Hello to both of you?

All these reasonings are relevant.Do you know if we could find the correct spherical volumes and the correct serie with the good probablistic method.The serie and its finite number and the volumes are the keys in fact logically.I read the works of Feynman about électrons.It is a wonderful discussion.The fine structure constant is relevant also.I study a little this constant and its meaning.Feynamn in all case was incredible, when we read his papper and his words ,it is so deep and general.He was an incredible thinker.Do you remember that he said these words " one day we shall see all the truth and we shall say all oh my god but how is it possible that we have not seen a thing so simple before ?" sometimes the complexity returns to simplicity :)

Best

Steve,

Thanks for the continued interest. Perhaps you will submit an essay?

Best regards,

Gary Simpson

You are welcome Gary,

My English is not good and I have difficulties to resume, furthermore I have not a program of maths.Best Gary good luck also.

Hi Gary,

I like your work involving complex numbers in relation to particle physics. I too believe particles can be constructed or modeled with a field of complex number vectors, though I think 3 1 dimensions is sufficient. I have such a model for electrons/positrons here:

http://gpcpublishing.com/index.php?journal=gjp&page=article&op=view&path%5B%5D=367

It would be good if you could explain how your work fits into the essay topic of wandering towards a goal resulting in goal oriented structures in the Universe. Clearly the formation of particles is the most essential step in this process (as I have discussed in my essay) so it would be good to explain this in the essay.

Overall: nice work and a well written essay. Good luck!!

Best Regards,

Declan Traill

    Declan,

    As I state in my essay, I address the "arrow of time". Essentially, I eliminate it and replace it with scalar time that operates upon the complex plane. This simplifies the methods whereby any system may evolve with respect to time.

    Both GR and QM are 4-D models. They share the same physical space. However, they treat time differently. The time in GR is not the same as the time in QM. Therefore, there is no 4-D model that can combine them. The least number of dimensions tat can do that is 5 which is what I present.

    The fact that I have accurately calculated the size of the proton should be considered a very strong piece of circumstantial evidence in support of a 5-D model.

    Best Regards,

    Gary Simpson

    Hi Gary,

    Can you explain what is different about time on GR and QM?

    It seems to me that formulating GR in terms of a scalar field where space is fixed and the speed of light and rate of time are variable (by the same amount - thus giving the impression to any observer that the speed of light doesn't change) fits in nicely with QM, and in the same space 3D particles can be modeled that agree with QM.

    What would the fifth dimension be?

    Best Regards,

    Declan Traill

    Declan,

    Please read my essay slowly and carefully. It is not light reading. Figure 1 presents the 5-D geometry. It does so in a way that can be construed as 3-D geometry for an inertial reference frame.

    In both GR and SR, time and space are presented together as a 4-vector. The 4'th dimension is presented as i*c*t. Essentially, i*c*t is added to a space vector and the result becomes Minkowski space-time. GR is presented taught using tensors. Thus far, I have not learned to use tensors competently.

    Time in QM is more simple. It is presented as a scalar rather than a pseudo-vector component of space time. Space in QM is also treated differently ... more like a scalar than a vector. The Schrodinger Equation presents time coupled with the complex i and it presents the space variables x, y, and z presented as scalars rather than as vectors containing the unit vectors i, j, and k.

    Wikipedia is a wonderful resource. I give Wikipedia a modest amount of financial support. But it is not a substitute for other sources.

    BTW, Einstein himself specifically rejected the idea of a scalar field. I mention this near the end of the essay. Space-time is not a vector plus a scalar as in a quaternion. Space-time is a vector plus a "time-vector" based upon the speed of light. That is not the time of QM.

    Best Regards and Good Luck,

    Gary Simpson

    I see you have an essay here. I remember an essay last contest with similar content, it dealt with quaternions. I presume you are the same fellow. I will have to read it tomorrow.

    As for spelling, I often write from and form and similar errors, drop s from plural words and so forth. It is just a glitch.

