Mohamed Haj Yousef

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The non-local phenomena in Quantum Mechanics, such as entanglement and tunneling, are in apparent violation of causality or the principle of Relativity, that nothing can travel faster than light. Even if the violation of Bell inequalities is only due transfer of information and not physical superluminal motion, this still means that non-local phenomena affect the fundamental structure of space-time.

In the Duality of Time Theory, because space and matter are perpetually being re-created in the inner levels of time, non-local motion, and not only transfer of information, can occur without breaking the speed of light limit, as we shall explain in chapters V and VI.

Locality and the Speed of Light

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 creation or the refresh rate of re-creation. This gives rise to Relativity because this velocity is independent of all observers, while also allowing instantaneous nonlocal physical change, and not only transfer of information, because there is no real continuous motion, but it is always 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, rather: it is by either 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 observers or measurements 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.

If the perpetual creative process of re-creation is conceptually “stopped” and taken in isolation, it will form a still picture of things around us, or a single frame of space that is created in one instance of time, as shown in Figure 5.1. In each following instance, this frame of space, with all its elements, will be re-created with possible slight changes that may occur at various positions. Therefore, the dynamic manifest Universe is the instantaneous and continuously renewed succession of these slightly changing frames. Motion, therefore, is observed because things may successively appear in different 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.

It follows, therefore, that measuring velocity as distance per time is only a macroscopic approximation that works just fine in everyday life, where the system is the whole world itself, or a significant part of it. This approximation can produce a huge error when applied on microscopic scales or when the system is very small, not in terms of volume but in terms of the number of particles even if they are largely separated in space, or even in time, i.e. when they are entangled. This is the reason why Quantum Theories are successful in this domain, while Relativity fails. Therefore, Relativity is a macroscopic approximation of Quantum Mechanics, and the opposite is not true.

In Quantum Mechanics we start with the wave function that describes the state of the whole system, and any perturbation will cause subsequent synchronization in the following instance of re-creation. Hence, nonlocal interactions can naturally happen when the system is very small, even when it is spread over different regions of space or time, because the change is limited by the conservation laws rather than distance. The effect of distance prevails in large systems because energy dissipates quickly over the large number of points when they are spatially connected, i.e. in an apparently continuous local region of space.

Therefore, microscopic isolated systems will always exhibit quantum interactions as a result of the laws of conservation. The EPR is one experiment that is able to demonstrate this nonlocal interaction in the case of two entangled particles that are spread over large distance. Another, kind of such weird quantum interaction is the single particle interference which can be explained in terms of temporal entanglement or coherence as a small isolated system that is spread over time. In both cases the effect can only be logically explained because the particles are simultaneously connected through the Single Monad that is their sole mutual source, as it is explained further in chapter VI.

In conclusion, the change is always limited by the speed of light, or the re-creation frequency. This universal constant frequency of becoming into existence is the speed of causality, and it can never be exceeded. In large systems the change occurs through smooth motion on which we can apply the laws of mechanics, i.e. velocity equals distance per time, in which case the universal frequency of re-creation is the same universal speed of light in vacuum. In small systems we can speak of frequency but not velocity, in the common sense as distance per time, because the re-creation in this case may cause nonlocal changes that are different from normal continuous motion. As an example we can consider quantum tunneling and the orbital jumping of an electron between the different energy levels in the atom, which cannot be studied in classical mechanics, i.e. we cannot speak of its velocity between the orbitals, because it does not exist “between”!

Logical Interpretation of Quantum Mechanics based on the Duality of Time Theory

The foundations of Quantum Mechanics were established during the first half of the 20th century, based on various experimental observations which confirmed that light, as well as matter, sometimes behave as spreading waves and sometimes as localized particles. Although it has been successfully applied in Quantum Mechanics, this wave-particle duality is still an ongoing conundrum in modern physics, and it is actually rooted in the ancient philosophical dispute between the continuum and discrete structure of space, or the atomic and substance theories of matter. The wave-particle duality is deeply embedded into the foundations of Quantum Mechanics, because all the information about a particle is encoded in its wave-function that evolves according to the Schroedinger equation. Even for particles with mass, this equation has solutions that follow the form of the wave equation, whose propagation leads to wave-like phenomena such as interference and diffraction.

What is even more perplexing, is that these wave phenomena are sometimes exhibited by single particles that are moving separately from each other, as in single-particle interference experiments. Feynman confirmed that such phenomena are absolutely impossible to explain in any classical way. The problem is that particles and waves are two contrasting phenomena, so they cannot describe the same thing at the same time. Einstein summarized this problem by saying: “We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.”.

