# ULTIMATE SYMMETRY:

Fractal Complex-Time and Quantum Gravity

# II.1.3 The Fundamental Interactions

There are four fundamental forces in nature, and they result from the various interactions between fermions as they are attracting and repelling each other. These four forces are also called the fundamental interactions. Two of them are long-range, while the other two operate only on the subatomic distances. The gravitational and electromagnetic forces can be observed directly in everyday life, while the strong and weak forces govern nuclear interactions. Some scientists speculated the existence of a fifth force, referred to as quintessence , but this has not been proven yet. It is worth mentioning here that the fundamental forces in the Duality of Time Theory are directed related to respective time-time dimensions, and there must be at least five forces, but the fifth is the magnetic force itself which is a result of the intrinsic spin property of each single point of space, so it is only manifest in nature coupled with other forces, thus is called electromagnetic and electroweak, and that s why the magnetic mono-pole has never been found, as it will be illustrated in section IV.4.3.

In the conceptual model of fundamental interactions, matter consists of fermions, which carry charges and spin, and they attract or repel each other by exchanging bosons. The exchange of bosons always carries energy and momentum between the fermions, thereby changing their speed and direction. This exchange may also transport a charge between the fermions, which turns them from one type of fermions to another. Since bosons are spin-one particles, they carry one unit of angular momentum, so the fermion s spin direction will flip during such an exchange from  to , or vice versa, in units of the reduced Planck s constant. The strong interaction is carried by a particle called the gluon, which is the boson responsible for the binding of quarks together to form hadrons, such as protons and neutrons. As a residual effect, this interaction also creates the nuclear force that binds the hadrons to form atomic nuclei. This is then called the weak interaction, which is carried by the  and  bosons, responsible for radioactive decay. These four fundamental interactions are summarized in Table ??.

The other two forces are long-range. The electromagnetic interaction is mediated by the photon, and it creates the electric and magnetic fields, which are responsible for chemical bonding and electromagnetic waves, including visible light, and forms the basis for electrical technology. Gravity is also expected to be carried by a particle called the graviton, but there is physical confirmation of such a theoretical particle. Although the electromagnetic force is far stronger than gravity, it tends to cancel itself out within large objects, so over the largest distances, on the scale of planets and galaxies, gravity tends to be the dominant force.

In General Relativity, the gravitational force is explained in terms of the curvature of space-time, while the other three are discrete quantum fields, and their interactions are mediated by the gauge bosons described by the Standard Model of particle physics. It is believed that gravity should be also quantized, but all the theories and models of such Quantum Gravity have not been fruitful yet. The essence of the problem is that most of these theories are trying to implement some kind of quantization in a continuous space-time background, which makes any prospective theory of gravity non-re-normalizable, thus impossible to test because it cannot make any meaningful predictions. The two serious approaches to this critical problem are Strings Theory and Loop Quantum Gravity (LQG), where the first is trying to develop an effective Quantum Field Theory of gravity at low energies, by postulating strings instead of point particles, while LQG uses spin networks to obtain granular space that evolves with time. This makes the latter closer to General Relativity that considers space-time to be dynamic, but here the smooth background is replaced by nodes. Therefore, while Strings theory still depends on the background continuum, LQG is trying to be independent of the background by quantizing space-time itself. As we shall discuss in section IV.4.3, in the Duality of Time Theory, all fundamental interactions are manifestations of the genuinely-complex time-time geometry which produce a granular and hyperbolic space as a result of breaking the original symmetry of the three-dimensional Euclidean space.

All four fundamental forces are believed to be related, and united into a single force at high energies on the Planck scale, but particle accelerators cannot produce the enormous energies required to experimentally probe this field. Maxwell s equations established the first integration of magnetic and electric fields, called electromagnetism, which also included the optical theory. Also the weak and electromagnetic forces have already been unified with the electroweak theory, and a good progress is made in uniting the electroweak and strong fields within a Grand Unified Theory (GUT). However, this is still not yet achieved, because the novel particles predicted by GUT models are expected to have masses just a few orders of magnitude below the Planck scale, which is well beyond the reach of any foreseen particle collision experiments. There is the possibility of a grand unification epoch in the early Universe in which the fundamental forces are not yet distinct at that extremely high energy density.

The photon, the particle involved in the electromagnetic interaction, along with the  and  provide the necessary pieces to unify the weak and electromagnetic interactions. With masses around  and , respectively, the  and  were the most massive particles seen at the time of their discovery, while the photon is massless. This difference in masses is attributed to spontaneous symmetry breaking as the hot universe cooled. Therefore, the theory suggests that at very high temperatures where the equilibrium energies are in excess of , these particles are essentially identical and the weak and electromagnetic interactions were manifestations of a single force. The question of how the  and  got so much mass in the spontaneous symmetry breaking, which is called a Higgs mechanism that requires a new field particle, called the Higgs boson, whose existence has been confirmed in 2013.

