Start typing, then use the up and down arrows to select an option from the list.

Physics36. Special RelativityConsequences of Relativity

Okay, one thing that we talked about in class earlier was this idea that E equals mc-squared. Okay, and that is rest mass. So this is the energy in the rest mass particle but when the particle is moving, we know it of course has kinetic energy, and so there is a more general relationship for E, which is this: E is equal to gamma MC squared, where again gamma is our 1 over square root 1 minus V squared over C squared. Okay, but there is a much more powerful relationship between energy, momentum, and rest mass, which is the following. If you take this, you can prove it to yourself but I'm just going to tell you the answer: E squared is equal to P squared plus M squared. Now you look at this equation and you say, wait a minute those don't even match up in units, right? M is kilograms, how does kilogram squared become joules squared? The what -- the reason I wrote it like this is because it's easy to remember if you let C equal 1. Okay, and this is how theoretical physicists think about energy momentum and mass, how do they relate to each other? E squared equals P squared plus M squared, but we know if we want to get the unit's in there we got to dump in some C's, and so in reality we would write the following: E squared is equal to P squared C squared plus m squared C to the fourth. Okay? Or E squared equals P C quantity squared plus M C squared quantity squared. What have we just written? This is a total energy of the particle. This is the momentum of the particle and this is the rest mass energy. Okay, and this is a very powerful relationship that tells you how all these different terms combine and I like to just think of it as that, E squared equals P squared plus M squared, you throw in some C's where you need to satisfy the unit's. Now this has interesting consequences not just for things with mass but also things without mass. And if I look at this equation here, particles without mass, meaning that this last term goes away. What is a particle without mass? Well, one of them is called the photon and a photon is a little piece of electromagnetic wave. Electromagnetic waves are made up of these particles called photons and so the energy of a photon is what? Well, it's P squared C squared plus zero, that term goes away, and so we just get the following relationship: energy is equal to P times C. Okay, this is the energy of a photon. Okay, and we know that photons have energy, we also know that they have momentum, right? We knew that before but this relationship tells us absolutely that if it has energy, it has momentum. Okay, and in fact we know what that momentum is. P is equal to energy over the speed of light, the energy of a photon is H times the frequency of the photon. Okay, C is lambda times f, and so look what happens, f drops out and you get h over lambda and this is something called Planck's constant. What's the energy of the photon? Its Planck's constant divided by the wavelength of the photon. All right, why don't we take a five-minute break and I will see you guys back here and a few and we'll have a little more discussion, all right.