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Anderson Video - Length Contraction

Professor Anderson
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Okay, so length contraction is the following. If you measure a stick at rest it's going to have a length L. Okay, here you are taking a look at that stick and it's going to have a length L. But if you are at rest with respect to it you get one measurement. If the stick is zooming past you at some speed V you get, in fact, a different measurement. And the scaling between those two is our good old factor gamma. Okay? So let's make sure we get the nomenclature the same as they had in the book. I think they want this one as L naught. That's the rest length. And this one is the one they call L, which is the moving length. Okay, and the relationship is the following. L is equal to L naught over gamma. Remember what gamma is. Gamma is 1 over the square root of 1 minus V squared over C squared. And gamma is always bigger than 1. If V is 0, it's 1. If V is something bigger than 0, then this number is bigger than 1. And so L is shorter than L naught. Okay, it's shorter by this factor gamma. And this is known as length contraction or Lorentz contraction. Okay, because Lorenz was one of the first to come up with all these mathematical principles. Okay, so this is kind of weird, but when you measure objects that are moving, they are in fact shorter than when they're at rest. Okay? It's only in the longitudinal direction, though. So for instance, if I have a box and that box has height H naught length L naught. And now I take that box and move it at some high speed V, the length contracts to L, but the H stays exactly the same. Okay, it only contracts in the direction of the velocity. Okay, doesn't contract in the transverse direction. Now in class we said that when Einstein started thinking about these problems he was thinking about the electrodynamics of moving bodies. And if you think about electric fields and magnetic fields due to chunks of charge then you have to take into consideration the length contraction that happens in these systems as well. Okay, a chunk of charge will in fact compress in the longitudinal direction, in the direction of V. And this has very strange implications, right? E fields can transform into B fields, B fields can transform into E fields. And if you continue on in physics when you get to upper division electricity and magnetism you'll see a whole set of relations that describe exactly how E fields transform into B fields, depending on the velocities that are involved and the directions of those velocities. It's really very fascinating stuff. I think. You may not. I think so. Okay.