Hi Edwin, it seems that many beer-mats and napkins later they left without agreement but at least had not come to blows. I don't think Einstein would have enjoyed the meeting.

We are, it appears, in agreement about there being no empty space.

You include some history but I think the most important background, which you do not point out, was that this development of Special Relativity was happening at a time when co-ordination of clock time at different places was becoming necessary for the successful running of railway timetables. After early time signal sending by pneumatic tubes, electric signals were used. It is easy to understand that the time signal is something different from passage of time. Just as a time signal can be sent and received, a light signal can be transmitted and received. The time signal is processed into a clock time and the light signal can be processed into an image. When the signal is processed is when the image is seen, not when the event it pertains to happened.

You know from your own experience of thunder storms and Doppler effect of a moving siren, that the observer's relation to the sensory stimuli affects the experience. Two observers different distances for the storm experience the thunder and lightning differently, there isn't simultaneity of the events, for them. The different time lines pertain to the different experiences. The observers are experiencing the universe differently. Those experiences are different from what is actually happening in external reality simultaneously with the 'present' experience. It is important to separate what appears to be Now from uni-temporal Now. Due to the way in which the senses work there is a causal order: production of potential sensory information, transmission, receipt, processing, experience. Thus present and uni-temporal Now can not be the same.

I can tell a lot of thought and effort has gone in to crafting your essay. It is well written. No disrespect is intended. Georgina

    Dear Georgina,

    Thanks for reading and commenting. You are of course correct about the contemporary history of signal timing and synchronization of clocks. One of my more informed adversaries always wants to formulate relativity problems in terms of clocks in space at every point in each inertial frame. This is based on the view that clocks measure time perfectly, and can be synchronized perfectly, then moved with no effects.

    A key problem is that none of the clocks, circa 1900, could measure any relativistic effects. Not until the advent of atomic clocks could one test relativity, and then the results depend on interpretation of what clocks are doing: measuring a moving time dimension or measuring the cyclic energy of a moving atom, etc.

    When you speak of observer's experience of time, this vastly complicates the "clocks" involved, and, while this is relevant to our perception, it's difficult to rigorously relate this to relativity.

    Thank you for your positive remarks. Good luck in the contest.

    Best regards,

    Edwin Eugene Klingman

    Dear Diogenes,

    Your essay begins by acknowledging the need for a conceptual basis and the basic or 'substantial' stuff from which stems everything that exists. The conceptual basis is 'mental structure' for imaging and image correlation entailing information-based limitations of finite channels and noise. From these derive our concepts of space, time, mass, and distance, all sensor based. The ontological basis of such is inherently unknown, but sensed correlations allow us to build up mental structures which we project onto reality. Since pre-existing space devoid of content seems unlikely to exist, the essential stuff entails space which leads to space and time, wherein events occur. You conclude that space cannot be continuous. My own concept is that the 'essential stuff' or field is a continuum. You note that the concept of time currently used in science is subjective. Having read my essay you know that I identify time as universal simultaneity.

    You discuss mass in terms of inertia, then define the most basic form of matter as 'energy', with self-consistent dynamic structure. This seems compatible with an energy-time conjugation interpretation that is basic to the measurement of time.

    Thank you for reading my essay and commenting. Good luck in this contest.

    Best regards,

    Edwin Eugene Klingman

    Edwin, the content of each observers reference frame, that which is deemed to be simultaneous, must necessarily be the product of processing of received sensory input. The content of the reference frames of organisms or devices can not in reality be the externally existing matter (outside of, and distant from the observer), independent of the function of observer's sensory systems, or function of the sensing device. As that can not be seen /has not been detected. The different time dimensions you mention are pertaining to the space-time generated by the observers.

    Edwin:

    I do not believe you've made much fundamental progress in the nature of time since, In my opinion, without properly including the subjective aspect of the observer and his relationship to our theories we will continue to be stuck in an old paradigm. However your critique of Einstein and emphasis on the great body of work based more on classical thinking is excellent and deserves to be praised since we must dislodge the constraints he his bigger than life reputation has trapped us in to make progress. I hope you win and will do my part to make that happen

    Wolfgang Baer

    Dear Edwin

    I just took pleasure in bumping your score up another point.

    I hope you will take the time to view my essay please? Darwinian Universal Fundamental Origin.

    And I also hope we will have occasion to discuss a theme common of both our works. That considerations which are traditionally delegated to times process, are better served as considerations of energy or force. Specifically, that relative motion and gravitational environments issue effects as a modulation of atomic energy or force. I understand my Darwinian scope will seam an unjustified leap to you, and I'm happy to bench that subject while we might discuss modulated atomic energy, and the theme I have already put to you regarding modulated Baryon mass and its prospect for predicting galaxy rotation velocity. Simply by issuing a modulated Baryon mass based on square law proximity of matter. Specifically, the proximity of stars to each other in galaxies. What did you make of this assertion please?

    Galaxies do rotate as though their mass density is constant from middle to edge. While infact star densities decline proportional to square of distance from galaxy center. Interesting symmetry to reflect on, dont you agree?

    Congratulations on a great essay. My favorite for a placing two years running.

    Steven Andresen

      Ed,

      Good to see your rating having tough, regardless of all other disagreements about time it does mean that there is a growing realism than the hitherto strictly Quantum Mechanical abstraction that Time emerges from pure random events piling up in a bell curve. jrc

        Dear Edwin

        I'm glad you liked my intro and I much appreciate your complement.

        I understand your grand effort contribution for this community, reading and communicating with a large number of essays and authors. I know you are extremely busy in this community service, and I feel guilty for demanding more of your time than you have already volunteered for me. But it is a relatively simple question I hope you can address for me please? An is more important to me than I might readily admit too.

        I have been going on about galaxy rotation velocities. That if atomic energy is modulated/dilated dependent on gravities square law. What do you think of applying consequence to dilated mass?

        Galaxies do rotate as though their mass density is constant from middle to edge. While infact star densities decline proportional to square of distance from galaxy centre. This illustrates the deviation from GR predictions. Its very tidy.

        If atomic energy/mass is dependent upon proximity of stars to each other, inversely proportional to gravitys square law. Then it applies mass precisely where it need be, so as to predict galaxy rotation velocity. It presents a mathematical fit. Do you recognize my reasoning in this regard please?

        Please can you tell me where you stand with this reasoning? and in light of your gravity / atomic energy considerations?

        I understand your misgivings concerning the use of "perfect clocks" in theoretical context. You made that point clear in your essay. And you said to me that mechanical clocks can't measure relativistic effects. I spoke loosely within terms of, near and afar large masses. Would you object in the same fashion if the mass was sufficiently large so as to have a dramatic effect on the mechanical clocks function? A neutron star or larger mass.

        Thank you once again

        Steve

        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