by David Colarusso - April 11th, 2007
Sorry for the delay, but it’s spring break. ;)
The bizarre consequences of special relativity arise from two postulates, two things which once accepted lead to Einstein’s space-time. In this series of five episodes, we will introduce and build upon these postulates to derive the consequences of special relativity.
The Tabletop Explainer
Episode Eight (8)
Special Relativity (1 of 5): Two Postulates
The bizarre consequences of special relativity arise from two postulates, two things which once accepted lead to Einstein’s space-time. In this series of five episodes, we will introduce and build upon these postulates to derive the consequences of special relativity. So are you ready? Okay then, fasten your safety belt and prepare for take off.
Imagine you’re waiting on the runway and decide to take a nap. When you awake all the window shades are drawn, and no one is in the cabin. So can you determine, without peaking out the window, whether you’re on the tarmac or flying in a straight line at a constant speed?
You might think that dropping something would help, but it doesn’t. Some people reason that if they drop something and it falls “straight down” they aren’t moving, but really all this does is establish that they aren’t accelerating.
This is sometimes known as Galilean relativity, and it’s why we don’t perceive the Earth’s rotation. For a sailor traveling at a constant speed in a straight line, a cannon ball dropped from the crow’s nest falls “straight down.” To a land locked observer, however, [black mask telescope thing] both the ball and the ship are moving forward, and so the ball is seen to follow an arch.
This means dropping something can’t tell you if you’re moving. It looks the same to you either way as long as you’re undergoing uniform motion. Now if the plane was to suddenly speed up after you released the bag of peanuts then it wouldn’t land directly below your hand.
However, this is what’s special about special relativity, we are concerned only with things standing still or moving in straight lines at a constant speed, what we call uniform motion.
This introduces the first postulate. There is no experiment you can perform to determine if you are standing still or moving in a straight line at a constant speed. Yes, you could have looked out the windows, but all you could have said for sure is that the ground and the earth were moving relative to each other. The plane could be the “still” one with the earth rotating below. It’s all a matter of perspective; it’s all relative.
Alright then, are we happy with the first postulate? The most one can say is that she is not speeding up, slowing down or changing direction. She cannot say whether this is because she is standing still or moving at a constant speed in a straight line.
It might help to consider that there is no absolute reference frame in the universe with which to compare one’s motion. Remember the earth is hurtling around the sun and the sun around the center of milky way. The best we can say is, “I’m moving relative to this or to that.”
Okay, let’s go to a parade.
You’re throwing candy to onlookers, and normally you throw candy at five miles an hour relative to yourself. The truck is trotting along at two miles an hour. So when you throw candy to people behind the truck you are throwing opposite the truck’s motion and the candy reaches them traveling slower than it would if you were standing still relative to them. How much slower? Well you subtract the truck’s speed from that of your throw and find three miles an hour.
When you throw the candy forward, it’s moving with the truck and so hits the spectators going seven miles an hour, your pitching speed plus that of the truck.
Got it? Good, ’cause now things get weird.
Light it turns out is special. It doesn’t behave like candy, trucks baseballs, or any material object for that matter. To see what I mean, let’s wait for nightfall.
Now imagine you’re standing still next to a stationary truck. We can think of the light coming from the headlights as little particles or waves, take your pick. What’s important is that we measure how fast they’re leaving the truck. This is like your pitching speed at the parade. When we do this, we find the light is leaving at 670 million miles an hour.
Now let’s have the truck zoom towards us at 10 miles an hour, and measure the speed of the light leaving the headlights. How fast do you think it’s going? 670 million miles an hour plus ten? Well, that would be wrong. No matter what, we measure the speed of light to be 670 million miles an hour. It doesn’t matter if the truck is moving at 600 million miles an hour, we don’t add its speed to that of the light leaving the truck.
That’s the second postulate. The speed of light is the same for all observers undergoing uniform motion, that is, standing “still” or moving in a straight line at a constant speed. This is an empirical fact. Yes, the speed of light changes when it moves through glass or water, but we’re not concerned with these complications. The speed of light in a vacuum is always 670 million miles an hour.
It might seem odd, but experiment shows this to be true. Now if you can accept this and the first postulate, you’re ready for relativity. They’re all you need. Everything else just follows.
For our purpose this means:
All uniform motion is relative. That is, you can not determine if you are standing “still” or moving in a straight line at a constant speed, and the speed of light in a vacuum is the same for all observers undergoing uniform motion.
You cool? All right then, now for some specialized nomenclature.