Dear Eckard

I was hoping to see a response to my post above. The more rigorous logical analysis is in a post I've just made to Tom in support of Georgina in the blogs (Time travel) but repeated in my string. I hope you'll look, as it identified conceptually and logically where our understanding and application of maths and SR was incorrect.

I note I haven't scored yours yet and will do so now with the far higher one it deserves, as time is running out. I do hope you will agree mine deserves the same, if you haven't done so yet.

Very best wishes.

Peter

    Dear Paul,

    In my understanding, foundational questions should not just include FOM (fundamentals of mathematics) but demand some clarification in FOM even if corrections might be painful to those mathematicians to whom aleph is a gospel and set theory the alpha and omega alias infinity of mathematics. I agree not just with David Joice in that the good old Euclidean notion number was abandoned in the 19th century. So far I seem to be the first one who makes this an issue. Cantor's "counterintuitive" infinities beyond infinity provoked distrust, and they got even used as to enforce purely formal thinking. I do not intend being considered one more crank who tries to disprove Cantor or Einstein. Having dealt with the foundations of the foundations, I see the necessity for tiny but very basic resurrections.

    When I tried to explain why discrete and in particular digital models are superior, I did not hide that any belonging abstraction and in particular linearizing implies a loss of realism. I do not yet see any possibility to decide whether or not the world is anyhow discrete at the lowest level. However, most likely such lower end of our scales for temporal and spatial distance would be as useless as an upper end. I never dealt with or believed in the big bang.

    Already when I was a child, I did not understand those who spoke of blowing up a point. To me numbers and continua are likewise abstract notions that do not have exact correlates in nature unless we define for instance how to count a pregnant cow. My Fig. 1 might illustrate how to imagine discrete values to be seen in a continuous function and how a non-linear transformation changes the scales. When I heard for the first time the expression negative signal to noise ratio, I was confused. How can it be negative? The answer is simple: SNR is usually given in dB.

    Best regards,

    Eckard

    Dear Eckard,

    I enjoyed the ideas in this essay. We are very much on the same line. Quantities are related to objects, negative and complex numbers are useful because they represent orientations of real objects. They represent common sense reality, nothing magical about them. We could do without complex numbers and replace them with their 3D analogs, the more powerful quaternions.

    I remember you also used examples of auditory perception in last year's essay to make your point.

    I especially liked the sentences:

    "Strictly speaking there are neither absolutely continuous nor absolutely discrete signals, because any tangible thing is finite."

    "Even begin and end of an animal's life are continuous while irreversible processes."

    "Peas are preferably treated as if they were uncountable. Uncountable liquids are measured in terms of countable gallons."

    "Both the foundations of mathematics and, to a larger extent, basic interpretations of implication for physics are not yet as mature as possible."

    "...unfortunately common identification of a number with just one point instead of the distance between zero and a virtual limit point..."

    "Foundational pragmatism outperforms pseudo-foundational formalism"

    Best wishes for this contest,

    Arjen

      Dear Georgina,

      Be not worried if I got anonymous. It costs me time to login. Nonetheless I did so again. The system seems to tend logging me out.

      I apologize for not reading most of the many responses you got. Admittedly I am a bit disappointed because you did not as clearly issue against spacetime as I hoped you to do.

      Edwin Klingman asked me about the same as did you: How to interpret ict and ih. Concerning the latter see my essay. What about ict and spacetime, I seem to be the only one here who claims that physics must get rid of the Janus head of a mathematics that claims to fit reality from minus infinity to plus infinity. This would not even fit to the big bang.

      I do not understand what exactly you meant with spatial change over time. Engineers like me have to understand their tools. Complex plane is a tool to me, not an extension of numbers. Already Bombelli wrote that a+bi always comes together with its complex conjugate a-bi. In order to get only a+bi, one has to arbitrarily omit the latter. Of course, complex calculus is utterly advantageous - provided one does either not forget to go back into the domain of reality or a complex solution can reasonably be interpreted, e.g. complex impedance Z = R +i omega L.

      Best regards,

      Eckard

      Dear Arjen,

      Even John Baez confirmed in principle that quantum physics can equivalently be expressed in terms of real or complex numbers, and quaternions and octonions.

