arrow of time

Time is an important concept in physics, but physics itself dosn't have that much to say about the why of time. Time shows up as a variable in most of the more complex physics equations, because often when you want to model something, you want to model something traveling through time.

Many such equations are "time symmetric", which means they work equally well for positive and negative values of time. If you plug a negative time value into the equations which define a black hole, you get a white hole (from which energy in indefinitely expelled rather then absorbed). It's not at all clear how you might get a white hole to appear in the actual universe, but if we find one we have the math to describe it. Most astrophysicists believe their existence is impossible, since despite that the math can deal with negative time values, they believe the universe cannot.

Perhaps more interestingly, if you plug a negative time value into the equations which define an electron (or any particle of matter) you get a particle which behaves basically like a positron (or whatever the corresponding anti-matter particle would be). We have found positrons and other anti-matter particles, which could (according to the math) just be normal matter particles traveling backwards in time.

So in most equations time can be treated as just another variable (which also means it can be graphed as just another dimension). It could actually be a vector of however many dimensions we wish, but we only notice time proceeding in one direction so it's almost always just treated as a scaler. The direction we always notice time proceeding in is always the direction which entropy increases, suggesting that our experience of time is highly related to the notion of entropy (though I at least have few ideas asto why this may be).

Another idea closely associated with time in most physicists mind is that of 'causality'. We really want to be able to say "one thing causes another," and we further want the cause to proceed the effect (i.e come before the effect according to our notion of time). Sadly, this is really more of a bookeeping convenience then anything else. You could, for example, say a forward time traveling positron heading north strikes a barrier which causes it to change direction so it is then traveling east. You could also say a backwards time traveling electron traveling west strikes a barrier, which cause it to change direction so that it is now traveling south. Both these explanations are equivalent as far as the math is concerned.

Referenced by Stephen Hawking in "A Brief History Of Time". There are three arrows of time: psychological, cosmological, and thermodynamic.

The thermodynamic arrow of time is defined as the direction in which entropy increases. A universe with a thermodynamic arrow of time opposite to our own would become more orderly (i.e., less entropic) with the passage of time. It is postulated that life could not exist in such a universe, as life as we know it is based on the consumption of resources (thus increasing entropy). However, it's possible that our definition of life is simply too narrow.

The psychological arrow of time is the way that we perceive time -- namely, that we remember the past and anticipate the future. It is postulated that the psychological arrow of time must always point in the same direction as the thermodynamic arrow of time, because our consciousness is a direct result of chemical processes in our brain, bound by the Three Laws of Thermodynamics. If in some way this arrow were reversed with respect to the thermodynamic arrow, we would experience time flowing backwards, essentially remembering the future and knowing nothing of the past.

The cosmological arrow of time points in the direction in which the universe is expanding. Some believe that unlike the thermodynamic arrow of time and the psychological arrow of time, this arrow could concievably point in a different direction, particularly if the universe stops expanding at some point and begins contracting in on itself. Others believe that if this were to happen, the other arrows of time would change directions as well: entropy would decrease, and time would run in reverse, though we wouldn't realize it since our minds would also run backwards. Hawking once thought that this would be the case, but has since retracted that belief.

In our universe, all three arrows point in the same direction, which we consider "forward".

One of the more persistent problems in the philosophy of time is determining the nature of the differences between the past, present, and future. This question is intimately tied to that of the logical possibility or paradox of time travel, and in resolving the latter problem we find a powerful tool for thinking about the former. Once we have established that logic does not forbid time travel, logical distinctions between the past and the future fall away. Functional time turns out to be an entirely thermodynamic construct with no inherent logical direction.

In "The Paradoxes of Time Travel," David Lewis explores probably the most troubling logical conundrum in backward time travel, the grandfather paradox. The standard argument runs that if time travel is logically possible, then I can travel back in time and kill my grandfather before he has any children, creating a logical paradox: I have killed my grandfather, so I am never born, so I do not kill my grandfather, so I am born, and so on and so forth. What Lewis argues is that I cannot, in fact, kill my grandfather. The fact of the matter is that I did not kill my grandfather before he had children, so no matter how well-prepared I come to do him in, he will survive. I will slip on a banana peel, or my gun will jam, or I will have a change of heart, or something. This cosmic bookkeeping argument is perhaps unsatisfying, but it remains logically consistent. The universe isn't "intelligently" preventing the murder--it simply didn't happen, and that's that.

If we accept then that backward time travel is logically possible (a fact which I do not claim to have rigorously established, but which has been thoroughly explored by much better philosophers than myself), what is perhaps the most obvious logical distinction between the past and the future disappears immediately: it is not true that the past and future are logically distinguishable because of the logical impossibility of travel into the past. (I take it as given here that forward time travel in the absence of backward time travel entails no logical paradox, since this fact seems quite transparent.) It then remains to explore exactly what distinctions do exist between the past and the future and to show that these are not logically inherent.

How exactly, then, do we distinguish between the past, present, and future? According to standard conception of time, the following definitions seem eminently reasonable: The past consists of those events that have already happened; the present consists of those events that are happening right now; and the future consists of those events that have yet to happen. In this picture the past has objectively happened, and the future has objectively not happened. This certainly seems like a powerful difference between the two, and it is one that will certainly need to be explained if we are to convincingly argue for the logical indistinguishability of past and future.

