Everyone has probably heard of Einstein's Special Theory of Relativity, but what is it, and what does it mean?
This is the first of a series of articles that will attempt to explore and explain Special Relativity and its slightly younger brother General Relativity.
We need to start with a bit of background to make sure we all understand the language. Don't go running for the hills just because we're talking about Einstein's Theory of Special Relativity. That doesn't mean it's complicated.
Well, actually, it is complicated if you want to use it professionally, but if you have a logical mind, I promise you that you can understand the basics.
First, a frame of reference is a technical term that simply means: where you are, where you are going and how long it takes to get there. That's a frame of reference. For what it's worth, it can be described with seven numbers: three to describe where you are (x1,y1,z1), three to describe where you going (x2,y2,z2), and one to describe how long it takes (secs).
What it boils down to, if you are standing on the ground, not moving, that's one frame of reference. If I come and stand next to you, not moving either, I share your frame of reference. If I walk over to the cooler to get a beer, I'm in a different frame of reference—one that happens to be moving. When I get to the cooler and stop, I again share your frame of reference. (To be picky, our frame of reference isn't exactly the same unless we stand in exactly the same spot. Close is good enough for our purposes.)
If we both walk, side by side, to the cooler to get a beer, then we share the same moving frame of reference, and our relative velocity is zero.
★ By the way, it's very important to understand the difference between velocity and acceleration. Velocity is a constant, unchanging speed (including zero!). Acceleration is when your speed is changing over time. Speeding up and slowing down are acceleration. Tooling along exactly at 55 MPH is velocity. Everything in this article assumes velocity, not acceleration.
☞ Technically, velocity is speed in a specified direction. 55 MPH is just a speed. 55 MPH going dead east is velocity.
If you are standing still, and I walk towards you, I have a velocity relative to you. If I stand still, and you walk towards me, I have a velocity relative to you. (That isn't what you thought I was going to say, is it!) If we both walk towards each other, I have a velocity relative to you.
The above paragraph works exactly the same from your point of view. In all cases, you can equally claim that you have a velocity relative to me.
★ Here's an important bit: absent other clues (like the ground moving past), so long as both our speeds are constant, neither one of us can claim to be the one that's moving. It's the old two trains thing: If you're on one train and you look out and see another train right next to you, you cannot tell which of you is moving absent other clues. If all you see is another train's windows moving past your window, there's no way to say who is moving (could even be both of you).
The last piece of this is that objects moving in a frame of reference have their own frame of reference.
▶ Suppose that I am on a train that is moving (let's call the train's speed T). Suppose also that I'm walking towards the front of the train (let's call my walking speed W). From my frame of reference, inside the train, my speed is simply W. If I turn around and walk towards the back of the train, my speed is still W.
▶ Suppose you are standing on the ground, while I go past you in that train. From your frame of reference, when I'm walking forward, my speed is the train's plus mine (T+W). And when I walk back, my speed relative to you is the train's minus mine (T-W).
Okay, so the deal is that the speed of light is the same regardless of your frame of reference. That's pretty special, because that's not the way it is with most things we know. Most things obey the laws of relative motion described above. Most things are like me walking up and down the train.
Light doesn't act like that, that's what's magical. Light appears to go the same speed to both of us, inside and outside the train. If I shine a flashlight up and down the train, we both see the light moving at the same speed. No material object acts like that. If you watch me fire a high-speed bullet, you see the bullet's speed in relation to the train's speed. But the light from the flashlight is insensitive to the speed of the train.
This is so counter-intuitive that it literally took an Einstein to figure out. He pondered the idea of moving very fast alongside light. What would it look like if you could move nearly as fast as light. Could you see the waves of light?
He decided that was impossible, so therefore, the speed of light must be constant regardless of your frame of reference. And if that was true, what were the consequences of that?
The end result of his musing is called The Theory of Special Relativity. What's "special" about it is that, as mentioned above, it applies to objects with a constant velocity with regard to each other. Things get more complicated when acceleration is involved. Complicated enough that it took him nearly a decade to figure it out and come up with General Relativity.
Special Relativity is basically about the equivalence of the speed of light to all observers in non-accelerating frames of reference. It has some astonishing astonishing consequences, one of which I'll explore in part two.
General Relativity is basically about the equivalence of gravity and acceleration. If there's interest, I might touch on it briefly in a third article. My grasp of it less firm, so I'd only cover the basics. To make things crystal clear to others, they need to be crystal clear to you!
© 2008 Chris from MN