The spheres of time

In the race for knowledge of nature and the workings of the universe, Galileo, Newton, Planck and Einstein have each been of decisive importance, propelling physics towards a new future.

In its voyage to the limits of science, sub-atomic research is now turning in two main directions, either continuing to study elementary particles and their interactions, or considering that there is nothing outside of space-time, which Einstein saw as a field covered with bumps and dips.

Here we will try to convey the meaning space-time of the three colour charges considered in the previous chapter as the ultimate components of the universe.

 

The expansion of the universe

Newton worked in a Euclidean space with three dimensions, to which Einstein added a fourth: time. Since then, new theories have imagined space-times with not only four, but five and even seven dimensions. These theories have variants which, among other things, depend on whether the corresponding universe is open or closed. In the former case, the universe expands indefinitely, while in the latter an initial explosion is followed, sooner or later, by final implosion. The average density of matter is the decisive factor.

The existence of a four-dimensional universe is quite probable, as it agrees with the Big Bang theory in which the expanding universe is traditionally represented by a hypersphere, a bubble of the present which swells with time, and whose interior corresponds to the past. In this model, space, from which a dimension has been subtracted, is represented by the surface of the bubble of the present.

In view of these three factors, the past, present and future, the surface of the bubble of the present, and thus of space, necessarily has a degree of "thickness". Its outer surface faces the future, while its inner surface faces the past. To avoid intermingling, the two surfaces have to be separated by a non-oriented layer of the present. The surface facing the future could be referred to as positive, while the surface facing the past could be referred to as negative, with the non-oriented layer being neutral.

Although sometimes criticized as too simple, the Big Bang model has the advantage of accounting for several observable characteristics of the universe, such as the background cosmic radiation, a vestige of the primordial explosion, or the red-shift of light emitted by galaxies which therefore seem to be receding from ours at high velocity. In actual fact, this is the result of the dilation of space, comparable to that of a balloon whose surface is dotted with points representing galaxies. When the balloon is blown up, the distance between any two points increases proportionally to their distance. The same applies to all the galaxies, but our instruments and ourselves do not dilate (which would prevent us from observing the phenomenon) because the cohesive forces within atoms oppose this.

 

The discontinuity of the flow of time

Is the expansion of the hypersphere continuous or discontinuous, which would quantify the course of time?

The structure of a quantified space-time is at present considered as uncertain due to the continual fluctuations which appear at the level of Planck units. We will nevertheless adopt the hypothesis that the expansion of the hypersphere is discontinuous, as it makes it possible to geometrically locate the past and future of the universe, as well as the present.

If its expansion is discontinuous, the hypersphere and all its components successively go through two alternating states, one of motion and one of rest.

At rest, the sphere of present is immobile in time, occupying a position between the past and the future. It is one of an infinite succession of spheres of probability of increasing size, virtual in a preliminary approximation, and nested inside one another like Russian dolls. These virtual spheres mark all the positions which the sphere of the present could occupy during its expansion in the future.

In a symmetrically inverse way, an infinite succession of spheres of decreasing size is contained within the sphere of the present, and thus in the past. However, real spheres have to be distinguished from virtual spheres, a point to which we will return.

The sphere of the present at rest is separated from the adjoining sphere of the future by an interval of time. It will cross this interval by moving towards the future under the elementary push of Planck's quantum of Action, which has the dimensions required for this purpose: the product of energy by time. This is Planck's constant, h, whose value is 6.66 x 10-34 Js.

The sphere of the present is not smooth. On its so-called positive side, the future, it has lumps - "Einsteinian" particles - with corresponding symmetrical dips on the negative inner surface, the past.

These lumps stick out into the future, where the pressure of their masses gradually deforms the succession of future spheres, which thus acquire a degree of reality. These deformations of the future by the mass of particles may be identified with the curvatures of space-time known as gravitational waves.

During the discontinuous expansion of the hypersphere, its component elements necessarily pass through a succession of states of rest and motion. However, it is not possible to simultaneously observe two successive events, and therefore to specify at the same time both the state of rest (position) and the state of motion (velocity) between two positions occupied by a particle. Perhaps this is the basis of Heisenberg's uncertainty principle.

According to Louis de Broglie, the discovery of wave-particle duality was "the great drama of contemporary physics". This duality can be explained by considering that the particle state corresponds to a state of rest, and the wave state to a state of motion.

Like all other components of the sphere of the present, the photon passes through alternate states of motion and rest, and thus of wave and particle.

In the first case, the quantum of Action, h, the constituent element of the energy of the photon, propels it from the sphere of the present to the adjoining sphere of the future. The energy of the photon under consideration is equal to the product of its frequency times h. Its frequency could correspond to the number of times that h crosses an interval between the sphere of the present and those of the future.

In the second case, the photon can be considered as a real particle, as is shown by the Compton effect, among other things, which is a true elastic collision between a photon and a free electron.

