In this post I intend to briefly look at a controversial topic, physical determinism. Whether I succeed in being brief (it will be a first) we will find out at the end of this post. It will certainly be brief compared to the vast monographs which have been written on these topics, and which ought to be written were I to do the topic justice.

I will begin, as I always should (but often don't) with my definitions.

Physical determinism is defined as the belief that the laws of physics are such that in principle if one knows the complete state of a closed physical system at one moment in time, and has the correct understanding of physics (and there was no intervention from "outside physics", if such intervention is possible), then one could calculate the complete state of the system at any other moment in time. More specifically, for every physical system in a state A, they will each necessarily evolve into a the same state, which we can label as B, a given time period later. Of course, the calculation might be possible in principle, but in practice we could never know the state of the system well enough to carry it out. The determinism is about the principle rather than the practice; it is a statement about the nature of the laws of physics more than it is about our abilities (or lack of them). As an obvious example, Newton's laws of motion are deterministic.

Indeterminism states that the laws of physics are such that it is not possible even in principle to calculate the state of the universe at the next moment of time, but only to assign probabilities to various outcomes. For example, given a closed physical system in a state A and perfect knowledge of an indeterminate laws of physics, we are saying that the result could be A, B, C or D, but not anything else. It does not imply a complete free-for-all where anything could happen; rather it states that instead of there being only one option, there is a finite number of possibilities. Knowledge of Physics then allows us to compute the probability (or likelihood) that each option is achieved.

Indeterminism is inconsistent with several different forms of causality, especially those which claim there is a necessary connection between cause and effect. If the original state might be preserved, and thus the change to a different state is spontaneous, then it is also inconsistent with those forms of causality which require that every event has a cause. It is not, however, inconsistent with the older view of efficient causality that each substance is caused by another substance, i.e. that the efficient cause of B was A regardless of whether the transition between A and B has a physical explanation (for example, to explain why it happened at one particular time rather than another). This version of efficient causality is the minimum required for the universe to be rational and it to be possible to formulate (useful) theories of physics.

Indeterminism is also not inconsistent with the idea that we can know future events. It states that we cannot predict future events from knowledge of the present, but it might be possible to know future events by some other means. For example, if we had a time machine capable of viewing the future. Or if we were in some way viewing the universe from a position outside time, and could see what is to us (for such a being these terms have no meaning) past, present and future in one glance as we might survey the surface of a wall or floor at one glance. Equally, we can think about past events. We know that at some past time the system was in state A and it later (but still in the past) went on into state B. That we know what happened in no way contradicts the idea that the laws of physics are indeterminate; that just means that we could not calculate that given A it would be B. But by examining our records of the experiment after the event, we see that it did in fact become B. But that's OK, because such knowledge did not come from calculation but from some other means, namely observation.

I should here mention the block (or B) theory of time. The philosophy of time has split into two camps; the presentists (or A theory), who claim that only the present is real, and the block theorists, who see all of the past, present and future as equally real. It views time as being like another dimension of space (although obviously with some differences). We have no difficulty in saying that the location where I am sitting is real and the location of the desk next to me equally real. There are of course also those who combine the A and B theories of time in various different ways, and there are different forms of each school of thought.

The B theory states that we should regard time in the same way; my desk one second in the future is just as real as the space dust located one light second away from me is now. After all, I don't perceive the desk next to me as it is now; I perceive it at the moment in the past corresponding to the time it took for the light to reach me from that desk, and for the signal to pass up my optic nerve to be processed by my brain. An incredibly short time, but still non-zero. In other words, I regard the time about a hundred billionth of a second ago as just as real as the present, so why should I not regard two hours ago as just as real as the present? Or two hours in the future? (While I can't see into the future, people in the future can see me as I am now; so if my moment of time is real to them, so their moment of time must be real to me.)

The B theory was formulated in response to the theories of special and especially general relativity, and in view of these theories I can't see how the A theory can be made to work. Even the statement that two events are at the same time doesn't make sense in the context of relativity (unless they are also at the same location), because it is coordinate system dependent; and which coordinate system we choose is entirely arbitrary. So we can't say (as the A theorist does) that events separated in space are equally real but events separated in time aren't, because there is no unique and objective definition of which events are separated in space but not in time. The A theory assumes Newton and Galileo's presumption (although the notion goes back long before these two thinkers) of an absolute space. But this notion is now outdated and disproven. We are left with two options, either to say that only what is local to me, in both space and time, is real, or adopt a block theory of space and time. (Of course, one may question this view by mentioning that what general relativity describes is not physical space time but a geometrical representation of physical space time. The B theory might apply to the representation but not the physical reality. But this doesn't strike me as tenable; the representation is connected to at least a part of reality by a bijective mapping; if we could not go from space/time to the geometrical representation and back again then physics wouldn't work. I cannot see how one can say that the whole of the geometrical space is real but only one slice of the physical space, since there is a firm connection between each point of the physical space and the geometrical space.)

