspects of special relativity, states about Einstein's postulate:

"Light propagates the same in all inertial frames... It is not for us to ask how!"

Well since Einstein' space time based on Minkowski's Paper - Minkowsky, Hermann, German paper Raum und Zeit (1909), Jahresberichte der Deutschen Mathematiker-Vereinigung, 75-88. In the 1920 English translation...We can clothe the essential nature of this postulate in the mystical, but mathematically significant formula 3x108(metre)=в€љ-1(second)....

Well Minkowsky made Einstein's postulates mathematical by making the speed of light the imaginary unit. Hence what the imaginary unit can do the speed of light can do -- and the imaginary unit closes the algebra on the geometry for any equation. That is, by making i equals c Minkowsky got space-time.

Clearly by making the speed of light by definition the imaginary unit, we imbue "the speed of light" with all the "properties of the imaginary unit" which are the properties that are necessary and sufficient to close all equations. That is, what the imaginary unit can do, the speed of light can do to. Clearly the imaginary unit via The Fundamental Theory of Algebra forces "c=i" to behave as a universal constant always timelessly available for all observers. That is, the imaginary unit is the "timeless" number that closes algebra on a geometric number field, all numbers are "forced" by the power of mathematical certainty (obtained by deductive proof) to obey the terms and conditions of the Fundamental Theory of Algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. That is, there are no "places" without the constant of closure for General Relativity of "c=i" that is, this "constant of closure" is universal and acts as a timeless initial condition for all polynomials that describe any interactions via single variable equations that are non-constant.

and recall What is fundamental in complex numbers - is how we define the imaginary unit in maths. Recall the imaginary unit is defined by solving uniquely the equation xВІ+1= 0. That is, i is a unique (i.e. distinguishable) number defined as the square root of minus one, i.e., i в‰Ў +в€љ-1. Since there are two possible square roots for any number +в€љ and -в€љ, clearly the square roots of a negative number cannot be distinguished until one of the two is defined as the imaginary unit, at which point +i and -i can then be distinguished. Since either choice is possible, there is no ambiguity in defining i as "the" square root of minus one.

Your essay uses these two imaginary units above since clearly +i(second)=c(meter) then elementary complex maths tell us that 1/i=-i, or that is -i(second)=h(Joules) that is why you say the clocks count energy not time. Clearly Joules ~ 1/time or (Quantum theory:minimum change О"EО"t~h/2ПЂ).

I feel using these basic facts you could of derived your ideas with less bother and not use the two-time and one-time frames. Since Minkowski used the +i for space-time and you include the qm -i. Yes I'm saying that our physics uses the indistinguishable imaginary units +i,-i and not the definitional i в‰Ў +в€љ-1

A marvelous read and the comments you are receiving are so great -- one of the best essays so far.

I hope you have time to read my essay "What is fundamental is the area of the imaginary unit" it goes into details about these two constants for the definitional imaginary unit

    Ed,

    Browsing your paper for the first time surprised by the opening implicit assertion that there is something wrong with light defining a 'preferred' reference frame. Isn't that exactly what it's supposed to do? Light is the fiducial in our definition of space. The laws of physics don't change when we take light as the fiducial. That's what SR tells us as I understand it. And I'm of the opinion that one needs to understand quantum gravity to properly appreciate why this is true.

    Having said that, I'm delighted by the way you set the scene in the tavern. Thank you for that.

    Didn't dig into the remainder of the paper in detail, see there is not much to do with the quantum in it. Logically it is perhaps good to keep in mind that SR is three body problem, Lorentz transform is just Pythagoreus. If seeking foundations exact general solutions don't exist (afaik) beyond two body. And QM is ultimately two body. Getting three things together in one spot simultaneously gets ever more difficult as one goes to every smaller length scales.

    The distinction you seek to make is between partial and total derivative? I don't know if it will help you to look at this from GA perspective, but pretty cool if it does:

    vacuum wavefunction in GA can be taken to be Pauli algebra of 3D space, comprised of point, line, plane, and volume elements. One scalar, three vectors, three bivectors, and one trivector. Assigning topologically appropriate electromagnetic fields to those fundamental geometric objects generates agents in the physical world.

    interactions of those wavefunctions/agents can be modeled by the geometric product, which changes dimensionality of the iteracting geometric objects. The product of two 3D Pauli algebras yields a 4D Dirac algebra, a geometric representation of the particle physicist's holy grail, the scattering matrix. The fourth dimension, time, emerges from the interactions. It is encoded in the 4D pseudoscalars of the Dirac algebra.

