Scott,

Thanks for reading and commenting upon my essay. I'll answer your questions in order.

I do not think that space-time is fundamental, but I also do not think that space-time can be reduced to something more simple. I realize that this seems contradictory. I think that space-time is EMERGENT from actions upon the vacuum. IMO, that is the meaning of Equation 5.2. I took a pair of 5-D conjugates and multiplied them. The result was a scalar that is equal to the base quaternion's length.

I cannot comment upon how the Octonion Group compares to other mathematical interpretations since I have only recently begun to study Group Theory. I can state that the group includes anti-commutation between the complex i and the unit vectors. This is what makes the 5-D conjugates work. Space-time emerges from the vacuum. The vacuum is more fundamental than space-time and it is more complex than space-time. Therefore, I am arguing that simplicity emerges from complexity rather than the reverse argument:-)

Best Regards,

Gary Simpson

Gary,

I view quaternions as the generalization of complex numbers from 2 to 3 dimensions. Just as complex number manipulation is simpler and easier than vector calculus in 2D, so are quaternions simpler and easier than vector calculus in 3D. The cost in going up a dimension is loss of commutativity when quaternions are multiplied. Clifford Algebra is the generalization to arbitrary dimensions, of which quaternions are the 3D version and complex numbers the 2D version. Dave Hestenes in Arizona has done great work in advancing this point of view. But if you want octonions and have a taste for unconventionality, try Peter Rowland's interesting book "Zero to Infinity: the Foundations of Physics". Good luck!

Anton

Anthony Garrett

Anton Garrett

    Anthony,

    Thanks for the comment. You should read my essay. I deal with a hidden variables. I see from your essay that you have an interest in this.

    Best Regards,

    Gary Simpson

    Yes, phase is not directly observable; only phase *difference* has an effect in physics. Do you think that there is such a thing as absolute phase?

    Hello Gary,

    Another well constructed argument in experimental theoretical mathematics.

    I can accept your premise that the most fundamental physical condition is the vacuum, IF we firstly distinguish that from the Void. That is to say that if there is existence at all, there existentially exists a vacuum from which the deconstructed elements we parameterize as energy and spacetime emerge. I can then accept that space-time is a parallelized co-existence of stress between a curved line and a straight light and the origin of energy. The rest is math. As you know, I do agree with your "two kinds of Time", represented as a scalar value in parallel with a vector value existing in S0. The hidden variable revealed as the Fifth Dimension. Glad you made the community ratings, Good Luck. jrc

      Anthony,

      I believe that there is an absolute phase angle that is based upon absolute velocity. Essentially, I begin with Euler's Equation and then substitute the Lorentz Transform for the cosine term and (v/c) or the sine term.

      You will no doubt ask why this is an absolute rather than relative velocity. I will reply that in order to match the observed mass ratio between the proton and the electron, it is necessary for the v term to be 0.006136 c.

      You will then likely ask what this has to do with the Mp/Me ratio and I will answer that the reference frame of the observer is built into the wave function of what is observed.

      Best Regards,

      Gary Simpson

      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