Zeno was an ancient Greek thinker whose mathematical paradoxes are of greater importance to modern thought than is generally believed. He was a disciple of Parmenides of Elea, whose followers belonged to the school of philosophers known as the Eleatics. The Eleatians produced brilliantly insightful arguments showing how other thinkers’ premises led to contradictory conclusions and therefore might not be true.
Zeno’s paradoxes have long interested mathematicians, 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 minimum unit of space? Is it possible to locate a mathematical point in space and time?
Tolstoy, in his War and Peace, 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 spacetime continuum, although ironically it was he who built on Planck’s work with the conjecture that 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 in their entirety. It was only after Einstein’s work that the word “quantum” and Planck’s constant (h) came to be 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 Heisenberg’s Uncertainty Principle interpretation and Schrödinger’s wave equation; and since then it has been the subject of extensive metaphysical and philosophical debate, since 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 the following: Consider a race between Achilles and the tortoise. Achilles allows the tortoise to have the advantage because he is faster. The race begins with Achilles at point A and the tortoise at point B. By the time Achilles reaches point B, where the tortoise started, the tortoise has moved a little further towards point C. By the time Achilles reaches point C, the tortoise has moved further to point D closer to C than C was to B. By the time Achilles reaches point D, the tortoise has moved to point E closer to point D than D was near point C; and so indefinitely such that Achilles will never catch up with the tortoise.
Zeno’s argument is more than amusing, since if our assumptions of a spacetime continuum were correct, then it’s hard to explain 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 significance of the Zeno Paradox is that we had had, for centuries, conceptual theoretical foundations, before Planck and Einstein, to believe in the idea of a quantized spatiotemporal universe. The discovery of quantum mechanics alone should have confirmed our clever hunch of the Zeno paradox that we live in a universe of broken or fragmented space-time. The question that Zeno unknowingly 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 would be impossible to accurately determine 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 only as a result of the experimenter’s limitations and the type of experimental setup with which, of necessity, he must deal. However, physicists have stressed that the uncertainty principle is not a consequence of the limitations of observation but a fundamental property of nature due to the fact of the finiteness of quantum action in nature.
Around the same time as Heisenberg’s work in the 1920s, Schrödinger developed what became known as wave mechanics (in contrast to “matrix mechanics”). In his wave mechanics, he addressed the problem of developing an equation for “matter waves”. He introduced the famous Schrödinger wave equation which, according to Bohr’s Copenhagen interpretation, measures the probability that certain observable quantities take on certain values at a specific location. The so-called quantum “leap” in mechanics is a probabilistic event in the sense that the motion of the particles came to be seen as obeying laws of probability.
The general philosophical implications of Quantum Mechanics are profound. To begin with, it would appear from Zeno’s paradox that we live in a quantized 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 a non-stop flow of transformations in space-time can be compared to the illusory appearance of a non-stop flow in an animated cartoon. One has not fully grasped the implication of comparing a broken stream or flow in space-time to an animated cartoon until one begins to realize that our naive materialistic notions of being, reality, and existence could, after all be wrong.
The unfolding of the strange world of subatomic particles, in the field of quantum mechanics, stretches the imagination and challenges long-entrenched and cherished materialist philosophies. If a fundamental particle constituting nature assumes a proper state 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 it is admitted that things are not? so real?”
Could ghost particles add up to ontologically substantial “things”? Why do some “theorists of mind” dogmatically continue to assert that dualistic philosophies have been consigned once and for all to the dustbin of history when physicists, like Stapp, borrowing ideas from quantum mechanics, are proposing dualistic theories? subject-object interactions that are merely dualistic? 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, in what are now “multiverse” theories, proposing that our world is a virtual reality projection. In his original “many worlds” theory, Everett suggests that the universe might be constantly dividing into a large number of branches, all the result of “measuring” interactions and (in his view) because there is no entity outside the system that can To designate which branch is the “real world”, we must consider all branches as “real”.
Multiplying variations of Young’s basic double-slit experiment (the delayed choice and the quantum eraser, for example), using subatomic particles, gives us a glimpse, from a new angle, into a world of causality we’ve never dreamed of. In the crazy world of subatomic particles, one could make a decision 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 have physicists come from the naive materialism of the 19th century world!