Chapter 3: Complex-Time Geometry and Ultimate Symmetry

“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

“Absolute non-existence is like a mirror for absolute Existence, so He is seeing in it His own (temporal) image(s), that are the entities of contingent things. That is why things have Constant Entities and thing-ness even before they actually come to be, and when they become, they appear according to this Image of (Real) Existence.” Ibn al-Arabi, The Meccan Revelations, III.47.32

“If non-existence could speak out, it would tell you: ‘you are created according to my image’, because it sees in you nothing but its own shadow, just as Existence has told you: ‘you are created on My Image’.” Ibn al-Arabi, The Meccan Revelations, IV.154.23

Both Special and General Relativity, as well as Classical Mechanics, consider space and time to be continuous, and although Quantum Mechanics is constructed on discrete quanta of energy and fields, they are still considered to be evolving in continuous background. Throughout all the previous century, there has been many attempts to quantize space and time, without any noticeable success at all! The main reason that is preventing any complete quantization of space-time is because, since we exist on the level of multiplicity with many surrounding objects and other entities, we always need to define some absolute background geometry or topology where these objects could be located and referenced.

In the Single Monad Model, this difficulty is eliminated, due to the re-creation principle, which is based on the fact that all things are being perpetually re-created in one chronological sequence at every instance of our level of time that we encounter. This principle was elegantly formulated in the Duality of Time postulate, from which all the principles of Relativity and Quantum theories were explained and derived mathematically in Chapter V of Volume II.

Therefore, in our normal level of time, as we have already mentioned in the Introduction, if this perpetual process of re-creation is conceptually “stopped” and taken in isolation, it will form a still picture of all things around us, or a single frame of space that is created in one instance of time. But if this process is stopped in the real inner level(s) of time, there will be only one single metaphysical monad, without any background space or time, since there is nothing else to be compared to it. The flow of time in the inner levels is creating space and matter, which then evolve in the outer physical level that we encounter. The dynamic manifest Universe is the instantaneous and continuously renewed succession of the slightly changing frames which are created at the succeeding instances. Motion, therefore, is observed because things may successively appear in different (adjacent) places, but in reality there is no actual infinitesimally gradual motion, or transmutation, rather: the observed objects are always at rest in the different positions that they appear in. This important conclusion is the key to quantize time and reveal the hidden discrete symmetry of space.

With this unswerving conclusion, Relativity will be fundamentally based on granular space, and Quantum Mechanics is a natural consequence with fully logical interpretation, and we can already notice straightaway that there would be no difference between inertial or non-inertial frames since all frames are effectively at rest in the normal (imaginary) level of time. Indeed, there is even no need to introduce the second principle of Special Relativity, which says that the laws of physics are invariant between inertial frames, neither the equivalence principle that leads to General Relativity. These two principles, which are necessary to derive Lorentz factor and Einstein’s field equations, will follow directly from the complex-time geometry as we shall see further below.

Discreteness implies interruption or discontinuity, and this is what the outer time is doing to the continuous flow of the inner time that is creating space and matter. Mathematically, this is achieved by multiplying with the imaginary unit which produces an abrupt rotation by 90 degrees, creating a new dimension that is perpendicular on the previous level. Multiplying with the imaginary unit again causes time to become real again, i.e. like space. Therefore, each space-time point is the product of seven instances of time, the first six of which make the three spatial dimensions and the seventh is the outer time. This is the Cosmic Week, that is the ultimate unit of space-time geometry. Surprisingly, the days of this week are identical with our normal days that we count, the same twenty-four hours’ day! Yet all these days, including Saturday itself, are occurring in Saturday. This extremely intricate conception is explained in Chapter IV of Volume I, and elaborated further in Chapter IV of Volume II.

It is not possible otherwise to imagine granular space-time without any background in which the topology is defined. The main pioneering theories that are trying to solve this fundamental problem are Strings Theory and Loop Quantum Gravity. The first is trying 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. Although there has been some considerable achievements, but 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 of Volume 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 of Volume I, the Single Monad Model endorses two harmonious perspectives of time; on the ontological level, time is discrete and uniform, but phenomenologicaly 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, as we mentioned above.

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.