Antonio Lao said:
Epsilon Pi,
The magnetic monopoles (H+ and H-) are quantization of spacetime (1D of space and 1D of time). When we add up H's, we get the value of charge. When we multiply H's, we get the value of mass.
There is one point I am thinking about, having in mind the basic unit system concept, which is a rotating system in the complex plane, where you have 1D for space if you want, and 1D for time.
The BUS concept has inherently a frequency when acquiring a steady state, I mean, when becoming a "mass", for example, as the BUS concept is in general a representation of the behavior of energy, a reason why we can find with it, the equations of energetic systems such as the pendulum, the electron and its SWE, the Lorentz transformation group, and those equations of gravitational fields.
If think of H+ and H- as being summed as in Euler Relation we can effectively have the magnetic field, as in fact with the BUS we can represent it, too, but is not clear to me how we obtain "mass", except by considering it a resonant state of energy at lower frequencies.
Antonio Lao said:
I am still reading your revised paper on "The Principle of Synergy and Isomorphic Units" as archived in xxx.lanl.gov. I can say that your idea about the concept of complex number is my idea about the directional property of a number. So a complex number is an Abelian group in addition of a scalar quantity and a directional quantity. This directional quantity is an imaginary number. The scalar part is inherently "oneness" and the directional part is intrinsically dual, it is the product of a scalar and a 1D direction (a unit vector or basis).
Yes a complex number has both a directional property and scalar property defined in its angle and its magnitude when represented in polar form, or in Euler relation. Oneness has to do with the fact that in that complex triadic unit I have the radical duality of time and space represented, and wholeness with the fact that with that same unit I can represent the behavior of different physical energetic entities, and openness with the fact that I have associated with it a field, or way to interchange energy with the environment.
Antonio Lao said:
The square root of negative one is a way of establishing the orthogonality of the real axis and the imaginary axis. This orthogonality validate the Pythagorean theorem for one dimension of spacetime and even for higher dimensions. Without the existence of right triangles, sine and cosine functions are meaningless since they are defined as the ratio of sides of right triangles as described in trigonometry.
Yes it is, but additionally the square root of negative one, is a symbol for differentiating two different orders of reality or the radical duality of time and space.
Antonio Lao said:
The principle of orthogonality is very powerful as it is the basis of forming physically covariant theories.
In differential geometry, the time derivative of the tangent vector is always orthogonal to the tangent vector. With this orthogonality, the motion of a point can be defined in 1D as well as in higher dimensions.
And with that principle of orthogonality what we obtain when having Euler relation in mind is precisely the complex plane, sort of canvas where we can represent energy and its behavior by establishing a complex dynamic differential geometry, whose main object is not necessarily to make, as it were, geometric representation but to obtain the state of an energetic system, with two main state variables, that of time and that of space.
Thank you so much again for your time!
Best regards
EP