    Cheers LC

    I just gave your paper an 8. The reason I did not give a 10 is that I think things go awry at the end. Up until equation 4.2 and page 8 things look very interesting. It is at the end when you write that the time is a scalar and not GR or SR and so this departs from GR. Actually this is a form of Clifford algebra CL_{3,2}(C) ~ SO(3,2) based on the interval

    s^2 = i^2 + ω^2 - (\bf i}^2 - (\bf j}^2 - (\bf k}^2,

    where for one of the "time" components constant (say i) this defines the anti-de Sitter spacetime AdS_5 ~ SO(3,2)/SO(3,1). This is general relativity! Spacetime can be described according to the spinor variables A and b with the interval

    s^2 = a·b + axb, x = times,

    so the scalar a·b plays the role of time and the "vector part" axb is spatial part.

    The equations 3.3 and 3.3.1 are a "biquaternion" version of the electromagnetic or Yang-Mills field tensor. The biquaterion form comes from the 2x2 matrices A_0 and A_i etc in eqn 3.3. I worked out a couple of years ago how the derivative

    d(f{\bf i} + g{\bf j} + h{\bf k}))

    ----------------------------------

    d(x{\bf i} + y{\bf j} + z{\bf k}))

    leads to the field tensor. This approach leads to a bi-quaterionic form that I think is connected to the Petrov-Penrose tensor.

    So there is a lot of good stuff here. Given that you are not trained to be a math physicists it is pretty remarkable.

    LC

      Hi Gary,

      I don't recall seeing the complex 'i' in GR for the time dimension, it is just c*t from my experience and thus a scalar time. Have you introduced the i in your work? I know it is in the Schrodinger wave equation and thus features in standing waves (i.e. for particles), but I don't see why the same notion of time cannot be used in an understanding of GR and QM (from a WSM standing wave perspective of the Universe).

      Regards,

      Declan Traill

        Lawrence,

        Many thanks for taking the time to read and comment on my essay. In the previous essay contest, I had an entry that dealt with using quaternions as a basis for Calculus. There were several other essays that dealt with quaternions also. Perhaps mine is the essay that you remember.

        Can you recommend a suitable textbook(s) for Clifford Algebra and de Sitter Space? Perhaps the time has come for me to learn these things. Keep in mind that I am an engineer by education and engineers do not study things like Group Theory ... perhaps there are some prerequisites necessary prior to Clifford and de Sitter ...

        Do you think that 6*pi^5 and the resulting proton diameter are coincidence, or could they have a physical significance? Or is it simply wrong?

        The concept of scalar time that I am presenting is a little different from what you have interpreted, but I did not really make it very clear. I am proposing that there is a "master" scalar time that is multiplied by Euler's Equation. This produces two time-like values. The product with the cosine is hopefully the time used by SR & GR. The product with isine is hopefully the time used by QM. I then interpret all of this geometrically by having the "master" scalar time operate on the complex plane. That is where the 2x2 matrices become essential and the bi-quaternion form of Hamilton's work presents itself.

        Best Regards and Good Luck,

        Gary Simpson

        Declan,

        Your statement is basically like saying that you do not see the unit vectors i, j, and k in Euclidian Geometry. It might be true, but it also misses the point. Minkowski space-time is based upon 4-vectors and that means i*c*t. The complex i is there whether or not you see it presented in writing. This is a prime example of how Wikipedia can unintentionally mislead people.

        Best Regards and Good Luck,

        Gary Simpson

        Dear Mr. Gary D. Simpson

        As you said:

        Even if you don't think you are a top thinker (hey, I'm not for sure) it is worth participating. You just never know how your thoughts might affect someone else who might then affect someone else ...

        If someone has only ten percent of good ideas, it's better than prosaic essay that supports the prevailing opinion. Your article is full of ideas and is useful and supported with math. Your math is certainly not numerology. But section, Proton Diameter leads to wrong conclusions. Your Calculated value is close (but not in the middle of the interval) from the CODATA value which is known to very few of significant digits. This means that the calculated value is likely wrong, but true.

        In my article "Cycle towards Methodology of Everything", http://gsjournal.net/Science-Journals/Research%20Papers/View/6731 I got value for the proton radius 8.764-16m.

