The Paradox of Time

exerpt from The Boundaries of Human Knowledge" by Steven Lehar

Consider our perception of time. It has long been recognized that physical time is very different than the time of our experience. In phenomenal time there is a past, present, and future, and we have the experience of our self as flowing through time, from past, through presesent, towards the future. In physics there is no such distinction, any instant of time can be set arbitrarily as the origin t = 0, but in fact that particular moment in time is no different in principle than any other moment in past or future. In physics, time is a dimension, much like space, and in modern physics space and time are combined in the notion of spacetime. Let us suppose, hypothetically speaking, that physics is right, and that there is no flow of time, every moment is like every other. We can imagine a series of events as a length of a movie strip, whose individual frames can be viewed in succession through a movie projector, but that the succession is actually illusory, and that real time underlying the illusion is the movie strip itself, as if laid out on a table, with past towards the left and future towards the right. This results in a deterministic view of reality in which the final outcome is predetermined, and there is no longer anything like "free will" as we normally conceive it. And yet the characters recorded in the movie strip behave exactly as if they do have free will. At one point one character decides to take this action instead of that, and every time we go back to that point in the movie we see that same character exercising his free will again by making the same choice. The free choice is frozen in time when viewed externally, outside of time, but to the character there is nevertheless a free choice that he experiences as occurring at that point in time, as when viewing the film strip in sequence through a projector. Every frame in the movie sequence is perceived as the present moment, framed between leftward past and rightward future events, and yet as in physics, this perception is illusory, because in fact every instant is equal to every other, the past and future directions being merely relative.

A persistent believer in free will might object that there are potential branch points along the stream of time, at which one choice would result in one sequence of consequences, while a different choice would result in a completely different sequence. In our movie strip analogy this would appear as forks, or branch points where, like a train at a fork in the tracks, events choose to follow one path or the other. Free will, in this analogy, is the switch that determines the final path only at the time that the train arrives at that point. But when the train actually gets to a fork, it does actually take one path instead of the other, whether it does so by "free will" or by random chance. And if in the end the train does choose one path over another, then the other paths do not really exist in the time line of real events that actually occur, but only as potential events that never actually occurred, and therefore they do not really exist in the final time line of reality, which again reverts to a single linear sequence. Alternatively, one might argue that the train splits at each fork, and in some sense takes both paths simultaneously. In that case our memory is of only one path from our past, every branch point of which leads to our present moment of existence, but the future of our own fate remains undetermined until we reach the future branchpoints. But if both alternatives are actually taken as real events that actually occur, then there must be other selfs on all of the other parallel branches of the time line that experience themselves as having taken all of those different paths. The linear movie strip has been transformed into a branching tree-like pattern of parallel time lines, all of which are equally real, and free will is again frozen to a meaningless static concept.

As in our perception of external space, our perception of time embodies a fundamental paradox that reveals a profound limitation in our ability to ever get to the real essence of things. The paradox of time was already recognized by the ancient Greeks, as embodied in their legend of the oracle of Delphi. If the oracle reliably predicts the future, then it is pointless to try to resist that inevitable outcome, because if that were possible, then the oracle would have predicted the different outcome in the first place. By extension, if there is an eventual outcome, whether it is predicted by an oracle or not, then it is pointless to try to fight that outcome, we might just as well go with the flow and see where it takes us. Immanuel Kant identified a number of these self-contradictory paradoxes inherent in our conceptions of space and time and causality, which he called the antinomies. Kant argued that these paradoxes cannot be inherent in the real nature of things. The universe follows its own inscrutible logic, even if that logic remains beyond the scope of human comprehension, so the antinomies provide evidence not of contradictions in the true nature of things, but rather they reveal paradoxical contradictions in our own perception and understanding of things.

