I.2.3 Fractal Dimensions and the Emergence of Time

The Duality of Time Theory exposes a deeper understanding of time, that reveals the discrete symmetry of space-time geometry, according to which the dimensions of space are dynamically being re-created in one chronological sequence at every instance of the outer level of time that we encounter. In this hidden discrete symmetry, motion is a result of re-creation in the new places rather than gradual and infinitesimal transmutation from one place to the other. When we approximate this discrete motion in terms of the apparent (average) velocity, this theory will reduce to General Relativity.

Accordingly, the dimensions of space are created dynamically in the inner levels of time, where each dimension is formed by the combination of two orthogonal time directions. Conversely, we can also say that the Cosmos is created by splitting one homogeneous dimension of space into two time directions, which then form the two complementary physical and psychical domains, that are necessary to accommodate super-symmetry and quantum gravity, as we shall discuss further in Chapter II.

However, since at every instance of the real flow of time there is only one Single Monad that forms the unit of space-time geometry, these two parallel Universes do not exist completely separated from each other, but they are entirely intermingled, and, at every individual instance, there is only one point connecting them together, that is the point of now , or the present time. Therefore, each point of the physical realm has a certain unique reciprocal point in the psychical realm, that together form unity, such that: , or: .

This splitting of the homogeneous dimensions of space into orthogonal arrows of time is referred to as the splitting of the seven heavens, or skies, from (the seven) earth(s), which produced the seven days of the week, that are the six spatial and one temporal directions, which together form the local space-time geometry. This same theory of creation can be found, with numerous variations, in most religions and ancient civilizations, but it is most complete and well preserved in Islamic texts, though it is greatly abbreviated in many short and interconnected Quranic verses and related prophetic narrations. Nevertheless, many Muslim sages and philosophers have frequently elaborated on these inspiring accounts in their innumerable books and other mystical discourses, and the purpose of this book series is to renovate these dispersed illuminations into precise model of cosmology with comprehensive theory of complex-time geometry.

The splitting of heavens and earth is breaking the otherwise perfectly symmetrical sphere, of infinite and homogeneous space, into two hemispheres containing the Universe and anti-Universe pairs, or the physical and psychical realms, so each part has a natural tendency to re-unite again into the initial harmony. This love, or passion, for unification is the most fundamental cause of motion, that we call the Principle of Love . All parallel particles are naturally seeking each other. In trying to overcome the barriers and obstacles, they are continuously and sequentially annihilating into their original unity that forms the homogeneous flat space, and separating back again into opposite arrows of time, at every instance of time.

If it were only for these two super-symmetrical pair of physical and psychical worlds, they would remain in their eternal unity, with which there would be no further motion, and no time, but only abstract homogeneous space, like what happens in the state of terminal death, or relatively in deep sleep, and even at the time of rest, when one is isolated in a calm place and doing nothing . That s why this state is often desirable and required, but then here it comes the role of the spiritual world, which acts from one higher dimension that make the level of hyper-symmetry, which mirrors the previous two levels together, such that: , so we can write the complete world formula as:

 (1.6)

From this simple cubic equation, that describes the whole world as well as every single space-time point in it, we can deduce the laws of super and hyper symmetry, including the Lorentzian invariance of Relativity. In Islamic cosmology, this trinitarian world , composed of the spiritual, psychical and physical worlds, is represented by the Kaaba, as illustrated in Figure VI.2 of Volume II.

Without the spiritual world, all motions will stop instantly, because the physical and psychical worlds would annihilate and remain in this state of vacuum or absolute rest. The spirit is exciting this ground state of vacuum by inducing the personal desire for further motion, in order to achieve certain goals that may not be in the immediate reach. This personal desire is what we call free will , but it can be generalized, with relative contexts, to all animate and inanimate beings, and it is directly related to consciousness, as we shall explain in Chapter III.

