The intent of this brief article is to answer the logical question, “What sort of mathematics could be used to explain how non-locality (entanglement) happens?” The interest here is that, although physicists agree that entanglement is a real phenomenon, thus far no physical or mathematical explanations of this phenomenon have been put forward. The present article takes a logical meta-mathematical approach searching for a plausible explanation. A Moebius topology is used to describe the relationship between matter and anti-matter, thereby pointing to an explanation of non-locality. What are the physical implications of this topology? How would it show up in the laboratory?
The intent of this brief article is to answer the logical question, “What sort of mathematics could be used to explain how non-locality (entanglement) happens?” The interest here is that, although physicists agree that entanglement is a real phenomenon, thus far no physical or mathematical explanations of this phenomenon have been put forward. The present article takes a logical meta-mathematical approach searching for a plausible explanation. A Moebius topology is used to describe the relationship between matter and anti-matter, thereby pointing to an explanation of non-locality. What are the physical implications of this topology? How would it show up in the laboratory?
The theory of Quantum Mechanics is one of the mainstay of modern physics, a well-established mathematical clockwork whose strength and accuracy in predictions are currently experienced in worldwide research laboratories. As a matter of fact, Quantum Mechanics laid the groundwork of a rich variety of studies ranging from solid state physics to cosmology, from bio-physics to particle physics. The up-to-date ability of manipulating single quantum states is paving the way for emergent quantum technologies as quantum information and computation, quantum communication, quantum metrology and quantum imaging. In spite of the impressive matemathical capacity, a long-standing debate is even revolving around the foundational axioms of this theory, the main bones of content being the non-local effects of entangled states, the wave function collapse and the concept of measurement in Quantum Mechanics, the macro-objectivation problem (the transition from a microscopic probabilistic world to a macroscopic deterministic world described by classical mechanics). Problems that, beyond their fundamental interest in basic science, now also concern the impact of these developing technologies. Without claiming to be complete, this article provides in outline the living matter concerning some of these problems, the implications of which extend deeply on the connection between entanglement and space-time structure.
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth" of the mathematical formalism of quantum mechanics and then proceed to investigate the theory's implications for the physical world. One of the outcomes has been endless discussions of the quantum measurement problem, wave/particle duality, the non-locality of entangled quantum states, Schroedinger's cat, and other philosophical conundrums. In this essay, I take the point of view that quantum mechanics is a mathematical model, a human invention, and rather than pondering what the theory implies about our world, I consider the transposed question: what is it about our world that leads us to a quantum mechanical model of it? One consequence is the realization that discrete quanta, the quantum of action in particular, leads to the wave nature and statistical behavior of matter rather than the other way around.
The article demonstrates how the properties of the quantum world can be noncontradictory explained without using mathematical apparatus. They are generally considered incompatible with the logic of classical macroscopic physics. Indeed, wave-particle duality, magnetic pulses, negative energy, non-locality, entanglement, and other phenomena are not fit into the usual picture of the world. However, just one assumption provides the key to understanding most quantum paradoxes. If we assume that there is real and equal forward and backward in time movement in the microcosm, then we can find a simple explanation that is compatible with the principles of causality, conservation and symmetry.
Quantum entanglement, a bizarre phenomenon where particles become linked regardless of distance, has captivated physicists and philosophers alike. This research delves into the potential of quantum entanglement to fundamentally alter our understanding of topological structures, exploring its implications for the study of quantum systems. We propose a novel approach – a non-linear topological structure analysis method – leveraging entanglement to model and understand the dynamic evolution of topological systems. Our core claim is that entanglement can lead to previously unforeseen topological structures, offering a pathway to new theoretical insights.
Abstract Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive interpretation: quantum entanglement of subsystems means that there are “strings” connecting them. More generally, an entangled state, or similarly, the density matrix of a mixed state, can be represented by cobordisms of topological spaces. Using a formal mathematical definition of TQFT we construct basic examples of entangled states and compute their von Neumann entropy.
Planck's constant h is considered to be a fundamental Universal constant of Physics. And although we can experimentally determine its value to great precision, the reason for its existence and what it really means is still a mystery. Quantum Mechanics has adapted it in its mathematical formalism, as it also has the Quantum Hypothesis. But QM does not explain its meaning or prove its existence. Why does the Universe need h and energy quanta? Why does the mathematical formalism of QM so accurately reflect physical phenomena and predict these with great precision? Ask any physicists and uniformly the answer is that's how the Universe works. The units of h are in energy-time and the conventional interpretation of h is as a quantum of action. But in this brief note we take a different view. We interpret h as the minimal accumulation of energy that can be manifested in our measurements. Certainly the units of h agree with such interpretation. Based on this we provide a plausible explanation for the existence of Planck's constant, what it means and how it comes about. We show that the existence of Planck's constant is not so much dictated by the Universe but rather by Mathematics and the inner consistence and calibrations of Physics.