How Many Solutions Are There For The Equation Descreate Math The Zeno Paradoxes, Metaphysics and Modern Quantum Mechanics

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The Zeno Paradoxes, Metaphysics and Modern Quantum Mechanics

Zeno was an ancient Greek thinker whose mathematical paradoxes are more important to modern thought than one might think. He was a disciple of Parmenides of Elea, whose followers were of the school of philosophers known as the Eleatics. The Eleatics produced brilliantly insightful arguments showing how the premises of other thinkers led to contradictory conclusions and therefore could not be true.

Zeno’s paradoxes have interested mathematicians for centuries, especially with the fundamental questions about the infinite divisibility, or not, of space and time that it raises. What is the smallest unit or instant of time? Is there a smaller space unit? Is it possible to locate a mathematical point in space and time?

Tolstoy, in his War and Peace, had argued from the point of view of the common assumption that space and time are a continuum. Einstein’s theory of relativity and his efforts at a unified field theory assumed a space-time continuum, although, ironically, he was the one who built on Planck’s work with the conjecture that the electromagnetic radiation is released in quanta of energy located at points in space and which (according to Einstein) come in discrete packages and can only be absorbed and emitted as a whole. It was only after Einstein’s work that the word “quantum” and Planck’s constant (h) was used to refer to the smallest quantity in which the physical quantity exists in nature and in multiples of which it increases or decreases.

Quantum mechanics was founded in the late 1920s from a reconciliation of the interpretation of Heisenberg’s uncertainty principle and Schrodinger’s wave equation; and, since then, it has been the subject of extensive metaphysical and philosophical debate, because Quantum Mechanics raises basic philosophical questions about our universe that are of the same essential nature as those raised by Zeno’s Paradoxes.

One of Zeno’s best-known paradoxes is: Consider a race between Achilles and the tortoise. Achilles allows the tortoise an advantage because he is faster. The race begins with Achilles at point A and the tortoise at point B. When Achilles reaches point B, where the tortoise started, the tortoise has moved a little further to point C. When Achilles reaches point C, the tortoise has moved further to point D closer to C than C was to B. When Achilles reaches point D, the tortoise has moved to point E closer to near point D than D was near point C; and so to infinity so that Achilles will never catch up with the tortoise.

Zeno’s argument is more than funny, because if our assumptions about a space-time continuum were correct, it’s hard to see why Zeno’s argument shouldn’t be true! But the fact that we don’t observe this paradox in nature raises questions about our assumptions that spacetime is a continuum. The importance of Zeno’s paradox is that we had, for centuries, conceptual theoretical bases, before Planck and Einstein, to believe in the idea of ​​a quantified space-time universe. The discovery of quantum mechanics should have only confirmed our intelligent intuition of Zeno’s paradox that we live in a broken or fragmented space-time universe. The question that Zeno inadvertently raised about whether space-time is a real or apparent continuum seems to have been resolved by Quantum Physics.

Heisenberg, in a very important paper in the late 1920s, showed that if the basic assumptions of quantum mechanics were correct, it should be impossible to determine precisely the position and momentum of a particle at any given time. Some had misinterpreted his argument to mean that the experimenter cannot determine the position and momentum of the subatomic particle simply as a result of the limitations of the experimenter and the type of experimental setup he has to contend with, by necessity Physicists, however, have emphasized that the indeterminacy principle is not a consequence of the limitations of the observer, but a fundamental property of nature due to the fact of the finitude of quantum action in nature.

Around the same time as Heisenberg’s work in the 1920s, Schrodinger developed what became known as wave mechanics (as opposed to “matrix mechanics”). In his wave mechanics, he addressed the problem of developing an equation for “matter waves”. He introduced the famous Schrodinger wave equation which, according to Bohr’s Copenhagen interpretation, measures the probability that certain observable quantities will take certain values ​​at a specific location. The so-called quantum “leap” in mechanics is a probabilistic event in the sense that the movement of particles came to be seen as obeying the laws of probability.

The general philosophical implications of quantum mechanics are profound. For starters, it would seem, by Zeno’s paradox, that we live in a quantified space-time universe because we have to. There is simply no way for magnitude to increase or decrease in physical actions except by one unit, h, greater than zero. Our impression of an uninterrupted flow of transformations in space-time can be compared to the illusory appearance of an uninterrupted flow in a cartoon animation. He has not fully absorbed the implication of the comparison of a broken stream or flow in space-time to a cartoon animation until he begins to realize that our naïve materialistic notions of being, the reality and existence could, after all, be wrong.

The development of the strange world of subatomic particles in the field of quantum mechanics stretches the imagination and challenges long-held and cherished materialist philosophies. If a fundamental constituent particle of nature assumes a state of its own only when a measurement is taken, to what extent can we speak of the particle as “real” in our naive understanding of that word? What sense does it make to speak, as some do, of a distinction between the classical world of macroscopic objects, in which things are ‘real’, and the microscopic world of ‘quantum particles’, in which things are admittedly not are they” so real?”

Could phantom particles add up to ontologically substantial “things”? Why do some “theorists of mind” continue to dogmatically claim that dualistic philosophies have been consigned once and for all to the dustbin of history when physicists like Stapp, taking information from quantum mechanics, propose interactive dualistic theories subject-object that are simply sophisticated? versions of the old Berkeleyan-type idealism. Some prominent physicists, such as Wolfram and Deutsch, have even suggested that we might actually be something like conscious brains immersed in the output of a virtual reality generator.

Everett’s “many worlds” solution to the “measurement problem” was the pioneering attempt at what are now “multiverse” theories, which propose that our world is a virtual reality projection. In his original “many worlds” theory, Everett suggested that the universe might be constantly splitting into a stupendous number of branches, all the result of interactions of “measurement” and (in his view) because there is no entity outside the system that can designate which branch is the “real world” we must consider all branches to be “real”.

Multiplying variations of Young’s basic double-slit experiment (delayed choice and the quantum eraser, for example), using subatomic particles, gives us a look, from a new angle, at to a world of causality that we had never dreamed of. In the crazy world of subatomic particles, a decision could be made in the future to determine an event in the past!

In fact, there is more under the sun than we ever dreamed of in our materialistic philosophies. How far the physicists have come from the naive materialism of the 19th century world!

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