Indeterminism


"If we imagine an intellect which at any given moment knew all the forces that animate Nature and the mutual positions of the beings that comprise it -- if this intellect were vast enough to submit its data to analysis -- could condense into a single formula the movement of the greatest bodies of the univese ant that of the lightest atom. For such an intellect nothing could be uncertain and the future just like the past would be present before its eyes" -- Pierre-Simon Laplace (Philosophical essays on probability)


Introduction

What is the nature of chance and indeterminism? I think many people have a false image of what random chance really is. To most people everything has a cause, and something happening uncaused may seem impossible and even absurd. The determinist position is that if one could set up two cases with the exact same set of circumstances we would get exactly the same result; or as Laplace's famous quote above indicates, that the future is embraced in the present. For the determinist, indeterminism is not fundamental, but lies only in our physical limitations to acquire complete knowledge of systems; if we could rewind history back to the big bang, the universe would evolve exactly the same way it has done today.

For natural reasons such an experiment is impossible to conduct, but determinism can be investigated indirectly. If the future was imbedded in the past, no new information would be introduced in the world, for all information would be contained in previous information. In this essay I will try to show that the determinist position is wrong -- that indeterminism is a fundamental quality of nature. "Noise" in the quantum world is amplified through dynamic processes and produces genuine new information at the expense of entropy.

The butterfly effect

When meterologist Edward Lorenz in 1961 made computer simulations on weather, he discovered what, in meterology, is now called the butterfly effect (the general expression in chaos theory is "Sensitive dependence on initial conditions"). It had been known previous to that, but not considered an important principle of science. To make a shortcut in his job, Lorenz typed in values from halfways on a previous run of the computer program, and discovered that the patterns of the two runs grew further and further apart until they showed no similarity whatsoever. He soon found out that the difference was not due to any error with the computer, but because he had typed in the rounded values of the printout instead of the more precise values used by the program (Gleick, 1987).

What the experiment showed was that, in non-linear systems, small differences of the initial condition will give rise to large differences in later stages. It is called the butterfly effect because, at least theoretically, it implies that a stroke of the wing of a butterfly could be the cause a hurricane. This effect is the reason why the weather is impossible to estimate with high accuracy for more than about three days and impossible to estimate at all after the fifth day. The reason for this is that the system gets so complicated that it in a limited amount of time has an infinite amount of possible states (or in mathematical language, infinite grades of freedom). No matter how fast computers we would ever use, it would still be impossible to calculate the future states before they happened (Davies, 1987). It can be mathematically showed that it is still possible to calculate the future state, but reality works faster than the simulation so it would be a prediction in second place (Davies, 1987).

Another reason why it is impossible to calculate the future before it happens is that we would have to know the initial figures, to give the computer program, with an infinite amount of decimals -- we would have to have infinite information of the system, an impossibility unless you are omniscient -- and since humans are not omniscient it is impossible to know the exact numbers to use. First because it is theoretically impossible to store a number with infinite precision in a computer (or indeed in any physical container), secondly since it is impossible to measure them, and thirdly because you would have to know the exact position and momentum of every particle and beam of energy in the whole universe to get exact values for any other quantum of matter. This was expressed before Lorentz, by Jules Henri Poincaré in Science et methode, in 1909:

"A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we then say the effect is due to chance. If we exactly knew the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secrets for us, we could still know the situation approxiamative. If that enabled us to predict the succeeding situation with the same grade of approximation, that is all we require, and we sould say that the phenomenon had been predicted, that it is governed by the laws. But it is not always so; It may happen that small differences in the initial conditions produces very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Predictions become impossible, we stand before a random phenomenon." (Gleick, 1987)

This impredictability of non-linear systems creates information. Since each new observation is a new bit, the system is a continous source of information.

Linear systems are exceptions

The butterfly effect is common in non-linear systems, but aren't linear systems in majority? No, in school students are taught mostly about linear systems, and non-linear systems are simplified into linear systems to be soluble; but actually, in nature, linear systems are exceptions and non-linear systems are fundamental. This has made the mathematician Stanislaw Ulam remark that calling chaos nonlinear science is like calling zoology "the study of non-elephant animals" (Gleick, 1987).

Quantum fluctuation

But since it can be showed mathematically that the future of a chaotic system is determined by the present, doesn't that imply that there is determinism? Does not the new information appear deterministically? Yes, the butterfly gives rise to what is called "deterministic chaos", but once again ponder the issue of the infinite amount of decimals. To know the present with certainity one would have to know the exact position of every particle and beam of energy in the whole universe.

If we would try to do so, we would have to investigate every object in smaller and smaller scale. First we would have to investigate the molecules, and then the atoms, electrons, photons, quarks and so on down to the smallest parts. When one tries to measure the exact position and momentum of a very small particle there is a huge problem -- Heisenberg's uncertainity principle.

Werner von Heisenberg deduced in 1927 that the product of the uncertainities of position and momentum equals Planck's constant divided by 4p (about 5.273 10-35 Js) [Where, p is the greek letter Pi]. Since the mass of large objects, such as tennis balls, is so big compared to Planck's constant we never see the effects of this in daily life, but in the thermodynamic world it is a very important factor making it impossible to calculate position and momentum with any accuracy for quantum particles, since the error in some instances will be larger than the measured quantity itself. It is possible to get a good estimation of momentum at the expence of position or the other way around, but never of both at the same time. For the same reason it is impossible to estimate the total energy of an object in a finite time span.

But isn't Heisenberg's uncertainity principle only a way of saying that our instruments cannot be made with the precision necessary to measure particles this small? Isn't it so that the error rises when we interfere with the investigated object so we change its momentum and position? Again no, most physics textbooks describe it this way, but it has been showed by quantum physics that particles don't even posess a distinct momentum and position. It is the reality behind Heisenberg's uncertainity principle that gives rise to phenomena like the second law of thermodynamics and Brownian movement, because it makes particles move randomly in a "theormodynamic dance". Some events, such as radioactive decay, happen by pure chance -- uncaused. There is, of course, a cause why a radioactive atom decays since it is energetically and statistically favoured to do so, but there is no way to explain why it happens at a certain time. This seemed Albert Einstein so absurd that he exclaimed the famous words "God does not play dice".

Einstein thought that a better model than quantum physics would develop, and proposed an experiment (The EPR, or Einstein-Rosen-Podolsky experiment. See Physics and Ultimate reality (1995)) that would prove that it was a false theory. Some years after his death physicists' instruments were good enough to carry out the experiment and it turned out at Einstein's disadvantage (Davies, 1983, 1987). So all evidence show, that for small objects there is no true distinction between wave and particle nature. This, in turn, makes complete knowledge of the position and momentum of any object impossible, and shows that indeterminism is a fundamental quality of nature.

Summary

I have here shown that Quantum particles give rise to small fluctuations which are amplified in a process known as the butterfly effect. This process creates information from entropy and consolidates the indeterminist position. Chaos theory and, particulary, Quantum physics have made the Laplacian "World Spirit" impossible.

References

  1. Paul Davies "God and the new physics" (1983)
  2. Paul Davies "The cosmic blueprint" (1987)
  3. James Gleick "CHAOS - Making a new science" (1987)
  4. PHYSICS AND ULTIMATE REALITY a debate between Kevin Solway and Paul Davies

Books I will read which probably will appear in the reference list afterwards

  1. I don't know the author Does God Play Dice?
  2. John Gribbin "In search of Schrödinger's cat"

Other views

  1. Chad Docterman's Essay on Determinism

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