Space-time and effect of Mass on a slice of it.

Relation between continuous and discontinuous space-time

One of the most complex "labyrinths" of human thought is the relationship

between continuous and discontinuous space-time. Since the days of Pythagoras

he had raised the issue of what was the space, which intuitively is continuous, but

we know that we can divide it indefinitely as the result of the division is always a

size that, as such, is further divided . The search for the fundamental building

block to fill the space so as not to leave gaps had continued for centuries, until

Leibniz introduced the concept of "monads", a particle so small that it was not

made up of parts and was filling the space, leaving no gaps. In my book: the

Talmud of Scicli ( which can be read in Google ) I refined the concept (I wonder if

I'm right) with the concept of "Logon", a particle not only of zero size, but also of

zero mass, whose only property is existence and which has only potential energy,

when it is immobile, but manages to create kinetic energy, then mass, when it

moves.

A Logon thus is the mass at rest, the size at rest and time at rest of the Photon.

The logons, being size zero could fill all the space without leaving any gaps

forming a continuum. All this is of course in conflict with the theory of quantum

mechanics, for which energy is manifested only as "quanta" of energy,

discontinuous and separated by the distance "h". A second dilemma is how to

balance gravity / inertia, which is a property of continuous space made of logons,

with quantum theory ( which is made of discontinuous particles ) that works

greatly to explain physical reality. No one so far has managed to put together the

theory of relativity, which is based on a continuous space-time, with quantum

theory which is based on a quantized space-time (therefore discontinuous).

I tried with the tetrahedron of Reuleaux, which consists of four spheres of

probability surrounding four quantized logons wedged into one another in such a

way that the center of each sphere is shared by the other three. I assumed the

distance between the quantized logons to be "h", Planck's constant. As each

logon can be found simultaneously in each point of its sphere of probability, the

tetrahedron theoretically becomes a solid filling completely space-time and

leaving no gaps. My quantized space-time is full of Reuleaux tetrahedra filling

completely all available quantized space-time and all together they create inertia,

gravity and nuclear forces. How ? I admit that I don’t know… because this is one

of the hidden variable mysteries foreseen by David Bohm and Albert Einstein.

Geometry of the Reuleaux tetrahedron

The picture above represents four interconnected spheres ( light blue ) of

probability surrounding four quantized logons wedged into one another in such a

way that the center of each sphere is shared by the other three. At the center of the

three spheres is a tetrahedron ( dark blue ) that contains a space-time common to

all the four spheres. This central tetrahedron that I propose to call “Aleph”, has

some interesting properties:

1- Each point of its volume is common to the four quantized logons.

2- The distance between its vertices is assumed to be equal to “h” the constant

of Planck.

3- Its total probability should be shared 1/4 among the four quantized logons.

4- Because the logons ( the atoms of space-time ) are dimensionless, this central

tetrahedron or Aleph, in spite of being limited in size, contains infinite atoms

of space-time and therefore its total probability is 1.

5- Any possible event that has a non zero probability to be verified within the

Aleph, will be verified in it, like if its space-time were continuous.

6- The sum of infinite Alephs fills all the available infinite space-time.

Here is the description of the Aleph of Borges:

"The diameter of the Aleph, will have been two or three centimeters, but it contained all

the cosmic space, without its vastness suffering from it. Everything ... was infinite,

because I could see it clearly from all points of the Universe. "

Jorge Luis Borges

Properties of the Aleph

1- The Aleph behaves like a spherical wave of probability because the probability

of finding the four quantized logons within its volume is always 1. It follows

that the space-time within the Aleph is a “continuum”.

In fact in Quantum Mechanics the uncertainty of the spatial position of a photon

that by definition is a quantized logon, which can be represented by a sphere of

probability, disappears when the wave collapses. The mechanism responsible for

this phenomenon is called the collapse of the wave function and can be understood

by studying what happens to a soap bubble.

. A

If the sphere of this design represents a

soap bubble, when the bubble comes into

collision with an object, (for example the

dot A, top right), the bubble bursts and the

radius r becomes zero almost instantly.

