Space when the Maxwell Equations are the axioms of physics
Let us give an example of how Space is defined when we are under the Maxwell Equations as axioms.
Before in physics, Space was considered a empty vessel for which matter and energy can enter and fill that vessel.
However, that view changes completely when we have axioms for physics.
Consider math as an analogy. In math, plane geometry is considered space, but when is it considered space? If we have a blank sheet of paper we would have the same notion of space as an empty vessel for which we then assign numbers as coordinate points making the Cartesian coordinate system.
So in math, Space or geometry comes into existence once we have coordinate points assigned to the Space. Before we have coordinate points, we had no mathematics, no geometry.
Now consider Physics without axioms, then space is in this view, the empty vessel that you fill with matter and energy. Space is independent of the Matter and Energy.
Now consider Physics with the Maxwell Equations as axioms. In this physics, there is no Space until there is coordinate points and if we look at the Maxwell Equations, they provide coordinate points as what is called the electric field E and the magnetic field B of which we can have E+ or E- and B+ (north pole) and B- (south pole).
So in Physics with Maxwell Equations as axioms, we no longer have the silly and stupid notion of Space as empty vessel wherein matter and energy can occupy or fill. In New Physics, Space itself is a form of energy or matter. And Space, if not matter, is Space that is E or B fields.
Now the Maxwell Equations never really pinpoint what the current is, whether they are electrons or protons and never really pinpoint the light wave or photon. The equations do show us what the speed of light is, but never tells us that light is a transverse wave. The equations never pinpoint a particle called the neutrino nor that it is a longitudinal wave, but we can figure out the photon as transverse wave from the equations having the E field perpendicular to the B field and we can figure out the neutrino is a longitudinal wave since the emf in Faraday's law must be longitudinal, not transverse.
The Maxwell Equations are general and we can pinpoint the specifics of electron, proton, photon, neutrino, neutron, atoms, transverse wave, longitudinal waves, and even Space.
The Old Physics, lacking axioms and thereby lacking logic in thought, had Space as an independent object for which we then have particles and energy that occupy that Space. In New Physics, we have Space and it is the E field of E- and E+ and the magnetic monopoles of M- and M+ (north and south poles). So in New Physics, we no longer have Space as a independent entity, but Space as part of the Maxwell Equations of the E and B fields. In New Physics the concept of vacuum is no longer existing. In Old Physics, the perfect vacuum was Space. In New Physics there is no vacuum, whether perfect or nonperfect because Space is the number of E and B fields.
So now, in New Physics, let us describe the motion of a photon and a neutrino, where the neutrino is a longitudinal wave of magnetic monopoles. And the photon is a double transverse wave of this:
E+ M+ M- E-
I suppose I could depict the neutrino longitudinal wave as this:
...M+ M- ... M+ M- ... M+ M- >>>
When a photon is created, the E- and E+ cancel in destructive interference leaving the photon particle in the direction of motion along the axis of the double transverse wave, and the same for the M+ and M- component.
When a neutrino is created, the energy is absorbed by a nearby magnetic monopole, either a M+ or M- and which of these two is chosen determines if it is a neutrino or antineutrino. And the energy compresses the M into the next M starting a longitudinal wave of that energy. Now the initial energy may form a brand new magnetic monopole that did not exist before.
Google's archives are top-heavy in hate-spew from search-engine- bombing. Only Drexel's Math Forum has done a excellent, simple and fair archiving of AP posts for the past 15 years as seen here: