John,

Many thanks for reading nd commenting on my essay.

I think we are on the same wavelength. I think that the vacuum fills the void. So, I definitely distinguish between those two concepts. In fact, I think that the vacuum might even be a single continuous entity. This would be consistent with non-locality.

Will you be submitting an essay?

Best Regards,

Gary Simpson

g.

not anytime soon. Thanks, also I see your suggestion that the existential vacuum is simply continuous. Nice distinction, underlying field theoretics. :-)jrc

Gary, I enjoyed your essay. If I understand correctly you see our 4D universe as embedded in a 5D vacuum, with the algebra of quaternions and octonions underlying the physics. You mentioned the cosmic microwave background and the Hubble bubble. Do you accept the big bang and if so how does that look in your model?

    Anthony,

    If I may. The question of an absolute velocity is commonly attached to a Cartesian space in Newtonian time, but that is not what Gary is saying. In any discrete energy field, the spacetime of that field will be 4 dimensional as conventionally held for both SR and GR globally. The Simpson 5th dimension is global which self-organizes to a local 4D spacetime of a particle (or photon). And in that 4D locality the direction vector relates to points within that isolate field, not necessarily to a point in the global 5D universe. Lorentz Invariance still holds across non-locality in the global measurement space, but the absolute velocity of a mass particle can theoretically be ascertained as a vector within the 4D field itself. jrc

    Philip,

    Thanks for reading and commenting. You do indeed understand my argument. The basis for this thinking is Equations 5, 5.1, and 5.2.

    I consider motion to be the best explanation for the observed red-shifts associated with distant galaxies. Therefore, I think that the observable universe was much smaller in the distant past. Whether it began as (a point followed by inflation then expansion) or as (a homogeneous sphere followed only by expansion) is less clear to me. It is hard for me to imagine a sphere that is so large being almost perfectly uniform. So, I favor the point beginning but I have some doubt.

    My knowledge of modern cosmology is fairly limited. As I understand the situation, we observe that almost all of these galaxies are moving away from us. Given the errors of our prior earth-centric thinking, we interpret this to mean that there is no center of the universe and that everything is moving away from everything else. This argument seems to me to be flawed. The simpler explanation is that there is a center to the universe and that everything is moving away from the center but doing so at various velocities. So, the fact that so many galaxies are moving away from us simply means that we are moving slowly compared to most of the universe.

    I would envision the expansion of the universe as being driven by the complex quaternion terms present in the Octonion Group. Essentially, I see those terms as being virtual electrons. Since like charges repel, the universe expands.

    Best Regards,

    Gary Simpson

    John,

    Many thanks. It is nice to have someone who understands the Math and Physics to act as an interpreter:-)

    Best Regards,

    Gary Simpson

    sure thing, g.

    I was pleased to see that you got a community member to provide a rating. The essay Topic(s) do seem to get stretched every year, and what you have submitted was at least recognized as a fundamentally organized effort. Not in the mainstream, but not without foundation in both Relativistic and the search for Quantum unification. Take hope in Topology coming into general acceptance as a practical measure to unify mathematics. I think John Klauder might find some agreement in conventional Cartesian space (the shoebox full of cubes) being analytically functional, but not being absolutely essential as the classical measurement space. Good Luck and Happy Holidays, jrc

    All,

    Here is an example to consider.The relativistic energy equation is:

    E^2 = (m_0*c^2)^2 (p*c)^2

    This can be produced from Equation 5.2 by setting Q and Q* as follows:

    Q = m_0*c^2 pc

    Q* = m_0*c^2 - pc

    Best Regards,

    Gary Simpson

    All,

    Here is an example to consider.The relativistic energy equation is:

    E^2 = (m_0*c^2)^2 (p*c)^2

    This can be produced from Equation 5.2 by setting Q and Q* as follows:

    Q = m_0*c^2 pc

    Q* = m_0*c^2 - pc

    Best Regards,

    Gary Simpson

    5 days later

    Hi Gary. I liked the introduction, especially where you talk about needing to consider the majority of the universe that isn't the ordinary matter. Please excuse my inelegant paraphrasing. Tied up again nicely at the end where you make clear that you consider 'the vacuum' fundamental.I don't personally think the 5D structure is needed but I like that you clearly explained the reasoning behind your thinking it would make a good model. Lost me rather in the middle where it got 'technical' but overall your essay is readable and clear. Kind regards Georgina

      Georgina,

      Thanks for reading and commenting. Will you be submitting an essay? There has been very little activity in the forum thus far.

      My apologies for the Mathematics. I have no other venue where I can reasonably present these ideas. So I use FQXi as a sounding board. I realize doing so probably has a negative impact upon my scoring, but I consider it worthwhile to do so. In this case, I considered Equation 5, 5.1, and 5.2 to be noteworthy along with the matrix inversion.

