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Complex-Time Geometry and Perpetual Creation of Space

by Mohamed Haj Yousef

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3.4.4  Copenhagen Interpretation

In the years between 1925 and 1927, Bohr and his assistant Heisenberg played a critical role in establishing the theoretical and mathematical framework of Quantum Mechanics, and they generated some definite rules for interpreting its mathematical formalism, that later became known as the “Copenhagen interpretation”, although the term itself was coined by Heisenberg after more than thirty years while he was criticizing the emerging alternate interpretations that had been developed afterwards.

According to the Copenhagen interpretation, physical systems generally do not have definite properties prior to measurement, and Quantum Mechanics can only predict the probabilities that measurements will produce certain results, while the act of measurement itself is what affects the system and causes the set of probabilities to reduce to the final eigenstate. This is known as the wave-function collapse, as we shall describe it further in section 4.4.4.

The wave-function:, represents the state of the system as it evolves with time. This function encapsulates everything that can be known about that system before an observation. Furthermore, the properties of the system are subject to the principle of uncertainty, as it will be described further in section 4.4.2, which means that they cannot all be fully defined for the same system at the same time. During an observation, the system must interact with the observer or the device, which is what causes the wave-function of the systems to collapse, or irreversibly reduce to an eigenstate. The results provided by measurements are essentially classical, and should be described in ordinary physics, as it was particularly emphasized by Bohr, and accepted by Heisenberg.

Therefore, according to the Born rule, the description given by the wave-function is probabilistic. This principle was established by Max Born who devised his own interpretation that will be described in section 4.5.1. Also, according to Bohr’s complementarity principle, that will be discussed further in section 4.4.3, and because the wave-function expresses a fundamental wave-particle duality, any experiment can show either the particle-like properties, or the wave-like properties, but not both at the same time. The Copenhagen Interpretation, however, denies that the wave-function provides a directly apprehensible image of the physical reality, or anything more than a theoretical abstract concept.

Also according to the correspondence principle, which is a general rule that must be fulfilled by any new theory, when quantum numbers are large, they refer to properties which closely match those of the classical description of particles and rigid objects.

In metaphysical terms, the Copenhagen interpretation views Quantum Mechanics as providing knowledge of phenomena, but not as pointing to really existing objects, which it regarded as residues of ordinary intuition and classical physics. This makes the interpretation an epistemic theory, in contrast with Einstein’s view, that physics should look for really existing objects, as any ontic theory.

Many physicists and philosophers have objected to the Copenhagen interpretation, because:

•it is nondeterministic, •and the measurement process is undefined and it is not known how the probability functions convert into determined values by measurements.

Because of this nondeterministic approach, the Copenhagen Interpretation had been widely criticized and exposed by a number of relevant thought experiments and paradoxes, such as Schroedinger’s cat and the Einstein-Podolsky-Rosen paradox. These will be summarized in the following subsections, in addition to the various fundamental conceptions, such as the wave-function collapse, the uncertainty principle, the complementarity principle, quantum entanglement, and the observer effect. We will mention afterwards how the other interpretations tried to solve and explain these riddles and concepts in alternative manners, focusing more on the Duality of Time approach that will be elaborated further in chapter VI.

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I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever!

By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.

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Mohamed Haj Yousef

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