    Does this means total or partial derivative to your Tavern Keeper? One or the other? Both? Neither?

      Hi Edwin:

      Thanks for your time in reading my paper and providing kind and thoughtful comments. Finally, I got a chance to read your paper and enjoyed throughout.

      I do not fully comprehend all mathematical detail of your model but notice your conclusion - "The effect of this belated recognition of 'ether' is the restoration of physical intuition and understanding of the fundamental nature of time as universal simultaneity."

      Your conclusion contradicts Einstein's relativity of simultaneity, while my photon model in my paper - "What is Fundamental - Is C the Speed of Light" supports Einstein as it is vindicated by the observed universe expansion data. My photon model shows that there is no unique time or clock in the universe as time is only a relative entity to the frame of the observer.

      I notice that you are in the bay area; I also reside in Cupertino, may be we can get together to discuss this further. You can contact me at avsingh@alum.mit.edu.

      Best Regards

      Avtar Singh

        Hi Edwin,

        With the effectively entertaining device of a stage play taking place in a bar, you've revisited a variety of "relativistic" debates from a range of perspectives (historical characters).

        As an indicator of where I stand in such matters, I'll begin by offering my translation of the recurring relativistic expression: "Relativity of Simultaneity." As used by Big Al and his troupe of loyal followers, what I think the idea really means is this:

        Fogification of the inevitability of the anisotropy of light propagation.

        As any competent ether theorist would argue, since light propagates as a wave in a medium, at every point in space there is a frame of reference (speed and direction) with respect to which light speed equals exactly c. Which means it equals something else in all other frames.

        A point not often enough appreciated in such discussions is the huge difference between one-way speed and back-and-forth average speed. Locally, the back-and-forth average speed has so far always come out to equal c (Lorentz invariance). Whereas the one-way speed is arguably impossible to measure, due perhaps most of all, to the problem of producing a pair of synchronized clocks at the endpoints of the path.

        Typically, the discussion gets very messy and fraught with all kinds of misunderstandings. In the interest of simplifying things, I've often conceived of a vast empty space with two props, considered one after the other: 1) a rotating wheel and 2) a massive sphere. In the first case light speed anisotropy can be measured because a light path can be made to follow the circumference in opposite directions. Return times to the same starting point are not equal. Also, time dilation is shown to be non-reciprocal: slowest clocks on the rim, fastest clocks at rest with respect to the axis. These are facts.

        In preparation for considering the second case, you may recall that, upon contemplating such problems, wherein Earth's gravity has to be accounted for, Phipps sometimes use the expression: "born-and-bred inertial clocks." I think this is a step in the right direction, as is your idea of conceiving "light propagating in local gravity defin[ing] the preferred frame."

        Neither approach, as I see it, is sufficient to the task, however, because of abundant evidence provided by motion-sensing devices (accelerometers and clocks) that almost all such frames still yield evidence of motion. Neither Phipps' idea, nor yours, are sufficiently restrictive.

        Intent on cutting through the complications, it long ago occurred to me that the answer is to identify the general (gravity-inclusive) analog of the rotation axis. The most strictly "born-and-bred inertial clocks" of all are members of the family of clocks that are falling from infinity. This is the collection of "preferred frames" whose trajectories I call maximal geodesics.

        Disentangling maximal geodesics that might serve as such with respect to one massive body from the influence of other bodies and all manner of rotational and linear motions in the real world is no trivial task. But I think it's the appropriate strategy.

        Upon pursing this route, I think it is interesting that, even accepting the possible fundamental significance of radial falls from infinity, we encounter a seemingly irreconcilable conundrum under the assumption that gravity is an attraction. If the paths are followed into a hole through the center of the source mass---if gravity is regarded as an attraction---then we'd have substantial speeds with respect to the center in every direction. Accelerometers on these trajectories NEVER gave non-zero readings. So how did they acquire any absolute (non-preferred) speed? Presumably, the rates of such clocks whipping past a clock at the center would be slower than the central clock. If these clocks never suffered an accelerometer-measurable acceleration, then what made this happen? Gravitons? Purple-winged horsies?

