By the way. Short correction.
A photon always has a nonzero longitudinal mass. I knew what I wanted to say, but it came out wrong.
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On 2001-12-05 04:22, SEG9585 wrote:
Ok, thanks very much Rosen1, it lays it out alot more clearly now.
2 more basic questions, though:
1. What is the "Lorentz factor" exactly? I never heard of this.
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I made the phrase up, assumming that you knew the basic formula and would understand it in context. The Lorentz factor that
I was talking about a factor F where:
F = 1/sqrt(1-(v/c)^2).
Note that according to SR,
m = F times m_0
where m is longitudinal mass and m_0 is rest mass.
You can see that if v=c, F becomes infinity. Well, actually, the precise way of saying this is that as v goes to c, F goes to infinity. There is a very fine distinction between equality and going to a limit which I don't want to get into until I absolutely have to.
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2. You say how the mass becomes infinite since energy becomes infinite, so why is the actual speed of light finite, and why can't it go faster?
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The longitudinal mass of a photon does not go to infinity. The longitudinal mass becomes infinite only if the rest mass is nonzero. For the reasons that I stated (infinity times zero is an indefinite number), the longitudinal mass is indeterminate only if the rest mass is zero and thus doesn't have to be infinite. What we measure isn't infinite, it is a finite longitudinal mass greater than zero.
The photon has a longitudinal mass greater than zero. The photon has inertia, characterized by the longitudinal mass. That is why there is radiation pressure.
A lot of Einstein's work was based on the apparent descrepancy of Newton's third law (for every action on a particle, there is instantly an equal and opposite reaction on another particle) with the fact of radiation pressure (if a particle emits light, the force it exerts isn't felt by the particle until later). He tried to resolve this. He didn't at the time know about photons (he later introduced the concept, for which he won the Nobel prize). However, most people at that time didn't know that light had mass. So where does the radiation pressure come from? Well, E=mc^2. Light contains energy, and energy has mass, so light has mass and can exert radiation pressure.
As some people will tell you, the formula E=mc^2 has a history before Einstein. However, they don't mention some caveats. Einstein worked it out in a different way and in a far more useful context. However, it is true as far as it goes. He wasn't the first. Nor did he get a Nobel prize for THAT particular formula.
A photon has a rest mass of zero, but a longitudinal mass greater than zero. The longitudinal mass goes into E=mc^2, not the rest mass. Unless they are the same thing, which only happens when v=0. If v=0, there is no difference between a rest mass and a longitudinal mass. Newtons Laws in their simplest form work well only when v is much less than c.
<font size=-1>[ This Message was edited by: Rosen1 on 2001-12-05 06:52 ]</font>