1.    Introduction:

The famous Michelson–Morley experiment in 1887 proved that light travels with the same speed regardless whether it was moving in the direction of the movement of the Earth or perpendicular to it [[1]]. This unexpected result initiated active research that eventually led to Special Relativity in 1905 [[2]]. The speed of light in vacuum is then considered the maximum speed which anything in the universe can attain. Photons and some other massless elementary particles propagate in vacuum at this terminal speed, regardless of the motion of the source or the reference frame of the observer. This constancy and invariance of the speed of light is an axiom that has been experimentally verified, but not yet proven in any fundamental academic sense.

On the other hand, and in parallel with the success of Relativity, Quantum Mechanics had also been proved successful in describing the interactions between fields and subatomic particles, despite the fact that it clearly contradicts the aforementioned central principle of Relativity, since it predicts various nonlocal interactions, such as quantum entanglement and tunneling, which have been also widely observed experimentally [[3]] [[4]].

This conceptual incompatibility between Relativity and Quantum theories triggered many research paths that tried to consolidate the fundamental forces of nature, leading to many differing and intersecting theories, such as Quantum Field Theory, Superstrings and Quantum Gravity. None of these theories, however, has ever been able to settle this fundamental conflict. On the contrary, this conflict manifested recently in the cosmological constant problem which was described by Hobson and Efstathiou in 2006 as “the worst theoretical prediction in the history of physics.” [[5]].

The Single Monad Model (SMM) is based on a research performed at Exeter University in 2005 [[6], [7], [8]], which presented a pioneering study of Ibn Arabi’s eccentric conception of time and its implications for modern physics. To resolve the discretuum-continuum duality, the SMM 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 accommodate instantaneous change without breaking the light speed limit, which by itself is a direct consequence of the 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 foundation, as it is inevitably the case in current models.

2.    The Single Monad Model:

Relativity and its classical predecessor are constructed on the notion that space and time, or both together, are a continuum, whereas Quantum Mechanics uses discrete quanta of energy. Both theories have already passed many rigorous tests, and it became clear that Relativity is quite successful on the macroscopic scale, while Quantum theory is equally successful in the microscopic domain. Nonetheless, when they are applied together, they inevitably produce enormous contradictions, such as the cosmological constant problem or what is known as the vacuum catastrophe. The source of this catastrophe comes from infinities that are always associated with the continuum. In the words of Einstein himself: “It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do” [[9]].

Accordingly, any successful Theory of Everything must not rely on either the continuum or discrete space-time. Rather, these two contrasting views must be the product of such theory, and they must become complementary in 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, all the phenomena of nature are manifestations of plurality, because a subject must act on an object in order to produce a result. In rational logic, therefore, multiplicity can only emerge at least from the trinity of: subject, object, and action. For this reason, the philosophers of emanation cosmology concluded that: “from (the simple) one only one can proceed” [[10]].

Consequently, if we want to build a creditable theory based on the notion of ultimate oneness, we need first to explain how the phenomenological multiplicity can proceed from this ontological oneness, and then exhibit various discrete and continuous impressions, such as particles and waves as they are widely observed in nature. This is the only way that may lead to a Theory of Everything, that is capable of providing full understanding of nature, and this is exactly what the Single Monad Model does, by adding a little alteration to the previous philosophical maxim, so it becomes: “from one only one can proceed at a time”, and then explaining the reality of “time” in a unique manner that has never been conceived before.

Hence, the SMM explains first how “space”, as a manifestation of multiplicity, is continuously being constructed by this conjectural oneness of the Single Monad. One of the invaluable rewards of this continuous space construction is that it reduces space into time, and time into number. Therefore, the speed of light, which will naturally emerge as a first constant, can be easily “calculated” based merely on the three dimensional structure of space, and it will be a unit-less constant, from which other constants will follow. So the cosmos as whole will be a simple arithmetic machine, or a cosmic computer, since we will also see that its fine structure is not only “quantized” but literally “digital”.

3.    The Re-creation Principle:

The SMM postulates that every entity in the cosmos intrinsically ceases in the second instance after its becoming, to be re-created in a slightly different state. This perpetual re-creation process is realized by the Single Monad which continuously and successively images all possible states to complete a comprehensive instance of space, with all its contents, just to start over a new instance and produce the flow of time and all associated phenomena of motion and change. In other words, the Single Monad appears in each state for one single instance of the “real flow of time”, thus creating an individual monad which is nothing but its own temporal projection. The succession of these individual monads, that occur one monad at a time, produces one frame of space, and the succession of these frames produces the dynamic universe.

