Amazing as it may sound, neither of us has a problem—we’re both right. What Einstein discovered is that the weird effects that he had already deduced from the constancy of the speed of light forced him, as it will force us, to reject yet another cherished Newtonian notion—that of absolute simultaneity. The principle of absolute simultaneity says that if you see two things happen at the same time, I’ll see them happen at the same time, also. But Einstein discovered that wasn’t the case most of the time; he discovered that we only agree if either (a) we’re at rest with respect to one another, or (b) the two events also occur at the same place, with respect to our relative motion.
In our little chestnut of a problem, neither (a) nor (b) is true. We’re not at rest with one another, and the two events—the front door closing and the back door closing—don’t occur at the same place, relative to your direction of motion (from one door to the other). So what “really” happens? As I see it, you and your 6-foot pole go into the shack, I close both doors at the same time, and then you and your pole continue on, busting through the back door.
What you see, instead, is the following. You and your 10-foot pole go partway into the 6-foot shack. Then the doors close, but from your point of view, they don’t close at the same time. Instead, the back door closes first, then your pole busts through it, and then the front door closes behind you. By rejecting the notion of absolute simultaneity, Einstein explained how either observer could see relativistic effects experienced by the other, relatively moving observer. In general, events ahead in the direction of travel are advanced in time, events behind us in the direction of travel are retarded in time.
This also explains how you could see my clock slowed down, and I could see your clock slowed down. Isn’t that some kind of impossible cycle? But it turns out that in order to synchronize clocks, you have to agree on simultaneous events. So long as you and I remain moving at a constant relative rate of speed, we can’t do that, and we can’t decide which one of us is “really” right—because we both are! It’s only when we come to a rest with respect to one another that we can again compare clocks. In a certain sense, one clock only “really” slows down with respect to another because it accelerates with respect to the first—inertial clocks don’t slow down. But that’s covered in Einstein’s general theory of relativity—and therefore a matter for another essay.
Is that all there is to special relativity? No! There is yet another transform that involves the same gamma factor, and that is an even more mysterious effect, that of mass dilation. Suppose that while you’re in the boxcar, moving along at 0.8c and tossing the tennis ball at 45 feet per second, it heads straight out of the boxcar, perpendicular to the train tracks. Meanwhile, the stationary observer on the ground throws a tennis ball back at you, also at 45 feet per second. Just by chance, the two balls happen to collide in mid-air. If the tennis balls are identical, what should happen? Does the observer’s ball knock your ball back toward the tracks, or do you knock his ball away from the tracks?
I’ll explain it one way to make you think it goes back toward the tracks, and then I’ll explain it another way to make you think it goes away from the tracks. The first way is, your ball, which travels 45 feet in each second from your point of view, takes longer to travel those same 45 feet from the observer’s point of view. In fact, Equation 8 says it should take 5/3 of a second to travel 45 feet, so from the observer’s point of view, it’s only 45 feet, divided by 5/3 second, or 27 feet per second.
Actually, that’s only the motion of the ball in the direction of the observer. It has a high sideways velocity—0.8c, and this speed is imparted by the train—but that speed is precisely irrelevant to the ability of your ball to knock his ball. Since your ball is going slower in the direction of the observer, his ball should knock yours back toward the tracks.
The problem is, you can reason the same exact way, but in reverse. From your point of view, it’s his ball that’s slowed down in time, and going only 27 feet per second. Therefore, your ball should knock his ball away from the train tracks. So what really happens?
Symmetry demands that neither ball knocks the other one back—both rebound equally from the mid-air collision. The ability of a ball to knock around other things depends on its momentum p, which is defined as
(15) p = mv
If its measured velocity is only 3/5 of what it “should” be, then in order to compensate, in order to maintain the same momentum p, its mass must be greater—5/3 of what it “should” be. In other words, the observer sees your ball as both slower (at least with respect to its motion toward him) and more massive than his ball, and the two factors exactly compensate for one another. You see the same effects with respect to his ball. To put it more generally, mass is increased in the same proportion that time is dilated:
(16) m / mo = 1 / sqrt(1—(v / c)2) = y
And that is the third and last of the Lorentz transform equations.
So now you know a little about how special relativity is derived. But do we understand why special relativity works? That is, why does time dilate? Why do objects compress in the direction of motion? And how on earth do objects somehow gain mass just by virtue of moving rapidly?
The answer is, nobody knows why! We know that it must all be true, because of the constancy of the speed of light and because the predictions of special relativity have been proven time and time again in experiments. But no one really knows why space and time work that way. It turns out that physics, and science in general, is not very good at answering those kinds of “Why?” questions. The best we can do is take nature’s clues and figure out as much as we can, and leave it at that.
Adapted from Astronomical Games: April 2001.
Brian Tung is a computer scientist by day and avid amateur astronomer by night. He is an active member of the Los Angeles Astronomical Society and runs his own astronomy Web site. His previous publications in Strange Horizons can be found in our archives.
Interview: Andy Duncan
By Mack Knopf
8/13/01
There’s a suburb somewhere in Hell called Beluthahatchie that I never would have known about except for Andy Duncan. Andy is on this year’s World Fantasy Awards ballot three times: his book, Beluthahatchie and Other Stories, was nominated for best short story collection, and two of his stories, “The Pottawatomie Giant” and “Lincoln in Frogmore,” made the short fiction category. He’s had novellas nominated for the Nebula Awards two years in a row, and other works nominated for the Hugo and by the International Horror Guild. This year’s novella, “Fortitude,” is a disturbing story about General George Patton’s déjà vu, and the previous one was an oddly reassuring tale called “The Executioner’s Guild,” about, well, a guild of modern executioners who make sure executions are as humane as possible. As you can imagine from the above, Duncan likes the weird, and he also likes the wonderful.
I first met Andy when I was in graduate school with him at the University of Alabama, and while I remember kind words and a friendly, Southern voice, the memory that sticks the most comes from a Southern Literature class we had together. Midway through the semester, we did presentations on a relevant area of interest, and Andy got up and did a talk on the wonderful movie version of Raymond Chandler’s The Big Sleep. I don’t know to this day how Andy tied in the movie with Southern literature, though he probably went by way of the Gothic and film noir. All I know is that I remember listening to him spellbound, and thinking, “This man can talk.”
And reading through his stories, that’s what comes across. Andy loves to talk, and he loves to tell us stories. He’s genuinely interested in the people in his stories, and they’re all interesting in turn, and they all feel real. Even characters who should be unlikeable, like General George Patton, become absolutely fascinating once he gets into their heads.
Mack Knopf: You love novellas, don’t you? Why the form?
Andy Duncan: I guess I’m working my way towards a novel, because the short stories just get longer and longer. “Fortitude” is a strange thing. It’s basically something I never read before. Someone gets the chance to change things, and changes almost nothing. Patton gets his life to live over, and knows it.