A real number system of 4-dimensions, R4, provides the fundamental coordinate system needed for a dynamical continuous charge path geometry. Moving up into dynamical structure we have rational numbers Q which are very useful for nested systems of spinning dipoles that synchronize on h-bar quanta of angular momentum.
These are dynamical systems. There is a background “floating ground” of potential and its gradients. A floating ground is the point charge equivalent of Mach’s Principle. How could we hope to have accurate N-body simulation when the real world has a floating ground potential? We have the void. We have the floating ground of potential from all charges in the universe. Then we have a floating soup of extremely lightly interactive spacetime aether structures. Any reaction of higher order structures takes place in this floating environment.
Helpful ideas and constraints :
- Charges exist in a Euclidean void of space and time.
- Charges continuously emit an electrical potential which expands spherically at the speed @.
- Point charge emergence is isomorphic to standard matter observations and effective patchwork math.
- Why are complex numbers useful in the mathematics of the universe? The reason is the context of point charges and rotations of assembled structures of charges. Imagine the dynamics of the three orbiting dipoles in each Noether core. See all the wonderful 3blue1brown lessons.
Note to self : It is incredibly interesting to think of GR and QM formulas as being the limit as a precise geometry zooms out in scale. The implementation of nature refines the mathematical approach.
The next step is to explore these options and attempt to build from first principles to very elegant math. If the emergent math doesn’t map all the constant factors properly that is easy to take care of through our choice of units. We can also look for clever opportunities to define units that incorporate constants of nature. An example here is one hertz of frequency is one cycle of a dipole. That is natural. One equals one. What about Planck’s constant? It is based on the unit increment of energy, i.e., angular momentum.
Is such discussion akin to syntactic sugar in software? No and yes. I presume that in mathematics, the parsimony of a powerful concept is itself a portion of the evidence in its favor, especially when shifting a paradigm from a more complex patchwork explanation. When a simple, logical, geometrical model is discovered and it is isomorphic to a complex patchwork, then this lends credence to the validity of the new model.
Here’s a cool idea. A field should be modeled as an object. It is a very simple object. It is centered at a location in space and time, such as x,y,z,t0 and it has a radius. Presuming,
- EM fields travel at a constant absolute speed throughout absolute space and time,
- whether local space and time are populated with moving point charges
- and presuming an immutable point charge casts no shadow in the passing field
Then, a field object is simple and we can calculate the vector direction and magnitude of the field at any x,y,z,t. Consider the field object E1 instantiated as a point charge that passes through x0, y0, z0, t0.
- Field object E1 is immutable
- Field object E1 expands as an outward moving field front presenting upon a spherical surface
- Note that the point charge moves continuously, not discretely.
- There is a precise mathematical equation for the field front.
- evaluate the vector radius r from x1, y1, z1 to xn, yn, zn
- does |r| equal the constant of field speed multipled by (tn – t1)?
- yes : E1 along the vector radius r|. E1| at x1, y1, z1 = q / |r|2
- no : E1 is zero other than the spherical surface. |E1| = 0
- For discrete time simulations with a delta t increment,
- there is a field object E0 that was emitted delta t before E1
- there is a field object E2 that was emitted delta t after E1.
- action may occur to another point charge if the wave front passes during the interval delta t.
- Fine granularity simulation is important for some applications and we may need to simulate some tiny fraction of a Planck time.
How do we define the energy of a point charge? Perhaps Einstein was directionally correct with E = mc2. We know that mass is an emergent phenomenon which can be understood as apparent energy. Composite particles structures generally employ shielding of the Noether core with standard superposition.
The Lorentz transformation is an enormous clue to the solution of nature. The tricky part is to interpret the clue properly. Physicists and cosmologists accepted the Lorentz transformation on face value and developed theories based upon Einstein’s spacetime geometry.
An alternate approach is to consider that the Lorentz transformation is exactly what it says. Transform from what exactly? The Lorentz transformation is not to make reality understandable to our Euclidean instincts formed in low energy spacetime. Oh no! It is a clue that our perception of nature is distorted from reality, by some aspect of nature that implements the Lorentz transformation. Lo and behold, the emergent tri-dipole Noether engine structure implements the geometry of the Lorentz Transformation in space and time.
One might consider the net electric potential throughout the universe, along its gradient and the gradient of its gradient to be the next level background above the Euclidean void. If you subtract away any local causal effects, every point charge still experiences the floating ground.
This floating ground renders to nonsense any notion of a deterministic universe. Local reactions are influenced by the floating ground which in turn is caused by point charges that are beyond causal contact for the reaction.
Therefore, we have free will.
J Mark Morris : Boston : Massachusetts