        As you know, my model avoids this conundrum by steadfastly adhering to the testable prediction that trajectories representing radial falls from infinity do not pass the center. A clock at infinity and a clock at the center always tick at the same rate because they are extreme members of the family of maximal geodesic clocks.

        I'll leave it at that.

        Best regards,

        Richard Benish

          Dear Edwin.

          This is quick notification for you and discussion that I shared Richard. Im reading this your essay and will comment later.

          Since Richard J. Benish told in his essay some interesting point of your ideas which I really appreciated.

          I think your essay is very interesting and important (one of the best I know so far) and therefore rate after reading it with great intention, Since it profoundly attacks most of current problems in physics. It really gives me a good answer about the questions related to prioritizing problems I faced.

          To address all problems and to put new forward going Idea are two very important actions, but I sometimes wonder which one is most important to focus on first?.

          Here is my essay in current contest; https://fqxi.org/community/forum/topic/3143

          Please feel free and comment, discuss, approve, disapprove or ... Truth is only important thing for all and forever.

          According to your essay, some points I really understand are;

          "How far into the foundations, when it comes, must the revolution penetrate?" [1]-- Thomas E. Phipps, Jr.

          "One of the current essay contestants, Edwin Kling-man, echoes some of Phipps' ideas by suggesting that the course of physics would benefit by rethinking the foundations back to Hertz and Maxwell. [2]".

          I absolutely agree with Edwin and woold like to comment, that at least some department of physics namely Theoretical Physics should go back 19th century by recombining to Natural Philosophy, in order to setup it's foundation and recover fundamental problems, or minimum point to 1932 and cancel Coulomb's charge statement and all fundamental interpretation Quantum Mechanics namely Nuclear force and hypothetical boson particles with its massles terms and profoundly rearrange everything.

          On the other hand the impact of above mentioned statements gives that the question of Fundamental Physicality would be incomprehensible without setting up its basics by addressing all problems in Physics (comprehensive environment).

          additionally Paul Dirac very few Physicists that have been worrying about this case since 1928.

          "2 . What's Not Fundamental About Modern Physics and Cosmology?".

          I think the Interpretation of Modern Physics (Quantum Mechanics) is Fundamental.

          Regarding to history of scientific development It has been something normal that scientists at time conclude their work and generalize to equation, based what they so far but second generations must be aware it's validity and if there is new discovery immediately must be profoundly interpreted while taking into account it Philsophical aspect, other wise misinterpretation may lead chain of misconceptions. A best example is tremendous situation of the separation (due to matter of misinterpretation) between Classical Physics and the Quantum Mechanics.

          Linking them to the Fundamental nature of Gravity, there is 232 years old PUZZLE namely Coulomb's Law which have no valid reason last 85 years (1932 last nucleon discovery), but I m not quite sure if today's Scientists are aware to it and it's consequences. I think the appropriate and inspiring question is;

          Regarding to Coulomb's law a statement that says "same type of charge repell and different type of charge attracts". How Coulomb would conclude his law, if he know that nuclei has protons that same type of charge are attracting each other and with the neutrons? and they can be divided into fractions of charge?.

          I agree many points of your conceptual explanation and would like to discuss it later. If you find more relevant essays/topics please share with me.

          The fundamental concept physics is based on three basic units Mass, Space and Time ( matter plus two related basic effects) which isn't interchangeable but their effects (derived) as energy, force an so are interchangeable since it agrees with our everyday experience.

          What is the difference between Fundamental and elementary?

          What is the name of fundamental penergy e?.

          The case of mass energy equivalence, in 2010 essay contest I have explained and quantized that mass of elementary particle (photon) but I have experienced that there is great misunderstanding due to confusion of terms over last hundred years, since photon is the first hypothetical boson

          http://fqxi.org/community/forum/topic/794

          Mass of photon m=E/c^2 = 1.78266173x10^-36kg.

          Wavelength = 1.239841857ﾃ--10^-8 m

          These results and perhaps more are also in Wikipedia. https://en.m.wikipedia.org/wiki/Electronvolt

          We are incoherently talking same thing in diffrent name. I would be thankful if one can comment.