      Don't fret too much about that 5'th dimension. It is scalar. It does not have a direction.

      Best Regards,

      Gary Simpson

      Yes essay submitted awaiting approval.

      I won't fret, or argue with you about the 5th dimension -or even the 4th for that matter. We are both just doing our 'own thing', in our own ways,(building sandcastles is my analogy). and trying to get it across to others as well as we can. Good luck with that. Hope you get lots more reviewers. Georgina

      5 days later

      I have not read your essay yet. I read a couple of your back essays. I will try to get to this soon. I too wonder why the entries are not showing up here.

      LC

      Gary,

      I just read your essay - interesting as usual.

      I noticed your question about the meaning of the complex numbers and I have found in my analysis of the electron/positron wave functions in my paper, the following (quoted from my comment on another essay):

      "The reason that the vectors are complex, is that the Schrodinger equation requires them to be, as it relates two vector quantities with a complex 'i' in the equation. The reason for that is that the two quantities are orthogonal - multiplying any complex vector by 'i' has the effect of rotating it 90 degrees around the origin in complex space. The vectors are actually real, but the Schrodinger equation uses this mathematical 'trick' to express orthogonality in a concise way."

      Hope this helps...

      Regards,

      Declan Traill

        Hi Gary,

        I enjoyed your essay, particularly your discussion of Maxwell and quaternions, and that the Octonions group encompasses all of electromagnetism and "something else". I suspect that the "something else" is gravito-magnetism, as represented by equations (5) in my essay. I hope to find time to try to apply the Octonions in this regard, and I think you might find it rewarding to think this through.

        As you probably know, the gravito magnetic equations are identical in form to Maxwell's equations, but the gravito magnetic field interacts with itself and is hence non-linear, thus differing from electromagnetic linearity. I do not see this as having any significance from an Octonions perspective, although it is vastly different for the physics involved.

        It's also worth noting that Maxwell's quaternions do not imply 4D space-time. That is Einstein's contribution, which I analyze in my essay.

        Thank you for reading and commenting on my essay. I am happy to see you pursue Octonion math and it's possible meaning for physics. I believe this is a very important topic.

        As for the meaning of 'i', I believe that the best interpretation is given in Hestenes' Geometric Algebra, where 'i' is essentially a duality operator.

        My very best regards,

        Edwin Eugene Klingman

          Ed,

          Many thanks for reading and commenting.

          I think you are correct regarding EM and gravity. The Kaluza-Klein Equation is a 5-D model that combines EM with gravity. It was abandoned because AE believed that the implied scalar field was not compatible with GR.

          I also think you are correct regarding quaternions and Minkowski space-time. The scalar term in a quaternion can be used to relate the dot product of a vector and the change in that vector to the length of the vector.

          Having stated that, I would like to point out that the relativistic energy equation can be produced by setting Q and Q* in my Equation 5.2 as follows:

          Q = m_0*c^2 p*c

          Q* = m_0*c^2 - p*c

          Here, m_0 and c are scalars and p is a vector.

          This implies a velocity quaternion as follows:

          V = c v

          Here, c is a scalar and v is a vector.

          I think this velocity quaternion is at the heart of the Hertz Equation Galilean Transform that you demonstrated.

          If I then integrate that velocity quaternion with respect to scalar t, the following results:

          Vt = X = ct vt

          If this is an indefinite integral then there could be a constant in there. If it is a definite integral, then this will be the difference between final and initial conditions.

          So, this is a quaternion that represents space-time, but not Minkowski space-time. Whether or not this is actually Physics is another question.

          I have given some thought to how to fit all of this together. The main stumbling block that I see is that when two bi-quaternions are multiplied together, the result has four terms (AC, BC, BD, and AD). Each of these must represent something that is physically real and measureable.

          I have begun to study Dr. Hestene's work. It will take me several years to build a satisfactory level of knowledge.

          Best Regards and Many Thanks,

          Gary Simpson

          Declan,

          See my reply to Dr. Klingman below.

          Best Regards,

          Gary Simpson

          Hi Gary,

          I always enjoy reading your works and your love for quarternions. I noticed this time you thank Wikipedia, instead of the brewmasters. :)

          For my essay, I put something together based on the wave structure of matter and how it relates a fundamental universe. Hope you like it.

          The Fundamental Universe

          Jeff Yee

            Ed,

            For one of the equations I presented, I should have added the following:

            Vt = X = ct vt = ct x

            Where c and t are scalars and x is a vector.

            Best Regards,

            Gary Simpson

            Hi Jeff,

            I'm still brewing beer. And drinking it:-)

            Best Regards and Good Luck,

            Gary Simpson