## F.INDEXING

Each and every spason must have an "identification" that is different, unique, distinct, from all other spasons, and it is these identification units, or indices that actually determines the "structure" of space time at each and every instant in time.  By the Pauli Exclusion concept, which also apparently applies to this more fundamental level, two spasons to be different must have at least one difference between them.  Any two spason having the same exact characteristics are not different but are the same spason. There must be some distinguishing characteristic between different spasons, spasons being different "quanta" of space-time.

These things that make up spasons and identify them may have neither the properties of mass nor energy, and also may not have any characteristic of space or time. They lie in the domain far below that of mass/ energy and also below the domain where space and time cease to be relevant at roughly 1 x 10-21 cm and 4 x 10-32 seconds.

The spasons are the smallest units of space-time that can have relevance. The new concepts which make up spasons and identify them will be called indices. They are pure numbers.  The name index is the name given to the full numerical identification of each spason. Indices have neither mass like nor space-time like properties, and they, as hinted by the name, are only pure numbers without any dimensional property in the normal sense.

If the universe is, as proposed, some 15.387 billion light years radius or 1.4557 x 1028 cm (x 1026 meters) and if the distance for one spason is 1.2737 x 10-21 cm (x 10-23 meters), then there must be 1.1429 x 1049 spasons possible in the radius of the universe.  To have that number of spasons requires roughly 2164 binary numbers in the radius. This implies that each index must be log 2.2857 x 1049 divided by log 2 = 163.9671 binary digits. From a pragmatic point of view all binary numbers must be integer, thus it must be 164 binary bits or more in each radial axis.

If the number were exactly 2164 then that would accommodate a diameter of 2.3383825 x 1049 spasons and a radius of 1.1691912 x 1049 spasons. This also corresponds to a radius = 1.4892306 x 1028 cm or time = 4.9675387 x 10 17 sec or 15.74 billion years (H=2.05941 x 10-18 per sec). This is a deviation of 2.3% from observed values which may or may not be real. The actual case probably is that our universe has not expanded yet to the full 2164 index. This radius is just enough to specify one dimension, let us call that x for convenience. Our space time requires position in three spacial dimensions. To specify that three orthogonal index systems, one for x one for y and one for z, must be present in each spason.

STATEMENT of ASSUMPTION: It is assumed that the index system is generally binary in form. I cannot prove this, but binary being the simplest form of distinction (+ or -,  yes or no, exists or does not exist) this seems to be a reasonable assumption. The binary form assumed here will be slightly different from the binary system we use in computers. This arises from the assumptions that now seem to match reality.

1) Neighboring NATURAL binary points must be no more than 1 index bit different from their neighboring points. To say this another way, {by comparison with our Boolean binary system where we shift from 1101 to 1010 with two binary bits of change, or even more where 1011 goes to 1100 with three bits changing}, in the "natural" system it would appear probable that one and only one bit changes from neighboring index to index.

2) There is no "Zero" or privileged index. All indices have absolutely equal equity. Zero is nothing, and nothing does not exist, it is non-existence. There can be no index of value zero.

3) From any one index, the others in both "directions" must be symmetric. An added 1 to the front of a sequence must be the equivalent of shifting from + to - or going from -1 to +1 in the old "Roman" number system without any zero.

4) This index also must "loop around, i.e. with only 5 bits 10000 must be "next to" or opposed to 00001; (i.e. 00000, "nothing does not exist"). This implies that the extreme ends of the radius going left meet or at least are next to the extreme end of the radius going right, and that the universe is not an open system at all, but a closed system. The radius would be the same measured from any point in the whole universe. This strange result is very like a line drawn on the surface of a balloon (sphere). It eventually gets as far as it can from the initial point, and all other points in any direction are closer than that furthest point. In our case we are trapped inside our universe and unless we move outside of it (which is not technologically possible at the present time) we cannot transverse the whole universe and "come back to the starting point" by going all the way around, returning from left by starting our right. The time vector prevents us from doing that in any case.

Partially repeating 2 there is no "unique" or special reference point. There is no "zero" or special reference point from which we can measure all other distances. Even more to the point zero is nothing, and in our universe things exist; so nothing can not exist, it IS nonexistence.

Starting at the beginning of the universe, well before energy has meaning, but as space time is coming into existence, (The universe was without form and void and darkness moved upon the face of the deep) one spason had to come into being; It is the first spason. It being unique might well be represented with the sole index 1.  The 1 signifies that it exists. In the first case only one point exists. A position (bit) that might exist but does not, will be represented as a 0.  Thus the index 0, or 00 or 000 is prohibited since they do not exist.

