Time and causality

In classical physics (including the General and Special Theory of Relativity), time can be conceived of as an additional dimension alongside three-dimensional space. Thus, motion in a physical system can be regarded as a static and continuous curve traversing through a four-dimensional spacetime. It is also reversible. If we turn all the particle's momentum backward, the motion can be completely reversed. As long as a snapshot (an event -- made up of the momenta and coordinates) in the spacetime is known completely, the equations of motions uniquely determine the past and the future evolution of the physical system. According to classical physics, if one knows the positions and momenta of all particles in the universe at a certain time, the future of the whole (physical) universe is completely determined.

If one additionally takes a materialist position, the implication for our lives may become very profound. For one thing, free will will be completely eliminated. According to this view, the future is not really open for us, it is just that we do not know what the future is. No matter how eagerly we may try, our knowledge and apparent free will cannot alter it one bit. Furthermore, since one does not actually have free will, there is no such thing as responsibility. There is only a false belief in it. Since there is no such thing as responsibility, there is no reason to punish a wrong-doing. Since there is no free will, there is no reason to advocate democracy or human rights or even science in a society.

The classical spacetime theory plus materialism (let us call it materialist determinism or simply determinism) also has a side effect on causality. Causes and effects become totally meaningless in this framework. According to determinism, an event is nothing but an immediate and necessary follower of another event in spacetime and the causal chain can be traced all the way back to the beginning of the universe (if any), as well as forward to the end of the universe. Thus, a statement such as:

Example 11   An atomic bomb in Hiroshima claimed hundreds of thousands of lives in 1945.

is meaningless (has no content) according to determinism. If we want to talk about causality, we have to be able to discern what is internal to the system in question and what is external. Without smuggling in the idea of mind, which an honest determinist cannot allow, he has to treat all the entities in Example 11 -- the human beings, the atomic bomb, Hiroshima, human lives, etc. -- as intrinsic properties of the material world, therefore internal. In fact, if a determinist must talk about causality in this case, he should probably say ``It is the physical laws that caused the loss of lives in Hiroshima in 1945.''

But this is obviously at odds with our experience. We really can, we firmly believe, in a broad range of situations, determine something in the future. For example, one can choose to stretch out one's left or right foot, if one is conscious of it. That ``explanation'' stating which foot is first stretched is in fact pre-determined seems extremely implausible. This causal inefficacy is a major embarrassment to cognitive scientists who subscribe to materialist determinism, explicitly or implicitly.

In fact, causal efficacy is particularly notable in our use of language. It is highly implausible to regard the works of Shakespeare as simply ``caused'' by the laws of physics. Espousing determinism, art, science and indeed most valuable human activities have to be reduced to nothing but mechanistic trivialities. It is no wonder that this particular problem has lured many to subscribe to one or another variation of Cartesian dualism.

However, Cartesian dualism is not the only solution if one takes quantum mechanics into account. For one thing, the classical view of time is not correct in quantum mechanics. In quantum mechanics, for example, the collapse of a wave function is not deterministic. It is also irreversible. In essence, quantum mechanics has set the four-dimensional ``frozen jelly'' in classical spacetime ``free.'' Now if brain really works according to quantum mechanics, it may be able to accommodate free will. This is because the experimental arrangement in the brain can be considered a result of a series of quantum measurements.

We should note, however, that the formalism of quantum mechanics alone is not enough to explain free will. A fatal criticism of a purely quantum physicalist account of free will is that free will of this kind is, in fact, a derived effect a quantum phenomenon, with the formalism of quantum mechanics being, mathematically speaking, still deterministic. Thus the whole enterprise simply surrenders the free-will problem to another deterministic framework (namely the formalism of quantum mechanics) and therefore eliminates causality as well^5.9. Nevertheless, if language (and thinking in an internal language) is to be treated as a quantum system, the explanation of free will may turn out to be irrelevant, for in order to pose such a question the original mental state must have been destroyed. ``Free will,'' as a symbol for genuine free will, is not free anymore once it is captured. In other words, genuine free will is an unthinkable issue.

In any case, physical cause(s) of a physical event can be technically regarded as the immediate and salient antecedent(s) of the event (let us call it causality stripped of free will). In this case, the inherent difficulty of classical spacetime becomes even more obvious, for in classical spacetime, the immediate antecedent (the infinitesimal deviation to the event) has to be the event itself, due the continuity of spacetime. Thus, technically speaking, the only cause of an event has to be the event itself. This does not explain anything.

It turns out that quantum mechanics can offer a much more satisfactory explanation in this regard. This is because to understand causality of this kind, we have to identify possibilities and actualities and establish an effective link between them. Therefore, a physical and/or cognitive framework capable of dealing with counterfactuals can explain ``$x$ causes $y$'' as well. Specifically, the causality embedded in the utterance can be transformed to a counterfactual argument as ``If it were not the case $x$, then it is necessarily not $y$.'' In quantum mechanics, we only have to examine the antecedent of the counterfactual conditional (the superposition of a state of affairs $\left\vert s \right\rangle$ in terms of all eigenbasis consisting of $\left\vert \neg x \right\rangle$) and look for the projection of $\left\vert s \right\rangle$ on $\left\vert \neg x \right\rangle$. If it is zero, the causal relation is established^5.10.

One should note that the causality discussed here pertains not only to states of affairs of physical nature, such as ``The revolution of the moon causes the tides on earth.'' but also to states of affairs which are highly cognitive, such as in Example 11. One should also note that a framework like this is often, if not always, multi-causal. In Example 11, we can surely assert that ``the law of physics is a cause of the loss of lives.'' This is correct, because the atomic bomb indeed has followed the law of physics. If it had not, the bomb would not have exploded. However, thanks to the counterfactual aspect of quantum mechanics, we can identify the relevant causes of a situation. For instance, if the bomb dropped in Hiroshima had been replaced with a normal bomb, it wouldn't have claimed so many lives. In this fictitious situation, ``the law of physics is a cause of the negation of the loss of many lives.'' Now it is clear that ``the law of physics'' cannot be very relevant in this case.

In fact, a quantum mechanical account of causality is not only qualitative but also quantitative. The strength of quantum mechanics comes as no surprise since causality can be regarded as disguised counterfactual conditionals with quantitative aspects. Furthermore, quantum mechanics can accommodate situations with mutually contradictory causes. It can also offer an account of probabilistic cause-effect relations, which are of particular practical interest. For instance, many causal explanations of medical science and engineering are based on statistical research.

We should notice, however, that a quantum mechanical account of a situation such as ``Smoking causes lung cancer'' should not be treated as the disguise of a statement such as ``80% of lung cancer cases are caused by smoking.'' A statement like this has a real number probability instead of the complex component of the cause. Some information is bound to be lost. In fact, this may be a dangerous practice, for there can be cases where an additional contradictory cause may cancel out the cause completely (for example if a fictitious antidote against cancer were taken). In quantum mechanics, this is a kind of destructive interference that is difficult, if not impossible, to accommodate in a probabilistic framework.