Stock Market is a Random Walk

My opponent presents strong arguments the Heisenberg Uncertainty Principle is non-deterministic but not random. However, the mathematics show that the Uncertainty Principle is derived from the random walk. I argue that it is therefore completely random. Probability density arises when we consider a slight modification of the random walk. Suppose that in addition to random choice of direction for each step (this is basically the random walk), the length of each step is also varied in an unpredictable way (in some sense, even more random than the random walk). If we call the length of a step S, then S may have any value at all, but most often will be near 1. We shall let = 1. When this is the case, the probability that distance D will be any value after N steps will always be 0. The probability is zero that D will be any particular value, since there is no chance at all that the sum of the backward steps (of varying lengths) would exactly equal the sum of forward steps. Now, to obtain the function for probability density, we ask not what the probability is of finding a particular value for D, but instead ask what is the probability of obtaining D near some value. We define P(x, delta x) as the probability that D will lie in the interval delta x located at x. We expect for small delta x the chance of D landing in the interval is proportional to delta x, the width of the interval. As a result, we can write P(x, delta x) = p(x)(delta x) The function p(x) is the probability density. So, when my opponent says the Uncertainty principle has nothing to do with randomness, he is actually wrong since probability density is derived from the random walk. Probability density does not guarantee predictability. And, as the equation I found in my first argument shows, the Uncertainty principle is derived from probability density for a particle's location. This result demonstrates that everything -- EVERYTHING -- is completely random. My opponent argues that quantum effects are irrelevant on the classical level. He raises the concept of a correspondence limit to argue that quantum mechanics reproduces physics in the limit of large quantum numbers. The problem with this argument is that the "correspondence principle" or correspondence limit is arbitrary. In other words, a correspondence limit arbitrarily limits the operators that correspond to physical quantities or measurements such that they reproduce classical mechanics. As my opponent himself states, it requires a limit of large quantum numbers. This limit is theoretical and arbitrary in that it is neither necessary nor wholly accurate. Also, another problem with my opponent's argument is that classical mechanics are inaccurate. They are an approximation of the behavior of the physical world. As a result, they are not applicable as any prediction with them will necessarily be inaccurate. It will never be a prediction because a prediction is something that is accurate and based off of theories that do model the physical world accurately. My opponent also argues that we do not experience quantum effects in our world. This is not true. We may not notice or be aware of quantum effects, but we do experience them. As evidence that we do experience quantum effects in our world, I present the findings of Andrew Cleland and colleagues of the University of California, Santa Barbara. In a remarkable finding, they showed quantum effects in a visible object. I present below the abstract of the article in which this finding was published: "Quantum mechanics provides a highly accurate description of a wide variety of physical systems. However, a demonstration that quantum mechanics applies equally to macroscopic mechanical systems has been a long-standing challenge, hindered by the difficulty of cooling a mechanical mode to its quantum ground state. The temperatures required are typically far below those attainable with standard cryogenic methods, so significant effort has been devoted to developing alternative cooling techniques. Once in the ground state, quantum-limited measurements must then be demonstrated. Here, using conventional cryogenic refrigeration, we show that we can cool a mechanical mode to its quantum ground state by using a microwave-frequency mechanical oscillator—a ‘quantum drum'—coupled to a quantum bit, which is used to measure the quantum state of the resonator. We further show that we can controllably create single quantum excitations (phonons) in the resonator, thus taking the first steps to complete quantum control of a mechanical system." http://www.nature.com... This experiment was able to show a strip of medal in a state of superposition. In other words, it occupied two places at once. This experiment demonstrates the reality that quantum effects do affect our world. We just do not notice them. Vote Pro, as I have shown quantum effects to be derived from the random walk and therefore be random. I have also shown that quantum effects do exist in our world.