The bubble collapses at the point where

the collision takes place and disappears.

Imagine that the bubble illustrated above is

the wave of the probability of a photon

that expands in the space-time at the speed of light.

Here's what says about this phenomenon Anton Zeilinger, famous quantum

physicist, in his book The veil of Einstein: "... in the case of quantum physics we

speak of probability waves. If a photon is emitted from a very small point source, it

corresponds to a spherical probability wave, the intensity of which in a certain

position indicates the probability of finding the particle in that point. With the

increase of the distance from the source, this sphere becomes larger and larger, and

thus its intensity decreases in each point. The probability calculated over the whole

sphere must be equal to 1, because the particle must be somewhere in the sphere

itself: it can’t disappear. What happens when we detect the particle at a given point,

that is, when the detector is triggered by the presence of the photon? If the particle

is detected in a certain point (for example in point A in the drawing, this comment is

mine) it can’t certainly be in another point. So, by the time the detector is triggered

the probability must immediately become zero in the rest of the sphere. "

Now, since this collapse happens at the speed of light, when time stops, the radious

of the sphere disappers instantaneously ( at infinite speed ). This phenomenon is

called non-locality, or by Einstein: spooky action at a distance.

2- The four quantized logons within the Aleph are entangled together, because

when one of them is detected, all the other three are detected and the total

probability of the Aleph is 1.

The sphere of Rieman explains this phenomenon.

Let's analyze the sphere of Rieman.

You can see the sphere of Rieman from different perspectives complementary to

each other. At the algebraic level we consider the point at infinity as a result of

the equation:

In other words it is possible, using the sphere of Rieman, to accumulate infinite

dimensionless geometric points of probability (points of zero dimension) only in

one point, because the sum of infinite zeros is equal to 1.

Studying the geometric design shown above we see that it is possible to project

all the infinite dimensionless points of a probability space enclosed by the Aleph

into a single point, the apex of the cone, where the four logons are entangled.

Exagonal symmetry of logons in space-time

I suppose that the Reuleaux Tetrahedron is the fundamental structure of a

quantized space-time ( i.e. a kinetic space-time ) and I suppose that the logons are

bosons ( like the photons ) and that they can gather in infinite number filling

completely all the available space-time. During Big Bang a small portion of the

compact Substance made of infinite logons that filled all the infinite space was

included in the first few Alephs of the original singularity and transformed first into

energetic photons and finally into a discrete quantized grid of fermions ( quarks )

separated by the distance “h”. (The transformation energetic photon/quark +

antiquark is possible in physics.)

During the first instants of the creation the distance between the quantized logons

(quantized logons = energetic photons = quarks) was probably the same in every

direction of space, therefore a tetrahedral arrangement is supposed, like in the

packing of oranges, cannon balls or marbles. As shown by experiments with

marbles, when randomly packed on a flat surface, they will preferentially form

sheets of equilateral triangles, with an hexagonal symmetry like that shown above.

If we cut a slice of space-time at the base of the Alephs resting on a flat surface, like

the plane of the present of the event Big Bang , the pattern above is what we

probably see. Here it’s evident the fact that the vertices of each equilateral triangle

forming the base of each tetrahedron are shared by six converging triangles (to form

an hexagon) and shared 1/6 with each neighboring triangle. If we place quantized

logons at the center of each six converging triangles, the logons will occupy the

centers of regular hexagons and the distance between the logons will be the same in

every direction (for example the constant of Planck “h“).

An interesting observation that probably reflects some hidden Law of Nature is this:

“ If each triangle formed by three logons contains a total amount of energy = 1 this

energy will be shared 1/3, 1/3, 1/3 by each logon.”

Note: As long as the quantized logons become only photons ( i.e. bosons ) what

we assumed above is probably valid, because one can pack as many bosons

together into an Aleph without any problem. The problem starts when the excited

photons become quarks, because now the Principle of exclusion of Pauli will have

to be taken into account, but let’s suppose that the laws of Nature will take care of

Pauli, for the time being, and let’s contitue to study the geometry of the Aleph.

