Hi Gary ,
Congratulations for your papper about geometrical algebras.It is very relevant these algebras and these diamaters and others Tools.Thanks for sharing and good luck in this contest.You are going to have a prize in logic.You merit it.
Regards.
Steve,
Thanks for taking a look and reading my essay. I think the geometric algebras will eventually explain everything to us. What is most interesting to me about what I have presented is that under some circumstances, an 8-D octonion can simplify to a 5-D space. I think this is very significant. It is necessary to take all of the concepts together as a single entity to understand fully what is happening with these algebras.
Best Regards,
Gary Simpson
Hi Gary,
You are welcome.I liked your method in playing with octonions and this 5D.I like also these geometrical algebras now.I try to formalise my theory of spherisation with 3D quant and cosm sphères with the spherical geometrical algebras and my equation about matter and energy E=mc²+ml² It is a big work Gary I search the good method.I like the quaternions, and others with the 3 vectors and the scalar and this and that, but we consider points for these algebras.If now we insert the spherical volumes and the motions more the geometrical algebras, that become relevant.Even for computing we can correlate with the bloch sphere for qbit.The strings are a beautiful tool for computing also.The convergences can appear after all.good luck in this contest.:)
Gary Simpson,
Your finding that the mass ratio of proton to electron is related to 'pi' is interesting; the observed deviation is attributed to absolute motion. In my opinion, the deviation may be due to quantum- continuous disparity.
For example, make a circle using small spheres. What is its effective circumference? A continuous line passing through the outermost points, or a continuous line passing through the centers of the spheres, or something in between. Here I think the Feynman diagrams may help, because these are used in the case of wave- particle duality, which is a case of quantum- continuous disparity. I regard the Feynman diagrams as approximation techniques. However, I have not used them till now.
As my approach is Newtonian, I take that the integration of grainy (quantized) matter follows "symmetrical spherical packing", and so 'pi' has a crucial role in deciding the masses of proton and neutron. The mass of neutron is slightly grater than 1838 electrons. This is not an arbitrary number; it represents the minimum number of spheres required to make a nearly spherical structure having perfect symmetry, when the spheres come in pairs (like electron-positron pairs). Here also, 'pi' decides the number. The surprise is that Fine Structure constant remains inbuilt in such a structure.
So the equation you obtained for proton radius cannot be a mere coincidence; it has something buried inside (however, in my model proton and neutron have sizes proportional to that of electron).
Jose P Koshy
Jose,
Thank you for commenting on my essay. I was beginning to feel a bit ignored. It is clear to me that you read and understood.
The coincidental value 6pi^5 is what set me upon a long journey. To the best of my knowledge, it was first noted by Friedrich Lenz in the April 1951 issue of Physical Review. I independently discovered it in April 2012 and I have been trying to make sense of it since that time.
You mention an alternative method of explaining the deviation of the empirically observed value of Mp/Me from 6pi^5. Your thinking seems to be very similar to that of Don Hotson. He authored three papers in the fringe web journal "Infinite Energy". The first two of those essays are excellent reading and very thought provoking. Regrettably, he has passed away. I would expect you could find his work using a Google search.
My present thinking is that the pi^5 term is the result of the 5 dimensions and that the coefficient 6 is the sum result of a scalar one value for each of the three real dimensions vector i, vector j, and vector k, plus a scalar one value for each of the complex dimensions (complex i)x(vector i), (complex i)x(vector j), and (complex i)x(vector k).
Best Regards and Good Luck,
Gary Simpson
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
