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This is a world-class physics question. Albert Einstein was very interested in this question, and it was the issue of randomness implicit in quantum mechanics that kept him from ever accepting quantum mechanics, he is quoted as saying, “God does not play dice.” [In fact, there are all kinds of Einstein quotes about God. He said once that he was trying to determine if God had any choice in how he made the universe, and another time he said, “God is subtle, but not malicious.” At one physics conference Einstein spouted another of these God aphorisms and one of his colleagues shot back, “Stop telling God what to do!”] We now are certain that any new physics that is discovered in the years to come will have to be consistent with quantum mechanics, so the randomness seems to be here to stay. I am drawing heavily from “The Feynman Lectures on Physics” in this answer. I’ll be talking a lot about quantum mechanics so I need to say a word about what it is. Under most circumstances, when we look at objects that are reasonably big, we do not need to invoke quantum mechanics to accurately predict the object’s behavior. For instance, the motion of a baseball, or an airplane, or a red blood cell, can all be described very accurately by classical physics. When you start to look at things that are about one billionth of a meter or smaller, which is the size of atoms and small molecules, we find that classical physics is at a loss to predict much of anything. So it is mainly when we consider things that are very small, such as atoms and their inner workings, that we need to come up with a new physics, which is known as quantum mechanics. Your question about radioactive decay is a problem that can only be treated on a fundamental level by quantum mechanics. [It is an oversimplification that quantum mechanics only shows up at the atomic level, and it is possible to find situations where quantum mechanics “shows through” into our classical world. For instance, lasers owe their existence to one of the most important principles of quantum mechanics. Similarly, superconductivity and superfluidity owe their existence to quantum effects, and they are easy to see in the laboratory on spatial scales that are large. We believe that neutron stars are very real, these are stars that are extremely massive and large by laboratory standards, and yet quantum mechanics is needed to explain their existence. So it isn’t true that quantum mechanics only takes over at small spatial scales.] Quantum mechanics had a difficult and protracted birth, with the first efforts starting around 1900 and fairly complete and accurate formulations of the theory being developed in the 1920s and the 1930s. First off, let’s talk about whether or not the laws of physics before quantum mechanics were deterministic or not. By deterministic, I mean that given accurate starting conditions of some system of particles, say, for example, the system of particles that makes up our galaxy, and knowing the laws of physics, is it possible to predict the future evolution of the positions and velocities of all these particles? If so, then the system is said to be deterministic. A random system would be one that was non deterministic. The first stunning success of Newtonian (classical) physics was Newton’s ability to apply his laws of motion and his law of universal gravitation to predict the motions of the planets and other heavenly bodies, such as comets. Newton was fortunate in that in our solar system the sun is much more massive than any of the planets, and therefore the problem of the motion of the planets nearly breaks down to a bunch of two- body problems. It turns out that if three bodies are interacting we cannot solve the equations of motion exactly, except in some special limiting cases. Newton had a terrible time trying to predict the motion of our moon accurately since both the earth and the sun interact strongly with the moon, which makes it one of the dreaded three body problems. Since we can’t solve a three body problem analytically (which means with just pencil and paper giving simple mathematical expressions that are easy to evaluate), consider how much worse it is when there are lots of interacting bodies. There is a good book written on the subject by Ivars Peterson entitled “Newton’s Clock.” I recommend it highly. Computers, in a sense, get us out of some of this problem. Even though we can’t compute solutions analytically for N body problems, we can compute the solutions to Newton’s laws of motion for N bodies interacting gravitationally with arbitrary precision. But there is a catch. It turns out that many systems that you might study have properties that lead to a very high sensitivity in their evolution to vanishingly small differences in their initial state. Consider balancing a pencil on its tip, an unstable situation. It will fall in one direction or another, eventually, but the direction it winds up falling in will depend extremely sensitively on its exact position and velocity when you let go of it, or perhaps it will depend on tiny air currents surrounding it. In many physical systems tiny differences get amplified enormously. Such systems are called chaotic. This has the operational effect that since you cannot know positions and velocities with perfect precision, after a very short while your ability to predict the system’s behavior is terrible. To explain the situation qualitatively, you might say that for every factor of 10 in precision that you improve your starting measurements you will increase the time over which you can accurately predict the system’s behavior by one second. [Don’t take the specific numbers seriously, they are just given to make the case concrete. Exponential growth of an instability holds for small perturbations in many sorts of systems.] So if you can measure to 4 decimal places, you can predict for 4 seconds, 10 decimal places worth of precision would allow you to predict accurately for 10 seconds, and so on. This is not good news, as it is not possible to go on adding precision to our measurements with ease. The most accurate physical measurement that we can make is not much more than 10 decimal places, which is pretty good but not good enough to stay ahead of an exponential growth in some instability. Therefore, since these nasty instabilities grow in lots of systems that we have studied, it means that while in theory we might be able to predict the future behavior of a complex system, in practice, we cannot. So the world was already random before quantum mechanics came along. An early pioneer in chaos theory was developing a simple model of weather and found this exquisite sensitivity to initial conditions and subtitled one of his papers “Can a butterfly in Brazil cause a tornado in Texas?” His conclusion was that it could. By the way, James Gleick wrote a very good and very readable book about chaos entitled, aptly, “Chaos.” When quantum mechanics came along, things only got worse. Now for even very simple systems we find that no matter how we prepare the system, the results have an element of randomness. We can predict very accurately, on a statistical basis, what will happen on average if we repeat an experiment millions of times, but we usually cannot say with certainty what will happen in one specific instance. You suggested that there might be an underlying layer that we don’t understand yet. If we could see to that layer, things would be deterministic again. That is a good idea, and Einstein held out hope that such a theory would prevail. Such theories are called hidden variable theories. However, none of these theories have been successful. In fact, it is believed that no hidden variable theory can be correct, and that we are stuck forever with the indeterminacy of quantum mechanics. Richard Feynman has said that no one who has thought deeply about quantum mechanics can feel comfortable with it. It is just too strange a theory, compared to how we experience the world. Perhaps if we grew up playing with quantum mechanical toys, the indeterminacy would seem right and natural to us. But in our, seemingly, cause and effect world, quantum mechanics is very strange. The test of a theory must be how well it predicts measurements we make. Einstein’s theory of relativity seemed to be very counter intuitive when it was first proposed, but it had the virtue of making very detailed predictions that check with what we see. We accept quantum mechanics because it, also, is a remarkably successful theory. In some cases, it is able to make predictions that are accurate to one part in 10 billion. Not bad. Perhaps in time we will find a deeper theory that encompasses quantum mechanics and makes more “sense” to us, and quantum mechanics will fall out of this “super” theory in a natural way. Then we might be able to see why the indeterminacy of quantum mechanics that we observe is right and natural, rather than the strange and unsettling thing that it appears to be.

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