# THE QUANTIZATION OF SPACE-TIME

By James H.L. Lawler

March 1998

## A.  INTRODUCTION AND ABSTRACT

There are seven key concepts involved in this work and over forty sub-concepts.  All of these concepts lead to a finer and more detailed description of our universe.  They link together factors which until now were considered separate, forming a unified picture of our space-time.

1.   The first concept, IRRELEVANCE,  is a part of the scientific method and is a new concept whose time has now become relevant. The concept of IRRELEVANCE is:  " Every variable or concept has a domain over which it is valid.   Outside of that domain the variable or concept is irrelevant and we must seek other variables or concepts with which to describe events or phenomena."   We should always seek to describe the domain over which our variables or concepts are valid,  and find the boundary of the domain so that we may know where to use those concepts or where they are not valid and when to seek other descriptors.

2.   The second key concept is a model of a photon.  It is proposed as an induction that a photon consists of two opposite charged "poles," one + and the other -, which rotate about one another such that the distance, d, between them is inversely proportional to the energy, E, of the photon, E= L/d where L = 3.443780 x 10-29 Joule meters (or 10-21 erg cm) (eq 1)  This then implies the poles have a charge of  6.19004 x 10 -20 coulombs or roughly 1/3 that of the electron.

3.  The photon model leads to the third key concept. It is proposed that “All mass,  all matter,  is made of photons and only photons”. Electrons, protons etc. are combinations of photons. The electron is made of three photons. The three + poles are in a core while the three - poles make up the charged – field, with the core repeat motion being the interpole distance, d. The proton is made up of five photons. The core has 4 – poles and one + pole. Thus effectively in the charged field there are 3 + poles (4 + and 1 -) that are free in orbit to give the same sort of + charged field in the proton equal in magnitude to the - charge field of the electron. Thus two pairs of + poles interactions are equivalent mathematically to the +2/3 charged "quarks"- the phenomena is  just being looked at differently. The repeating element in the proton is the photon wavelength. Mathematical models allow calculation of mass ratios, the charges and magnetic moments of several particles with considerable precision. The most precise of these predicts that the mass ratio of proton to electron should be:

Mp / me  = 6p5 = 1836.1181 ... eq 16 versus:  1836.152701(37) ±0.020 ppm observed.

* (For more precision  Mp / me = 6p5 (1+{6p/106}) = 1836.152719

versus 1836.152701(37)±0.020 ppm accounting for the actual spason "sizes" of {6p/106} in the cores of the two particles.

This concept that all mass is photonic was originally done as an induction but it also may be derived deductively from strict symbolic logic applied to prior well accepted concepts.  Max Planck in 1902 proposed that "All energy is quantized"  E= hf, or E = hC/l, (eq 2) with the quantum of energy later being named the photon. Albert  Einstein in 1905 stated that mass and energy were inter-convertible: mC2 = E, (eq 6), so that we may deduce that  all  MASS  is quantized,   m = hf/C2 = h/lC  and the quantum of MASS is the photon.  Quantum means the smallest indivisible unit and implies that the concept of energy or mass should not be used below the level of photon since it is the boundary, the end of the domain, of mass or energy where they become irrelevant.  This requires abandonment of all mass or energy containing variables such as momentum,  force, and angular inertial terms below this level.

4.  The fourth key concept is : "Space-time is quantized" into discrete units named  SPASONS. The spason is pure position in a four dimensional sense (including x,y,z, and t) and does not display the characteristics we call mass or energy, but its properties do give rise to mass and/or energy.   The spason expressed in space units,  x, is about:

x = 1.2737272175 x 10 -21 cm (or x 10 -23 meters)(eq 52) or in time units, T, it would be about  T = 4.2486966942 x 10 -32 seconds (eq 48).  Note the ratio of x/T = C, the speed of light = 29,979,245,619.3 cm/sec (eq 26). This is the boundary or the end of the domain where distance and time have meaning.  Between roughly 10-15 and   10-23 meters it is improper to say that we are describing mass or matter, but rather the description of the universe and its properties must be done in terms of space and time variables and pure numbers. Below the domain of roughly 10-23  meters even distance, or time at less than 10 -32 sec. becomes irrelevant and we are forced to use just pure numbers.