Actually, the wave-particle duality is a fundamental fact of nature that cannot be explained on the level of physical multiplicity, where things are either discrete or continuous, not the two together. However, according to the Single Monad Model and the complex-time geometry that resulted from the Duality of Time postulate, discreteness and continuity are two emergent properties of the same one linear flow of time, which is perpetually re-creating objects in the inner continuous levels, as waves, and displaying them in the outer discrete level, as particles. Originally, the real flow of time is infinitesimally continuous because it is a result of the continuous revolution of the Single Monad that is perpetually re-creating the cosmos at the speed of light, but as this Single Monad “turns” from one individual state to the other, each one individual state will encounter a discrete interval of time, which is the second level that is encountered outwardly, and that is why it appears imaginary with relation to the previous level. So, on the primary level of time, space is being continuously created, and each instance of the whole space will appear as one point in the secondary level of time, that we normally encounter.

Any kind of measurement or detection necessarily means that the Single Monad at this particular instance of measurement is manifesting as the observer that is now acting on the system, and since there is only one real state, at the real flow of time, the system must necessarily collapse at this particular instance of the real time. Of course, this collapsing is not fatal, otherwise particles and objects will disappear forever, but they are re-created or excited again right after this instantaneous collapse, at which time the observer now would have moved back into an indeterminate state, and become an object amongst other objects. Therefore, uncertainty in position is inversely proportional to the number of monads that constitute the particle, and that is why small objects or particles suffer greater uncertainty. So the number of monads is actually the number of discrete states at the time of measurement with relation to a stationary observer. This number decreases as the object accelerates, because the states that are at C are indistinguishable, so the number N tends to one when velocity tends to C, in which case the momentum will be defined at M-C but the uncertainty in position becomes 100%, so all the states will overlap until they become completely indistinguishable as in the case of Bose-Einstein condensate. Inversely, when the mass tends to infinity, the number of monads tends to infinity too, and the uncertainty in position becomes zero, which describes a singularity in space-time geometry, but in that case the momentum, or energy, will be completely undefined. In any measurement the measured entity which was in the superposition state, or subject, has now collapsed into the eigenstate, or object. by the act of measurement by the observer that has just took over this instance of existence and became the subject at this very real instance of measurement.

The whole cosmos is then built on these three entities: subject-action-object, or: energy-force-matter, or: wave-operator-particle, that are three different aspects of the same reality of the Single Monad, that is the only player who is unceasingly performing these three consecutive movements whose outcome would create an individual monad that is nothing but its “shadow” which would act as an object in the next scene. The perpetual recurrence of this three-fold operation results in the accumulation of these shadows or objects that are eventually spread spatially and temporally to make the whole dynamic matter and energy in the cosmos. In total, therefore, the Single Monad performs seven primary revolutions, because each movement of the above three-fold operation consists of two states of existence-nonexistence, which in total makes the six directions or three dimensions of space, and the seventh revolution is what makes a one directional instance of the outward level of time, and this will be like resetting the instance of space to start anew. In terms of Quantum Field Theory, the first six revolutions create massive particles that becomes localized in space, which will be either the subject or the object depending on which one is current excitation, and the seventh revolution creates a massless particle that is the action or energy.

For this reason, energy is directly related to time, while mass is related to space. In other words in the inner levels of time things behave as waves, and in the outer level they become localized as physical particles, but only for the indivisible instance of time when they are observed. If we suppose the particle is composed of N individual points, or monads, each of which is an instance of the Single Monad, that is the only entity that exists in the real flow of time, then the total velocity of the particle is the time average of the velocities of all individual points, each of which is either at rest or moving at the speed of light at the particular single instance of the time of measurement. Therefore, in an object or particle of N individual points, because only one point exists in the real flow of time on the inner level of perpetual creation, the position of one of these points will be completely uncertain, because its velocity is equal to C, while the rest have been already defined, because they are now in the past, and their velocities have sequentially and abruptly collapsed from C to zero, after they have made their specific contribution to the total quantum state. When the number N is very large, as it is the case with large objects and heavy particles, the uncertainty will be very small, because only one point is completely uncertain at the real instance of time. But for small particles, such as the electron, the uncertainty could be considerably large. This uncertainty will also increase with momentum, because higher physical velocity simply means that on average more and more points are in real motion rather than rest.

This explains all the puzzling features of Quantum Mechanics, such as uncertainty, the measurement problem or the effect of observers and consciousness, as well as the reality of wave-function and its collapse; as it has been demonstrated in more detail in Chapter VI of the Duality of Time Theory.

For more information, please visit the Single Monad Model Website: http://smonad.com.

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