If we go from the world of marbles to that of “quantized logons”, which kind of packing would the quantized logons of a given portion of space-time prefer?

If the quantized logons placed on a flat surface (like the plane of

the present of the Big Bang) are identical and are bound

together mainly by inertial/gravity forces, which are completely

non-directional, they will favor a structure in which as many

quantized logons can be in direct contact as possible. This will, of course, be the

hexagonal arrangement of equilateral triangles, as shown in this picture.(Hereafter

for brevity the word logons will be used to mean naturally quantized logons.) If a

second sheet is added on top of the first, regular Tetrahedra will be formed by the

juxtapositions of the two sheets, because this is the packing that most naturally fills

the space available. If the logons are tightly packed in a three-dimensional space, they

will be arranged as regular tetrahedra.

The pyramid shown above gives an idea of “cannon balls” packing of marbles of

equal size. The top of the pyramid shows very clearly a regular tetrahedron formed

by four marbles and the alternating layers of blue and pink marbles show the

different layers of this structure. It may be only a coincidence but there is a strange

relation between the structure of a tetrahedron and that of the neutron.

The neutron consists of two down quarks with charge −⅓ e and one up quark with

charge +⅔ e, and if we suppose that the up quark consists of the sum two

hypothetical +1/3 e quarks ( linked together ) we will have four 1/3e quarks of

different charges occupying the vertices of a tetrahedron, and distributed in a

possible arrangement of couples + 1/3 and – 1/3 that would satisfy the

requirements of the exclusion principle of Pauli. We don’t know how exactly but

let’s suppose that Nature takes care of this trick as well.

It follows that from one tetrahedron of logons it is geometrically possible to form a

neutron, with a quark charged +2/3e ( the sum of two + 1/3e hypothetical quarks )

and two quarks charged -1/3e.

Close-packed lattices in three dimensions

I want to demonstrate now that not only a neutron, but also a proton has a

structure that is compatible with the symmetry of the Aleph. Two tetrahedra are

needed to form a proton, but the two tetrahedra should be close packed on top of

each other in a special way, compatible with an ABA hexagonal symmetry.

Close-packed lattices allow the maximum amount of interaction between logons. If

these interactions are mainly attractive, then close-packing usually leads to more

energetically stable structures. These lattice geometries are widely seen in metallic,

atomic, and simple ionic crystals.

As we pointed out above, hexagonal packing of a single layer is more efficient than square-packing, so this is where we begin. Imagine that we start with the single layer of green logons shown below. We will call this the A layer. If we place a second layer of logons (orange) on top of the A-layer, we would expect the logons of the new layer to nestle in the hollows in the first layer. But if all the logons are identical, only some of these void spaces will be accessible.

In the diagram on the left, notice that there are two classes of void spaces between the A logons; one set (colored blue) has a vertex pointing up, while the other set (not colored) has down-pointing vertices. Each void space constitutes a depression in which logons of a second layer (the B-layer) can nest. The two sets of void spaces are completely equivalent, but only one of these sets can be occupied by a second layer of logons whose size is similar to those in the bottom layer. In the illustration on the right above we have arbitrarily placed the B-layer atoms in the blue voids, but could just as well have selected the white ones. An interesting question would be: what fills the void spaces ? If it is a vacuum, it could generate the tremendous force to glue the logons together, as the force of inertia of the infinite space-time would not be balanced.

Two choices for the third layer lead to two different close-packed lattice types

Now consider what happens when we lay down a third layer of logons. These will fit

into the void spaces within the B-layer. As before, there are two sets of these

positions, but unlike the case described above, they are not equivalent.

The logons in the third layer are represented by open blue circles in order to avoid

obscuring the layers underneath. In the illustration on the left, this third layer is

placed on the B-layer at locations that are directly above the logons of the A-layer,

so our third layer is just another A layer. If we add still more layers, the vertical

sequence A-B-A-B-A-B-A... repeats indefinitely.

In the diagram on the right above, the blue logons have been placed above the

white (unoccupied) void spaces in layer A. Because this third layer is displaced

horizontally (in our view) from layer A, we will call it layer C. As we add more

layers of atoms, the sequence of layers is A-B-C-A-B-C-A-B-C..., so we call it ABC

packing.

These two diagrams that show exploded views of the vertical

stacking further illustrate the rather small fundamental

difference between these two arrangements— but, as you will

see below, they have widely divergent structural

consequences. Note the opposite orientations of the A and C

layers

Only the Hexagonal closed-packed structure preserves the same “h” distance between the logons in every direction.

The HCP stacking shown on the

right takes us out of the cubic

crystal system into the

hexagonal system, so we will

not say much more about it

here except to point out that

each logon has 12 nearest

neighbors: six in its own layer,

and three in each layer above

and below it.

We will not consider the ABC

face-centered cubic structure

because it does not preserve

the distance “h” in every

direction of space-time.

Construction of a Proton

If we direct our attention to the diagram below showing a regular

tetrahedron where four logons occupy its vertexes we will clearly see

that if two logons are linked together in the NW – SE diagonal and are

charged positive, the other two, charged negative are located on the axis

linking the top of the tetrahedron with the NE corner.

If we add a second identical tetrahedron of top of it, respecting the

hexagonal close packing symmetry ABAB, we will have the following:

2 ( + 2/3e ) up quarks with positive charges, and one down quark with negative

charge ( -1/3e ), to form a proton of positive electric charge +1e. In addition there

will be 3 (-1/3e ) charges forming one electron of -1e charge that will neutralize the

positive charge of the proton. Again let’s hope that Mother Nature will take care of

the requirements of Herr Professor Pauli, for example combining on the other two

diagonals (-1/3e ) and (+1/3e ) quarks to satisfy the Principle of exclusion.

The above describes exactly the atom of Hydrogen, the most abundant atom in the

Universe and certainly the first to be created after God created light and the photons.

Conclusion

The logons are imaginary particles, described in the Talmud of Scicli as atoms of

space-time filling up all the space-time available, which is infinite. They are

supposed to form the substance of God from which everything was created with a Big

Bang. The quantized logons created after the Big Bang form an hexagonal closed

packed structure consisting of Alephs of Reuleaux tetrahedra filling up all space-

time available in the kinetic Universe. The distance between all the quantized logons

is equal to the Planck constant “h”, but their hexagonal close packing symmetry

ABAB leaves some small voids in the centers of their structure. These voids,

presumably filled with some sort of unknown vacuum, maybe cause the force that

glues the quantized logons together ? From these Alephs it is assumed that neutrons,

protons and electrons were formed. I don’t know all the details of this creation, in

particular I ignore the causes of the electrical charges of quarks and electrons, I can

only speculate that they are due to the rotation of the logons that create electro-

magnetic forces. Special vacuum forces of unknown nature may keep the quarks

glued together within the neutrons and the protons, and I have to admit that this

theory has a lot of hidden variables to be answered in the future.

In spite of all the unknowns, I have to admit that at least the geometry seems to be

right and appears compatible with the assumptions made. To conclude it takes two

Alephs to make a proton ( two up quarks and one down) (2⁄3 + 2⁄3 -1⁄3 = +1 charge)

and one electron ( three down quarks ), 3 (-1⁄3 e ) charge that together with the

proton will form an atom of Hydrogen. Only one Aleph is needed (two down quarks

and one up) to make a neutron (2⁄3 - 1⁄3 - 1⁄3 = 0 charge).

But this conclusion, shocking as it is, does not describe the full implication of the

initial conjecture. Because a logon was described as a “photon asleep” with this

equation:

logon = inert photon ( or logon = rest mass and rest dimensions of the photon )

it follows that an activated and quantized logon must become an energetic photon

and a quark. So the conclusions are that:

active logon = energetic photon = quark

and if this assumption is correct, all the substance of the Universe is made from very

energetic photons that were transformed into quarks !! This is precisely what the

Bible tells us: then God said, “Let light be “, and there was light (Gen. 1, 3 )

Any theory must make predictions. If what is said above proves to be valid, it will be

one day discovered that the electron is made by three down quarks of -1/3e charge

each tightly glued together by some kind of vacuum forces.