Authors: Joseph P. Farrell, Scott D. de Hart

continued by Dr. Volodymyr Krasnoholovets of the Institute of Physics of the Ukrainian National Academy of Sciences in Kiev. Notably, Krasnoholovets has been led by his research to posit a “sub-quantum mechanics” with some peculiar properties that recall our own speculations about the tetrahedral properties of the medium

Noting that the electromagnetic, the weak, and the strong forces of current quantum mechanics intersect at a scale of 10- 28 cm, Krasnoholovets then takes this measure as the size of the building blocks of space itself. Space thus has a cellular structure... where particles appear as deformations of this structure. 24

These elementary perturbations of space itself, these “fundamental particles”, Krasnoholovets very suggestively calls “inertons.” Without going into the complicated argument of his paper, it is worth noting that Krasnoholovets makes mention of the “ ex nihilo” characteristics:

“Of special is the approach proposed by Bounias (1990, 2000) and Bounias and Bonaly (1994, 1996, 1997). Basing on topology and set theory, they have demonstrated that the necessity of the existence of the empty set leads to topological spaces resulting in a “physical universe.” Namely, they have investigated the links between physical existence, observability, and information. The introduction of the empty hyperset has allowed a preliminary construction of a formal structure that correlates with the degenerate cell of space supporting conditions for the existence of a universe. Besides, among other results we can point to their very promising hypothesis on a non-metric topologcial distance as the symmetric difference between sets: this could be a good alternative to the conventional metric distance which so far is still treated as themajor characteristic in all concepts employed in gravitational physics, cosmology, and partly in quantum mechanics.” 25

I then observed the following:

Behind the obtuse technical language lies a series of very unique insights:

1. The current mathematical “languages” used to describe the interactions of sub-atomic particles with space is inadequate;

2. It is inadequate because it is based on a form of mathematical language where measurements of distance , or more simply, vectors are the primary thing in view;

3. A more adequate way to account for the peculiarities of quantum and sub-quantum mechanics is via set theory, that is, a mathematical language that compares the properties of systems or sets wherein properties of distance and vectors are only sub- sets of a greater set of properties. Simply put, Krasnoholovets is saying that the fundamental language of physics must change from a linear mathematical language — points, lines, planes, vectors and so on — to a non- linear language inclusive of such things but not limited to them. Hence his emphasis on information . Sets of physical properties, on this view, are a much fuller description of the “information in the field.”

Note now that Krasnoholovets is thinking in the same terms as our previously discussed topological metaphor, which also employed differentiations on the empty hyper-setto model the emergence of observable entities from a primordial Nothing.

Thus...Krasnoholovets introduces the idea that the fundamental relationship between a particle and space itself is harmonic in nature, since a particle, by moving, exhibits inertia and sets up an oscillation in space itself. Or as he puts it, “It is the space substrate, which induces the harmonic potential responding to the disturbance of the space by the moving particle” 26 itself that is in primary view.

Again, we must pause to note how well our topological metaphor corresponds to this idea of harmonic relationships between the various cells in space-time, for it will be recalled that by differentiating that primordial nothingwe ended with two regions distinguished by a common surface:,, and. Note that each expression

Noting that the electromagnetic, the weak, and the strong forces of current quantum mechanics intersect at a scale of 10- 28 cm, Krasnoholovets then takes this measure as the size of the building blocks of space itself. Space thus has a cellular structure... where particles appear as deformations of this structure. 24

These elementary perturbations of space itself, these “fundamental particles”, Krasnoholovets very suggestively calls “inertons.” Without going into the complicated argument of his paper, it is worth noting that Krasnoholovets makes mention of the “ ex nihilo” characteristics:

“Of special is the approach proposed by Bounias (1990, 2000) and Bounias and Bonaly (1994, 1996, 1997). Basing on topology and set theory, they have demonstrated that the necessity of the existence of the empty set leads to topological spaces resulting in a “physical universe.” Namely, they have investigated the links between physical existence, observability, and information. The introduction of the empty hyperset has allowed a preliminary construction of a formal structure that correlates with the degenerate cell of space supporting conditions for the existence of a universe. Besides, among other results we can point to their very promising hypothesis on a non-metric topologcial distance as the symmetric difference between sets: this could be a good alternative to the conventional metric distance which so far is still treated as themajor characteristic in all concepts employed in gravitational physics, cosmology, and partly in quantum mechanics.” 25

I then observed the following:

Behind the obtuse technical language lies a series of very unique insights:

1. The current mathematical “languages” used to describe the interactions of sub-atomic particles with space is inadequate;

2. It is inadequate because it is based on a form of mathematical language where measurements of distance , or more simply, vectors are the primary thing in view;

3. A more adequate way to account for the peculiarities of quantum and sub-quantum mechanics is via set theory, that is, a mathematical language that compares the properties of systems or sets wherein properties of distance and vectors are only sub- sets of a greater set of properties. Simply put, Krasnoholovets is saying that the fundamental language of physics must change from a linear mathematical language — points, lines, planes, vectors and so on — to a non- linear language inclusive of such things but not limited to them. Hence his emphasis on information . Sets of physical properties, on this view, are a much fuller description of the “information in the field.”

Note now that Krasnoholovets is thinking in the same terms as our previously discussed topological metaphor, which also employed differentiations on the empty hyper-setto model the emergence of observable entities from a primordial Nothing.

Thus...Krasnoholovets introduces the idea that the fundamental relationship between a particle and space itself is harmonic in nature, since a particle, by moving, exhibits inertia and sets up an oscillation in space itself. Or as he puts it, “It is the space substrate, which induces the harmonic potential responding to the disturbance of the space by the moving particle” 26 itself that is in primary view.

Again, we must pause to note how well our topological metaphor corresponds to this idea of harmonic relationships between the various cells in space-time, for it will be recalled that by differentiating that primordial nothingwe ended with two regions distinguished by a common surface:,, and. Note that each expression

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