The three immanent, inherent, inseparable, equally essential, axiomatic properties of space are:

- the length(s) (distance(s))

- the lengthwise capacitance, a.k.a. electric permittivity 

- the lengthwise inductance, a.k.a. magnetic permeability 

The space is essentially an electromagnetic phenomenon.

This is the new, proper axiomatic definition, the true definition of space. Scientific definition, based on measurable physical facts, and reduced to essential components (essential properties).

 and   are not properties of any material (including the hypothetical aether – as it was demonstrated with the Michelson-Morley experiment, there is no such thing as aether) –   and  are fundamental properties of space, equally fundamental as the length(s), and inseparable from the length(s). They do not require any “internal structure of space“ in order to be „understood“. Do we understand the length property of space? Actually, no. It is something that we take as the existence-fact, as the existence-axiom. Well, that is what the  and   are, too.

We can notice the lengths (distances), and we can measure lengths (distances). They are part of our everyday experience. We are accustomed to them. That is all that we can fundamentally say about the distances. That is the essential, the fundamental apprehension of the length-property of space. That, and the fact that there can exist maximally 3 straight line segments (lengths) which are mutually orthogonal (perpendicular) and which cross each other at the one and the same point, is all we fundamentally „understand“ about the distances in our 3D space.

Concerning   and  , we can only measure them. Not directly, as we can measure a length (distance), but we can measure them. And they are fundamental, essential properties of space.
The material devices known as capacitors and inductors have the capacitance and inductance only and exclusively because the space they occupy has the properties    and  . 
Each and every material object does not have    and   properties. These properties are the properties of the space between and within the atoms of that material. Their values are higher than    and   of empty space because that is the way the space reacts to the presence of matter, that is, to the presence of energy in the form of that what we call matter.

This new, fundamental axiomatic postulation/definition of space is an oversighted option, an option which was missed to be considered, an option which stood between the wrong aether hypothesis and the highly abstract hyper-geometry-based postulations.

Space is the most basic, the essential medium for energy propagation, the essential energy manifestation enabler, container, sustainer.

The elementary energy is the photon – the photon is the elementary EM-energy. Photon is an elementary EM oscillation which propagates linearly through space in time. For some given oscillation frequency, the elementary energy is

I.   ,

 is the Planck’s constant,  is the EM-oscillation frequency

Prefix  in front of  denotes the finite, non-infinitesimal elementary energy for a given frequency , the elementary packet of energy for a given frequency  . “Elementary” means that it cannot be less than it is, and it is

This equation was theoretically derived (precisely, deduced) by Planck, and it represents the fundamental, basic, elementary equation of universe, the axiomatic law of existence. The axiom of existence. The „that’s-the-way-it-fundamentally-is“. It describes the most elementary form of existence (the photon, the elementary energy) and its basic connection/relation with another axiom of existence: the time:

 is the time period during which the photon’s EM-oscillation completes.

It is the time period in which the photon passes the length which is equal to the length of that photon:

Velocity of EM-energy propagation is determinated by the properties of the medium through which EM-energy propagates. The medium for EM-energy propagation is the space, either the so called free space (that is, the space which is not affected by some material), or the space affected by some material (the space around some material, and the space inside the material, that is, the space between the atoms/molecules of some material).

Fundamental EM-properties of the space are   and  , and these properties determinate the velocity of a photon in it:

II.  

This is the most fundamental discovery of James C. Maxwell, broadly known in the form

Any photon which moves through the  ----space has the velocity

In other words, no matter what the energy of a photon is, the velocity will be the velocity which the  ----space allows (imposes, determinates), and that velocity is

There where the space properties   and   have higher values,

i.e.: 1) between the atoms of an optical prism, 2) in the gravitational field,

the velocity of photon-propagation is

In order to be able to impose, to determinate the velocity of a photon’s propagation, the space has to have the means to interact with the photon, with that elementary EM-energy-entity. These means are   and  , the essential EM-properties of space.

That what is inevitable, what is essential in the process of energy-space interaction is: the energy, the space and the time.

“The change of a photon’s spatial location takes time (requires time, axiomatically includes time)”

= “The interaction of a photon with space takes time”

= “The propagation of a photon takes time”.

Length,  , and   are fundamental, axiomatic properties of space, and time is

and that is the true, fundamental, and the only reason for using the term spacetime. That is the true reason to state that time is inherently contained within space. Or, time is essential, axiomatic property of space, that is, of spacetime.