          Another amazing fact is that I have noticed that it agrees with Einstein's proposed photon as particle with energy of 1eV.

          What means to answer the question Fundamental in such kind of environment?

          Sincerely.

          Bashir

          Dear Edwin.

          This is quick notification for you and discussion that I shared Richard. Im reading this your essay and will comment later.

          Since Richard J. Benish told in his essay some interesting point of your ideas which I really appreciated.

          I think your essay is very interesting and important (one of the best I know so far) and therefore rate after reading it with great intention, Since it profoundly attacks most of current problems in physics. It really gives me a good answer about the questions related to prioritizing problems I faced.

          To address all problems and to put new forward going Idea are two very important actions, but I sometimes wonder which one is most important to focus on first?.

          Here is my essay in current contest; https://fqxi.org/community/forum/topic/3143

          Please feel free and comment, discuss, approve, disapprove or ... Truth is only important thing for all and forever.

          According to your essay, some points I really understand are;

          "How far into the foundations, when it comes, must the revolution penetrate?" [1]-- Thomas E. Phipps, Jr.

          "One of the current essay contestants, Edwin Kling-man, echoes some of Phipps' ideas by suggesting that the course of physics would benefit by rethinking the foundations back to Hertz and Maxwell. [2]".

          I absolute with Edwin and would like to comment, that at least some department of physics namely Theoretical Physics should go back 19th century by recombining to Natural Philosophy, in order to setup it's foundation and recover fundamental problems, or minimum point to 1932 and cancel Coulomb's charge statement and all fundamental interpretation Quantum Mechanics namely Nuclear force and hypothetical boson particles with its massles terms and profoundly rearrange everything.

          On the other hand the impact of above mentioned statements gives that the question of Fundamental Physicality would be incomprehensible without setting up its basics by addressing all problems in Physics (comprehensive environment).

          Paul Dirac was one of very few Physicists that have been worrying about this case since 1928.

          "2 . What's Not Fundamental About Modern Physics and Cosmology?".

          I think the Interpretation of Modern Physics (Quantum Mechanics) is Fundamental.

          Regarding to history of scientific development It has been something normal that scientists at time conclude their work and generalize to equation, based what they so far but second generations must be aware it's validity and if there is new discovery immediately must be profoundly interpreted while taking into account it Philsophical aspect, other wise misinterpretation may lead chain of misconceptions. A best example is tremendous situation of the separation (due to matter of misinterpretation) between Classical Physics and the Quantum Mechanics.

          Linking them to the Fundamental nature of Gravity, there is 232 years old PUZZLE namely Coulomb's Law which have no valid reason last 85 years (1932 last nucleon discovery), but I m not quite sure if today's Scientists are aware to it and it's consequences. I think the appropriate and inspiring question is;

          Regarding to Coulomb's law a statement that says "same type of charge repell and different type of charge attracts". How Coulomb would conclude his law, if he know that nuclei has protons that same type of charge are attracting each other and with the neutrons? and they can be divided into fractions of charge?.

          I agree many points of your conceptual explanation and would like to discuss it later. If you find more relevant essays/topics please share with me.

          The fundamental concept physics is based on three basic units Mass, Space and Time ( matter plus two related basic effects) which isn't interchangeable but their effects (derived) as energy, force an so are interchangeable since it agrees with our everyday experience.

          What is the difference between Fundamental and elementary?

          What is the name of fundamental penergy e?.

          The case of mass energy equivalence, in 2010 essay contest I have explained and quantized that mass of elementary particle (photon) but I have experienced that there is great misunderstanding due to confusion of terms over last hundred years, since photon is the first hypothetical boson

          http://fqxi.org/community/forum/topic/794

          Mass of photon m=E/c^2 = 1.78266173x10^-36kg.

          Wavelength = 1.239841857ﾃ--10^-8 mm.

          These results and perhaps more are also in Wikipedia. https://en.m.wikipedia.org/wiki/Electronvolt

          We are incoherently talking same thing in diffrent name. I would be thankful if one can comment.

          Another amazing fact is that I have noticed that it agrees with Einstein's proposed photon as particle with energy of 1eV.

          What means to answer the question Fundamental in such kind of environment?

          Sincerely.

          Bashir.

            Dear Steve,

            Thanks for your gracious compliment. The interactive commenting is one of the most valuable features of these FQXi contests. I learn a lot from participation.

            It's difficult to address the 'flat rotation curve' problem in a single comment. Even tougher to analyze your specific model and address the pros and cons. A few years ago I treated spiral galaxies as 'mass current loops', which induce an axial gravito-magnetic dipole similar to the electromagnetic dipole induced by a charge current loop. This 'gravito-magnetic moment' pierces the galactic plane and exerts a Lorentz type force mv x C, where v is the velocity of the orbiting star with mass m and C is the gravito-magnetic field vector generated by the rotating spiral galaxy. Physically, this acts in exactly the correct manner, with faster objects experiencing greater force inward toward the central axis of the galaxy. Quantitatively, I have no results to compare to anything.

            Therefore, since I have a qualitative theoretical explanation for 'flat rotation curves' from gravitational equations of the type seen in equation (5) of my essay, but I have no quantitative reason to believe it, I tend to stick with my own qualitative theory unless and until someone comes up with a qualitative explanation with quantitative calculations that are convincing.

            As for whether mechanical clocks in massive gravity would exhibit relativistic effects, I don't know.

            I hope this answers your question.

            Best regards,

            Edwin Eugene Klingman

            • [deleted]

            • Post #146

            Dear Jouko Harri Tiainen,

            It's very rewarding to read comments such as yours. You express your appreciation of my essay, and suggest that I could derive my ideas with less bother if I had expressed

            +i(second)=c(meter)

            or

            -i(second)=h(Joules)

            to express that clocks count energy, not time.

            I am most impressed, but my first response is that bringing the 'imaginary' i into the picture instead of the physically intuitive arguments would've gotten me nowhere. The expression i = sqrt(-1) does not usually 'clarify' things for people, even physicists. Even Minkowski, in your quote, referred to the 'mystical' formula.

            Nevertheless, my own interpretation of the 'imaginary' i is as represented in geometric algebra, i.e., i is the duality operator that transforms one element of geometric algebra into its dual.

            Thank you for observing the quality of the comments I'm receiving. Yours is exemplary. I look forward to reading your essay and will comment on your page.

            Thank you very much,

            Edwin Eugene Klingman

            Dear Jouko Harri Tiainen,

            It's very rewarding to read comments such as yours. You express your appreciation of my essay, and suggest that I could derive my ideas with less bother if I had expressed

            +i(second)=c(meter)

            or

            -i(second)=h(Joules)

            to express that clocks count energy, not time.

            I am most impressed, but my first response is that bringing the 'imaginary' i into the picture instead of the physically intuitive arguments would've gotten me nowhere. The expression i = sqrt(-1) does not usually 'clarify' things for people, even physicists. Even Minkowski, in your quote, referred to the 'mystical' formula.

            Nevertheless, my own interpretation of the 'imaginary' i is as represented in geometric algebra, i.e., i is the duality operator that transforms one element of geometric algebra into its dual.

            Thank you for observing the quality of the comments I'm receiving. Yours is exemplary. I look forward to reading your essay and will comment on your page.

            Thank you very much,

            Edwin Eugene Klingman

            Some embedded character is messing up my responses and others responses. I will ask FQXi to help me solve this problem. - Edwin Eugene Klingman

            I have asked FQXi to find the embedded character or other source of the formatting errors appearing above. - - - Edwin Eugene Klingman

            Dear Edwin

            Thank you

            Ok I had hoped or assumed that your correlating clock cycle counts to consideration of energy value, resulted in our works having an equivalence. The only difference being you speak in terms of a variation of energy as clocks increase or decrease their cycle count, while I relate the same principle with term of force dilation.

            However, when you convey to me that you don't know if mechanical clocks can measure relativistic effects near massive gravitating bodies, then I realize I have misunderstood something within your work. That you must have divorced Theory of General Relativity in preference of original concept. For the answer to my question within scope of GR is a trivial one. "This is not a criticism, as I value original opinion, especially yours"

            I take your point concerning qualitative research for exploratory purposes. That a predictive solution is not worth more than mere curiosity, if it can't be related to a reasoning whether conventional or not. You offered a good example of a hypothesis which stands alone as an island, detached from conventional theory or unique justifications. However that example entirely neglects two points of my essay.