Most people, whether A theorists or B theorists, seem to regard the B theory as saying that change is impossible. The block universe, after all, is just there; it cannot change because there is no notion of time external to it to measure that change. However, I have never understood why people say this. Change is not a matter of becoming and ceasing to be. Change is the actualisation of a potential; the movement between one state and another; or actual existence at one time becoming potential existence at another time, and potential existence at one time becoming actual existence at the other. Something was one state at one moment in time and is in another state at another moment in time. This is no more inconsistent with the B theory than it was in the A theory. Time itself might be fixed, but objects in time can change from one moment to the next, just as they can change from one location to another. Nor can we discount the definition of time that it is a measure of change. It can play this role in the B theory just as well as in the A theory.

And, of course, to get back to my main discussion, the B theory of time is not inconsistent with indeterminism. If the future is fixed in the B theory, that does not mean that it is predictable. Thus there is no contradiction between the idea that the future is fixed and equally real as the present, and the idea that the future is in principle unpredictable through calculations of the sort done by physicists.

Both deterministic and indeterminate physics are self-consistent and rational. So how can we tell which one holds? We have a few hints from the philosophy of mind. Surely, for example, free will is more compatible with an indeterminate physics than a determinate physics. One cannot choose to deny free will (since the denial of free will contradicts the choice of coming to that belief). If a belief in free will is not through a choice grounded on rational thought and examining the evidence, then it is meaningless and has no guarantee of being true. Thus to deny free will is not only in contradiction to our most basic experience, it is irrational as well. Many modern studies of the brain have been based on the assumption that neurons and synapses are too large for quantum effects to be significant. To suppose this is, I believe, foolhardy. Quantum causes can have macroscopic effects. Equally I have little time for Cartesian or similar dualist philosophies, which might allow for an deterministic physical world and an indeterminate mental world, for the usual reason that they can't adequately explain how one influences the other.

But the test of whether the real world is determinate or indeterminate is experiment. And in principle, a direct experiment is easy. Set up a physical experiment, exactly the same way each time. Repeat the experiment a large number of times. If you get the same result every time for every experiment, then the world is most likely determinate. If on at least one occasion you get a different result, then the world is certainly indeterminate.

However, in practice, it is not as easy as this. Firstly, every experimental measurement carries imprecision. So if your experiments all get the same result, then that means that they agree to within that precision. You can't tell whether or not they are all exactly the same number, or have slight differences but below the resolution of your experiment. You can't tell whether the system is indeterminate, but one outcome is possible but so rare that you by chance haven't measured it in your finite number of experiments. Equally, how do you know that you have exactly the same set up each time? If you see differences in the results beyond the experimental precision, it could be because of differences in the original set-up in qualities you couldn't measure, either because they were below the experimental precision, or for some other reason. So you have to do a bit more work.

One way of avoiding this is not to rely on experiment directly and alone, but the combination of experiment and theory. Find a theory that matches the experiments as a whole, and ask whether that theory is determinate or indeterminate. Or rather, is there any deterministic physics that matches up with the whole corpus of your experiments.

Quantum physics, fortunately, allows us to resolve this issue in another way. If physics is indeterminate, then that means that we cannot say what the outcome will be with certainty. That means that we need some measure to parametrise our uncertainty. If the differences we can see in the experimental outcome arise from minute differences in the experimental setup, and the physics is deterministic, then the uncertainty should be governed by classical theory of uncertainty, probability. The number of results you get in each outcomes should be proportional to the number of times you started in each possible initial set-up. Quantum physics is, however, governed by the rules of quantum uncertainty, which is a little bit different. These differences have experimental consequences, particularly when combining two different results.

Experiments up to the twentieth century gave repeatable results, within errors, which strongly suggested physical determinacy, in agreement with Newton's laws. Thus most of the early modern philosophers (baring those who denied the applicability of physical theory entirely, such as Hume and the empiricists) assumed a deterministic metaphysics and built that into their systems. However, subsequent experiments have shown that results aren't exactly repeatable. The same set-up won't lead to the same outcome every time.

Last time, I showed that one leg of the mechanical philosophy which dominated the philosophy of science for most of the modern period was inconsistent with experiment, namely that the fundamental corpuscles are indestructible. This time, I have said that another leg of the mechanical philosophy, namely that physics is deterministic, also contradicts experiment.

It looks like the mechanical philosophy is in bad shape.

But the Aristotelian philosophy, which mechanics replaced, is looking better. Aristotle can cope with one form of matter changing to another type of matter. Aristotle causality is the one solution which allows us to maintain both the rationality of the universe and physical determinacy. Efficient causality, which links one substance with another, still applies. Final causality, which lists the possible outcomes that a physical state tends towards, becomes useful again. Indeed, it is inevitable that physicists will have to introduce final causality back into their work. We use the term 'decay channels' to describe pretty much what Aristotle meant by 'final cause'.

So we need to develop a theory of physics that both allows us to describe the creation and annihilation of particles and physical indeterminacy.