5.   A fifth key concept is the interdependence of space and time.  TIME IS CHANGE.  To have change implies that there is something there to change.  Time can not exist without space. Space might  conceivably exist without time, but it would be unchanging and therefore rather un-interesting.  Since space and time are so linked the word SPASON is meant to imply this interrelationship, and the prior names of hodon for the quantum of space and chronon for the quantum of time have been reserved for space like and time like behavior. The word spason is the combined linked concept reminding us of this link.  The basic unit of change gives rise to all motion and thus is linked and discrete - one to one- one new hodon equals one change in the fabric of space-time, and one change is precisely one chronon, one digital quantum of time.

6.  A sixth key concept is that of INDEXING which describes position in pure numerical relationships.  Each spason thus has a unique "index" of approximately 452 binary bits (164 bits for each x, y, and z) and these binary indices obey certain rules, somewhat different from our Boolean binary system.  It is these rules that at a higher level give rise to the conservation laws, and that control the properties of space-time. In addition indexing predicts the existence of tachyons, which transmit pure information at velocities of about 4 x 1058 meters per second.

7. The seventh key concept is: Everything in the universe is interdependent.  Everything, all mass and all forces, if looked upon with the proper perspective are part of the same phenomena. The universe is a consistent whole. This theory is not quite the "Unified Field Theory" sought by Einstein and others, since it is not a field theory, but it accomplishes the same purpose and unifies our continuum of space-time into a single unified theory. It also implies the existence of a very large number (1032) of other closely related continua (Multi Universe Theory, MUT), and an even larger number (1064) of not so closely related universes.

From the above statement there are no forces at a distance, but only direct interactions.  The gravity and electromagnetic theory is a two body interaction, proportional to l/r2 while the strong nuclear force, Fs, is seen to be a three body interaction proportional to l/ r6 , letting B1 be the proportionality constant:  Fs = B1/ r6 (eq 80) and the weak force, Fw, is a four body interaction proportional to  l/r12., letting B2 be that proportionality constant   Fw = B2 /r12(eq 81). The proportionality constants are found from experimental data as B1 = 960 and B2 = 328460 where distance is expressed in Fermis and the Fs or Fw units are in charge density of      10 -19 Coulombs per cubic cm. (with apologies for the badly mixed units).

With proper perspective gravity is seen to be a two body interaction linked to the same process as electromagnetism and not separate from it, i.e. the same equations apply and it is exactly equivalent to say:

A) Gravity exists, in Newtonian form,  Fg= G m1 m2/r2                         eq 76

B) The universe is expanding, dt= do exp(+Ht) + B exp (-Ht)                         eq 69

C) Time is passing, and time is change

D) The energy of time flow, DEt, is DE = t  m  DT, t = HC2 = 0.18509  J/kg sec (or m2 / sec3)

= 1850.908 ergs/ gm sec  (or cm2 / sec3 )   eq75

E) Entropy is increasing or things trend to disorder

F) Red shift velocity, V, will be observed at large distance, d, specified by the Hubble Constant = H,  V= H d (eq 74) but where:

H2 =(4/3) p r G (eq 79) where r is the density of mass in the universe and Hubble's constant, H = 2.05941 x 10-18 per second which also corresponds to an age of the universe of (1/H) = 15.387 billion years (4.85575 x 10 17 sec), and a diameter of 15.387 billion light years (C/H).

From the general equation for the expansion of the universe, there is a contra terrene universe associated with our own universe. In that universe there are anti particles (positrons and anti-protons) making up anti-matter; that universe is contracting, the time vector is reversed, and entropy proceeds to increasing order, with blue shift as the universe contracts. This paired universe accounts for the “missing” anti-particles in our system.

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