The conceptual conflict between the Quantum and Relativity theories is the modern version of the recurring ancient philosophical competition between the continuum and discrete views of matter. The problem is that these two contrasting views are mutually exclusive, yet each one alone is not capable of describing the whole reality.
Therefore, 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.
This book explains how “space” is continuously being constructed by the Single Monad that is the Heart of the Cosmos. 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 its fine structure is not only “quantized” but literally “digital”.
The Single Monad Model of the Cosmos (SMM) is THE Theory of Everything, it is not by chance that traditionally one of the names of the Single Monad is "Everything". This is simply because it is the Source of all existence, and it is re-creating every entity in the universe every instance of time.
The SMM is a non-background theory that demonstrates the origination and construction of space-time. The Re-creation Principle in this model provides an innovative philosophical explanation of the constancy and invariance of the speed of light, while also allowing nonlocal quantum mechanical phenomena, without breaking the light speed limit, which makes it an essential common foundation for both Relativity and Quantum theories. Therefore, this model offers a new interpretation of Quantum Mechanics that clearly demonstrates why Relativity dominates as soon as the system becomes complex. Based on these new concepts, Einstein’s mass-energy equivalence relation is deduced directly from fundamental classical principles.
All major problems in physics and cosmology can be resolved with minor efforts based on this innovative model:
- why the speed of light is constant and invariant in all directions and all inertial reference frames?
- why the speed of light is the maximum cosmological speed limit?
- how nonlocal quantum mechanical phenomena can happen in nature without breaking the light speed limit?
- what is the real nature of the wave-particle duality?
- how the wave function collapses into the eigenstate?
- the SMM can prove the existence of the magnetic monopole and explains why it can not be observed.
- the SMM can prove the existence of the mass gap.
- the SMM can solve the vacuum catastrophe.
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 [ ]. This unexpected result initiated active research that eventually led to Special Relativity in 1905 [ ]. 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 inertial reference frame of the observer.
This constancy and invariance of the speed of light forms the main principle in the Theory of Relativity, which predicted peculiar relativistic phenomena such as time dilation and length contraction. Even though they were confirmed by many experiments and explained mathematically according to Maxwell equations and Lorenz transformations, there is yet no philosophical account that could explain the ontological reasons behind these counter intuitive phenomena. In other words: the constancy and invariance of the speed of light in all frames of reference is an axiom that has been experimentally verified, but not yet proven in any fundamental academic sense.
Traveling faster than the speed of light would violate the causality principle, and accelerating to light speed or exceeding it would also violate certain energy conditions, but such justifications are actually a result of Einstein’s main relativity principle and do not explain it in any philosophical sense. Later developments in elementary particles and field theories showed that particles move in “the Higgs field” and may interact with it. As a result of this interaction, particles acquire their mass. This explains why some particles are heavier than others, and because they do not interact at all with the Higgs field, photons have no mass and therefore they move at the fastest possible speed. This, however, does not explain why there is such a maximum speed in nature. The SMM is the only model that will give a profound ontological reason of this cosmological speed limit.
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 [ ] [ ].
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.” [ ].
In a previous research performed at Exeter University in 2005 [ , , ], we presented a pioneering study of Ibn Arabi’s eccentric conception of time and its implications for modern physics, where we proposed the Single Monad Model (SMM) and suggested some ideas for its verification. Here we want to extend this analysis to explain the ontological reasons behind the universal speed limit and how nonlocal quantum mechanical phenomena can happen instantaneously, without breaking this maximum speed!
To resolve this 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 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.
The SMM ultimately offers a new interpretation of Quantum Mechanics by describing how actually the wave function collapses into a single eigenstate and what is the role of the observer in determining this state, in addition to the aforementioned realistic illustration of nonlocal interactions. In its current formulation, the SMM does not give any direct insight of gravity but since space and time are constructed and quantized in a unique manner that has never been conceived before, it can therefore initiate new research on Quantum Gravity and set the stage for the Theory of Everything.