This is schematically demonstrated in Figure (1), where space is shown conventionally in two dimensions. In reality, however, we can conceive of at least five levels or dimensions of time: 0D, 1D, 2D, 3D and T, where each level is nested inside the higher dimension, and all are nested inside the outward normal time dimension T.

Figure (1): The inner and outer levels of time.

Because of the various degrees of freedom, the interactions are different from one level to the other, so in total we have five different fundamental forces: magnetic, electric, strong, weak, and gravity, respectively corresponding to the above five levels of time. Although the metaphysical 0D, which is the quanta of space-time, is the building block of all subsequent dimensions, it does not exist alone on the multiplicity level where all the physical phenomena are eventually observed, so this is the magnetic monopole that exists everywhere, attributed to spin, but cannot be isolated because it is always coupled in higher dimensions. The first level of physical manifestation of the magnetic monopole is the electromagnetic force, then the strong nuclear force, then the weak nuclear force, and then gravity, which can potentially explain the relative strength of these forces and why gravity is very weak, since it is exhausted in the volume. Moreover, this can open the door for converting magnetism into other forces including gravity, which will be naturally quantized, because they all emerge from the actual discrete primary flow of time.

The structure of space-time in this model is effectively similar to the lattice approach of quantum chromodynamics (QCD), but the main idea here is that its points are being perpetually constructed in chronological sequence.

To explain this further, we can consider the world in analogy with a movie that is displayed on a computer monitor. The screen of a classical computer monitor is normally composed of a large number of pixels that spread as a matrix over the horizontal and vertical dimensions of the screen, for example 800 by 600 pixels. On its part, the movie is made of succeeding frames, that pass rapidly before the eye at very short intervals. Each frame is produced on the screen by an electric current that starts at the lower left corner by forming a pixel, with specific color and intensity, and then leaves it to make another pixel next to it with its own specific color and intensity, and so on 800 times until it completes a horizontal line, just to switch back to the left again and make another line above the first one, and so on 600 times until it scans the whole area of the screen. When this full frame is displayed, the beam starts over the same process again to make a new frame that displays a slightly different image, and so on, as long as it is running. Even when it is displaying a blank or blue screen, the image is continuously being refreshed at a high rate that we cannot normally follow. The details just stated here for the purpose of this analogy are summary of traditional computer display system, but in reality there could be a variety of many other diverse methods.

Therefore, the movie is generated on the screen frame by frame, and each frame is generated pixel by pixel; one pixel at a time. When the frames are swiftly changed at a suitable rate, the human mind observes (by illusion) as if objects or characters are moving on the screen. If we suppose that the screen has no visible edges, especially with modern holographic systems, it would be very hard initially to distinguish this illusion from reality.

Of course, things in nature are much more sophisticated than this simplified view, but essentially the SMM envisages the whole world as a digital code, composed of one dimensional sequence of data, that is being interpreted in the mind(s), although in the end it still as objective as we are. In other words, the Single Monad takes the form of every entity -or monad- in the world, one monad at a time, thus creating it as an excitation in the abstract vacuum field, and when it completes the creation of one frame it starts again a new frame by re-creating the same excitations, which will be eventually interpreted as objects moving in space-time, hence producing the dynamic universe in a similar manner as the movie is displayed on the computer monitor.

We should notice, however, that the perpetual alternation of the Single Monad creates the whole space with all what it contains, and it does not itself move through the expanse of space as we may imagine. Everything in the world, including matter, space and time, do not have any persistent objective reality in themselves. Although for us they are as objective as ourselves, but with regard to the Single Monad nothing else exists. As Special Relativity predicted, space and time will form a singularity for anything travelling at the speed of light. So the Single Monad for itself is everywhere at once, encountering no time and no space, but with relation to other temporary monads it looks moving with the speed of light, due to the process of re-creation that is a discontinuation or interruption of existence. Motion is therefore like trying to catch up with the continuous existence of the Single Monad, so when a monad is changing more frequently it will appear moving faster than others which are changing less frequently due to their inertial mass that resists such change, whereas massless monads, during their limited lifetime, will appear moving with the same speed of the Single Monad, but they can never surpass it because it is their ultimate ontological cause.

