Time Flies and Stuff Happens

Jim Holt has written a nice article on that eternally perplexing subject: the nature of time. As expected, it left me properly perplexed.

Consider this passage:

Events judged to be in the past by one observer may still lie in the future of another; therefore, past and present must be equally definite, equally “real.” In place of the fleeting present, we are left with a vast frozen timescape—a four-dimensional “block universe”… Nothing is “flowing” from one event to another. As the mathematician Hermann Weyl memorably put it, “The objective world simply is; it does not happen. Einstein, through his theory of relativity, furnished a scientific justification for a philosophical view of time [called] “eternalism.” Time, according to this view, belongs to the realm of appearance, not reality. The only objective way to see the universe is as God sees it: sub specie aeternitatis [“under the aspect of eternity”].

But wait (if it’s appropriate to use that term). What is the ultimate fate of the universe?

Ever since its birth in the Big Bang, some 13.82 billion years ago, the universe has been expanding. If this expansion continues forever … the stars will burn out; black holes will evaporate; atoms and their subatomic constituents will decay. In the deep future, the remaining particles … will spread out into the void, becoming so distant from one another that they will cease to interact. Space will become empty except for the merest hint of “vacuum energy”. Yet in this future wasteland of near nothingness, time will go on; random events will continue to occur; things will “fluctuate” into existence, thanks to the magic of quantum uncertainty, only to disappear again into the void….But there is another possible cosmic fate. By and by, at some point in the far future, the expansion that the universe is currently undergoing might be arrested—maybe by gravity, maybe by some force that is currently unknown. Then all the hundreds of billions of galaxies will begin to collapse back on themselves, eventually coming together in a fiery all-annihilating implosion.

Well, you might ask, which is it? Does time belong to the realm of appearance, not reality? Or has the universe been expanding for 13.82 billion years?

Is it correct to say the “objective world simply is; it does not happen”? Or should we say that stuff happens all the time?

Holt is probably correct when he says that “most physicists … agree with Einstein that time’s passage is an illusion; they are eternalists.” Here’s how the “Time” article in the Stanford Encyclopedia of Philosophy defines eternalism:

Eternalism says that objects from both the past and the future exist just as much as present objects. According to eternalism, non-present objects like Socrates and future Martian outposts exist…, even though they are not currently present. We may not be able to see them at the moment, on this view, and they may not be in the same space-time vicinity that we find ourselves in …, but they should nevertheless be on the list of all existing things.

The idea here is that the history of the universe may be thought of as a series of events on a continuum that stretches from the past to the future, but which never includes a moment that is “now”. We can say that one event is earlier or later than another (e.g. the Big Bang is about 14 billion years earlier than December 1, 2014), but it’s wrong to think that the moment you or I perceive as “now” has any special significance, so far as the universe is concerned.

It’s as if the timeline of the universe were a long, straight line between points A and B. Between A and B there are many other points, but none of them is more real than any other. Instead, each point on the line and each moment in the history of the universe (and every object that has ever existed or ever will) exists in the very same way.

Nevertheless, as Holt goes on to say, some physicists are “presentists”. So are some philosophers (as well as most “normal” people who have ever thought about the issue). Presentists believe that “now is a special moment that really advances…; this would still be true, they believe, even if there were no observers like us in the universe”. In the words of the Stanford Encyclopedia:

Presentism is the view that only present objects exist. … According to Presentism, if we were to make an accurate list of all the things that exist … there would be not a single non-present object on the list. Thus, you and the Taj Mahal would be on the list, but neither Socrates nor any future Martian outposts would be included.  

I confess that I find presentism much easier to understand than eternalism. In fact, eternalism sounds sufficiently crazy that there must be extremely good reasons for very smart people to believe it.

Is every object and every event in the history of the universe equally real, so that the biggest triceratops who ever lived and the dinner you’re going to have next New Year’s Eve are just as real as the chair you’re sitting on? Holt says Einstein answered that question and the answer is “Yes!”:

What Einstein [showed] was that there is no universal “now.” Whether two events are simultaneous is relative to the observer. And once simultaneity goes by the board, the very division of moments into “past,” “present,” and “future” becomes meaningless. Events judged to be in the past by one observer may still lie in the future of another; therefore, past and present must be equally definite, equally “real.” In place of the fleeting present, we are left with a vast frozen timescape—a four-dimensional “block universe.”

Maybe that’s the conclusion to be drawn from the scientific evidence. On the other hand, quoting the Stanford Encyclopedia again:

Perhaps it can be plausibly argued that while relativity entails that it is physically impossible to observe whether two events are absolutely simultaneous, the theory nevertheless has no bearing on whether there is such a phenomenon as absolute simultaneity.

Thinking about what might be the case beyond our powers of observation may qualify as metaphysics rather than physics, but it seems to me that change is a fundamental feature of the universe, time is the rate of change, and wherever and whenever changes occur, time is passing. My “now” is different from your “now” in the same way that my “here” is different from your “here”. But each “now” marks a real point in time (a point in the overall history of the universe), just like each “here” marks a real point in space (the universe’s overall expanse).

Eternalism, however, treats time as if it’s one more spatial dimension, a dimensioin in which all locations are equally real. I don’t think time is like that at all. Some moments (or temporal locations) were real, some will be real, and when a moment becomes real, it’s now. Not merely from our perspective, but in reality.

Anyway, that’s my opinion. If you and I aren’t more real than Socrates or the 75th President of the United States (whoever she turns out to be) in a very significant sense, meaning that we exist and they sure don’t, well, this isn’t a universe I want to spend time in.

Bet on Achilles to Beat the Tortoise

Many are the times I’ve thought about Achilles and the tortoise:

Zeno concluded from this and other paradoxes that motion is an illusion, so it’s important to show why Achilles will beat the tortoise. Otherwise, we’ll all have to sit very still.

Zeno’s argument goes something like this:

1) When Achilles starts running at point A, the tortoise is already at B.
2) By the time Achilles reaches point B, the tortoise is at point C.
3) By the time Achilles reaches point C, the tortoise is at point D.
4) This series can be extended forever.
5) In order to catch up, Achilles will have to perform an infinite series of tasks in a finite amount of time.
6) It’s impossible to perform an infinite series of tasks in a finite amount of time.
7) Therefore, Achilles can never catch up to the tortoise.

But we know that mighty Achilles is going to catch up to the tortoise and win the race. Fast runners beat slow walkers. Hence, the paradox.

In his book A Brief History of the Philosophy of Time, Adrian Bardon suggests that Aristotle had a good response to Zeno. Aristotle apparently argued that Zeno’s paradox rests on confusing “an abstract value (i.e. time), which is mathematically divisible into instants, with actual change, which is not literally composed of infinitesimal units of change”. In other words, Aristotle distinguished between “the rules for time (as a mere abstraction) and those for change (as a real phenomenon)”. Maybe Aristotle was right, but I’m not sure Zeno would have been convinced.

Bardon also discusses the mathematical concept of a “limit”, which “allows for an infinite number of finite quantities to add up to a finite sum”. That’s the idea mentioned at the end of the video. Many have concluded that Zeno can be answered using this concept, although Bardon asks: “Can a limit be a real endpoint to a real process, or is it just a new mathematical convention that disregards the metaphysical question about time and change with which Aristotle and Zeno are struggling? Does it really help matters to say that [motion or change] represents convergence on a limit? That wouldn’t have sounded like real motion to either Zeno or Aristotle”.

Maybe Zeno’s argument does require a subtle and sophisticated response. But what struck me as weak about his argument was one of the premises listed above:

6) It’s impossible to perform an infinite series of tasks in a finite amount of time.

Really? Who says? Isn’t that what we do every time we move from point A to point B? Having arrived at point B, haven’t we also traveled 1/2 of the distance, 1/3 of the distance, 1/4 of the distance, 1/5 of the distance and so on? Isn’t this a clear example of performing an infinite series of tasks in a finite amount of time? Granted that the tasks overlap, but it seems fair (albeit boring) to describe what we’ve done this way, without having to explain what the mathematical concept of a “limit” is or draw a distinction between the rules for speaking about time and the rules for speaking about change.

Perhaps this is mere sophistry and Zeno would have considered it such, since he and the Sophists were contemporaries. I think it’s a simple truth that moving around involves doing many little things by doing one big thing. Take that, Zeno!

On a similar note, the English philosopher G. E. Moore wrote a famous article called “Proof of an External World”. In that article, he said he could prove the existence of the world outside our minds by drawing our attention to his two hands: “by doing this, ipso facto, I have proved the existence of external things”. Whether that’s a great argument or not is an open question. Moore defended his argument, however, by pointing out that skeptical philosophical arguments (such as proving motion to be an illusion) often rely on philosophical intuitions or generalities (such as premise 6 above) that we have much less reason to accept than the common sense beliefs they supposedly refute.

All right, it’s safe to start moving again.