In addition to Relativity, Einstein also formulated the famous mass-energy equivalence relation: E=mc^2 that explains the relationship between mass and energy. This relation was originally a paradox described by Henri Poincaré [ ], but in 1905 Einstein was the first to propose that this equivalence is a consequence of the symmetries of space and time [ ]. However, no one had ever been able to derive this essential relation from fundamental principles. Einstein himself spent more than forty years trying to prove it, but he never constructed a general proof [ ]. Therefore, to support the rationality of the SMM argument, we shall give a straight mathematical deduction of this relation based on the principles of classical mechanics, in the light of the Re-creation Principle.
To establish the hypothesis in this article we only need to explain the Re-Creation Principle which is the main principle of the Single Monad Model that will also be briefly described. This model is based on solid metaphysical foundations that are beyond the scope of this article, so we shall deal with it here just as a pure hypothetical postulate and then demonstrate its astounding conclusions. Nevertheless, a succinct introduction to the philosophical principles of the SMM is imperative and will be given next. But a more detailed discussion and elaboration can be found in the previous references [7, 8, 18].
The Single Monad Model:
The conceptual conflict between the Quantum and Relativity theories is in fact a modern version of the recurring ancient philosophical competition between the continuum and discrete views of matter. The problem is that these two contrasting views are mutually exclusive, so they cannot be applied together in the same domain. Yet each one alone is not capable of describing the whole reality. This was first manifested very clearly in the wave-particle duality nature of light, which eventually lead to Quantum Mechanics, because in Newtonian Mechanics and Relativity the classical view of particles as points or spheres localized in space becomes inadequate on the microscopic scale.
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. 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 Albert 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" [ ].
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” [ ].
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”.
The idea of the oneness of the ultimate reality of nature is not new. It can be traced in many ancient philosophies. Parmenides, who is the founder of the Eleatic school of philosophy, distinguishes between the reality of the unity of nature and its unreal variety or multiplicity [ ]. He describes his two-ways view of reality: “the way of truth” and “the way of opinion”, that in the way of truth reality is one and unchanging, and existence is timeless and uniform, unlike what we normally observe in the world of appearances where our sensory faculties lead to conceptions which are false and deceitful, hence the second view.
Parmenides had an immense influence on Plato, who named a dialogue after his name, and always spoke of him with veneration. In effect, Parmenides’ monistic views were deeply characterized in the whole history of Western philosophy, and he is often seen as its grandfather. In “Nature and the Greeks”, Erwin Schrödinger identified Parmenides’ monad of “the way of truth” as being the conscious self [ ], which was an important part of the development of Quantum Mechanics in the twentieth century.
However, Parmenides was not able to convince other prominent philosophers, such as Socrates and Aristotle, so his student Zeno tried again by reformulating the same argument in terms of what to become known as Zeno’s paradoxes, that can be considered the first thought experiments in which he demonstrated the deficiency of both the discrete and continuum views. Zeno basically showed that both views will inevitably lead to infinity problems, which was in fact the main motivation that eventually lead to the development of calculus by both Isaac Newton and Gottfried Leibniz in the 17th century.
Calculus and other modern theories in mathematics were very successful in describing the phenomena of nature, but they could only do that by applying various kinds of approximations which normally work very well in most situations, but may produce terrible errors in situations which include singularities or infinities. For example, in calculating the instantaneous velocity or acceleration we must use derivation or integration which can only be applied in the case of infinitesimally continuous change. This condition is fulfilled in almost all practical situations, but the reality is different.
Newton, therefore, became most famous for his pioneering work on gravity, that he published in the Principia in 1687, with encouragement and financial help from Edmond Halley. In this work, Newton stated the three universal laws of motion, laying the foundation for Classical Mechanics, that is essentially built on the concept of an absolute and continuous space and time. Leibniz, on the other hand, was most known for his theory of monads, that he exposited in Monadologie [ ]. According to Leibniz, monads are elementary particles that can also be compared to the corpuscles of the Mechanical Philosophy lead by René Descartes [ ].
Unfortunately, Descartes and Leibniz theory of monads had not received adequate attention, unlike Newton’s Mechanics which quickly found many industrial and practical applications, and was eventually developed by Einstein into the Theory of Relativity. Although, in essence, had it been given similar consideration, Quantum Mechanics would have been a natural successor of monadology. It is only because of this historical break that Quantum Mechanics came out with new terminology, and physicists had to wait many decades after the beginning of Quantum Mechanics until the Standard Model of the Quantum Field Theory established the fact that elementary particles are the quanta of field excitations, which are nothing but the monads as we shall see below.
