## Monday, March 30, 2009

### light is a bandit

I've started learning about special relativity in school. I've heard a little about relativity in the past and had previously developed a sort of blind trust that space and time are relative to frame of reference, or something like that. I knew that if you go really fast then time doesn't pass at the same rate, I had no clue how. Recently when working with optics I read that light travels away from the source at a constant speed and even if you were moving away from the source, as far as you are concerned, the light still approaches you at the same speed. This concept totally blew my mind because as you all know: when someone throws a ball at you and you run away, it then appears to you that the ball is coming at you slower than if you just stood still. If the ball behaved as light does then as soon as you start running it would speed up to its initial speed plus your speed. So how is light an exception to the laws of mechanics? Maybe it has something to do with light being a wave of energy stored in electric and magnetic fields, also light has no mass like a ball does. It turns out that this curious behavior of light is Einstein's second postulate of special relativity and because of it, crazy things happen. Things I don't yet understand so I won't try to explain.

I do however want to share what I think is an interesting example of current in a wire from 2 different inertial frames of reference. We have observer 1 who is stationary with respect to the current and observer 2 who is moving with the same direction and velocity as the current.

Observer 1 experiences a magnetic field (it can be calculated by Biot-Savart, or Ampere's Law).

If we imagine the current as individual positively charged particles then to observer 2 the so-called current becomes an electrostatic line of charge.

Observer 2 would experience an electric field due to these charges (we find this by Coulomb's or Gauss' Law). This might lead to a nasty disagreement between the two observers as observer 1 would insist that there was a magnetic field and observer 2 would be quite certain that it was actually an electric field and they both would be right. I must give credit to Gary Adams who showed that to me (and 170 other people in the room) last semester and is a really great physics professor.