Therefore, the SMM conceives of only two primordial states: existence and nonexistence, the spatial and temporal combination of which is what produces the multiplicity of states or monads. This means that in the real flow of time each simple monad can either have zero speed or move at the speed of light, while the apparent limited velocity of massive compound particles or objects is the average of this combination that may also change as they are re-created over the outward space and ordinary time.

Accordingly, as it is the case in Strings and Quantum Field theories, vacuum or empty space is the ground state, while other particles are various excited states, but because they are all discrete and sequential instances of the linearly progressing inner flow of time, the vacuum energy should be calculated from the average of all these states, and not their collective summation. This remarkable notion can potentially solve the vacuum catastrophe that is the huge disagreement between the value of the cosmological constant that was first measured in 1998 and the zero-point energy suggested by Quantum Field Theory [[11]]. Actually, dark matter and dark energy may also be potentially resolved in this model in which space itself is continuously being constructed in the same manner as other matter particles, so it must have its own intrinsic background mass and energy. In effect, this model brings back the concept of aether and quintessence in a novel way that does not require it to affect the speed of light or matter particles, since it is now the background space itself, and not something in the background. Moreover, this one directional and linear progression of time that is continuously creating space and its contents can also provide a straightforward explanation of entropy and the arrow of time.

4.    The Duality of Time:

According to what we have described above, there are two levels of time where at every instance of the outward normal time level, space is perpetually being constructed in a uniform chronological sequence, which forms the inward level that is also nested inside each lower dimension of space. This means that at every instance of the real flow of time there exists only one metaphysical entity, that is the Single Monad, or the Quintessence, whose chronological recurrence is constructing the three dimensions of space and what it may contain of matter particles in local curled dimensions. With regard to observers who are habitually living in the outward normal time level, this process of space construction is instantaneous, and the reason why this does not contradict any laws of physics is because it is performed by a massless metaphysical monad. Mass, energy and other physical properties, including velocity, acceleration and even the dimensions of space, are only observable on the outward level of time, as a result of the temporal coupling between at least two of those metaphysical monads.

As Niels Bohr has remarkably anticipated, the wave-particle duality is a metaphysical fact of nature [[12]]. This metaphysical fact is the Single Monad, and the essential underlying principle in this model is that no two entities can ever co-exist together in a real single instance of time, so multiplicity can only emerge by sequential production through its inner levels. This can even be proved with simple logic, as follows:

We can conceive of seven different instances of space: < up | right | front | here | down | left | back >. The observer who is at a particular instance of space, denoted as <here>, cannot realize any of the other six instances without moving through time. So, with regard to the observer, what actually exists of space at every instance of time is only <here>. Time, on the other hand, is made from three different instances: < future | now | past >. The future does not yet exist at the present moment, which is denoted by< now>, and the past has already ceased. Therefore, what exists “here” and “now” is all what exists at the moment for any particular observer, and this is not physical because it has no extension in space or time, i.e. it has no dimensions. Dimensions and other physical properties are a consequence of the recurrence of this metaphysical reality that exists alone at every single moment and is only multiplied with the flow of the inner level of time, creating space and matter which then evolves over the outer time dimension.

One possible objection to this logic is that we can actually see multiple things around us at the same single instance of time when we open our eyes. This is easily refuted because, even in thought, without any physical movement, one needs at least three moments to conceive of two different things and their possible relation to each other, but because time is extremely fast the whole picture is viewed as though it is happening in one instance. Moreover, what is actually perceived when we see multiple things is light, as the image of those physical things, and not the physical things themselves, and according to Relativity: light does not encounter time or distance; that is why the image of multiple things reach the observer at once even though they are created at different instances with relation to each other.

We must stress, however, that this model does not deny the objectivity of physical things, but it concludes that they are produced by the sequential multiplication over the inner dimension of time. Being part of this physical multiplicity that we describe as the universe, the other parts are as objective as ourselves, but we cannot conceive of them without the flow of time. The universe becomes nonobjective only if we suppose we are watching form outside.