Monadology, or emanation cosmology, is based on the Greek philosophy, that they inherited from the Babylonians, and it was later first expounded by the Asharites and developed further by some later scholars such as Alpharabius, Avicenna, and Averroes . Nevertheless, Ibn Arabi was the only scholar who was able to use these concepts to formulate a unique cosmological model that is capable of explaining many physical phenomena, although his work on this subject is extremely scattered and remained undiscovered until it was collected and analyzed recently in the Single Monad Model .
In order to explain the relation between oneness and multiplicity, the SMM endorses two types of time, or two levels of presence. On the primary level, the continuous globular revolution of the Single Monad produces the individual monads that are spread over space as temporary excitations in the vacuum field. Then, on the secondary outward level, this whole presence will be perceived as an instance of time that contains one frame of space. The dynamic universe is then the succession of these temporal frames. We are normally not aware of the primary level of presence, because interactions, as phenomena of multiplicity, occur only on the secondary level.
Therefore, understanding the real flow of time is the key to resolve this dilemma of oneness-multiplicity duality which keeps manifesting in science in different ways, such as: particle-wave, mass-energy, discrete-continuous, finite-infinite, etc. This real flow of time is realized through the complex intertwining between the primary and secondary types of time. Although we shall not need to explain this complex intertwining in this paper, but it can be shown that this innovative concept is the only way to demonstrate the construction of space-time in a manner that allows us to “calculate” the theoretical value of the speed of light from the first fundamental principles, and then it will be truly dimensionless constant because initially the motion that created the extension of space is the same motion that created the impression of time, but the distinction between them happens only because they are perceived on the above two different levels of presence, otherwise existence is a linear progression of events that are consequently spread over space and time.
Furthermore, we shall see that the SMM allows only two primordial states: existence and nonexistence, or motion and rest. Absolute existence moves at the speed of light, and nonexistence is at rest, while the limited velocities that we normally encounter are due to the superposition of these two primary states that each monad can have, as we shall explain shortly below. In this way, the universe is literally a digital computer, that combines these two states of zero and one in various manners in order to produce the multiplicity of natural phenomena of motion and change.
Although this SMM might look extravagantly philosophical or metaphysical, the purpose of this article is to provide strong experimental justifications and suggest some possible methods to test its consistency and credibility.
In summary, the SMM consists of three complementary hypotheses:
The Single Monad: There is only one Single Monad that can be described by real continuous existence at any given instance of the real flow of time. Multiplicity is then created by the successive projection of this Single Monad that revolves in seven distinctive movements where the first six will manifest the six directions, or three dimensions, of space, while the seventh movement is resetting back in order to start a new instance. The Single Monad is a compound but indivisible reality, that is essentially composed of the “Greatest Element”, or the Quintessence, that is the ultimate simple substance of existence. The structure of the Single Monad and its relation with the Greatest Element will not be discussed further in this paper.
The Re-creation Principle: Each individual monad ceases to exist intrinsically right after the instance of its creation, and then it is re-created again in a different state, which causes the phenomena of motion and change.
The Actual Flow of Time: Since the Single Monad performs seven distinctive revolutions in order to create each point of space, and because of the sequential re-creation process, there will be two intertwining levels of time: on the first primary level one frame of space is created that will then make only one instance of the outward flow that is the second level that we normally encounter. These two levels of time are intertwined in a complex manner but this will not be discussed further in this paper.
Therefore, the purpose of this paper is to show that the Re-creation Principle, as an independent postulate, is enough to explain and combine the foundations of Relativity and Quantum theories, and solve major conflicts between them. Therefore, we will only need to concentrate on the Re-creation Principle, without discussing the structure of the Single Monad or the complex intertwining between the two levels of time. There will be some detailed philosophical analysis because we are introducing completely new concepts that have not been discussed or formulated before. A mathematical formulation of these concepts will be the subject of a forthcoming paper.
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” [see section: 4 below], 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.