Therefore, whereas the physical and psychical worlds have the natural tendency to unite, as they are doing at every instance of time, the spiritual world is breaking their super-symmetry by causing the individual entities to move further according to their own relative free will, though it is significantly constrained by the surrounding environment. As a result, although everything is returning to rest at every instance of time, motions continue because of the conflicts between the various opposing desires of individual entities. In more scientific terms, due to the hyper-symmetry of complex-time geometry in the spiritual world, free will is the ability to control the collapse of wave-function into a specific state, whereas this collapsing is completely nondeterministic in super-symmetry.

In contrast with the previous description of super and hyper symmetries, the ultimate symmetry of the absolute oneness of God does not act from any higher level of space, but from within all these levels of creation. This is represented by number one in the previous world formula , which means that God exists everywhere within all entities, but without any reference to spatial dimensions, as we shall explain further in Chapter IV. The existence of God is always manifested in every individual entity of creation, and that is because this number one in the previous formula is the dimension of time, which exists only as one single indivisible instance, at a time, whereas the three dimensions of space are composed from the recurrence of these complex-time instances.

Therefore, this simple cubic equation  contains all the information about the World, with its three spiritual, psychical and physical domains, each one represented here as one dimension of space , as well as the absolute oneness of God, represented here as number one, which is the reference to ideal time. However, in order to reveal the details of this ideal equation, the first thing we need to realize is that our world is not perfectly three dimensional, but it has a dynamic multi-fractal dimension that change between zero and three: , and that is why time is flowing and the World is evolving, thus the practical equation becomes:

 (1.7)

Based on the concept of re-creation according to the Duality of Time Theory, the Universe is constantly being re-created from one geometrical point, that is , from which all the current dimensions of space and matter are re-created in the inner levels of time before they evolve in the outer time. Therefore, the total dimension of the Universe becomes naturally multi-fractal and equals to the dynamic ratio of inner to outer times, because spatial dimensions alone, as an empty homogeneous space, are complete integers, while tractability arises when this vacuum state starts oscillating in the outer time, which causes all types of evolving elementary particles.

The dynamic fractal dimension  is the ratio of inner to outer times, and that is the same as the speed of light, which only needs to be normalized in order to express the fractality of space-time; to become time-time. For example, if the re-creation process, that is occurring in the inner levels of time, is not interrupted in the outer time, i.e. when the outer time is zero, this corresponds to absolute vacuum, that is an isotropic and homogeneous Euclidean space, with complete integer dimensions, that is  in our normal perception. So the speed of light, in the time-time frame, is a unit-less constant that is equal to the number of dimensions that are ideally  for a perfect three-dimensional vacuum, but it may condense down to  for complete rest, or void.

The standard value of the speed of light in vacuum is now considered a universal physical constant, and its exact value is  meters per second. Since 1983, the length of the Meter has been defined from this constant, as well as the international standard for time. However, this experimentally measured value corresponds to the speed of light in actual vacuum that is in fact not exactly empty. The true speed that should be considered as the invariant Speed of Creation is the speed of light in absolute void rather than vacuum , which still has some energy that may interact with the photons, and delay them, but void is real nothing . Of course, even high vacuum is very hard to achieve in labs, so void is absolutely impossible.

Because we naturally distinguish between space and time, this speed must be measured in terms of meters per second, and it should be therefore exactly equal to . The difference between this theoretical value and the standard measured value is what accounts for the quantum foam, in contrast to the absolute void that cannot be excited. Of course all this depends also on the actual definition of the meter, and also the second, which may appear to be conventional, but in fact they are based on the same ancient Sumerian tradition, included in their sexagesimal system which seems to be fundamentally related to the structure of space-time, as we noted in Chapter VII of Volume II.

Therefore, the actual physical dimensions of the (local) Universe are less than three, and they change according to the medium. For example the fractional dimensions of the actual vacuum is simply , and the fractional dimensions of water would be , and so on for all transparent mediums according to their relative refraction index. Opaque materials could be also treated in the same manner according to their refraction index, but for other light wave-lengths that they may transfer. Dimensionality is a relative and dynamic property, so the Universe is ultimately described by multi-fractal dimensions that change according to the medium, or the inner dimensions (of space), and also wavelength, that is the outer dimension (or time).