So, spacetime is fundamentaly the EM phenomenon – lengths and time are its aspects which are intrinsically related to   and  .

Namely, all of the axiomatic properties of spacetime:  , , length, time, are all equal (equally fundamental) and interrelated aspects of spacetime.

We could actually say that the elementary energy manifests itself as electromagnetic because the spacetime is essentially electromagnetic phenomenon – while interacting with the  -spacetime-property, the elementary energy produces (manifests as) electric EM-component, and while interacting with the -spacetime-property, it produces (manifests as) magnetic EM-component. 

The more general description would be: when elementary energy interacts with fundamental properties of spacetime   and  , that interaction manifests as a linearly propagating EM-oscillation, that is, as a photon.

The general mathematical model for interaction is the convolution. The most basic, elementary convolution is the simple product, the simple multiplication of elementary values which interact. 
Hence, the process of elementary appearance which we call photon, is the elementary interaction (convolution) of elementary EM-energy with elementary EM properties of spacetime, the interaction which consists of elementary interconvoluted  elementary EM-energy and   and   :

III.   

 is the measure of EM-coupling, the (total) amount of EM-coupling of elementary EM-energy of a photon and elementary EM-properties of spacetime. 
The appropriate name for this equation would be the embodying equation.  is the essential-physical-manifestation property, the embodyment, which arises from (is the result of) interaction of elementary EM energy and elementary EM properties of spacetime. The embodying equation is the fundamental, basic, elementary equation of universe.

This is the proper, the primary (primordial) definition and derivation for that what is generally known as the mass. Essentially, the mass is an electromagnetic phenomenon. And, in the case of a photon, it is the non-inertial mass, or, the proto-inertial mass. 

This was also the proper, the fundamental derivation of Einstein’s most famous equation.

The fact that the equation

is the fundamental equation, whose validity starts from and including the photon, is experimentally almost explicitly supported by each and every experiment conducted so far and in which this equation was used for explanation of these experiments (i.e. nuclear reactions, „annihilation“, Compton’s experiment, gravitational red-shift of a photon, etc.).

And, the fundamental origin of this equation presented here is strong and sound in every scientific aspect: logical, and physical, and hierarchical (the mass-energy relation is established in the most fundamental way it is possible to be established). 
As already stated in The gem (1), the first proper derivation of this equation – electromagnetic derivation – was done by Poincare, and here that equations is derived in the most essential way possible. 

This equation has nothing to do with relativity theories.
Let us imagine the following scenario: we are in a small spaceship, far away in space, i.e. at the outskirts of our Solar system (that is, there where there are almost no general-relativity-effects (“space curving”)). 
Our spaceship has the lab equipped to accurately measure the mass of electron, of positron, as well as the energies of  -photons. 
We have measured the masses of electron and positron. 
And then, we setup the collision of one slow electron and one slow positron (hence, there are no special-relativity-effects), and we measure the energies of two  -photons, which are the result of that collision. 
If we then divide the sum of energies of two  -photons with the sum of masses of electron and positron, we will get that their ratio is

Hence, this result is neither the consequence of special relativity, nor of general relativity

– the equation III.,  , is the fundamental, elementary, quantum-level equation. The same as are the equations I. and II.

So, we have covered all fundamental properties of existence, all axioms of existence:

• the fundamental properties of space
  (length(s),   and  ) (in the most basic sense, the lengths are electromagnetic: each length (in each direction in vacuum), has the hidden flavors, background flavors, fundamental flavors, essential flavors, electromagnetic flavors: the lengthwise capacitance , and the lengthwise inductance )
• the time,
• the fundamental energy,

including the three elementary equations, axiomatic equations, the essential relations among the axioms of existence:

I.   , or  

II.  

III.  

The existence is essentially electromagnetic, and continual.

The infinitesimal calculus is the essential tool, the best tool, intellectually achieved tool, the result of sapience, of rational thinking about the physical phenomena, the tool which best describes/models the reality. 
The reality, in its essence, is the electromagnetic energy-space-time-continuum. 
That is why the infinitesimal calculus describes it so perfectly. That is why the infinitesimal calculus was the result of reasonable thinking about the reality.

So, this was the proper axiomatic postulation of reality. The complete set of the primary axioms of existence. Based exclusively on known, detected, confirmed facts.

To be continued in the next posts, with the proper, simple, clear derivations, explanations, …, proper  demystification and proper unification of physics.