Chapter V: Complex-Time Hyperbolic Geometry

“The Moving Finger writes; and, having writ, ...

Moves on: nor all thy Piety nor Wit, shall lure it back to cancel half a Line.

Nor all thy Tears wash out a Word of it.”Omar Khayyam, trns. Edward Fitzgerald

“The time of anything is its presence; but I am not in time, and You are not in time; so I am Your time, and You are my time!”Ibn al-Arabi, The Meccan Revelations: III.546.16

“You should know that some of (the levels of) time are above Nature and some of them are below Nature [I.377.12], ... (the time that is below Nature) is defined by the motion of orbs ... and the time that is beyond Nature is defined by (spiritual) states. [I.477.12].”Ibn al-Arabi, The Meccan Revelations: I.377, 477

As we have seen in chapters II and III, Relativity and its classical predecessor consider space and time to be continuous, whereas Quantum Mechanics is constructed on discrete quanta of energy and fields, albeit they still evolve in continuous background. Although both theories have already passed many rigorous tests, they inevitably produce enormous contradictions when applied together in the same domain. This was manifested very clearly in the cosmological constant problem, which was described as “the worst theoretical prediction in the history of physics” Hobson et al. (2006). As we have already summarized in chapter III, most scholars believe that this conflict may only be resolved with a successful theory of Quantum Gravity, which seems to be beyond the current scope of Relativity because it is primarily based on dynamic space-time continuum.

Many innovative concepts have been investigated in this regard, but none has ever been able to settle the discrepancy, including the two most serious approaches to this critical problem: Strings Theory and Loop Quantum Gravity (LQG). 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-renormalizable, thus impossible to test because it cannot make any meaningful predictions.

Strings Theory tries to develop an effective Quantum Field Theory of gravity at low energies by postulating strings instead of point particles. On the other hand, LQG uses spin networks to obtain granular space that evolves with time. This makes LQG 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 tries to be independent of the background by trying to quantize space-time itself.

However, as a matter of principle, quantizing space is impossible on the physical level of multiplicity, because the objects cannot occupy positions between the discrete points of space, and they cannot move between these points, otherwise they won’t be discrete, as it had been long demonstrated by the irrefutable Arrow Paradox of Zeno, as we have explained in chapter II. Furthermore, if space is considered to be somehow discrete, how the distance(s) between its nodes are going to be measured without considering any abstract space-time reference frame according to which measurements are made! This same contradiction also applies if we choose the abstract space-time continuum of General Relativity, because this dynamic space-time becomes curved and its curvature cannot be realized without some more abstract reference frame, and so on ad-infinitum.

Therefore, any successful theory that could combine Relativity with Quantum Mechanics must not rely on either the continuum or discretuum structure of space-time. Rather, these two conclusive and contrasting 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 are either discrete or continuous, there is no other way. However, we need first to explain how the 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 continuously being generated and layered into the three spatial dimensions, which then evolve throughout the “outer level of time” that we encounter.

As we have described in chapter IV, the Single Monad Model endorses two harmonious perspectives of time; on the ontological level, time is discrete and uniform, but phenomenologically it appears potentially continuous and relative because of the global perpetual re-creation that is captured locally at a fixed refresh rate. As a result, there is no gradual motion in the common sense that the object leaves its place to occupy new adjacent places, but it is successively re-created in those new places.

With this unique approach we can also accommodate instantaneous change without breaking the speed of light limit, which by itself is a direct consequence of re-creation. This will also creatively explain all kinds of dualities such as the particle-wave duality and the mass-energy equivalence, as well as the most profound philosophical issue of discreteness and continuity, which will be a consequence of the theory rather than its starting foundation as it is inevitably the case in all current models.