This is my final paper for my Paradox class, (in three parts). It discusses the ideas on motion. What is motion? Is there motion at all?, etc. It discusses Zeno, who postulated that there is no such thing as Motion. Enjoy.
*References on request
In Zeno's paradox of motion, which he states that there is no motion, he gives an example of an arrow being shot, indicating that from the time the arrow is released to the point in which it hits its target, (let's say a tree) there is no actual motion that takes place. Zeno pictures an arrow in flight and considers it frozen at a single point in time. He argues that at that instant it is stationary, and because it is stationary at that moment it is stationary at all moments in time. Therefore, there is no motion.
The argument is as follows: (1) when the arrow is in a place just its own size, it's at rest; (2) at every moment of its flight, the arrow is in a place just its own size; (3) therefore, at every moment of its flight, the arrow is at rest. (Aristotle 239B5-7) Our understanding of reality and the now rests on Zeno's conceptualization of motion.
“For when does the arrow move otherwise if not in the now? If it is only over a period as a whole that it can move, motion is not a real phenomenon, since reality is enclosed in the now, that is, in each of the nows separately. Conversely, if the arrow does not move in the now, it does not really move over a period either. ” (Hasper 13)
Our understanding of time and space can be greatly effected and has been widely discussed because of Zeno's arrow paradox, making it a very important and interesting topic, even today.
There are many theories, experiments and debate still today, regarding this paradox. These differing opinions argue at even a quantum scale and reach from the quantum to consciousness and experience. Zeno's paradox has brought about a great number of speculation as to what motion really is, if anything at all.
I will be focusing on two views discussing the issue: the first, the Quantum Zeno Effect, or the notion that at a quantum level there is no motion, supporting the ancient philosophers idea's of a lack of motion in all objects. The second stance will be discussing ways in which we can see that in any instance the arrow is in fact moving. Finally, after discussing the above views, I will give my own thoughts on the matter, discussing the belief that through human consciousness and observation we see objects moving through space, therefore supporting the belief that there is motion, going against Zeno's paradox.
The Quantum Zeno Effect The concept of motion is hard to define, in fact, in regards to Zeno's argument saying what is wrong exactly can be difficult because by theory we can disprove the idea of motion, or that is to say, by theories in quantum mechanics we are able to see that objects move like pictures move in a 64 bit game—there is no motion, only changing of pixels to give the illusion of motion. Another example can be given with a movie reel: the human eye can comprehend, on average 24 frames per second, however we cannot see the black between each of the frames that slide through during a movie. When you look at the individual frames you see only frozen moments. Quantum mechanics has show that this is how motion acts at the quantum level and is called the Quantum Zeno Effect.
“The quantum Zeno effect is the inhibition of transitions between quantum states by frequent measurements of the state. The inhibition arises because the measurement causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state.” (Wayne, et al 5168)
This is the general idea behind the quantum Zeno effect. That an object moving through time, in quantum states, does not in fact move, but rather shifts between each collapsing wave function.
“Tobias Dantzig, the twentieth-century author of several popular books on mathematics, put it beautifully: 'When we see a ball in flight we perceive the motion as a whole and not as a succession of infinitesimal jumps. But neither is a mathematical line the true, or even the fair, representation of a wire.'” (Mazur 35) He, by example, shows that although we cannot see the jumps that are being made at a quantum level to give the illusion of motion does not mean that there is in fact motion. We cannot make assumptions through mere physical observation alone on physical examples of motion. That is to say that what the naked eye sees does not prove or indicate what is actually, physically, taking place.
Rather, by direct experiment and mathematics it seems as though we can prove motion does not exist. I find this troubling as Quantum Mechanics is quickly overtaking classical physics and in this it is evident that what we discover in quantum mechanics must be right, (or very near the truth). However there are other methods of measuring or observing motion other than at a quantum level and still yet a scientific level.
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