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 other quantum events and hence are entirely random, and cannot be predicted. So in calculating the path of a billiard ball also, we cannot actually predict a single path, we can predict only multiple paths out of which the ball will take any particular path in a random manner, though we can still predict the most likely path, the second most likely path, and so on. The pertinent point though is that these paths vary by quantum fluctuations. The fluctuations are of a quantum amplitude and so on the macroscopic scale the fluctuations are totally irrelevant and in fact undetectable and we do not have to consider them at a practical level.
Hence this is not true determinism but pseudo-determinism. These are actually random events that we consider as determined events because we regard them only at a practical level and not the theoretical level.
But in theory the paths do in fact have very minute, quantum random fluctuations and so they are not determined. So determinism fails. This was well recognized by Einstein and other scientists who protested against the randomicity introduced by quantum physics. They recognized that once randomness is proved at one level, it will be true for all levels.
This point about the macroscopic path of a ball being random is not just a logical point. It is well recognized in mathematics and mechanics. The quantum fluctuations are well studied, and it is the work of Feynman which led to many breakthroughs in the study of such quantum paths.
For example, the same point which I have made is made mathematically in the following way:
“In this way, the classical trajectory is qualitatively important. In general, the region of coherence is related to the “classical” nature of the system. On the (macroscopic) classical scale, (pi-nh) is a frighteningly small amount, making the principal contributing trajectories those in a narrow band around the classical one. On the quantum scale, however, the action is small enough that (pi-nh) is enough to allow significant quantum deviations from the classical trajectory. Intuitively, this corresponds to the fundamental uncertainty in the particle’s position at any given time..”
– “Path Integrals in Quantum Mechanics”; Dennis V. Perepelitsa, MIT Department of Physics. Link
Now, in a single instance of a single ball, the quantum fluctuations are insignificant for practical purposes. But in a very large system, say a billion balls hitting each other, the quantum fluctuations would begin to have a significant effect and make the end result unpredictable and random.
Even if we have a perfect computer which could make all the calculations, it still would not be able to predict exactly the result of such a system as randomness would ensure that the results are unpredictable.
Similarly, if we take a wave crashing on the sea shore, even theoretically a perfect supercomputer would not be able to predict the results of how many bubbles are formed and their pathways because of this randomicity.
Phenomena like the toss of a coin in practice are indeterminative because they are similar to the chaos effect. This is because the slightest change in initial conditions can cause very large changes in later conditions, and also the number of factors influencing the whole thing are so complex, that the events are unpredictable. There is no way that the toss can be determined.
But it may still be argued that if the conditions were favorable, the toss could be predicted. Thus if we have a machine which can use exactly the same force each time at exactly the same angle, and the coin was thrown in vacuum, and the floor was perfectly even, then we would be able to determine the coin toss. But this is where quantum uncertainty steps in. it ensures that we could never build conditions like this. We could never ensure exactly the same force, exactly the same angle, or exactly an even floor, to the perfection that would be required to have a determinative toss. Hence the coin toss would naturally remain undetermined under any practical and theoretical conditions that we can dream up.
The above is of course a very simplified, intuitive application of quantum theory to classical mechanics. Physicists grapple with much more complex theories like the Coherence principle and quantum chaos. But the basic principles of this argument stand true.
So determinism fails at all levels. It cannot be that we have randomness at one level and determinism at another level. The determinism that we see in our practical macroscopic world is only pseudo-determinism, a practical determinism as opposed to true determinism, and finer calculations show that in fact there is randomness.
If you wish to read more on this topic, you can look up my book, The Circle of Fire- the Metaphysics of Yoga. You can also read similar articles on Quantum Physics, Mass-energy equivalence, etc. from the Articles page on my website, www.thecircleoffire.com.