      However, so far he did not even mention the - as I maintain - reasonable tailor-made description in terms or only positive real numbers (R).

      My argument is simple: Any finite interval in R can be completely shifted into R, and this shift merely reverses the original physical relationship. For instance, any analysis of measured data has nothing to do with what will possibly happen after the measurement.

      Some consequences imply a lot. For instance, there is presumably no a priori given block of spacetime, no Higgs boson and no SUSY. MP3 works well with cosine transformation. This does however not mean that negative and complex numbers are unnecessary. On the contrary, they are utterly advantageous if correctly used and interpreted.

      Regards,

      Eckard

      Dear Peter,

      I did not yet read what you just wrote in your string. Time travel is impossible to me. What about the somewhat simplistic explanation you gave by means the metaphor of a river, it did not yet immediately convince me. With acoustic waves in a single medium one can also not exceed the velocity of sound by means of superposition.

      You might read what Tom Van Flandern wrote: "Is faster-than-ligth propagation allowed by the laws of physics?" and "Lorentz Contraction" in http://metaresearch.org/cosmology/gravity/LR.asp .

      Does it agree with your ideas? I see it agreeable with logic and all pertaining experiments I am aware of. It also seems to agree with the many convincing arguments collected by Ekkehard Friebe.

      Yan Flandern recognizes a universal time, a universal instant of now. Lorentz transformation works just one way and therefore without paradoxes. Minkowski metric seems to loose its basis. Physics becomes less mystic, and my touch stone seems to work: We do perhaps no longer need ict.

      Regards,

      Eckard

      Dear Eckard,

      I am very pleased with your new found popularity. Hope your essay makes it to the panel, as it appears it will. I am equally (if not even more) pleased, but not with my rating position (38) of my essay. But rather, by a very significant result I just posted yesterday. I consider you a friend and a supporter. So I just had to tell you of this directly.

      Two very key assumptions in physics (dating back to Einstein) are

      1)The constant speed of light (CSL)

      2)The Photon Hypothesis (PH)

      The first lead to Relativity, while the second lead eventually to Quantum Physics.

      In my very short paper "If the speed of light is constant, then light is a wave" I give a simple mathematical proof that CSL contradicts PH.

      I look forward to your always insightful comments.

      Best Wishes,

      Constantinos

        Dear Eckard,

        I really have not thought enough about these questions of the fundamentals of mathematics and how best to use mathematics to model reality. Which is one of the reasons I am very glad that you are.

        I was just trying to say that I think there may be a legitimate use for i as explained and hopefully clarified below.

        In my essay I have tried to show that space-time mathematics relates only to the recieved image of reality and incorporated temporal distortion. There is no change within the space-time model as it is a static geometric model, where time is a part of the geometry.

        However to have casality and passage of time there has to be a foundational reality where there is spatial change giving a sequence of earlier and later. Hence time appears as earlier and later in a sequence of spatial arrangements or positions. The spatial sequence is Mc Taggarts C series; the earlier later passage of time is B series; (space-time) past , present future expereince is Mc Taggart A series time. See his paper on the unreality of time in my references.

        So if One wishes to have that passage of time type change and -also- relate this to what is observed (in static space-time) one needs to have a change of position that can not be represented within the 3 spatial dimensions of space-time and that is a spatial distance that can not be a "real" measurement of distance because it can not be observed as a distance, within the observers scale and frame of reference.

        Dear Constantinos,

        While I maintain my support for you, I would like to clarify that the constant speed of light does not date back to Einstein but largely to Maxwell. Likewise the principle of relativity does not date back to Einstein but at least to Galilei. Planck's quantum (1900) predates Einstein's (1905) PH. Planck's appreciation might be to blame for his decision as editor to accept Einstein's paper "Zur Elektrodynamik bewegter Koerper" which omits any reference to Poincaré.

        Best regards,

        Eckard

        Dear Georgina,

        Use of i is of course legitimate. I trained a lot of students to use it. However, all physics except for quantum theory can in principle be reduced to differential equations instead. More precisely, the latter can be abstracted from original integral relationships as I tried to explain. Pauli raised the question why quantum mechanics is the only lonely discipline for which i is essential. I gave references that demonstrate his mysticism.