            1. That I anchor my hypothesis to an observation and measure I term "force Dilation". It is incontestable within scope of GR, although you might argue beyond its bounds.

            2. And I follow through with metaphysics within context of why nature would behave this way. That atomic force dilation occurs because space contains the substance which provides atoms with the capacity for force. That Baryonic systems are evolved to harvest this energy potential, and all the agencies of matter are directed towards an optimised structural theme.

            I wont revisit these arguments now because that's what the assay was for. But for your example of qualitative exploration to stand comparative to my work, well it would seem to dismiss all of my crafted arguments and justifications.

            To me at least, the complex systems of this world serve as a glaringly obvious clue. A clue that nature is serviced by an organisational principle, the types of which we are only aware of one. It surprises me that others are so blind to this evidence, even when I can articulate a scenario which rationalizes universal agencies and structures within its context.

            What I believe my work is deserving of at the very least, is curiosity, on the mere basis that such a rationale can be crafted at all. Surely a relatively simple task would be to test such an idea, attempt to pull a card out from under the house, see if and where it might break down? I feel my ideas are well prepared for such a challenge, but it is not forthcoming so far. I would hope this much might occur at an international science essay contest questioning the fundamentals of universal existence. Even on the basis of it being a novelty theory.

            Anyway, I'm off sailing now. I'm going to find a quiet little cove, dive for lobsters and scallops, and spend the rest of my time reading and rating essays. You are destined to do well in this contest, and probably all future contests to come. You're an asset to this event.

            Steve

            Edwin,

            Seems to be sparse reviewing and rating in this essay contest. I am revisiting those I have reviewed and see if I have scored them before the deadline approaches. I find that I have rated yours on 1/19. Thanks for reviewing mine.

            Jim Hoover

            Ed,

            There is something that always bothered me about SR and relative motion being the same irrespective of whose frame of reference was used. Specifically, let's say that I jump up from the ground. My vertical leap is ... well, not much. But I do get a few inches off the ground. Knowing this, I can calculate the force needed for the jump and the amount of energy needed for the jump. Surely the amount of force and energy needed to move me by 6 inches is less than the amount of force and energy needed to move the Earth by 6 inches. So, it seems to me that part of your preferred reference frame is the result of a minimum energy principle associated with action.

            Best Regards and Good Luck,

            Gary Simpson

              Edwin,

              That was a bit of fun but I felt I needed a drink listening to those three. I also felt a bit sorry for Einstein not getting much of a word in. It seemed a bit 'scripted' somehow.

              Your different views were interesting to read but I must say I could't get me head round the concept or point of 'deriving SR with just one frame'. Surely the wholw point of SR is that it handles transitions BETWEEN states of motion. You may not recall my 2012 essy but I showed that can be done with CSL with solid evidence. Our conceptions of 'frame transitions' must be very different. I still need that drink!

              A nice refresher of Hertz's views anyway.

              Best of luck.

              Richard

                Dear Steven,

                This essay contest provides a forum for us to showcase our theories and explanations of nature. Almost by definition, everyone who publishes his essay has faith in his idea and wants to share it with the world, but the author always understands more about his theory than anyone else, for obvious reasons.

                One may or may not assign the same meaning to keywords as others, and may or may not be aware of all competing theories and how they stack up. This list could go on and on, but with 200 contestants, all of whom believe in their approach, it is tough to recognize the truth immediately. In my case, I focus on fundamentals, which to me means fields, photons, electrons, etc. A mechanical clock is to me so complex that I make almost no assumptions about it. Even if I understood your theory exactly, I would hesitate to apply it to such a macro, mechanical, system.

                You are blessed to be able to find a quiet little cove, dive for lobsters and scallops, and relax in that way. I do see that your essay has shot to the very top, so congratulations!

                Thanks again for your kind words about my essay.

                Edwin Eugene Klingman

                Dear Jouko Harri Tiainen,

                By equating i to the speed of light (i=c) you suggest that the speed of light is a "constant of motion" if "the laws of physics (or the equations) are the same in all inertial reference frames."

