if you really want to know about e=mc2, check out the song “E=MC Hawking” at http://www.mp3.com/mchawking
the site is a bunch of hip-hop songs, using a voice-simulator which sounds like steven hawkings. and this isn’t just some stupid funny thing, all of the songs are full of sound scientific knowledge, and “E=MC Hawking” actually has a great explanation of einstein’s most famous formula. it’s not in-depth, but it serves it’s purpose.
For the sake of those who do, no, Millikan did determine the charge itself. The charge/mass ratio had been roughly known right since J.J. Thomson’s original paper on the electron. You may remember that Millikan was actually measuring the charges on the oil drops and it was the mass of those that he had to worry about (and measure). The mass of the electrons didn’t come into his experiment at all.
First, a bit of background: Before Einstein came around (in fact, before General Relativity, which is well after E=mc[sup]2[/sup]), there was nothing in physics that defined an absolute zero point for energy. You always just put the zero point whereever it was convenient in your problem. For instance, the gravitational potential energy of an object near the surface of the Earth is proportional to its height. Height above what? The floor? The top of the table? Sea level? It doesn’t matter; you use whichever is most convenient.
Well, Einstein happened to notice that the math for relativistic energy was much simpler if you said that an object at rest had energy equal to mc[sup]2[/sup], rather than saying that it had zero energy. It turns out that this also works in GR, where you can define a zero point for energy.
Oh, right. Thanks for the clarification. You’re right in guessing that I was thinking of the charge/mass for the drops themselves.
From what I remember of Modern Physics, Einstein did not really think up E = mc[sup]2[/sup] in a scientific epiphany. It is a result, ultimately, of the two assumptions of Special Relativity. First, the laws of physics work in every inertial reference frame (IRF). Second, the speed of light is the same in every IRF.
From these, it is not terribly difficult to derive the equations for time dilation and length contraction. Although it is not terribly intuitive, the mass dilation equation also comes pretty easily.
From there, you can derive the proper expression for kinetic energy. KE = mc[sup]2[/sup] - m[sub]0[/sub]c[sup]2[/sup]. Here m is the “relativistic mass” and m[sub]0[/sub] is the “rest mass”. Because, if you put something on a scale, you’re measuring its relativistic mass, I prefer to call this one the mass, but I think most people call rest mass the mass.
Now traditionally, total energy is the sum of the kinetic energy something has when moving, and its internal or potential energy that it has just by existing. It thereby makes sense to call mc[sup]2[/sup] E, the total energy, and m[sub]0[/sub]c[sup]2[/sup] E[sub]0[/sub], the “rest energy”. This leads to some neat results, like what g8rguy posted. In my notation, it’s E[sup]2[/sup] = (pc)[sup]2[/sup] + E[sub]0[/sub][sup]2[/sup].
How do you figure? Suppose I have a train, with a full laboratory on board, and it whizzes past me at .99 c. As it’s going past, I take a look through the windows at a Standard Kilogram sitting on a scale. Surely, I read the same value on the scale as the person sitting inside the train, correct?
By reading the scale, you are not measuring the mass in your co-ordinate system.
I believe the relationship comes from the Lorenz transformations, which have to do with the algebraic geometry of frames of reference. Lorenz was a pretty bright guy who worked out some equations that were readily adopted by Einstein. It seems odd to me that he didn’t take his ideas to the next level (special relativity), but then that’s what genius is about, and Einstein obviously had it.
Right. I meant, a scale in your IRF. If you had a train running on a track, and the whole thing was on an enormous scale, the scale would read heavier than if the train were still. That is kind of ridiculous, but what I really meant by scale is any classical means of measuring mass, like shooting a particle at sheets of gold foil. Of course, whatever experiment you do to measure the mass, the measuring device would need be in your IRF.