If time were a frozen dimension as proposed above, that would do considerable violence to our everyday notions of causality, and thereby radically alter our view of all causal explanations. For example the first, most basic feature of causality is that matter that exists has a tendency to continue to exist. (unless it happens to decay into energy, which then also continues to exist) In frozen space-time, this means that particles of matter no longer appear as points moving through empty space, but they become long spaghetti strands extending continuously through the time dimension. The causal property of persistence has thereby been transformed into a geometrical or structural feature in frozen spacetime, something like the logic of static structures, whereby a block will never be found hanging unsupported in space, but must always be supported by other blocks that rest on still other blocks all the way down to the supporting ground. Likewise, the explanation for the logic of evolution is dramatically altered when viewed in frozen spacetime. It can no longer be said that if an organism adapts to its environment it will continue to propagate, otherwise it will go extinct. Instead, we would have to say that there are many parallel and branching threads of life from the first living thing stretching on toward the future, together with countless side-branches of life that peter out because they don't stretch forward in time toward the future, but break up into disorganized lifeless matter. The conventional causal explanation becomes as tautological in frozen spacetime as saying that the only branches of a tree that grow to great heights are those that grow upward, otherwise they never grow to great heights. A causal law has been transformed into a structural feature of the time-line of life.

I do not propose that the static formulation of frozen space-time is necessarily more correct or veridical than the conventional flowing time explanation, but rather that there is no way in principle for us to comprehend something as fundamental as time, and the frozen time explanation may well be just as far from the "truth" as the conventional flowing time explanation. The point is that there can be alternative explanations of reality that are as profoundly different in their assumptions and their manner of explaining that reality as are the flowing and frozen time explanations, and yet they are also in some sense equivalent, because the structural laws of the frozen time explanation correspond exactly to the causal law of the flowing time explanation, although expressed in a completely different form. So it may be that the realist explanation of the world in terms of flowing time and causality is both an accurate reflection of the causal laws of the nouminal world, while at the same time being as fundamentally different and thus "wrong" in its expression of those laws as the difference between the flowing-time and the frozen-time explanations of reality. Thus the realist and the idealist are both right, our perception of the dimensions of reality are both an accurate reflection of the world as it really is, as must necessarily be the case for perception to be evolutionarily adaptive, and at the same time there is truly nothing we can know about the true nature of the nouminal world as it really is, it may be as different from our phenomenal experience as is the frozen spacetime world to the flowing-time causal world.

In answer to the idealist's objection therefore that there is nothing we can possibly know about the external world, we must admit that this is true, and yet the very best model of that unknowable reality available for human understanding is the realist interpretation, that the nouminal world has the familiar three spatial dimensions and time. Whatever its ultimate un-knowability might be, this view is as good a working hypothesis as any that can be fathomed by the mind of man. So in the absence of a better alternative, that model is the very closest we can come to knowing an external world which is in principle unknowable.

The paradoxical cracks or seams in our world of experience offer solid clues to the disparity between that experience and the ultimate reality that it attempts to replicate in effigy, in the same way that the discrete phosphor dots on our television screen, and the flickering shadows seen when we wave our hand in front of it, reveal the television picture to be an indirect replica of the world it depicts, rather than a direct window onto that world. Kant (1781/1993 pp. 317- 340, A424/B352 - A460/B488) identified a number of additional antinomies, some of which were discussed in chapter 1. The world must have a beginning in time because if it has always existed, then up to any given moment in time an eternity must have elapsed. But an eternity can never have an end, so it is impossible for an eternity to ever have elapsed. Alternatively, if the world did begin at a certain point in time, then there must have been an empty time before that point in which the world did not exist. But in an empty time nothing can begin to happen because no part of such a time contains a distinctive condition of being in preference to that of non-being, whether the supposed thing originated by itself, or by means of some other cause. Similarly, the world cannot be infinite in spatial extent because the world as a whole is the sum of its parts, but the finite parts of an infinite entity can never be fully tallied; they are, by definition, endless in number. However, neither can the world be finite in extent, because if the world were bounded by nothing, then there are no boundaries to the world, which is to say that it is unbounded, and thus infinite. Again, these antinomies do not highlight the inconsistencies in the external world itself, but merely the limitations of our conceptualizations of that world.