Friday, August 22, 2008

Whoda Thunk It? Einstein Was Actually Right!

Einstein's theory of relativity-An hour sitting with a pretty girl on a park bench passes like a minute,but a minute sitting on a hot stove seems like an hour.
Special relativity is one of those psych your mind subjects in physics. For the longest time I though there would be no way to observe it in nature. The 2 basic ideas in special relativity are that when an object is going a significant fraction of the speed of light it's length contracts and time dilates from the point of view of an observer. Length contraction means that if a space ship was flying by you at half the speed of light (0.5c) it would look shorter than it would if it was sitting at rest right next to you. Time dilation means that from your point of view time in the space ship will look
like its time is passing slower than it would if the space ship was sitting right next to you. This theory was founded by Albert Einstein as many of you already knew.

How Do We Really Know That Relativity is Special if We Can't Observe It?
The problem with special relativity is that you can't see any effects until an object is moving really really really really really really really really really really really really fast. The speed of light is 670,616,629.4 mph. Since most of us have never gone much faster than 500 mph this speed is pretty much impossible to imagine. But what about really small particles that are really light and very energetic like electrons. In fact electrons can travel at a significant fraction of the speed of light. But how might we observe length contraction or time dilation for an electron since it's impossible to image one?

Holy Flying Electrons Batman!!!!
One way to think about electrical current is to imagine a bunch of positive charges and negative charges inside a wire. The positive charges are moving very fast in one direction and the electrons are moving very fast in the other direction. The charge density of the positive charges is uniform and the charge density of negative charges is uniform also.

Why Does My Compass Keep Pointing at The Canadians?
One really strange and cool thing that is associated with moving charges is the magnetic field. We have all played with magnets before which produce a magnetic field. The magnetic field is due to tiny little charges moving around in circles throughout the material. If you make a material so all these circles are parallel you can make a strong magnet. It turns out that a wire carrying an electrical current also produces a magnetic field. The field points in circles around the wire like the rings on a tree. The farther from the wire you get the weaker the field is. Magnetic fields only affect moving charges. Where does this magnetic field come from?

Rubbing Your Hair With a Balloon-An American Pastime
We are also familiar with electric fields. The easy example of that is when you rub your hair with a balloon. This pushes charges to the balloon and the imbalance of charges causes the balloon to be attracted to your hair. Any imbalance of charges will create an electric field which causes attraction or repulsion depending on what the charges are. Where do electric fields come from? They come from charges positive and negative charges produce electric fields.

Do Magnetic Fields Come From Mars or Jupiter?
We still don't know where the magnetic field in a current carrying wire comes from. Let's look at our model of positive charges moving very fast in one direction and negative charges moving very fast in the other direction. According to special relativity, if something is moving very very very very very very fast it will appear shorter from the point of view of a stationary observer. From a stationary point of view both current densities are the same because the charges are moving at the same speed in opposite directions. No magnetic or electric field can be observed by a stationary observer. Let's pretend you are a positive charge outside of the wire. If you are moving at the same speed and same direction as the positive charges in the wire positive charges in the wire look stationary but negative charges are moving really really fast in the opposite direction. So if you believe special relativity you would see electrons with a higher charge density than the positive charges. Now if the two charge densities were the same, there would be no electric field coming off of the wire because they would cancel out (+1 + -1=0). But now that we know the charge density of negative charges is higher, there is some electric field. The E-Field from negative charges is greater than the E-Field from positive charges (from your moving viewpoint) so there is a net electric field (+1 + -2=-1). A field from negative charges will be pointing inward which means that the E-field will pull you (a positive charge) towards the wire.

But we were always taught that is was the magnetic field that would pull the moving positive charge towards the wire!! Well, guess what, Magnetic fields are just electric fields caused by length contraction. So there you have it, magnetic fields are a result of special relativity. Special relativity can be observed in nature and has been observed for a really long time. It just took a while to realize that it was due to relativity.

Saturday, August 2, 2008

The Most Fundamental Science

Now, I know all of you realize that physics is the most important and most fundamental science but, let me remind you of why it is so amazing. Biology, Chemistry, Geology, Engineering, Paleontology, etc. are all based on physics. According to the almighty Wikipeida, Physics is the science of matter and its motion, as well as space and time. Good attempt wikipedia but physics also describes light which isn't really matter. There is no denying that all things physical are made of matter or waves. So, that alone proves that physics is the best of all sciences. But I'm going to continue telling you about the wonders of physics.

An Imaginary Universe Where Gravity Will Psych Your Mind
In physics 1 we learned about gravity, acceleration, newtons laws, conservation of energy, harmonic motion etc. It seems that lots of people immediately think about launching projectiles when they hear the word physics. That is, in fact, physics but there is so much more. The equation that describes the gravitational attraction between two objects with mass is:

Imagine living in a world where things with mass repelled each other. Sure, God could have created the world like this but He didn't. If things with mass repelled eachother we could not be orbitting around the sun and we would all freeze to death. God gave the universe order by making gravity an attractive force.

