Bert Bates--
Good question kicking off this
thread. I have posted on this topic in a number of forums before and I will reprint one of my posts below this message for your perusal.
The problem with your statement that kicked off this thread has to do with a misunderstanding of what "relative" means in the Special Theory of Relativity (I myself don't understand Einstein's theories well enough to claim I have an understanding of "relative" as it applies to the General Theory).
The best thing I can say that will help you along (which I refer to in my reprint below) is to think about two spatial dimensions and how they are related. If you picture a horizontal meterstick, how is its x-dimension "relative" to its y-dimension? The stick is 1 meter long, and if its exactly horizontal it makes a projection onto the x-axis of 1 meter (if you were a one-dimensional person who lived in the universe comprised of the x-axis, you would see a stick of one meter in length and not be confused at all). Now if a 2-D person, who lives in the x-y plane started rotating the meterstick, what would the 1-D x-axis person see? He'd see the meterstick start to shrink, and would be boggled if the 2-D guy explained that the stick is still 1 meter long.
Where's that extra distance going, asks the x-axis guy. The 2-D guy tries to explain that there's a trade-off...when he rotates it, it *does* shrink in the x-dimension but grows in some proportion in the y-dimension to account for the rest of the 1 meter that's disappeared (from the x-axis guy's point of view). Oh, ok, says the x-guy...so if I see 0.5 meters here in my world, that means there's 0.5 meters in the y-world, right?
Well, no. When 2-D guy rotates the stick to 45 degrees, that's when 1-D x-guy and 1-D y-guy would see the same lengths--but they wouldn't add up to 1, would they? Pythagoras tells us that the square root of the sum of their squares would, though. WHAT!? says the x-guy. Why should THAT be?
I'll let you take over explaining the meterstick to the x-guy because that's where he really starts to boggle.
However, now if you think of one axis being x (space), and the other being t (time), you'll get a great understanding of the relativity between the two dimensions--with a scaling factor thrown in, it's exactly the same relationship between x and y. (You have to have a scaling factor because in the 2-D space example both axes are in meters...with time and space, one is in seconds and the other is in meters, so it would be amazing coincidence if we had just happened to hit upon equality when we invented the second and the meter...and then there's another subtle difference besides that having to do with i, the square root of -1.)
The relevant part of this analogy, though, is that you and I are the 1-D guy, except we're in 3-D, and Einstein is the 4-D guy trying to explain what he's looking at on the other t-axis we don't physically see...and we're mostly boggling in response.
Anyway, here's my repost now which hopefully you'll find instructive.
sev
Repost:
----------------------------------------------------------
At a very basic level, the theory of relativity is based on the idea that no matter how fast you go towards or away from a light source (in a vacuum), the speed of light you measure will always be the same, c.
So if you are in a space ship, and you are not moving with respect to the sun, you can start a stop watch the instant a photon passes the nose of your ship, and stop it the instant it passed the tail of your ship. If you divide the length of your ship (d) by the time (t0) you measured, you'll get d/t0=c. If you head towards the sun and repeat the experiment, you would expect to measure the speed of light relative to your ship to be the distance of your ship (d) over the time you measure (t1) to be d/t1=c+v, where v is the velocity of your ship. You do not -- you get d/t1=c once again. Einstein says this happens because time runs slower for you. So the t1 you measure is greater than it "ought" to be by tDelta. You can figure out what this tDelta factor is simply by substituting the correction (t1-tDelta), the time you "should" have measured, for t1, the time you did measure. If you had measured the time you expected (t1-tDelta), then your guess about light's velocity relative to your ship, c+v, would have been correct:
d/(t1 - tDelta) = v + c
So now we can solve this equation for tDelta to figure out what this correction factor is:
=> d/(v + c) = t1 - tDelta
=> tDelta = t1 - d/(v + c)
So what this equation says is that you logically expect this correction factor to be 0. The time you measure, t1, should be equal to d/(v+c). But when you do the experiment, it's not. The time you measure is *greater* than what it ought to be -- in other words, time "dilates" for you. It takes longer for everything to happen than it should.
Let's say that, alongside the route of your spaceship, I've set up a looooong row of clocks. They all read the exact same time, to the nanosecond, and they're all going. As you rip past them, you note the time on one of them is, say, noon and you start your stopwatch at that instant. After your stopwatch reads 1 minute, if you look out at the clock you're passing at that moment, you will see that it hasn't reached 12:01 yet. It says it's still noon and some number of seconds, like 12:00:45. Your stopwatch got to 12:01 before the clocks outside did. Time runs slower for you -- where you ought to be measuring light's speed at c+v, you're measuring the lower speed of c. This is because time is running slower, therefore in the equation v=d/t, t is increased for you (by how much?), which makes v go down.
Outside, if there's an observer watching you perform this experiment, he might notice that your ship, when stationary, is of length d. However, at the instant you zip past him, the length of your ship appears to him to be contracted. The speed of light v is still c for him, so if he tries to figure out how quickly you zip past a sun's photon, it *would* have been c plus the speed your ship is travelling -- except that your ship appears shorter to him than it ought to be. So the photon and your ship pass each other, from his perspective, faster than c plus the speed of your ship (how much faster?).
If you notice, I asked two questions in parens in the last two paragraphs. Relativity is concerned with answering those questions. It lays out a means of calculating these answers by mathematically explaining what's going on.
If you'd like a conceptual viewpoint, then here ya go. Try not to think of space and time as independent things. Think of a single entity instead, called space-time. Think of holding a meter stick up to an x-y plane, at a 45-degree angle to the axes so that one end is at the origin (along the line y=x). Now, drop down a vertical line from the other end to the x-axis, and a horizontal line from the tip to the y-axis. The distance along the axis represents the "projection" of that meter stick onto that axis. Now give the meter stick a slight rotation, and see what happens to it's projections. If you rotate it 5 degrees in the clockwise direction, you've slightly increased the x-projection and decreased the y-projection.
Think of the x-axis as representing the motion of direction of your space ship, and the y-axis representing the rate that time flows. When you are going towards the sun at 0.5c, what you have essentially done is rotate the meter stick some number of degrees clockwise. In actuality, outside observers will tell you that you contracted your ship -- but you see it as being the same length as always. So you are seeing an elongated projection along the x-axis of our graph. The rate that time flows for you has slowed down as you can see by comparing notes with the outside world (in the same way you compared notes for distance), so your y-axis projection has been shortened.
A lot of people get confused keeping track of what's been seen from what perspective, yadda yadda. This meter stick way of thinking about it is a good thing to remember, because it keeps the perspective the same, and the process of comparing your notes with the outside world is the same, so it becomes clear what has happened. You have slowed time flow (diminished your y-projection) in
exchange for elongating space (increased your x-projection). The confusing thing here is that you are likely to say, wait a minute, I did not elongate space -- from my perspective the ship didn't change at all! But you have to remember, you cannot tell anything from one perspective. You can only tell what's happening in your world by comparing it to another. From your perspective, time didn't slow either -- that is, until you compare, you don't realize it because all of your bodily processes, cognition, reasoning, etc, have slowed as part of the time slowdown too. Distance appear to have remained the same to you, though they have actually shortened.
sev
----------------------------------------------------------
[ March 20, 2004: Message edited by: sever oon ]