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 :) )
Tuesday, November 07, 2006
A Glimpse of Time Dilation
Thursday, November 02, 2006
Gravity and the Fabric of Spacetime
We all know the story. One fateful day, Newton was sitting under a tree when an apple fell on his head. He proceeded to pull a piece of paper out of his pocket and write down the entire theory of gravity.
While that's not exactly how it worked, Newton's theory of gravity worked for quite a while. Gravity was like an invisible rope that tethered everything in the universe to everything else.
And then all of a sudden comes Einstein, who has to come over and change everything, right? He realizes something in Newton's plan that doesn't exactly fit. And in solving that problem, Einstein wound up overturning physics completely, destroying the established worldview, and creating the most (and the only) well-known physics equation - E=mc².
The Problem -
First, let's show you how Newton saw gravity.
Let's say that you're the the sun, and you have a long string. At the end of the string is a little ball...that's the Earth. Say you hold the string up above your head and start spinning it around.
So you're spinning the Earth around your head, like a helicopter. You realize that the Earth wants desperately to escape your tyrannical grip. After all, it is getting quite dizzy spinning around like that.
However, something keeps the Earth from flying away from you into oblivion and hitting someone nearby on the head: the string. The string is the only thing keeping the Earth from flying away from centrifugal force. As long as you hold onto that string, the Earth will stay forever tied to you.
That string is, of course, gravity. Newton's gravity, to be precise. Or as the fancy scientists call it, "Newtonian Gravity". With me so far?
Now let's say that you're spinning the Earth around your head, and all of a sudden you let go of the rope. The Earth, itching to fly off somewhere, leaves immediately after you let go (at least, it did for the purposes of this model). As soon as the gravity disappeared, the Earth flew off. The Earth flies off into nowhere immediately after the gravity is gone.
We can apply that to the solar system. The Earth is tied by a tether to the sun. If the sun were to all of a sudden disappear, then according to Newton, the Earth would immediately be free of the gravitational tyranny of the sun, and fly off into space immediately.
Wait...instantaneous reaction? I'm not sure if you know this, but in the early 1900's, Einstein proved that nothing traveled faster than light. So how can gravity (or the lack thereof) travel instantly, surpassing this universal speed barrier?
The Solution -
For now we'll bypass Einstein's roundabout path to solving this paradox (I might go back to this later, though), and go straight to his solution.
In the end, he found out that gravity wasn't an invisible tether...instead it was caused by the "warping of the fabric of spacetime".
...What? Well, allow me to elaborate.
Imagine that you have a piece of fabric stretched out taught, forming a sort of stage for the universe to play out on. Now place, say, a billiard ball on this fabric. You'd get something like the image to the right.
Excuse me for using a picture off of another site, but it helps illustrate the concept. The grid is the fabric of spacetime, and the globe would be the billiard ball...or a planet/star.
Let's go back to our fabric. Placing a billiard ball onto the sheet will curve our fabric. The fabric....of spacetime! Fancy, eh?
So now we have a good ol' fabric of spacetime that is curved by the weight of a billiard ball. We'll have that represent the Sun.
Now, take a marble (that's the Earth), and roll it along the fabric. You can see that the marble makes a curvature of its own, but it's not nearly as big as the Sun/billiard ball does. As you can see, this shows that Bigger Mass = Bigger Curvature, and Bigger Gravity.
Say that this marble were to roll somewhere near our Sun. What would happen?
The Earth would fall into the depression formed by the billiard ball. It would get "sucked into" the billiard ball's curvature, like a marble rolling into a hole in the ground. And that, my friends, is Einstein's Gravity. That is his theory of Special Relativity.
So does this solve the paradox of gravity instantaneously traveling across the universe? You bet it does. Say the fabric of space time were thick and foamy, like those new fancy TempurPedic Mattresses. Those are the neatest things ever. They mold to your body :)
Anyway, when you place a bowling ball on the mattress, it actually takes time to sink in before it curves the TempurPedic Mattress of Spacetime, and creates a depression of gravity.
So what happens when you remove the bowling ball? What happens when it just disappears?
The marble trapped in its gravity well won't all of a sudden be free. No, it takes time for the curvature of the TemperPedic Mattress of Spacetime to become flat and normal again. So it doesn't travel instantaneously -- instead, there's a speed limit, depending on how thick the matress/fabric is.
Surprise, surprise. That speed limit just happens to be the Speed of Light.
a quick summary - Gravity is created when objects are put into the "fabric" of spacetime, creating a little depression in the fabric. Other objects fall into the depression, and that sucking-in effect is gravity.
The fabric is sort of thick, and movement of gravity (the speed at which the depression forms) is at the speed of light, and no faster.
There you have it. This was Einstein's second major discovery about relativity (after Special Relativity, which has to deal with the speed of light and whatnot). Although he claimed it was more complicated, I actually think that it is much simpler. The two theories are closely intertwined. But both of them COMPLETELY re-wrote the science books and changed the way that scientists looked at the world.