Why That Newton's Cradle Toy is So Cool
Probably the most beautiful law of physics is Conservation of Energy. This law states that energy is not lost or gained. It doesn't matter how an object is changed, gained energy for an object comes from somewhere and lost energy from an object goes somewhere. This thing we call energy can occur in two different forms. Kinetic Energy and Potential energy. And really, potential energy isn't real we just made it up so we could have this beautiful law. Most of you have seen that toy that rocks steel balls back and forth and the knock into each other clicking back and forth for a long time. This is an excellent example of conservation of energy. When you pick up one of the balls and drop it you give it an initial kinetic energy. It hits the other balls and stops in place. This loss in energy has to go somewhere so the force translates to the other side and gives the last ball kinetic energy. The equation for kinetic energy is:

You can see that it is dependent on both mass and velocity. When you pick up two balls and drop them they have the same speed but twice the mass. In order to conserve energy 2 balls on the other side are given a velocity.

Now, if you watch the toy long enough it will stop moving. Eventually all of the balls will come to rest. "Aha!!! that disproves conservation of energy," you say. You initially gave the balls energy by applying a force from your hand and it seems like all that energy goes away since the balls stop. But you forgot something. The balls make that beautiful clicking noise as they collide into each other also, the collisions heat up the balls slightly. The lost energy is turned into sound and heat which are 2 forms of kinetic energy. Heat is the movement of particles on a smaller scale so it is also kinetic energy. Sound is a more ordered vibration of matter and in this case the air is vibrating. The sound we hear is just the vibration of air that is caused by two balls colliding. So we have now shown that all the energy is conserved it just goes into slightly different forms.

I will tell you the story of where all the energy came from and went. Well the morning before you tried this experiment you ate food. Food has calories which is chemical potential energy. When you eat the food the chemical reactions inside your body give off energy which you and I use to move around, talk, listen, look, etc. So with this new energy that was given to you you had the ability to pick up the ball on one side of the toy. By putting the ball in an unstable position with gravitational potential energy it falls converting the gravitational potential energy into kinetic energy. The ball hits the others and its kinetic energy is converted into 1. Kinetic energy on the other side, 2. Sound, and 3. Heat. All sound is converted into heat eventually. These last steps are repeated until all the energy has been converted into heat. Vuala!!! Now you see how energy can be conserved.

Quantum Weirdness or Why Everything is a Bunch of Waves
There are tons of things that we can talk about having to do with physics but this note is getting long so I will talk about my final subject. The wave, particle duality of everything. You may have heard that light is made of photons. You may have also heard that it is a wave. But which one is it? Well it is both kind of. Light has both particle and wave characteristics. We have all seen rainbows before. Rainbows are absolutely a characteristic of waves. Different wavelengths of light are bent differently depending on how much of a water droplet they pass through. Also, some stars look blue and others look red. this is a wave characteristic called the Doppler Effect where blue corresponds to a star moving towards the observer and red corresponds to a star moving away from the observer (this is why ambulance sirens change pitch when they pass you since sound is also a wave). But if we make a kind of light that has a really really high frequency like Gamma radiation it looks like a particle. Some radioactive elements will emit gamma radiation which comes out one at a time like a particle. When you look at the signal you see one pulse at a time like a particle. Another particle like characteristic is the ability of light to move things. If you have no friction and light is absorbed correctly the sunlight can move an object. So we see that light acts both as a wave and a particle.

This is all very confusing because to us particles and waves seem soo different. Now we've all heard of electrons before. They are very tiny particles that are much much lighter than protons. Interference is a sure characteristic of a wave. If you have two speakers for your entertainment system you can move around the room and find quiet spots and really loud spots. These are characteristics of waves called destructive and constructive interference. This can be seen with light if it is passed through the correct size slit. You can shine a laser through the slit and see lines on the wall where the light spots are constructive interference and the dark spots are destructive interference. Well some crazy physicists decided to try doing the same experiment with electrons. So they shot the electrons through the slit and what do you know? The electrons showed interference when they were detected on the wall. We thought for sure that electrons were particles but this new evidence suggests that it is a wave also. This effect brought about all kinds of things like quantum mechanics, Heisenberg uncertainty principle, and more. This showed that even the things we call particles have wavelike characteristics. If you try the same experiment with protons (Hydrogen) you won't see an interference pattern. This shows that the less massive an object is the more its wave like features are exhibited. That is why you and I hold together really well and are not moving around like a wave all the time. Since we have a lot of mass (compared to electrons) we don't really show any wave like characteristics. If you have a particle travelling through space it has a wavefunction that describes the particle's behavior. If you add up a bunch of different frequencies correctly you can get something that looks like:

This pulse can be thought of as a particle. A single wavelength wave looks like a sine wave and just goes up and down periodically. But given the correct frequencies you can get pulses like this that can represent a particle. You can imagine a very light particle would have a wavepacket that is longer and looks closer to a sine wave because we know that light particles act more like waves than heavy particles. A heavy particle would have a wavepacket that is more compact and goes to zero very quickly. This makes sense because a wavefunction like that doesn't look much like a sine wave so it's hard to observe wavelike characteristics with a wavepacket like that.

I have only brushed the surface of why physics is so cool and hopefully I will feel inspired in the future to tell you more about the wonders of physics.