I propose then that the above definitions be modified (or if you will, clarified) as follows: the past consists of those events for which we are prepared to believe our best available records and memories; the present consists of those events that are immediately available to our physical senses; and the future consists of those events for which no believable record can exist. These certainly seem like sensible extensions of the standard definitions, and they help a great deal in explaining the nature of our perception of time. Note the pivotal nature of memories and records--the only reason we feel more confident in knowing past events than we do in knowing future events is that physical records exist (in the form of histories, pictures, synaptic pathways, and so on) that suggest rather strongly to us that the past went a certain way. And looking to physics we find that the entropy of our universe must increase over time, so we could theoretically delineate the passage of time from future to past by noting the trend in universal entropy. There is clearly something thermodynamically fundamental about the direction of time. What is not clear is whether this has anything to do with logic.

Now, if we examine these new definitions of past and future in light of the fact that time travel is logically possible (which I am taking here as given), it bears out immediately that our definition of the future is quite simply vacuous. If I can logically travel to the future and back again, I can bring with me a believable record of future events. This realization collapses the definitions of past and future into each other, lending significant weight to the idea that the two are not logically distinguishable entities. Really, what we are hitting on here is the relativistic picture of space-time: the future is just as fixed as the past, and time travel merely consists of shifting our personal present in such a way as to view different time-slices of space than we would normally be able to view. In doing so, we are certainly allowed to bring back snapshots of the past and future to what we normally think of as the present.

At this point, the possible objection that the future becomes the past, while the past never becomes the future becomes moot. With time travel, we can shift the past into the future. Better still, with continuous time travel (i.e. without discontinuous breaks between our personal time and what we perceive as external time) we can cause external time to flow backward with respect to our own personal time. Of course, this brings up the question, "What about personal time? Aren't past, future, and present much less subjective ideas in this context?" The answer to this final question proves to be very illuminating on the whole subject.

Up until now, I have been applying without explanation a concept I have called personal time. This is a fairly intuitive notion that Lewis explores more thoroughly (146), but I will let it stand on a simpler (if less rigorous) footing: one's personal time is the time marked off by a perfect watch kept on his person at all times. This concept is intimately tied in with the concept of a psychological arrow of time. In this sense, one's rightful age would be measured in personal time. It may seem that internal to each person's personal framework there is an absolute past and an absolute future that we can do nothing to reverse, but such is not the case:

Consider John, a hypothetical time traveler who keeps a perfect wristwatch on his person at all times to keep close track of his personal time. Through any time travels he may embark upon, his watch faithfully counts off the seconds of his life. However, both John and his watch are physiochemical constructs with definite physical properties. It is theoretically possible, given the necessary (finite) resources, to reconfigure John and his watch to some previous personal state accurately enough that John cannot realize by memory or reference to his watch that any intervening time has passed. That is, we can in fact reverse John's personal time by reversing the thermodynamic processes that have occurred in his vicinity.

Once we realize this fact, there is no observable scale so large that we cannot imagine uncertainty about the linear progression, or even the direction, of the passage of time. It is logically and physically¹ possible that without our knowledge, just as we did to John, some godlike force could rearrange all the matter and energy in our observed universe into some previous state as referenced to this force's personal time. Our memories and observed records would all agree that yesterday it was yesterday, that 5 seconds ago it was 5 seconds ago, and so on, even though it may turn out that 5 seconds ago (as referenced by the external force's personal time) was seven million years in our future, and that yesterday (again, as referenced by the external force) it was in fact our year three billion B.C.E. Our personal time could even be externally forced to flow continuously backward, and our memories, records, and observations would still inform us of the standard forward passage of time, since we may only directly view the present.

Viewing the problem like this, it becomes impossible to give a useful account of time on any observable scale that is not wholly dependent on thermodynamics to mark its passage. It seems compelling to conclude that there is not in fact any predefined logical direction to the flow of time, and so the past and the future become logically indistinguishable.

References were taken from The Paradoxes of Time Travel, by David Lewis, appearing in the American Philosophical Quarterly, April 1997, pp. 145-152.

¹There has been some strenuous complaint about this wording. Bear in mind that I use the specific example of a person in our universe for illustrative purposes only. For the sake of this argument, this kind of memory rearrangement need not be practical. It need not even be physically possible in our universe. As long as there exists some set of logically consistent physical laws that allows for such a procedure (that is, external memory rearrangement is not in direct violation of said laws), the point carries.

It should be stated that for most of physics, there is no real preference for the arrow of time. Most of the processes which are described in physics are symmetrical over time, including all of quantum physics and relativity. The uncertainty principle, and relativistic length contraction/clock slowing work exactly the same in a time-reversed world as compared to our own. This is due to the fact that most basic physical processes as described in those theories are reversible. Richard P. Feynman was once asked during one of his lectures on QED about time-reversed particles. He noted that if you have a film of a person who is merely flipping dominos on a table, the process looks the same whether the tape is going in forward or reverse.

In all of the sub-atomic world, there is only one (current) example about the preference for the forward arrow of time: neutral Kaon particles decay into their constituents about one trillion times more rapidly than Kaon particles can be created from their constituents. Needless to say, (due to the rarity of Kaon particles in the everyday world) this one example does very little to help explain why time seems to go in a forward direction.

Enter thermodynamics and statistical mechanics. In short, it was derived that in a large system of many small reversible processes the entire system has the highest probability of evolving into the state with the highest entropy. This behaviour is labeled the second law of thermodynamics. According to statistical mechanics, there are no real irreversible processes, just unlikely ones. So, it's possible to have a broken egg reform itself, it just has a infinitesimally small probability of occuring. Comparing the probabilities of egg breakage to egg formation it would seem that there is a preference to the forward passage of time (the direction of greater entropy).

Interestingly, in a time reversed world, a person would not remember the future and gain memories of the past as he/she went back in time. Memory formation is linked to the second law of thermodynamics, the process of making memories increases the entropy of the universe. If we lived in a time reversed world, people would lose memories instead of gaining them.