        I have it determined, as well as all other relations without using dimensions.

        Therefore, I argue that the debate about the number of dimensions is waste of time.

        In this year's essay I confirmed the importance of Mach principles and values of Proton shift, which I calculated. I would appreciate if someone finds errors in formulas.

        Regards,

        Branko

          Not necessarily. There is nothing magical about Tensors, they are simply 4 dimensional matrices - a way to neatly encode equations involving 4 dimensions. The time dimension need not involve the complex i. If you say that i, j and k are unit vectors in the 3 physical dimensions, you could say that complex i is a unit vector in the time dimension, but it need not be a vector at all. The equations work just fine treating time as a scalar even though it occupies a 'dimension' (in the mathematical sense, rather than a physical sense) in the 4D matrix.

          I rather think that the complex i vector comes into play when 3D standing waves are involved (i.e. in the case of particles comprised of 3D standing waves). In standing waves the medium moves in circles. In the case of Electromagnetism these circles are traced out by complex number vectors (this is where the complex i comes in) and so time itself is scalar, but as it determines the rate of these complex vector rotations in particles the complex i and t are closely coupled.

          Anyhow, I have given your essay a community score of 10 because your essay is well written and I like your work on complex numbers and quaternions and I think there should be more of it.

          Best of luck in the competition...

          Regards,

          Declan Traill

          Dear Simpson

          Your Harmony essay is very good. You envisaged, 5 axis coordinate system. , which are x,y,z,t and i the imaginary. You used it to derive the Diameter of proton and other results nicely.

          Is that really necessary to have that i axis? Why should we need imaginary things to derive real things.....? Both the classical Physics and QM are for real matter at different scales.

          Hope you will clarify me....

            Dear Simpson

            I modified the text and FQXi server did not take that change(modifications) even after 10 times trying and restarting my computer.... So I am putting another post...

            "Is that really necessary to have that i axis? Why should we need imaginary things to derive real things.....? Both the classical Physics and QM are for real matter at different scales."

            Hope you will clarify me....

            The coincidence you cite I am not sure of. Where things went I think a bit awry is with the interpretation of time as a scalar being different than that of relativity.

            I am going to try to carve out some time to work on this. I will present a bit here.

            The book by Hestenes and Sobczyk is good. Hestenes writes in a straight forwards way that avoids overly pedantic stuff.

            Cheers LC

            Branko,

            Many thanks for reading an commenting upon my essay. Perhaps I have given you an idea? If so, please use it wisely and freely.

            Regarding the proton diameter, the value that I estimate is in the lower part of the NIST data range. It is very close to the value determined using muonic hydrogen. Having said that, I should also say that my value is outside the range published by the Paul Scherrer Institute as part of their study. I also claim that the Earth's reference frame is in absolute motion. I have not yet determined the correction for this motion.

            I have briefly read your essay but not carefully enough to make any sensible comments. I'll study your work more closely and comment.

            Best Regards and Good Luck,

            Gary Simpson

            Satyavarapu,

            Thank you for taking the time to read and study my essay. Do we really need imaginary things? I will simply say this ... if the universe is truly 5 dimensional, then the extra two dimensions are not imaginary. The evidence that I offer in support of this is the proton diameter calculation. Admittedly, this is only circumstantial evidence, but if correct then it seems to be pretty good evidence.

            In some ways it is unfortunate that we use the term "imaginary" when speaking of a certain set of numbers. It is better to think of the complex i as an operator that causes direction to be reversed when applied twice.

            Think of it like this ... in the Michelson-Morley experiment, no aether drift was observed. The presumption is that motion with respect to the aether is the same as motion between two physical objects. But what if we really don't know how to describe or measure this motion. What if motion with respect to the aether is in the direction of the complex i? What if we are moving in such a way that we do not even notice the two extra dimensions? I realize this seems very speculative. I will simply ask how does the proton diameter work if there are not 5 dimensions?

            Best Regards and Good Luck,

            Gary Simpson