Friday, March 30, 2012

Special Relativity at its Simplest

Albert Einstein in his glory year of 1905 published many papers which changed modern physics against its will. One of those papers discussed the idea of Special Relativity. Since at the moment I have no idea how the theory's math works, and Im guessing you guys wouldn't really care about the math anyway, I will just give you the basic idea behind Special Relativity.

Lets begin by imagining yourself floating in a starless space by yourself where in every direction you look its pitch black. Lets assume that you are still, but wait, can we assume that? At this very moment you can say you are sitting still on your chair. The reality is that its all relative. Relative to the room, your still. Relative to the Earth, your rotating along the Earth's axis at hundreds of miles be hour. Relative to the sun, your moving at thousands of miles per hour as the Earth rotates around it. Eventually you get to the point to where you are moving at around 500,000 miles per hour as the Milky Way galaxy moves outwards into space as a result of the Universe's inflation property. So to connect back to the earlier scenario, you cannot say you are completely stationary in space because you have no reference points to tell you whether you are moving or not. Its like when you are on the freeway and you look outside the car window. As you see a road sign approaching, you perceive it as though it were moving towards you. Obviously we know thats not the case because we know we are moving. We know because we feel the bumps of the road as the car wobbles to them. We also feel the acceleration that the car produces, (but that applies to General Relativity which I will save for the next post). We know for a fact that we are not stationary and that the road signs aren't the ones moving past us. This is due to the forces we feel in the car. However the scenario above doesn't include forces in it.

So now that we understand that key analogy lets jump back to the earlier scene. So your in space were nothing is visible. You don't "feel" like your moving and in affect you feel still. This feeling of stillness is a lie though. When someone is floating in space at a constant velocity, they don't feel like they are moving. This means that someone could be traveling at 500,000 m/s in a frictionless space and not know they are. So there is no way of knowing whether you are moving or not in a colorless space if no forces are felt.

Now lets change the scene a little to give you a little more understanding. Lets say you get a buddy called Derpina. Lets also say you are both given a light to wear thats always on. A blue light for you and a red one for Derpina. Lets say your both floating in space and you guys have never seen each other before; completely unaware of each others existence. Now lets say you are in space and feel stationary. All of a sudden you see a red light in the distance. You start to panic as it gets closer and closer. Then for a couple of crucial seconds you see as Derpina whizzes by you. There goes the love of your life lol just playing XD. Anyway, right there and then you believe that you just saw Derpina move past you. You believe this because you felt stationary and therefore the only one who could have been moving was her. Remember however that in a frictionless space, if one goes at a constant velocity no feeling of moving is detected. Therefore we don't know which of you was moving. For all we know Derpina could have felt still and you could have beem the one moving past her. And as strange as this might sound, thats exactly what she experienced too. Once again neither will ever know whether one or the other was moving. The only way to know is if one felt a force which is as I said earlier, not a part of this discussion but of a future one. Now one more point, what if both you and Derpina feel like your both stationary and your both next to each other. We can either say your both stationary or your both moving at the same constant velocity.

So now that we have that out of the way lets take a break from all this space mumbo jumbo and head to a more "realistic" scene. Lets say that we have just entered a town who is having an intense confrontation between two political parties. One wants chocolate cake to be served on Mondays in and the other one wants pizza served every Monday. These two parties are both locked in a see-through train where a table is placed in the middle of it. The table has a light bulb fixed at its center giving both sides of the table an equal amount of distance from it. There are cameras all around the roads that the moving train is going to pass by. Both the left and the right side of the table contain a buzzer which sends a light beam to the light bulb in the middle, both equidistant from the light bulb (remember that light always goes at 3*10^8 m/s no matter what). There are people crowed all over bars waiting to see whats about to happen with the confrontation. Turns out the parties stuck a deal. Each party will have one representative sit at their corresponding side of the table and they will press the buzzer at the same time as the other one. If both of the light beams (which are passing through a see-through optical cable on the table) hit the bulb at the same time, then the parties will settle with switching Monday's lunches back and forth. However if one light beam hits the light bulb before the other, then the parties will go in an all out war.

Its the day of the decision and the parties are ready. Each side has their representative ready to press the buzzer at the same time. Since cameras are watching the event through the see-through train, the public watching the event through the bar's television can tell whether one light beam hit the light bulb first. The treaty is about to start but the train starts to move at a constant velocity of 30 m/s on frictionless tracks. The parties give each other the sign and press the buzzer at the same time. All the men on the train from both parties agreed that each beam hit the bulb at the same time and both the parties sign the treaty. Something very strange happened though. The public who supported chocolate cake swears that the cameras that broadcasted the event showed that the pizza party's beam hit first and therefore showed it wasn't going to comply with the treaty. As a result the cake party members at home start bombing the pizza party and a war starts between the two parties.

So how could such a problem be true if all the men on the train witnessed the light beam from each side hit the bulb at the same time? Who is right in this situation? The men on the train, or the men outside the train who saw the event through the camera's broadcast? Oddly both. Since the men on the train are moving at the same constant velocity on the frictionless tracks. We can say they all feel stationary and therefore relative to the train, all the men on the train are indeed stationary. So if both representatives hit the buzzer at the same time, which they did, then logically both light beams will hit the bulb at the same time. This truth however only holds true to the men on the train. Since all the men on the train are moving at the same constant velocity, they all experience and view the same thing. But what about the people watching the event at the bars which are not on the train moving at a constant velocity? They see one light beam hit the bulb first because its true relative to them and the train. Since the train is moving, one side of the table has a light beam moving towards the bulb faster while the other one has a light beam moving away from the bulb and therefore is slower to hit the light bulb.

