Posted January 9, 2001
Last week I brought up the idea of time and space being interchangeable. If two people are in different places, they're also in different times. This sort of makes sense, in that if you want to meet someone, then first of all you have to be in the same place, but you also have to be there at the same time. It doesn't help much to arrange a meeting time without also choosing a place, or to choose a place without deciding on a time.
Normally we think of time as being fundamentally different than space, partly because we can only move through time in one direction, and also because we can't seem to help how fast we move through time. Or can we?
Last week I said that time goes slower if you're moving fast enough. So you might spend a year on a rocket ship, and come back to find out that, according to everyone else, you've been away for two years. So your time can slow down, relative to everyone else's time, but it will still feel the same to you.
I have a great little book of vignettes called, "Einstein's Dreams" by Alan Lightman. Each story is a short exploration of what the world would be like if some fundamental aspect of life was turned upside down. It's somewhat reminiscent of John Wyndham. John Wyndham wrote about things like invasive telepathic alien children, and gigantic man-eating plants that make everybody blind; Alan Lightman wrote about things like: a world where time goes backward.
The particular story I'm thinking of, is about a world where time moves slower at higher altitudes. People become obsessed by spending as much time as possible at high altitudes, so that they can stay young, and live longer. They build houses on stilts and pillars and towers, and they go to great lengths to avoid ever having to come down to ground level, where all the poor people live, who can't afford these expensive high-altitude houses. They create little villages way up in the air, so they don't have to come down as much. You get the picture.
The story is a bit depressing because it's about people who let the pursuit of youth dictate how they live, which seems to defeat the purpose of staying young.
But I'm not here to talk about wasted youth, I'm here to talk about physics. First I want to point out that this story is not far from the truth; it's just an exaggerated depiction of the fact that time moves slower from the point of view of objects that are moving at high speed.
As you probably know, the earth rotates at approximately one revolution per day, relative to the sun. I say "approximately" because it has to do one extra revolution per year to compensate for the fact that it's in orbit around the sun. If the earth were to orbit the sun, without rotating around its own axis as well, we would still get one day and night. The earth rotates in the same direction as its orbit, which is counterclockwise as viewed from the north ... and by the way, the fact that the earth rotates counterclockwise is not a coincidence -- that's why clocks go clockwise.
And this is the point where you unexpectedly figure out why a pendulum would start to turn clockwise if you left it alone for six hours...
Anyway, every year, the earth rotates counterclockwise, once to compensate for its orbit, and again about 365 and 1/4 more times to give us one year. It would be convenient if it were exactly 365 and 1/4 times, or even better, exactly 365 times, but that particular coincidence is not ours to enjoy, so in order to prevent our seasons from going out of whack, we have invented something called February 29, which gets inserted once in a while to compensate for the last four years worth of 1/4 - revolutions. If it were exactly 365 and 1/4, we would have a leap year, but it's even less convenient than that, so there are more exceptions. 2004 is a leap year because it's divisible by 4, but 2100 isn't. I think 2400 is a leap year, but you might want to verify that before basing any important decisions on it.
That might be a bit more detail than you need, but hey, isn't that what physics is for?
Don't worry, I haven't forgotten that I was talking about relativity; I'll get on with that after we hear a little more music. Hey, you deserve it.
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So, about relativity. If you build a house on stilts, you're effectively putting yourself in orbit around the earth. For that matter, you are effectively in orbit around the Earth even if you don't build a house on stilts. But if you do go to a higher altitude, you'll still go around the Earth's axis once per day, but you'll be further from the centre of the Earth, which means your orbit will be bigger than before, so you'll cover more distance in the same day. So those clever people with the houses on stilts are right that they're moving faster, and that should make time go by a bit slower for them.
The difference will be very small, but let's assume that these fictional people, aside from being clever, are also very sensitive to small changes in the speed of time, so they are willing to spend all that effort to achieve a miniscule benefit.
There is one other problem though, and perhaps the people in the story will think of this someday: when you move very fast and time goes slower, you don't actually gain time or youth. As time slows down, and you start to age slower than other people, your mind slows down right along with it. So you don't get to appreciate the benefits of slow time. In fact, it's impossible to tell whether time is moving slowly or quickly for you at any given moment, because you yourself are the only reference point by which you can measure time.
I said there were two reasons why we are inclined to think that time and space are different. One is that we can't control how fast we move through time. But as it turns out, we can, to some extent, but it doesn't matter how fast we're moving through time, because everything appears exactly the same regardless. Likewise, we can control how fast we move through space, but if you've ever fallen asleep at the wheel -- sorry, if you've ever fallen asleep on a train, you've probably noticed that things feel exactly the same regardless of how fast you're moving through space.
The other thing that makes time and space different, is that you can't move backward through time, whereas you can move backward in space.
Or can you?
I think the only thing to say at this point is, it's not space... it's "space-time".
If you move from point A to point B, then back to point A, are you really back in the same environment where you started? I say no. Point A has changed irreversibly since then. For example, you can be sure that entropy has increased, just as you can be sure that some time has passed. So there are two distinct possibilities here: the Point A as it was before you left, and Point A as you find it when you return.
Rather than using "point A" to refer to a point in space, which is ambiguous because it doesn't say whether we're talking about point A before or point A after, we might as well say that "Point A" is a point in space-time. So if you leave Ward and Baker at 3:00, that's Point A, and you get to Fort Shepherd by 3:30, that's Point B, and then you return to Ward and Baker at 4:00, are you at point A? No, because Point A is Ward and Baker at 3:00, not Ward and Baker at 4:00.
You can't get back to Point A. You can only get to new Points like Point C and Point D. They might be in the same space as Point A, but they won't be there at the same time. So, consider yourself to be living in space-time, rather than space alone. You might find that this point of view is a pretty good representation of how we see our world in day to day life.
For example, now you know why things never seem to stay just the way you left them. And never again will you have to say that you're "back to square one."
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