Peter,
Many thanks for reading and commenting upon my essay. I am flattered that you would read it several times and consider it so carefully. Also, many thanks for your vote of support. It appears that you have offset one of the 8 one-bombs I have received.
It is clear to me that you understand exactly what I intended with this essay. In answer to the question at the end of your post, the answer is YES! In fact, this is why my essay only loosely fits the essay topic. I have no other means of reaching a technical audience.
The coincidences here are several. First, is the value of 6*pi^5 itself. I think the exponent five corresponds to the system dimensions and I think the value 6 corresponds to the 3 real dimensions plus the 3 complex dimensions.
The second coincidence involves the calculated values for diameter and velocity. The calculated proton size is accurate. However, the calculated velocity appears not to be accurate. But this could be a matter of interpretation.
In a post above, Colin Walker states that the velocity associated with the Cosmic Microwave Background is much smaller than the value that I state and he gives a numerical value. The value I present is exactly 5 times the value that he states. You might be able to assist here. I remember from either math or statistics that there is a type of average where a value is divided by the number of degrees of freedom that a system has. So, in this case, that would be 5. So, if the problem is formulated correctly, the velocity associated with the CMB would be the velocity I calculate divided by 5. That makes a third interesting coincidence.
The question is exactly as you state it ... Is 3-D space curved within 4-D space-time, or is 4-D space-time curved within 5-D space (quantum-space-time?)?
Your statement regarding time being a plane is correct in my opinion. I think that we experience a scalar time that then operates upon the complex plane to produce two time values. One is used by GR and the other is used by QM. Dr. Crowell commented in a post above that I have presented a bi-quaternion. That makes sense since it is the sum of a real and a complex quaternion. That also means that there are only 5 dimensions needed vs the 8 dimensions of the complete octonion group. Equation 2 seems natural to produce these two time values since it adds a term to the Lorentz Transform to produce a form of Euler's Equation.
There is a rather subtle point that I should also mention. When applying the Lorentz Transform to mass for example, we would normally apply it to the entire mass of the atom ... meaning the nucleus and the electrons. What I propose differs from this in that the LT is only applied to the nucleus. The electrons of a neutral atom are taken to be stationary vibrations that arise from the vacuum. They do not move with the nucleus but rather are pulled from the vacuum as the nucleus passes through space. This provides a tangible medium for light and for action at a distance. Since all particle accelerators use charged particles rather than neutral atoms, I am not sure how to falsify this by experiment. Perhaps there is some way to apply the photo-electric effect to something moving at high speed. Or perhaps there is some way of modifying the Stern-Gerlach experiment.
Best Regards and Good Luck,
Gary Simpson