                If one believes as Einstein, that "space does not exist absent of field" and that the gravitational field fills space, then the Galilean invariance of the Maxwell-Hertz equations implies only one time dimension, and this is consistent with constant speed of light in a local gravity frame. Coordinates fixed in the gravity frame see constant c. But for other objects moving in the frame with velocity v, the constant local c appears as c+v from the perspective of elapsed time. This preserves the geometry of the Minkowski differential, without implying different time frames.

                You then postulate that the mathematical definition of +i and -i can be associated with GR (c=i) and QM (h=i). That is truly fascinating. My own interpretation of the relativity of a self-interacting field (such as gravity) leads to unidirectional time. I will try to see how to understand this in terms of your postulate. The Minkowski geometry does not imply multiple time dimensions. It is compatible with 'same time' Lorentz formulations in one inertial frame.

                You interpret h=i in Schrödinger's equation to satisfy 'Planck's quanta is constant' and "all time is equal for all observers", compatible with time as universal simultaneity. As I mention above, my own interpretation of the 'imaginary' i is as represented in geometric algebra, i.e., i is the duality operator that transforms one element of geometric algebra into its dual.

                I think your essay is very deep and requires much thought. I plan to give it much thought and will score it accordingly. Congratulations on writing an essay deserving much thought.

                Best regards,

                Edwin Eugene Klingman

                Dear Jouko Harri Tiainen,

                After reading Armin's comments on your page, I want to expand on my remarks. I admire Armin's work very very much, but I don't think I agree with all of his statements, perhaps because I ignored your use of bra and ket, and also your treatment of entanglement. I pretty much ignore everyone's treatment of entanglement, for reasons I have already published, but as it is a common belief today, I do not generally downgrade essays for expressing this belief, or even a novel way of trying to make sense of it. Armin makes some good points, such as E=-m if i=c. Perhaps i~c would be more appropriate? You do use +i and -i so one might get E=m. Or perhaps this can relate to the negative energy of the gravitational field. I simply need more thought on this matter.

                Nevertheless, my perspective here is that you are simply letting the speed of light take on a unit value and similarly Planck's constant take on unit value and you are trying to make sense of the imaginary i in key physics equations.

                Why is that i there?

                I have concluded, with many others, that geometric algebra is the most powerful tool available for physicists today. In geometric algebra the function of i is that of a duality operator, which transforms the element it is operating on into its dual. That is how I'm interpreting your work. As I say below, your essay (for me) requires more study, but I do not dismiss it out of hand. Perhaps because physicists are so comfortable with complex analysis and so used to using the imaginary i in Minkowski geometry and Schrödinger's equation they see no need to think further. For pure geometry this is probably reasonable, but physicists tend to treat the i in quantum mechanics as somewhat mystical. Again, I want to spend more time thinking about this, and I will do so in the framework of the geometric algebra duality operator.

                By equating i to the speed of light (i=c) you suggest that the speed of light is a "constant of motion" if "the laws of physics (or the equations) are the same in all inertial reference frames."

                If one believes as Einstein, that "space does not exist absent of field" and that the gravitational field fills space, then the Galilean invariance of the Maxwell-Hertz equations implies only one time dimension, and this is consistent with constant speed of light in a local gravity frame. Coordinates fixed in the gravity frame see constant c. But for other objects moving in the frame with velocity v, the constant local c appears as c+v from the perspective of elapsed time. This preserves the geometry of the Minkowski differential, without implying different time frames.

                You then postulate that the mathematical definition of +i and -i can be associated with GR (c=i) and QM (h=i). That is truly fascinating, and may relate to the energy-time conjugation I develop in my essay. My own interpretation of the relativity of a self-interacting field (such as gravity) leads to unidirectional time. I will try to see how to understand this in terms of your postulate. The Minkowski geometry does not imply multiple time dimensions. It is compatible with 'same time' Lorentz formulations in one inertial frame.

                You interpret h=i in Schrödinger's equation to satisfy 'Planck's quanta is constant' and "all time is equal for all observers", compatible with time as universal simultaneity. As I mention above, my own interpretation of the 'imaginary' i is as represented in geometric algebra, i.e., i is the duality operator that transforms one element of geometric algebra into its dual.

                I think this part of your essay is potentially very deep and requires thought. I plan to give it more thought and will score it accordingly. Congratulations.

                Best regards,

                Edwin Eugene Klingman