In addition to the previous computer monitor analogy, as another illustration of this instantaneous creation of space, and to illustrate the complementarity between the apparent discrete and continuous properties of multiplicity and how do they emerge from the single metaphysical oneness, we can think of the continuous revolution of the Earth that creates days, months and years; so locally time looks continuous but it is divided globally into days and other discrete periods that are defined only with relation to other celestial objects. If we suppose that we are inside the Earth without knowing how it is moving in space, as we are now inside the universe without realizing its dynamics, we would only encounter continuous existence and continuous flow of time. But if we suppose we are watching the Earth from somewhere far away, with a constant source of light shining on it while it is revolving, we would only see its fluctuation between day and night, which will be interpreted as existence-nonexistence. Now if we suppose many such spheres close to each other and extending infinitely in space, they will appear popping in and out of existence at various intervening time durations. Especially when the variations are extremely fast, the total picture will form some varying patterns that we will describe as a dynamic universe, while in fact they are all created from the superposition of the only two primary states of day and night that are perpetually recurring on these revolving spheres.

Therefore, the universe is always coming to be in “zero time”, and its points are sequentially fluctuating between existence and nonexistence, which means that the actual instantaneous speed of each metaphysical point in space can only change from  to , and vice versa. This instantaneous change of speed does not contradict the laws of physics, and it is the usual process that is encountered by the photons of light and other massless particles on the normal outward level of time. Hence, this model of continuous construction extends this process onto all other massive particles and objects, but on the inner primary level of time where each point is still massless because it is metaphysical, while “space” and “mass” and other physical properties are actually generated from the temporal coupling of these metaphysical points, which is exhibited on the outward level of time.

Accordingly, normal limited velocities of massive physical particles are a result of the spatial and temporal superposition of the various dual states velocities () of their individual points . Individually, each point is massless and it is either at rest or moving at the speed of light, but collectively they have some non-zero inertial mass , energy , and limited total velocity .

Consequently, 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, i.e. motion occurs as a result of change and not transmutation, so the observed objects are always at rest in the different positions that they appear in. This is the same conclusion of the Moving Arrow argument in Zeno’s paradox, which Bertrand Russell described as: “It is never moving, but in some miraculous way the change of position has to occur between the instants, that is to say, not at any time whatever” [[13]].

5.    Locality and the Speed of Light Limit:

It is quite obvious from the above description of the inward level of time that there is a terminal cosmological velocity, which is effectively the speed of space construction or the refresh rate of re-creation. This gives rise to Relativity, while also allowing almost-instantaneous nonlocal physical change, and not only transfer of information, because there is no real continuous motion, but it is re-creation in the new place which could be at the other end of the Universe right in the following instance, as it usually happens with the two entangled EPR particles, or in quantum tunneling.

On the other hand, because the re-creation does not deliver any new contents; rather, it only may change some of the different states of existing space and matter, this means that the whole universe is like a global manifold standing wave, or a closed system of quantized excitations, where any perturbation at a particular location will cause subsequent coherent synchronization in other locations. This is usually expressed through the laws of conservation, of energy and momentum for example, that are normally applied only in local or connected space-time. With this novel view of re-creation, the conservation laws can be applied in any isolated system, but the isolation is not necessarily by direct connected spatial proximity, but by spatial and temporal entanglement. This also means that causality itself can now be logically explained in a way that is not directly related to space or even time; i.e. it allows non-local and even non-temporal interactions.

Naturally, the constituents of solid objects are closely entangled, so in ordinary macroscopic situations, the perturbation causes gradual or smooth, but still discrete, motion or change; because of the vast number of neighboring points, so the effect of any perturbation will be limited to adjacent particles and will decease very quickly after short distance, when energy is consumed. This kind of apparent motion is limited by the speed of light, because the change appears to be propagating through continuous space.

In the special case when a small closed system is isolated as a small part of the universe, and this isolation is not necessarily local spatial isolation, as it is the case of the two entangled particles in the EPR, then the effect of any perturbation will appear almost-instantaneous because it will be transferred only through a small number of points, irrespective of their positions in space, or through time. Furthermore, when the observer or gauge is part of such a small closed system, it will have a significant effect on determining the state into which the wave-function of this system will collapse. In normal macroscopic situations, the effect of the observer is not noticeable for the very same reason that enforces the speed of light limit, i.e. it is dissipated over a large number of points that are normally locally isolated. So in the macroscopic situations the effect of the observer or measurement will be limited only through physical forces, but in small isolated or entangled systems consciousness may have a considerable effect on the outcome of the collapse of wave function.

6.    References:

 [1] Michelson, Albert A.; Morley, Edward W. (1887). "On the Relative Motion of the Earth and the Luminiferous Ether". American Journal of Science. 34: 333–345. doi:10.2475/ajs.s3-34.203.333.