Physics: A Clock Story

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In special relativity, we're always talking about events. And event is something physical that happens at a position and a time. We describe an event by stating what are x, y, z, and time T. Now, it's easy to just write this down and go on and do all the calculations of special relativity, but if you really start worrying about what's going on in relativity, we are calling into question the nature of space and time. It's just not obvious exactly how one goes about measuring positions and time of an event when we're saying that positions and time are now relative concepts. How do you actually go about measuring these things?
There's a prescription. It's kind of a sought experiment for how you could quite rigorously define x, y, z, and T for an event in a particular reference frame. You're always going to work in a reference frame when you write down the coordinates. So let's think about it. It's not all that complicated. It's reasonably straightforward. But it's just worthwhile having a definite way, a program for figuring out x, y, z, and T for an event.
So first of all, x, y, and z are really not hard at all. I just lay out a grid of rulers. I lay x rulers and y rulers and z rulers, and you imagine filling space with this three-dimensional grid of rulers. And I get a bunch of buddies, imaginary physics buddies, who go out and there's one buddy at each intersection point on my grid. And they all just stand there taking notes. Whenever an event happens right next to them, they write down because they know where they are. They just look at the ruler intersection where they're standing and jot down x, y, and z, and that never changes. And then whenever an event happens, all they've got to do is write down, when did that event occur? They've got a little watch in their hand, and they write down the time, and we're all set. The event occurred and the nearest observer--not really an observer. The nearest grid point to it records x, y, z, and T, and then later I can just go at my leisure and collect everybody's notes, and I know what x, y, z, and T are for any event in my reference frame.
I'm sneaking one little thing by you. X, y, and z are straightforward. T is a little bit harder. What time does an event occur? I said my little observer friend who's standing right next to it looks at their watch, but this only makes sense if we've got calibrated watches. We've all got to agree that at a certain moment in time in my reference frame, all of our clocks read zero. I want all of our clocks to be doing this. They want to be running in sync. And how do you do that? How do I make sure that my friend over there's clock is synchronized with mine? And how would you do it in the real world?
One thing you might do is, you've got a stopwatch and you say, "Ready, set, go!" That's a bad way of doing it because I say the word "go!" and it takes some time for that sound to propagate over to them. And so if they hear me say "go!" and they press their watch, it's going to be lagging behind mine. So you certainly don't want to use sound to communicate. You want to use the fastest signal you possibly can. If we could communicate instantaneously, that would be great. I'd just say "go!" and send out this instant signal. But there is no such thing. Nothing in the world travels faster than the speed of light. So the best I can do is to flash a light. And the convention is, when I flash the light, that means I've started my clock at the origin.
Now, there's a buddy who's over there somewhere at position x, y, and z. They are at distance d away from the origin. They know where they're standing so they know what d is. Now, when they see that flash of light, they don't want to start their clock. They need to start their clock earlier because velocity times Time is distance. If they're at distance d away and my light pulse is traveling at the speed of light, which all light does--3x10^8 meters per second--there's a certain amount of time, which my buddy can calculate, it's just , and that's the lag time. So when they get that flash, they don't want to start their clock at T=0; they just set their clock at T= and now we're synchronized. So that's the trick. It's a conceptual trick by which you could imagine having a large number of observers who all have synchronized watches. Now we're all in lockstep. We're all rest to one another, with respect to one another, so our time is running the same, and now all events can be easily recorded and collected.
You know, when people are talking about relativity and you start to realize that time is relative and space is relative, it can get very confusing thinking about measuring these things. And sometimes people get a little bit confused when they're working relativity problems because they're thinking, "You know, I'm sitting over here and an event happens over there, and I'm trying to talk about the time of the event. And just by this formula, it would take a while for that light to get to me. So is that what relativity is about, this time lag?" That's not at all what relativity is about. That's just a classical velocity times Time equals distance effect. The amount of time it takes for the signal to get to me is just a practical issue, which I worked out by synchronizing clocks. And that's really got nothing to do with the strange fact that time itself is relative in the Theory of Relativity.
Relativity
Relativistic Dynamics
A Clock Story Page [2 of 2]