The Grand Unified Theory is the unification of the three fundamental non-gravitational forces: electromagnetism, the weak nuclear interaction, and the strong nuclear interaction, into a single quantum field interaction characterized by one larger gauge symmetry, with several force carriers but one unified coupling constant. Unification theories require restoring the broken symmetry. In trying to unify the strong and electroweak forces, the problem is that leptons don t have color and the strong force works only on colored particles, so we need to be able to convert quarks to leptons and vice versa, which violates the conservation of baryon number, which is a strong experimental nuclear physics principle. Baryon number minus lepton number would still be conserved as a quark is changed to an anti-lepton, but the required mass of the exchange boson is very massive, which is called the X-boson.

The bigger challenge, however, is to find a way to quantize the gravitational field, resulting in a theory of Quantum Gravity, which would unite gravity in a common theoretical framework with the other three forces. The unification of the strong force is well beyond our reach at the present time, and the unification of gravity with the other three is out of reach of any earthbound experiments.

Unifying gravity with these three interactions would provide the Theory of Everything (TOE), which would explain all the four fundamental interactions in terms of one unified Quantum Field Theory. Einstein spent most of the latter part of his life trying to create a quantum form of the general theory of Relativity. Currently, the two serious approaches in this regard are Strings Theory and Loop Quantum Gravity, where the first tries to develop an effective Quantum Field Theory of gravity at low energies by postulating strings instead of point particles, while the latter uses spin networks to obtain granular space that evolves with time.

The essence of the problem is that most of these theories are trying to implement some kind of quantization in continuous space-time background, which makes any prospective theory of gravity non-re-normalizable, thus impossible to test because it cannot make any meaningful predictions. In addition to the two most celebrated approaches to resolve this discrepancy, which are Strings Theory and Loop Quantum Gravity, some other space-time theories, such as Causal Dynamical Triangulation, Quantum Einstein Gravity and Scale Relativity, attempted to relax the condition of differentiability, in order to allow for fractal space-time, which was first introduced in 1983 [24]. In addition to the abundance of all kinds of fractal structures in nature, this concept was also supported by many astronomical observations which show that the Universe exhibit a fractal aspect over a fairly wide range of scales, and that large-scale structures are much better described by a scale-dependent fractal dimension, but the theoretical implications of these observations are not very well understood, yet.

However, as we have already introduced in Volume II, any successful theory of Quantum Gravity must not rely on either the continuum or discretuum structures of space-time. Rather, these two contrasting and mutually-exclusive views must be the product of such theory, and they must become complementary on the microscopic and macroscopic scales. The only contestant that may fulfill this criterion is Oneness , because on the multiplicity level things can only be either discrete or continuous; there is no other way. However, we need first to explain how the apparent physical multiplicity can proceed from this metaphysical oneness, and then exhibit various discrete and continuous impressions. The key to resolve this dilemma is in understanding the inner levels of time in which space and matter are perpetually being re-created and layered into the three spatial dimensions, which then kinetically evolve throughout the outer level of time that we encounter.

Due to this dynamic formation of dimensions, in the inner levels of time, the Duality of Time Theory leads to granular and self-contained space-time withfractalandgenuinely-complexstructure, which are the key features needed to accommodate both quantum and relativistic phenomena. Many previous studies have already shown how the principles of quantum mechanics can be derived from the fractal structure of space-time [22], but they either do not justify the use of fractals, or they are forced to make new unjustified assertions that may lead to fractal space-time. On the other hand, imaginary time had been successfully used in the early formulation of Special Relativity by Poincar , and even Minkowski, but it was later replaced by the Minkowskian four-dimensional space-time, because there were no substantial reasons to treat time as imaginary. Nevertheless, this concept is still essential in current cosmology and Quantum Field Theory, since it is employed by Feynman s path integral formulation, and it is the only way to avoid singularities which are unavoidable in General Relativity.

The Duality of Time Theory does not only unify gravity with the other fundamental interactions, but also unifies all the corporeal and incorporeal phenomena into one theory of complex time-time geometry. All entities in the physical and non-physical realms are objects created in various levels of the inner flow of time, so the four fundamental interactions correspond to the four levels of the inner time that is creating the physical world, and there are another four interactions in the orthogonal time direction that is creating the psychical world, but they are expected to be the same kinds of interactions. However, it is also anticipated that another four completely different kinds of interactions would be operating when the higher level of time is achieved to make the World developing in  space, and this may happen when a physical object moves at the speed of light, which could be achieved under certain conditions similar to quantum tunneling. In such cases, there would be positive and negative masses, in addition to more complex mass structures, just as electric and color charges can now be considered some simple forms of mass exhibited in lower dimensions.

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• ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...

• ## ... Standard Mode =>:

• ... ional force is explained in terms of the curvature of space-time, while the other three are discrete quantum fields, and their interactions are mediated by the gauge bosons described by the Standard Model of particle physics. It is believed that gravity should be also quantized, but all th ...

• ## ... Critical Problem =>:

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• ## ... Particle Collision =>:

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• ## ... Called Electromagnetic =>:

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• ## ... Dynamical Triangulation =>:

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The science of Time is a noble science, that reveals the secret of Eternity. Only the Elites of Sages may ever come to know this secret. It is called the First Age, or the Age of ages, from which time is emerging.
Ibn al-Arabi [The Meccan Revelations: Volume I, page 156. - Trns. Mohamed Haj Yousef]

### The Sun from the West:

Welcome to the Single Monad Model of the Cosmos and Duality of Time Theory

### Message from the Author:

I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever!

By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.