A Glimpse of Time Dilation

Before Reading This, see -
Chasing a Beam of Light (Nov. 1st, 2006)

Hey, all. I'm posting my first ever "sequel" post. This post can be thought of as a direct sequel to Chasing a Beam of Light, which is one of my favorite posts so far.

When confronted with the paradox of light's never-changing speed, Einstein decided to rethink exactly what time was. In this quest he completely redefined physics with something called Special Relativity.

Let's see each step of his reasoning in a simple, logical way.

(Note - this article is a bit more complex than the others. So if you can't handle it, try reading some of my other, simpler articles)

First, we'll be using the world's simplest and most impractical clock - the Light Clock. Basically, you have two mirrors facing each other, attached by a bracket, and a single photon (the stuff that Light is made out of) bouncing back and forth between the two mirrors. There's a detector that clicks whenever light makes one complete round trip.
So you have a piece of light bouncing back and forth between two mirrors, with a counter counting the amount of time it bounces.

Let's say that our two mirrors are far enough apart so that one second passes for every billion clicks of the timer. So when the light bounces back and forth one billion times, then a second has passed.
We can use this like a stopwatch. Say that after you run a track, thirty billion clicks have passed on the light clock. You can then deduce that you ran the track in thirty seconds.

Great clock, eh? And because light will always travel at the same speed, it seems to be perfect, never wavering.

So you're staring there, watching your little fancy light clock on the table. Then someone comes and gives you another one, and you decide to do a little experiment.
What would happen if you moved one around?

Here's the trick - it would take longer for a photon to make one complete trip on a moving clock!
Notice in the picture to the left (which, I am proud to say, I made myself). You can click it to make it larger, but you can kind of see the gist here.
As you can see, as the Light Clock moves, the light must travel a farther distance to keep up. It's no longer just going straight up and down...it's also going side-to-side as well.

To make one complete cycle, the light has to travel farther in a moving clock than a stationary clock.

Because light cannot speed up or slow down, then we can say that it takes longer for light to complete one cycle when the light clock is moving.
If there is a little digital counter on top of a moving and a stationary light clock, you can see that the moving light clock ticks a tiny bit slower than the stationary one.
You see why? Because it takes longer for light to complete a cycle on the moving clock, the moving clock "ticks" less often. As a result, its counter is slightly slower.


There you have it. The simplest proof of Time Dilation. Objects in relative motion travel slower through time than relatively stationary objects.


Let's say that you and the moving clock are moving at the same speed, the same direction. Here, you don't see the diagonal movement of the light as in the previous picture. We have shown that the for the moving light clock, 1 billion ticks is slightly greater than a second.
But if you don't see the diagonal movement of the light, then nothing is being delayed. Light doesn't "take longer to travel", because, well, to you, it's still bouncing straight up and down, without that side-to-side motion that you saw when you were stationary. So to you, 1 billion ticks still equals one second!

Someone looking at you from a stationary vantage point would see you moving in slow-motion. Because, you see, what is 1 second to you is actually a bit more than 1 second to him.

...Did I lose you?

Just to sum everything up -
Time passes slower for objects in (relative) motion.

Wow. Am I saying that when you're driving a car, you're going through time slower than someone who's walking? You're time traveling?
...Yes. But the difference is so tiny that you don't even notice.
But say, if you were traveling in a spaceship at 502,500,000 MPH (3/4ths the speed of light), then boy, the difference would be astounding! You'd be moving in slow motion compared to the rest of the world. One second for you would be 1.5 seconds for someone standing still. If you travel for two years at that speed and come back, then you'd find out that 3 years had passed on Earth. Time travel indeed.

The closer you are to the speed of light, the larger this delay is.

-

All of that may seem too abstract. But let me give you a more concrete example.
A Muon is a special type of elementary particle. It's so rare because the instant that one is formed, it disintegrates after two millionths of a second. It's like a muon lives life with a suicide bomb strapped to its chest with a countdown set at two millionths of a second.