        I appreciate your insight that spacetime cannot be a physical reality. I would not call the Doppler effect a temporal distortion, and I maintain: Future data cannot be perceived.

        What about Mc Taggart, I do not consider him worth mentioning if we intend to explain to ordinary people what everybody understands anyway, the distinction between past and future. It is just the unrealistic model of blocktime that causes trouble. You are quite right calling it "a static geometric model".

        Only elapsed time can be measured.

        Regards,

        Eckard

        Thanks for that historical clarification, Eckard. I am always impressed by your vast knowledge and your deep insights. And that is the reason I seek your comments on the result I linked in my last post.

        I am aware that Maxwell's equations (considering light as a wave) determine that the speed of light is a constant. My just posted result does the opposite. With the assumption that the speed of light is constant, I mathematically demonstrate that light must be a wave. Thus, under all circumstances, light is a wave. In my view, this contradicts the Photon Hypothesis and the 'physical view' it lead to. It makes a strong case for a continuous universe.

        Good luck,

        Constantinos

        Dear Constantinos,

        Hector Zenil claims the opposite: "The World is Either Algorithmic or Mostly Random". This is understandable since he imagines the world like a computer created by God out of nothing and switched on at the Big Bang. So far I cannot see any reason to invoke such capitalized items into physics. Who is correct?

        I agree with you on that light is a continuous function of time, an electromagnetic wave. However, does this exclude a discrete spectrum of frequencies alias energy levels? So far, it is commonly assumed that a function of time relates to its spectral representation via the Fourier transformation.

        I maintain: The original and therefore non-arbitrary and non-redundant relationship is not the complex Fourier transformation but rather its real part, the cosine transformation.

        Because the cosine transformation is its own inverse and a discrete function of time corresponds to a continuous spectrum and vice versa, it is not obvious which one is the primary one. Moreover, in reality there are neither ideal continuous nor ideal discrete functions of time or frequency because the width of window is always finite, see also the essay by Ken Wharton.

        Andrej Akhmeteli is certainly correct when he appreciates that "a more precise future theory may reverse the verdict" that declared reality discrete or continuous.

        Engineers like me, pysiologists, and others need not something to believe in but best matching tools. We are even ready to choose different most appropriate tools according to the special case of application if we know that among them are just approximations.

        Given you did find out that the world is continuous, who will benefit from that?

        The decision for digital signal processing was definitely a profitable one.

        Best regards,

        Eckard

        Dear Eckard,

        on the contrary Mc Taggart's very clear and unambiguous definition of the elements neccessary for time as we know it are very useful. The everyday notion of past, present and future is not adequate.

        As I have tried to explain in my essay for the distant observer events that have already occurred and are to the near man already the past, are yet to be experienced and are in that distant observer's future. Though beyond what has already occurred everywhere (even though it has not been experienced) the future is un-written. So you see from this that some parts of the future, not yet experienced, are preordained, as they have already happened, and others are not.So there is partial determinism allowing causality and free will.

        The everyday notion of a present experienced by all simultaneously is not sufficient to explain observations, where there is observed to be non simultaneity of events. (See the dog on the hill example in the essay.) However simultaneity is necessary at the foundational level to permit causality.The differentiation of (Foundational)object and (Reconstruction from received data)image reality allow both to co-exist without contradiction or paradox.

        The experienced present is formed from the data that is -received-, not the objects or events that exist or the data immediately it is formed. So objective or uni-temporal Now (Where foundational objects exist and interaction occurs) is different from the experienced space-time present. There is transmission delay according to distance from object or event which causes temporal distortion of the image reality experienced.

        Best regards, Georgina.

        Dear Georgina,

        You wrote: "The everyday notion of a present experienced by all simultaneously".

        Sorry, I am not aware of anybody who is stupid enough as to not understand that it is impossible to see or hear without a delay what happend elsewhere. I am also sure that the huge majority of people who easily understand that for instance thunder takes some time of flight never heard the name McTeggart.