If you have any questions or are unclear on one of the models, please leave a comment :)
EDIT: I would also like to point out that gravity warps space and time. It's hard to visualize how it warps time for now, so I'll just say the main effect - As gravity's pull on you gets stronger, time slows down around you. So a clock near a black hole (strong pull) would tick slower than a clock far away from a black hole (weak pull)
Wednesday, November 01, 2006
The Stuff the World is Made Of
I'm going to take a break from the mind-boggling and exciting paradoxes and explain what the universe is actually made of.
We've all heard about the molecule, and the atom, and the electrons, protons, and neutrons. Are those the building blocks of the universe? And what about these darned "photons"? Are they a brick also? Ever heard of a "graviton" or a "quark"? How do they all fit together?
Well, it all fits together seamlessly, like a cosmic orchestra. And here, you might see the slightest glimmer of the hottest thing in physics right now -- The String Theory.
What happens when you cut a block of salt in half? You get something a smaller block of salt. Cut that in half again...and it's an even smaller piece. You can do that again and again until you find a single molecule of salt...if you cut that down any more, it ceases to become salt. If you cut a molecule in half, you get two different atoms - Sodium and Chloride. Those nightmares from Chemistry coming back to you?
Pretty much, everything is made up of atoms. For quite a while, scientists thought that atoms were the smallest thing you could have. You can't cut an atom in half, because...well, there's nothing smaller to make it out of, the same way that you can't cut a pixel on your monitor in half.
But eventually, as scientists looked deeper, they found out that Atoms were made out of even smaller things put together. Basically, you have a bunch of electrons orbiting a dense nucleus, which is in turn made out of protons and neutrons.
Protons, Neutrons, and electrons. Are they the smallest building blocks of everything? Is everything in the world made out of a combination of them?
That was truth, until scientists found out that protons and neutrons were actually made up of brothers and sisters of the electrons - quarks (or, up quarks and down quarks). Electrons and the Two Quarks were now elementary particles. As of right now, science holds electrons and the two quarks to be a smallest, indivisible form of matter. The quarks are bigger than the electron, but basically they were like siblings in the cosmic family tree.
There you have it. The most common elementary particles are Electrons and Quarks. You could make pretty much anything in the world with them. Now let's run down the family -
Electron - Has an electrical charge of -1. Has a mass of 0.00054 u.
Up Quark - Has an electrical charge of +2/3. Has a mass of 0.0047 u.
Down Quark - Has an electrical charge of -1/3. Has a mass of 0.0074 u.
So...now that we have our puzzle pieces, let's construct an atom :)
Let's build an atom of Gold with our building blocks. We know that stable gold has 79 electrons, 79 protons, and 118 neutrons.
First, electrons -- there are 79 of them. Easy enough. But what about our 79 protons?
Scientists discovered that protons, with +1 charge, are made out of two up-quarks and one down-quark. And it makes sense, right? The electrical charge of two up-quarks (4/3) added to the negative charge of one down-quark (-1/3) comes out at 3/3, or an even 1. So we add 79 protons, each with two up-quarks and one down-quark.
So then what are neutrons, with 0 charge? They are simply one up-quark and two down-quarks. The charge of one up-quark (+2/3) added to the negative charge of two down-quarks (-2/3) adds up to 0. We add 118 neutrons, each with one up-quark and two down-quarks.
That's a brief exercise with adding up elementary particles.
Scientists have actually discovered a total of 12 elementary particles, arranged into three generations of four each. The generation we just discussed consists of the electron, the quarks, and a "neutrino", which isn't all that important.
If you have any questions, please ask them in the comments. I'd be happy to simplify or elaborate.
a quick summary - Most of the matter in the universe is made out of electrons and the two quarks. Protons are two up-quarks and one down-quark, and neutrons are one up-quark and two down-quarks.
I know this post seems like a boring chemistry lesson, I'm sorry...but I just wanted to get this established long before we go into the String Theory, which is where the real fun begins.
I'll be talking on the Force Carriers (protons, gravitons, etc.) later. They're a completely different breed.
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.
--
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.)
The Double Slit Experiment
Ah...the infamous Double Slit Experiment. For those of you who have heard of it before, it probably gave you a headache. For those of you who have no idea what it is, then prepare to be rocked.
There is no mathematical formula, no fancy theory that needs to be known to fully appreciate it. The experiment in itself is enough to be appreciated by someone who doesn't know a thing about quantum physics...or normal physics, for that matter.
At first glance, this is what you see. No mirrors, no magic -- tiny balls of matter acting more like waves in water, "sentient" electrons (although as we will see, that's a bunch of BS), and objects that are apparently two places at once.
In fact, it can be said that the easiest way to fully grasp what quantum physics truly is is to see this experiment. It's often one's first glimpse into the world of Quanta...and often not the last.
There's a famous video from the movie "What the Bleep do we Know?" that's been circulating the internet. If you watch it, I don't have to go through the process of explaining it. It actually does a pretty good job! I'd recommend anyone to watch it, even if they know nothing about quantum physics.