But scientists found that if they sent the muon flying nearly at the speed of light, the muon would live a lot longer.
What's happening here?
At, say, 667 million mph (about 99.5% of the speed of light), the "clock" on the suicide bomb slows down! Just like the moving light clock slows down. In fact, here it is moving so fast that the clock ticks about ten times as slow!
In fact, the muon's life expectancy is about ten times as high. When the muon finally dies, the lab clocks would say that ten times the life expectancy had passed since the muon was born...but in the muon's clock, only one time the life expectancy has passed.

Mind-boggling? It's supposed to be. Einstein completely shattered the world.

(Note - while this is supposed to be mind-blogging, it's not supposed to be mind-boggling so much that you don't understand a word I just said. So if you have any questions or comments, please leave...a comment. Thanks :) )

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Chasing a beam of light

Another paradox :) Scientists couldn't accept it. Einstein embraced it. Don't worry, we're not going to see how he solved it quite yet...we're just going to see the paradox. Which is always more fun.

About a hundred years ago, scientists were sort of embarrassed. You see, they had just discovered something wierd about the speed of light -- it's always the same to you, no matter how fast you're going. But it didn't make any sense to then.
Baby Einstein wondered...what would happen if you ran the speed of light? You could "race" a beam of light, catch up to it, and run alongside it (like running alongside a bike).
What would stop you?

Unfortunately, as they found out, light is pretty stubborn.

First, a few notes -- We're going to be discussing the speed of light in a vacuum, unaffected by outer forces. We're not talking about light slowed down or sped up by the materials it is traveling in, or even reversed as some have claimed it. You'll see why later, but basically we're talking not so much about light itself but more about the "universal speed limit".

So, one day our friends Steven and Anne were once again bored, so they decided to play Catch. Things were going fine until Steve all of a sudden decides to throw a rock at 25 mph towards Anne. Anne, being a girl, runs away at 5 mph.
How fast will the rock approach Anne? Well, to Anne, the rock is catching up to her at 20 mph (25-5=20). As you run 5mph away from a 25 mph object, then it catches up to you at 20 mph. With me so far?

So now Anne is mad. She pulls out a rifle and lets one loose on her pal Steven. Steven runs away a bit faster...10 mph. However, the bullet is traveling at 900 mph. Steve is running away at 10 mph, so the bullet approaches him at 890 mph.

Then Steve pulls out a flashlight and shines it at Anne. He knows that Anne has spontaneously developed a severe allergy to light...so she doesn't stand a chance! The light travels at 670 million mph. She starts running away at 5 mph...so then the light should approach her at approximately 669,999,995 mph...right?
Until she comes to a starking realization. Even though she's running away at 5 mph, the light is still catching up to her at 670 million mph!

So she jumps on the Millenium Falcon, which speeds away at 170 million mph. So the light should be catching up to them at 500 million mph, right (670-170=500)? Just like how if you run away from a 67-mph car at 17 mph, the car catches up to you at 50 mph.
But, to Han Solo's surprise...this isn't true. Light is still catching up to him at 670 million mph!
Impossible?
In response, Han picks up the speed some more...and pumps the falcon's speed to 570 million mph. At this rate, light should catch up to them at a feeble 100 million mph. But...no! The light again catches up them at 670 million mph, again.

Did light speed up? No...from Steve watching from the sidelines, the light has been going at the same speed all along. But it's obvious that the light that Anna sees is traveling faster than the light that Steven sees...

WTF is going on?

a quick summary - No matter how fast you go, light always catches up to you at 670 million mph.

It's a simple fact. But do you have trouble believing it? So did the scientists 100 years ago. You can see why they were all jealous of Einstein when he cracked the mystery...which is what we'll be doing later.

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If there is anything here that you didn't understand, if you believe that I am dreadfully incorrect on some accounts, or if you just want to comment, please leave a comment :) I'd be happy to take it, and I'd appreciate it a lot.


(Note - On November 7th, 2006, I finished the sequel to this post - A Glimpse of Time Dilation.)

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