        Regards,

        Eckard

        Yes Eckard,

        you are correct that most people do understand there is an information delay. However it does seem that there has been a general difficulty reconciling this knowledge with the notion of the present. Most are not conscious that the present experience is not a singular simultaneously occurring collection of events, or objective slice of reality happening right Now - but a composite image formed from received data with incorporated time delay, that is unique for each observer.The amount of delay being variable according to the distance from the origin and the nature of the stimulus.Smells taking longer than sound taking longer than light.

        I suspect experiments are designed without the subjective, relative nature of the present being taken fully into account. The two ends of the laboratory are not seen at precisely the same time by the experimenter standing at different ends of the room.It takes time for the light reflected to reach the experimenters eyes and be processed.

        Such considerations are important for example when quantum physicists start to talk about time travel. On a minute scale due to the high speed of light and tiny scale of particles under consideration, the far end of the room is seen in the past compared to what is actually happening at the far end of the room. The yet unobserved event might be said to be occurring in the future as it has not yet been observed, but so it is with all distant observations.It becomes the experienced present when the observation is made ie the data is received and processed so that there is an awareness of it.

        This gets really messed up for astronomical observations because it takes a vast amount of time for the data to arrive so it is obviously not something happening right now but yet it only now a part of present experience.Until it is observed it is something that has happened but is not yet observed, like the event at the end of the room. Still in the future until it is seen even though the event has happened. After the event is seen it becomes the past consigned to memory or other records.

        Those events that have happened but are not yet observed are only a part of the future, the determined part. Beyond what exists at the uni-temporal objective Now (That is right now in objective reality) there is nothing so the future is open and unwritten. Allowing non determinism and free will.I think confusion over this is what lead to the writing of the Andromeda paradox. It can be understood either as I have explained here or by using the Lorentz transformation to calculate what would be observed. The event becomes a part of the present when the data is received by the observer not when the data is formed.

        I do not know if you have actually talked to many people about their concept of the present. I seem to have had great difficulty getting others to accept the composite nature of an experienced present moment which is an image of reality formed from received data, rather than an objective reality made from objects and events as they are in space. If you are now saying this is the common everyday perception of the present then I am surprised at that.

        I too have only recently become aware of Mc Taggart. I have found his A, B, C series helpful because I have myself been trying to describe how a spatial change can become a sequence in time, which is necessary for passage of time and how this is different from experienced and geometric space-time. As his A, B C series are very clear and unambiguous so I am using his series to explanation what I mean.

        Dear Georgina,

        If special relativity is true, then each observer will have their own plane of simultaneity. Otherwise the Andromeda paradox is one more indication that Einstein's synchronization is rather a desynchronization. Did you decide whether or not SR is correct?

        Because I do not read French, I am not yet sure to what extent Einstein's theory goes back to Poincaré. Maybe Einstein was indeed not aware Poincaré's 1904 paper. This does not matter. Maybe already Poincaré 1898 is to blame. Anyway I see the Galilean principle of relativity violated by the ABA synchronization.

        All this is pretty independent from my own work. I merely got aware that there is no plausible explanation for ict.

        Again, do you believe in SR or not? And if so, how do you defend the logical asymmetry of ABA synchronization?

        Regards,

        Eckard

        Dear Edwin,

        Having repeatedly faced punishment by getting rated one, I am nonetheless not ready to hide the unwelcome results of my perhaps compelling reasoning even if this is seen an attack on holy grails in mathematics and also in physics. If no experiment will provide accordingly expected results, then I see no way but to deal with really foundational question not in the sense of more and more excuses and speculations but readiness to look for and admit very basic mistakes.

        I would highly appreciate the same courage. What is your opinion concerning aleph_2 and concerning fair synchronization?

        Eckard

        Hello Eckard,

        congratulation for your essay!

        I don't know if we are on the same line (at least mathematically) but I think you'll enjoy reading my essay because of my proposition for "simplexity" as a good answer to "ict" (for the best one) in your sentence:

        "When Minkowski's introduced ict as fourth dimension, he confessed not to understand why it is imaginary..."

        (see my essay here http://www.fqxi.org/community/forum/topic/952)

        Best regards, good luck for the contest

        Ayind Mahamba