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 [as described in section 9 further below], 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.
The observed world is nothing but the temporal excitations of the individual monads that are perpetually re-created in series, one by one, by the only one Single Monad, that alone can be described as having real continuous existence, while the existence of the multiplicity of individual monads is discrete, because it is a collection of instances of the continuous existence of the Single Monad. In this innovative view: oneness and multiplicity, discreetness and continuity, matter and energy, waves and particles, or, Quantum and Relativity theories: are two complementary phenomena of the same unique single reality that is multiplied and revealed over space-time. Both waves and particles are phenomena of this same unique reality, but particles are the spatial distribution of the temporary monads, and waves are their temporal progression. For this reason, particles are always associated with a wave function that describes their spatial probability and evolution in time, but only when detected or measured they will act as particles in defined positions.
On the other hand, individual monads do not have to be identical, rather, the elementary particles are themselves various kinds of monads, so we can call them Elementary Monads. Furthermore, the SMM even provides various insights of the types and number of these Elementary Monads, in full agreement with the Standard Model of Quantum Field Theory, but this also will not be discussed in this article.
However, we should notice 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 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 except itself. 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.
Accordingly, “rest” corresponds to void, or nonexistence, that is the background abstract “field”, or the ground state of an abstract “string”, and all individual monads are temporal excitations perpetually being re-created by the Single Monad in this field or string. Now again the SMM provides various intricate perceptions of the properties of this abstract field, but also we will not need to discuss that in this introductory article.
Furthermore, one of the striking conclusions of the SMM is the fact that it 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 [see section 4 below] 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. This novel view of the reality of motion can provide the ultimate mathematical proof for this model, because it can be used to deduce the famous equation: E=mc^2, based only on the fundamental principles of classical mechanics. This will be discussed in detail in section 8 below.
Therefore, when a monad emerges out of void, it always moves with the speed of light, i.e. the actual instantaneous speed can only change from v=0 that corresponds to void or nonexistence, to v=c that corresponds to existence, and vice versa; in the real flow of time there can be no continuous change in speed, because this necessarily implies endurance and permanent multiplicity on the highest ontological level that is reserved only for the Single Monad. The essential concept of the SMM is that no two entities can ever exist together, so multiplicity can only occur by reproduction through time. For this reason, the individual monads are always fluctuating between existence and nonexistence, as a result of the perpetual re-creation. This re-creation changes the states of some individual monads; so monads which change more frequently will appear faster than those which change less often, simply because the latter will spend more instances of rest.
However, monads which have been excited into existence, i.e. into the speed of light, cannot stay in this excited state forever, but also they never return back into complete nonexistence, so they keep fluctuating between these two primary states. Monads which remain long time without new excitation will slowly damp into the void but they will not completely disappear. This inactive or low energy state is the state of vacuum that is distinguished from abstract void that is the absolute nonexistence.
Just as the continuous existence is attributed to one Single Monad, vacuum is then also “one” changeless monad, the vacuum Monad, that still has a potential to be re-created, or excited, while void is absolutely changeless. This crucial concept can potentially solve the vacuum catastrophe which is the huge discrepancy between the quantum zero-point energy of vacuum that can be calculated in Quantum Field theories, and the small measured value of the cosmological constant Λ that is also expected according to General Relativity.
For example, a massless simple monad, such as the photon, during its lifetime, changes as often as the Single Monad itself, so its speed will be v=c, as far as it is moving in relation to complete vacuum, until it is absorbed or decomposed into pairs, which means that it falls back into vacuum, hence its energy will be converted into other monads because this “falling” excites the ground state of the vacuum field, and the new generated monad(s) are those excitations themselves. Conversely, when the state of existence of a monad is interrupted more frequently, it will be closer to vacuum, so it gains inertial mass which is a reflection of its resistance against continuous existence, in which case it will appear moving slowly, so its velocity will be: v<c, but this is the average quantized velocity of its instantaneous dual-state velocity that is either the speed of light or zero. For large objects that are composed of a large number of such massive monads that will eventually form complex particles and atoms, the apparent velocity could be very close to zero, but absolute zero velocity is only attributed to the Vacuum Monad.