Matter is rigid and discrete, as defined by its extents. The word “rigid” is used in the sense opposite to “flexible” meaning “firmly fixed or set”. And the word “discrete” is used in the sense opposite to “continuous” meaning “apart or detached from others; separate; distinct”. The dimensions of matter are depicted as rigid and discrete by Euclidian geometry. We can talk about the dimensions of matter in terms of units that are fixed and discrete, but we cannot do so for space that is empty of matter.
Space that is empty of matter, is not empty of energy. Energy flows like a fluid, and it can thicken up from a dilute state like a fluid; the only difference being that energy is not made up particles like atoms. The quanta of energy do not refer to a particle but to thickness (viscosity) of energy. As energy thickens up it increasingly becomes rigid and discrete like matter. Thus, there is a gradient of rigidity and discreteness. Space is defined by what it is filled with. “Empty” space is defined not by the rigidity and discreteness of matter (as we do currently), but by the flexibility and continuity of energy.
A location is considered fixed in space and discrete by Euclidian geometry; but this is true only for space filled by matter. When space is empty of matter, we cannot fix or pinpoint a location in it. A location in space is not discrete but continuous with the space around it. Mathematics considers a discrete point to be a primitive notion. This now comes under question. Rather continuous space should be a primitive notion.
A certain quantum of energy may be defined more correctly as a certain “viscosity” of energy. This “viscosity” of energy increases with frequency until it collapses into mass at the center of the atom (as its nucleus). We, may, therefore, say that, from the viewpoint of mathematics, a location in space shifts from continuity to discreteness on a gradient. This provides a new dimension to Calculus.
The new calculus will approach discreteness from continuity the way condensing energy would approach matter. The infinitesimals of this calculus are, therefore, shrinkable from the flexibility of continuity to the rigidity of discreteness. Currently, the infinitesimals of Calculus are assumed to be rigid like matter, regardless of how small they get. But as matter divides it does not stop at atom; it starts to become more “viscous” in the form of electrons, quantum particles and the electromagnetic field beyond.
We cannot use the rigid infinitesimals of Calculus for the electromagnetic fields, that is why we have a different mathematics for Quantum mechanics. If we can add the dimension of “viscosity” (or frequency) to the infinitesimals, we may extend the use of Calculus to Quantum Mechanics. Physics is struggling to get rid of conditioning due to matter. It cannot get rid of that conditioning unless mathematics gets rid of it first. We need mathematics that approaches discreteness from the direction of continuity.
We cannot use the dimensionless Euclidean point as primitive notion because it is not seen as expanding into a continuous space. But we can use continuous space as primitive notion because we can see it as shrinking to generate a dense point that approaches discreteness. It is this “viscosity” of infinitesimals that can be associated increasingly with discreteness.
As the “viscosity” of energy increases, rotational fields start to form within the electromagnetic fields. The first stable form of such rotational field is the electron. As these rotational fields grow, their center starts to collapse to form a hard nucleus due to high “viscosity”. The next stable form of this rotational field appears to be the hydrogen atom.
As we can see, the space contracts as energy condenses with increasing frequency (viscosity). The theory of special relativity talks about contraction of space at speeds approaching the speed of light. This conclusion is subjective because Einstein’s observer is not using the context of the whole universe as its reference.
Objectivity exists to the degree observer uses the whole universe as its reference. This means using all physical and mental senses. The moment one uses part of the universe as its reference one’s viewpoint descends into subjectivity. Thus, mathematics employed by Einstein’s theory of Special Relativity is subjective.
Objectivity is the consistency among inputs from all physical and mental senses. To the degree this consistency is missing, observation is incomplete and subjective.
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