Chaos theory tells us that complex systems are critically sensitive to initial conditions, and are therefore impossible to predict.
Simple systems (at least systems that appear simple to us) are not like that : A brick-laden cargo truck smashing into a stationary mobile home at 60 miles an hour will demolish that home. It doesn’t matter at all whether the truck is actually a brick or two short of a full load, the result will be the same. This dynamic is therefore NOT (critically) sensitive to initial conditions: there can be significant measurable differences in the weight of the truck and we can still “pretty much” tell what is going to happen.
On the other hand, a couple of weeks from now, a particular afternoon may be sunny or overcast, and there really is no way to predict which it will be. That is because changes to initial conditions that are actually too small to measure will create gross changes in outcome. Pushing even one particular atmospheric atom, just a trifle to the left or to the right on the first day of June (the mere stroke of a butterfly’s wing, to employ that popular imagery), will not just mean that a sunny day on the Fourth of July will be “pretty much” the same, such a tiny change to starting conditions may result in a completely washed-out holiday.
Therefore, given the complexity of the system prediction becomes impossible.
BUT (as will object the typically determined Determinist), the inability to PREDICT a future event does NOT mean that the event is any less inevitable.
Well… yes, it does actually ! Because this is where Quantum Physics intervenes.
Quantum physics does not predict particular events ; quantum physics predicts only the PROBABILITY of a particular event occurring. In the real world, quantum physics is invaluable for predicting all sorts of simple things, because, as in the truck and trailer example, all we care about is the overall situation within a large margin of error.
For instance, if we know the average size and weight of a brick, and the volume capacity of the truck (knowing also the speed of said truck), we can confidently predict the damage (Newtonian force at impact) sustained by the mobile home.
However, in a complex situation like weather, EVERY detail counts. It is not enough to know what the probability of a butterfly flapping its wings is (and hence how many butterflies, overall, will be flapping at any given time), to predict the weather you would have to know exactly WHICH butterflies are flapping and which are not. To be perfectly clear : two butterflies can be sitting side by side, and if butterfly ‘A’ flaps her wings, then you had better board up your store fronts on a pacific island thousands of miles away ; but, if butterfly ‘B’ flaps, you will be able to go out collecting clams on a perfectly calm day ; and quantum physics cannot tell us which (if any) particular butterfly, of this pair, will flap.
With reference to the truck, this would be like saying that if two bricks have a trivial difference in weight between them, and if the positions of those two bricks were to be reversed on the truck bed, the trailer would be destroyed in one case, but unharmed in the other (with no way of knowing which brick is where). THAT is the difference between a system that is “simple” and a system which is “complex” (under the sway of quantum probabilities).
So, obviously, we will agree that a complex system, which is critically sensitive to initial conditions, (and that these depend on particular quantum events), will indeed be unpredictable. But quantum theory does not simply say that a specific quantum event is unpredictable. The dominant interpretation of these facts now states that there is no explanation for why such an event HAS occurred. In other words, as far as we know, there is no reason for the event to have happened. To the best of our knowledge, nothing CAUSED that event.
Of course that is where our deep prejudices come into play, because everything has a cause, right ? Well… no, not as far as we can tell, (and as you may easily imagine, a great deal of work has been done trying to find some sort of “hidden” causes for quantum events — and this for the better part of a century — without any success at all).
To take a simple example, radioactive atoms such as Uranium, decompose ; which is to say : their nuclei split into smaller parts which become the core of new and different (smaller) atoms.
Quantum physics tells us the probability of any particular Uranium atom decomposing, and it tells us with great precision exactly what proportion of a larger Uranium sample will decompose in a particular time span. We possess no means, however, of either predicting which specific atoms will decay, or what is more, explaining why any particular atom DID decay. Again, as far as we know, there is no reason — no cause – for any particular decay.
In fact, the whole idea of an “atom” is that it is absolutely identical to all other atoms of the same element. So there would seem to be nothing setting one off from another. And as for the atoms in a sample, so also for all the uranium atoms in the world (or in the universe) : We know that a certain number will decay, but we don’t know which ones (and to pose an obvious question that we will consider in another place : how do THEY know whether they should decay or not ? How CAN atoms on opposite sides of the universe know whether the over all probability curve will be respected if they decay, or if they do not ?)
In any case, the point is simple : with each individual quantum butterfly making up the universe, there is no reason or cause for why, or why not, she will beat her wings. This means, that for any complex system like the weather (or the neural interactions in the brain, or the behavior of people in a group), outcomes are critically sensitive to initial conditions which are tied to events which have NO CAUSE. Which is the same thing as saying that the weather (not to mention human thought and behavior) have NO CAUSE that can be found in mechanical interactions of the sort described by Newton.
There are, to be fair, three possibilities : 1) there may be physical reasons for quantum events that have yet to be discovered (although the likelihood of this becomes less with the passage of time, and ever more detailed observations) 2) reality may be determined and constrained by forces that are not open to physical examination (many religious people, like Calvinists and Muslims believe this to be true, and more will be said on this subject elsewhere) 3) it may be true (and this is indeed the inevitable empirical conclusion of the scientific facts cited) that the future is open and free.
The articulation of this simple argument on behalf of an indeterminate future, relying on the interaction of Quantum Physics and Complexity Theory, represents a large part of the significance of the present work. I first arrived at this reasoning in, or around, 1997. I have never seen this idea advanced elsewhere. I have discussed this theory with several people possessing the relevant scientific experience and none has even attempted to argue seriously against it. I would be most grateful to anyone who might demonstrate an error therein. But in the absence of such demonstration, I must conclude that this proof is valid, and of the greatest importance to many of the foremost controversies in contemporary human thought.