The concept of a photon at rest is extraordinarily difficult to accept, as the alternation between states of rest and motion is so rapid, a bit like frames in a film, that one has the impression that the state of rest does not exist. However, might this not be the reason for the limit on the speed of light?

 

The colours of time

In quantum physics, colours are not the same as those used by painters. They characterize three charges, believed to be the ultimate building blocks of both the present universe and its predecessor, the primordial universe, as we shall soon see.

At present, the primordial universe is defined as a spatio-temporal singularity of infinite density. But how could such a singularity, reduced for the sake of argument to a point, give rise to myriads of galaxies separated by billions of parsecs? A partial answer is given by set theory applied to relative set numbers.

Relative set numbers are components of the set Z which includes all positive set numbers, all negative set numbers, and zero, the neutral element. In fact, as a member of both sets, zero is where they intersect, and is therefore a set in its own right.

The spheres of time are numbered by making those of the future correspond to positive set numbers, and those of the past to negative set numbers. The present is represented by zero, which lies between the positive and negative set numbers. In this scenario, the Z set is a mathematical model of our universe.

To go back to the primordial universe in this model, we have to imagine a mathematical Big Bang in reverse, adding each member of Z to its opposite. The positive set, the negative set and their intersection would then be combined in a single primordial mathematical set. As the sum of the positive and negative set numbers, Z would become a sort of mega-zero, in which the positive and the negative would be neutralized.

The primordial universe which corresponds to this model would not have any conceivable dimensions, as there would be no external reference to measure it against. Although it is currently believed to have been minuscule in size (maybe the size of a single photon with infinite energy), this is because we compare it retrospectively with the immense, constantly-increasing volume occupied by the products of its disintegration, spread across our universe today.

In summary, Z represents both the primordial and the present universe. In the former, positive and negative set number groups are added together and combined, while in the latter they have an intersection: zero.

The corresponding addition of the spheres of the future, present and past also combines them in a new, single set, homologous to the mega-zero. This is time, which by definition encompasses before, during and after, or the past, present and future. Here, time alone is referred to rather than space-time; as seen above, space is an aspect of time, the present.

In this configuration, what do chromodynamic colour charges correspond to? The three colour charges presented in the previous chapter as the building blocks of the universe correspond to the three components of the hyperspherical model of the universe, and the term "colour charges" should be replaced by temporal charges, of the past, present and future.

In the table of elementary particles and antiparticles, the colour charges should be replaced by temporal charges. For example, red would become a present charge, yellow a future charge, and blue a past charge.

But in that case, how could a particle such as an electron (which in this hypothesis has the same temporal charges as its antiparticle, the positron) travel into the future, while the positron travels into the past?

The rotations, already discussed above, of the equilateral triangle a, b, c, the geometric interpreter of the G3 group, provides the answer: a is replaced by a present charge, b by a future charge, and c by a past charge. If rotation from a b takes place in the direction present future, the particle is an electron; if rotation from a b takes place in the direction present past, the particle is a positron. The direction of rotation will therefore determine which way the particle travels through time.

Particles and antiparticles are not the only temporal charges which form the hypersphere. The three non-ordered colour charges of the photon must also be replaced by temporal charges.

The photon is therefore a temporal set, non-ordered, of three past, present, and future charges. Its image in Z is a set in which three components, positive, negative and zero, are added together, as in the primordial universe.

 

Return to the Big Bang

During the Big Bang, time's three sub-sets, the past, present and future, and their members, were created simultaneously, since one cannot exist without the others. However, only the sphere of the present is real. The spheres of the past and present which mark its possible positions are virtual, and according to the Z model, are infinite in number, both towards the past and the future.

At this decisive moment, the sphere of the present had the option of dilating, thus climbing the steps which symbolize the spheres of the future on the staircase of time. Or it could have contracted, and climbed down the steps which symbolize the spheres of the past.

If the sphere of the present had climbed down the staircase, time would have run backwards, and the past would have become the future of the present.

As mentioned above, we will now explain the distinction between real and virtual spheres of the past.

Observation shows that the hypersphere is expanding, and has decided to climb the steps of the future, the positive steps. It has therefore not gone down the negative steps into the past, which therefore remain virtual. In its ascent, on the other hand, it has transformed steps of the future into steps of the past, which are now behind it. However, these steps were indeed climbed, and can therefore be referred to as "real" steps (spheres) of the past.

In summary, it has been proposed that the three colour charges are the ultimate building blocks of the universe, and a temporal charge has been attributed to each of them. Just as the elements of unit Z are in an infinite number, in the same way the elements of its physical counterpart, the cosmic singularity, are in an infinite number, which would explain its infinite energy and the multiplicity of the elements resulting from its big-bang.

Without contradicting it, this hypothesis extends quantic physics. It will not be discussed further, as its lessons are enough to steer research into the origin of the universe, the subject of the next chapter.