Anyway, this video can explain it better than I can ever do it without pictures. So until I get around to making pictures, please watch it before you continue.
What actually happens? Why does matter behave like a wave? That question deserves an entire post for itself.
Then video tries something that I think is completely absurd. It puts a little eyeball next to the slit and goes "Okay, which one does it go to? We'll watch with the eyeball." Then they fire another electron...and the result is no longer an interference pattern, but two bands, again.
Woah, did the electron know it was being watched, and decided to act like a particle instead of a wave?
While there are obvious psychedelic properties to that theory, it is unfortunately total sensationalism. The video is just hyping things up.
How do they actually observe the electron? Basically, they do the same thing that we do with our eyes. They bounce things (light light rays/photons) off of the electron and observe how the things bounce back. But Electrons are so small that shining light on it will affect its movement. That is, the strength of the light will actually push the electron, just like a wave of water pushes a bouy.
So the electron doesn't change by "just observing", as if by magic. The electron is changed by the way that we observe, as a side-effect.
This is the basicness of the Heisenberg Uncertainty Principle...which warrants a whole post of its own.
A quick summary - When you fire tiny bits of matter through two slits, it behaves like a wave instead of like matter. Why? It's complicated and I'll demonstrate it in simple terms later. So which slit does it actually go through? When they try to observe exactly which one, the electron appears to "decide to become matter again because it knows it is being watched". This isn't exactly true, but it sounds cool. Freaky. Sentient electrons, particles acting like waves...this isn't the last of the Double Slit experiment for this blog. This is just a basic overview.
Hm...well, this article isn't as great as some of my others. You probably have alot of questions about the video. Please leave them in the comments,a nd I'd be glad to answer. Or if you're just passing by, I'd love to see hear your opinions.
Elephant into a black hole
I guess there will be two kinds of posts in this blog - Paradoxes and Solutions. One type of post will show you two facts that are both true, yet state opposite things. The other will look at these paradox and provide apparent solutions.
To be honest, I like paradoxes more, because (ironically) they're alot easier to understand.
Here's a story that was posted recently on Digg - The elephant and the event horizon. Don't try to read the article unless you want your brain to explode or melt down. But there are some shiny pictures.
The idea here is simple - what happens when you throw an elephant into a black hole?
For one, you'll probably get a bunch of animal rights activist on your tail. And maybe some Thai warrior/protector will try to run after it to take it back. But aside from the social repercussions, what happens...physically?
I'm going to introduce a pair of characters that I'll be using a lot in this blog. One day, two friends named Steve and Anna got bored and decide to throw an elephant into a black hole. Anna will watch the elephant entering the black hole from a safe distance, and Steve the daredevil will ride the elephant into the black hole.
So what winds up happening? (Note - if at any time you get lost, just scroll down to the bolded "quick summary")
Anna watches as the black hole pulls the elephant towards it at super-fast speeds. But then something strange happens when the elephant reaches the Event Horizon (the point of no return) -- it vaporizes.
That's right...Steve and Mr. Elephant are just sailing through space when BAM, they get vaporized when they hit the event horizon. Anna detects some radiation coming out from the black hole, and thinks that the elephant smashed into a brick wall and shattered into pieces that is contained in the radiation.
That's all nice and well...but what about poor Steve? Can we travel with him during his last moments?
Steve, on the elephant, flies through space towards the black hole. Having heard about the vaporization thingy, he braces himself before he hits the event horizon. But when he finally hits it...nothing happens. Instead it's just business as usual. He and the elephant continue flying towards the black hole. Eventually the immense gravity shreds them, but overall, nothing happens at the event horizon.
Wait...what just happened?
Anna just saw the elephant get vaporized at the event horizon, its remains coming off as radiation.
Steve just went through the event horizon, and nothing special happened.
So where is the elephant, or its remains? Is it flying through space like normal, or is it no longer even tangible, existing as radiation?
From what we see, it must be at both places at once! Steve sees that it's normal, Anna sees that it's vaporized. And according to relativity, they're both right in thinking so. So the exact same elephant is in two places at once?
Wait...what if...going through the event horizon cloned the elephant? So it's not the same elephant...it's just two different elephants that have the same matter!
...but that can't be. Even the most basic laws (the first laws of thermodynamics, for example, which states that matter, energy, and information cannot be created or destroyed, only rearranged) forbid it. Quantum laws state that it isn't so, either.
So...there's the paradox, isn't it?
A quick summary - From someone looking on the outside, the elephant is vaporized when it hits the event horizon. From someone looking from the inside, the elephant goes through as normal. And science says they're both right.
What the heck is happening?
Don't try to make sense of it. Just take it all in, just as it is, piece by piece.
This, my friends, is what makes this stuff amazing, elegant, and beautiful.
---
Please leave a comment if you have questions or something to say. This is mny first post, and I'd appreciate feedback :)
