Archive for January, 2010

Determinism would seem to be seriously challenged by quantum theory, which has proved randomness in as far as quantum events are concerned. This is however rejected by determinative thinkers who hold that determinism still holds at the macroscopic level.

Thus a determinism adherent would hold for example that if we could have a sort of supercomputer, he would be able to predict every bubble in a wave or every toss of a coin.

So a determinism adherent would say that in a macroscopic case, say a billiard ball hitting the side of the table and bouncing back, we could predict exactly by knowing the angle at which the ball hits the table and its initial velocity, the resultant angle and velocity after hitting the table.

But is this so? In fact, this is not really true and randomness still enters the picture. The path of the ball is not in fact totally predictable but has random fluctuations in its path, but these fluctuations are of a quantum proportion and therefore are not measured in macroscopic measurements.

If we take the toss of a coin for example (ignoring for the moment the question of whether the toss is actually random or not as it is not relevant right now), we can see that we get a probability factor of 50-50. It is because the toss is random that we get this probability. If we get two heads in a row for example, it does not mean that the third throw has a higher chance of turning up tails, the chances for it are still 50-50. however, because it is random and the chances of both are equal, in a large amount of throws, the two cancel each other and we get this 50-50 probability. If we throw it a hundred times, we have a good chance of getting a 50-50 result or a 49-51 result, we would not expect a 45-55 result. If we throw it a thousand times, we would get even less fluctuations proportionate to the number of throws, for example, say, 495-505. the fluctuation of 5 would be significant in 100 throws but of much less significance when compared with a thousand throws. Similarly, if we throw a million or a billion times, the fluctuations would be even further dampened compared to the total overall throws.

A chance observer presented with the results of only a billion throws at a time and not individual throws would say that there is a determinism which dictates that the coin would fall equally on both sides each time. He might be tempted to say that, if a coin shows head at one throw, it is virtually certain that the next throw would show tails. But of course he would be wrong, there is no determinism here, it is a pseudo-determinism based on randomness at its heart.

Similarly, we can consider a giant insurance company. Some peple would die early and some would die late, but most people would die around a certain age, and a mean age can be calculated, say 72 years. A manager in such a company can make his calculations for his offers taking the age of 72 and would be correct. But based on this, no man can remain sanguine that he would die at 72 and no other age.

Such processes where the overall result can be predicted on the basis of probability even though the individual processes are random are called stochastic processes.

Now, we can take take the case of a billiard ball. We know that the surfaces of both the billiard ball and the side rails of the table edge are in fact composed of billions of atoms with their electrons. Now, according to quantum theory, the electrons are not at a fixed position but can appear randomly at certain points when they interact with other electrons. So when it is considered at the level of quantum events, there is no predictable outcome, instead we can predict a number of outcomes and give their probability. So when the electrons of the billiard ball hit the electrons of the side rails of the table, there are in fact a huge number of random events taking place. But the randomicity adds up, as in the case of an insurance company or the toss of a coin, to give a path which is weighed heavily in favor of the most probable path and which is the macroscopic path of the ball.

But here, the most important point is that there are still random fluctuations in the path. Despite the ball going in the most probable path, the elements of randomicity would not usually add up perfectly and so there are always random fluctuations in the path. This is similar to the event of throwing, say, a million tosses of the coin. We would not expect always an exact 500,000-500,000 heads or tails, and there is bound to be a minor fluctuation of say,10 or 20 throws or even a bit more on either side. So also in the case of the ball, there is a minor fluctuation in the path and it does not follow strictly the laws of macroscopic mechanics, there is always a strong likelihood of deviations from the path. These deviations, moreover, are derived from the deviations of the electrons in their path and (more…)

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