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.

No comments:

Post a Comment