Next a second related spason comes into existence next to that with index in our Boolean binary system of 10 would come into existence while the index of the first also had to change to 01. Note the symmetry, and the required change so that the "first" now cannot be told from the second one since there must be no way to tell the priority or 1's from 0's and 01 and 10 are mirror images. We require that they be different. But those also required TWO changes. This requires in the “natural” system that 11 be next not 01 so a difference can exist at each and every unit of time in space-time. In the natural system the first point is 1 with all other positions not even being in existence. By our assumptions the second point is 11, and the third is 10. If we allowed 10 second that changed two binary bits, not just one.  With three indices it would now add 01 which now would be different, i.e. symmetric: i.e.  01, 11, 10.  Thus it is necessary to propose a rather different “natural” binary system for indexing spasons.  The information in our universe appears to be conveyed by these pure binary numbers.

The natural system is shown below, compared to the Boolean and decimal systems:

binary natural binary  decimal   change      sum

prior

00001             00001                         1                      +1                    +1

00010             00011                         2                      +1                    +2

00011             00010                         3                      -1                     +1

00100             00110                         4                      +1                    +2

00101             00111                         5                      +1                    +3

00110             00101                         6                      -1                     +2

00111             00100                         7                      -1                     +1

01000             01100                         8                      +1                    +2

01001             01101                         9                      +1                    +3

01010             01111                         10                    +1                    +4

01011             01110                         11                    -1                     +3

01100             01010                         12                    -1                     +2

01101             01011                         13                    +1                    +3

01110             01001                         14                    -1                     +2

01111             01000                         15                    -1                     +1

10000             11000                         16                    +1                    +2

10001             11001                         17                    +1                    +3

10010             11011                         18                    +1                    +4

10011             11010                         19                    -1                     +3

10100             11110                         20                    +1                    +4

10101             11111                         21                    +1                    +5

10110             11101                         22                    -1                     +4

10111             11100                         23                    -1                     +3

11000             10100                         24                    -1                     +2

11001             10101                         25                    +1                    +3

11010             10111                         26                    +1                    +4

11011             10110                         27                    -1                     +3

11100             10010                         28                    -1                     +2

11101             10011                         29                    +1                    +3

11110             10001                         30                    -1                     +2

11111             10000                         31                    -1                     +1

100000                       110000                                   32                    etc.    returns

etc.                                                                                 to +1

The natural system in the 31 units shown above shifted from 00001 to 10000 via all possible intermediate binary combinations, but with only one bit changing at any one shift. It also is symmetric about each and every index in the whole system, i.e. the added and lost binary bits all cancel out in the long run. Thus they do not "occupy" space-time, nor shift the index in any preferred direction. They are "democratic" or at least there is no preferred position.

### 1.                  The CURL or rotation of the photon from Spason index specification

There is also a "curl" of indexing.  This gives rise to the rotation in photons. If in the motion of a photon, one pole encounters a given spason from a prior photon path which already exists, and if the linear motion of the photon would normally have caused this spason to come into existence next, then it can not “re-specify” that which already exists. Some other spason position must be specified. There are rules which determine which possible spason will next exist instead of that one which can not be re-specified.

A new spason must come into existence, but in some other “direction”. This three dimensional relationship between the three possible indices, can take two and only two forms within the assumptions; - one gives rise to the + pole and the other to the - poles; one "rotates" clockwise relative to the C vector and the other rotates counterclockwise relative to the C vector. These must be paired, i.e. for each pole that rotates + the index demands that another rotate - to "conserve" indices in the normal pattern. This shifts bits between x, y, and z indices. As this shift of bits occurs, the new spason index is offset from the linear “preferred” or “most probable” index which already exists to that of a spason position offset by one unit in an orthogonal direction from the preferred linear index. In one set the x bit goes to y the y bit goes to z and the z goes to x  a (+) rotation OR in the other set the x bit goes to z, the z bit to y and the y bit goes to x; a (-) rotation.

The probability of this happening is on the average one part in 5768=(6p6) in our universe. Thus, on the average in free space, a spason encounters an old previously designated spason position once in every 5768 times and thus the photon rotates with that fraction.

In a location with more mass, then probability goes up, and this causes the refractive index of gases (slightly more mass than vacuum), liquids (generally much more mass than vacuum compared to gasses), and solids such as metals with the density of osmium being the practical density limit for atomic density, the rotation rises, the linear motion decreases and this is precisely the refractive index, with metals having the highest refractive index;

Note this concept also accounts for the optical activity of chiral organic chemical compounds where the Carbon atom having four different functional groups with differing "densities" or polarities rotates light in optical activity. These come in d and l (or R and S) forms and the CIP

(Cahn, Ingold, Prelog) rules really only re-enforce the above hypothesis as they would naturally arise from this indexing scheme. The fact that polar rotation is observed suggests that the hypothesis is on firm basis.

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