To better illustrate this lets imagine you roll a ball on movable table. First you roll the ball left and keep the table still. Then you roll the ball left once again at the same speed but now you also roll the table left too. The effect? The ball has to travel a longer distance to reach the left edge of the table. Same goes with the train and the light beam. Since one light beam is going left and the train is also going left, the bulb in the middle of the table is moving away from the light beam moving left. Therefore the light beam has to travel a longer distance to reach the bulb. In contrast one light beam is moving to the right while the train moves the bulb on the table left. Here we can say that light beam is moving towards that light bulb quicker for it has to travel a shorter distance to get to it. So for the public seeing the event through the tv are right too. Since the people on the train are moving at a constant speed, they all feel stationary relative to the train and therefore its like they aren't moving. This makes the perception that the bulb (which is moving to the left) is not actually moving away from the light beam that is also moving left. So as the title of Einstein's theory suggests, the way you see this event is all based on its relativity. Both of the perceptions are correct, but only one is true based on your position of viewing the situation.

Im guessing your brain is probably fried right now and your about ready to flip a table all the way to China. Its alright though, not everything is understood the first time. Just try to re-read what I've wrote so far and try to understand the situation till you get it. There will also be some videos at the bottom to provide some visual aid. For those who understood it great. Let us continue with the rest ;)

Ok lets go back to the space scene with Derpina. You both still have your lights and are still in this pitch black frictionless space. Lets say you each have a clock and some super powerful binoculars. Lets say you see Derpina coming towards you once again and you quickly pull out your binoculars and check her clock while seeing your clock at the same time. Turns out her clock is moving slightly slower than yours. Wait what? Hold on it gets weirder. Derpina from her point of view sees you floating towards her and sees your clock moving slower than hers. WTF is going on!!!? This ladies and gentleman, is what we call Time Dilation. When someone is moving they go through time slower than people who aren't moving. In effect their clocks tick slower than people who relative to them, are stationary. However the people who are moving don't experience life in slow motion from their point of view. They perceive time passing by at normal speed like when they were stationary. The people not moving see the people in motion pass through time in slow motion because they aren't moving and therefore they move through time at its normal speed while the people in motion go through time at a slower speed.

Back to the scene between you and Derpina in space. Both of you see the other's clock moving slower, but which one of you is moving and therefore has the slower moving clock? Neither of you can tell since no force is felt by either. Therefore yall can each say that the other's clock was moving slower than yours. So once again we are stuck in a situation where both the perceptions are true. To elaborate more on how time slows down as you move faster, imagine a graph. The Y axis is "distance covered" and the X axis is "time". As you cover more distance over a smaller amount of time your velocity increases. As a result the more your velocity increases the less you move on the time axis. Eventually you hit the limit to how much distance can be covered over an amount of time. This limit is the speed of light. Once the speed of light has been hit the line on the graph will be parallel to the y-axis. You will no longer be moving on the time axis and time ceases to pass for you. In conclusion the higher your velocity, the less you move on the time axis and the slower time goes for you. Once you hit the speed of light, time stops and you don't move through time anymore. This is why scientist say that the light particles (the photon) created at the big bang are still flying through space inflating the universe. All while not going through time at all. Apart from Time Dilation there is also something called Length Contraction, where your length is shortened the faster you go. I won't any more in depth on it because this post is already lengthy.

 This post is just some of what Special Relativity has to offer. The theory's name fits its self because the situations it uses like the ones above require them to have special conditions. They require you to be at a fictionless location where your moving at a constant velocity. This is not however how the real world works. We don't all move at constant velocities, we experience acceleration and forces. Something which ties into General Relativity and my next post's topic.


P.S. Most of this was taken from Brian Greene's "The Elegant Universe".

If you want to learn more or better understand Special Relativity watch the vids below or read Brian Greene's book above.

Vid 1: A nice and simple video.




Vid 2: A quick but confusing video :s

Vid 3: You really want to dive deep and learn about Special Relativity. Take your chance and start with the basics. Let Stanford's own Leonard Susskind show you some physics!!!

Wednesday, March 14, 2012

Pie day and Albert Einstein

Today ladies and gentlemen, is Pi day :). Since its discovery back in Babylonian times, it has remained an iconic symbol in math. Pi derives from the ratio of a circle's circumference over its diameter. The Babylonians thought that the ratio was just three, but we know today that Pi is a three with an infinite amount of integers after its decimal point. We just use the convention 3.14 to simplify things. Now why is today Pi day? Because today's date is 3/14/12!  Now why is Pi called pie? lol because of its orientation when you reverse 3.14. Look at the picture below to see what I mean.




Apart from being pie day, its also Albert Einstein's birthday!!! Happy B-DAY Mr. Einstein. Your contributions to the world of science will never be forgotten :)  

 So below me will be some interesting videos on Pi. This post was just a quick post to celebrate todays two important events. Hope you have a good day and eat a piece of pie!!! >:)

Video 1:



Video 2:



Video 3:



Video 4: