Can someone give a simple explanation of why in Einstein’s famous equation e=mc^2, the speed of light is squared, when we know that it is impossible to go faster than the speed of light?
Because that equation is not talking about velocity, it’s talking about energy, which just happens to be related to matter by a factor of c^2. And it’s not impossible to go faster than light at all; neutrinos do it all the time - though it is impossible to accelerate past the light-barrier.
“it is impossible to accelerate past the light-barrier.”
Explanation? If you can’t accelerate past the light barrier, how do you get by it?
If you start out already going faster than light, as in a neutrino. 
Those little buggers have no mass, so the whole speed-of-light thing doesn’t apply to them. (Light does have mass). Beyond that, I don’t know the specifics; I’m not a particle physicists and I don’t have my physics textbook handy.
Ha ha ha. I get to post to a Physics thread to clear this up before anyone else does. Neutrinoes do have mass (although not much) and they do not travel faster than c. (Technically speaking, it is possible to go faster than the speed of light, but it is not possible to go faster than the speed of light in a vacuum, which is called c.)
I think I know one thing that’s causing a little confusion here, but I don’t know if I should try to explain it. Oh heck, I’ll try anyway. In Classical Physics, when something is moving, it has the same mass as when it’s at rest. In Relativity, when something is moving, it gains a little mass. When it goes really fast, it gains a lot of mass. If it ever hit c, it would have infinity times what it had when it was at rest. The mass that any object has when it’s at rest is known as its rest mass, and it’s called m[sub]0[/sub]. The actual mass of something is just referred to as its mass, m, and this is the quantity that gets larger as something goes faster. It’s also the m in your equation there. So, one thing that E=mc[sup]2[/sup] says is, when soemthing goes faster, or gets more mass, it also gets more Energy.
This is also why photons can have mass. They do travel at c, but their rest mass is 0.
There is no known particle which travels faster than c. There have been theories batted around, but they are even stranger than the neutrino. If something’s going to go faster than c, a rest mass of 0 won’t do. The particle needs to have an imaginary rest mass.
“c squared” is just a number. A constant. Einstein’s equation in English is:
“mass is equivalent to energy”
or: e=m, if you redefined your units!
The c squared is just the constant of proportionality relating the units of energy to the units of mass. It doesn’t imply that anything is actually moving faster than c.
Interesting! As I understand, then, the energy equivalent of any given mass is that mass multiplied by the speed of light squared. Then is is entirely a coincidence that the number c squared is the constant? It might have been something else like c squared plus 5? How did Uncle Albert come up with that number anyway? Obviously, he could not have performed an experiment.
Well, no, it’s not a coincidence. As a certain wise man who lived long, long ago and far, far, away once said, “In my experience, there’s no such thing as a coincidence”. The way that Einstein came up with that equation, was by looking at the relativistic formula for kinetic energy. In relativity, KE = 1/2 mv[sup]2[/sup] isn’t right… it’s KE = gamma*m[sub]0[/sub]c[sup]2[/sup] - m[sub]0[/sub]c[sup]2[/sup]. Well, if you expand gamma in a power series, you get 1 + 1/2 v[sup]2[/sup]/c[sup]2[/sup] + some other (usually small) stuff, so if you take that term with the gamma in it, it’s m[sub]0[/sub]c[sup]2[/sup] plus something that looks like the old-fashioned KE. Einstein decided that this term represented the total energy, and that there was therefore a “rest energy” to the object of m[sub]0[/sub]c[sup]2[/sup] , even when it was at rest.
There are other thought experiments that can verify that matter/energy conversion can occur, but this was allegedly how he came up with it.
As an example of the logical error in this question, I will propose another question. In the above quote, you say that “we know that it is impossible to go” - Obviously, it is not impossible to go. Can you explain why you would say that it is impossible to go?
(I know it’s cruel and sarcastic. I just hope it’s funny enough to overlook that.)
Not funny enough, Dystopos. It remains stuck in cruel and sarastic land.
“In my experience, there’s no such thing as luck.” Get your quotes right man!
Anyway, this relativity stuff just trips me out. Achernar gives a very lucid explanation of part of it, but sort of glosses over how to define “rest” for the rest mass. In a vacuum, is it possible to tell what’s moving and what’s not? Let’s say the distance between particle A and particle B is decreasing. Which one is moving? Do they both increase masses over their rest masses by an equivalent amount? What if particle C is right between A and B, and its distance to both is decreasing at the same rate? It can’t be moving in both directions at once, so can we say it is at rest and A and B are moving? Yet if B wasn’t there, could we say that both A and C were moving?
Part of the problem, is that relativistic motion doesn’t really follow classical understanding. Obviously, light approaches earth at the speed of light, but at what speed does it approach a rocket hurtling towards the sun? At the exact same damn speed! (Albeit with a shorter wavelength.) I just don’t get that.
This may be a stupid question, but…
can a photon have a velocity other than c?
Sure. C is velocity of light in a vacuum. A photon passing through glass (or water, etc.) slows down. I can’t remember but I think scientists have slowed light down to speeds below 100 mph.
But I thought that the decrease in the speed of light as it passes through a substance was the result of photons being absorbed and re-emitted, rather than the photons actually slowing down. If that’s not true, someone tell me what exactly happens to the photon in a medium to cause it to actually slow.
Greg Charles, I can clear up your qualm (I hope). Of course you’re absolutely right in that it’s impossible to define “at rest”, as per Special Relativity. When I said that, I mean “at rest relative to some observer”. The thing about it is (and here comes the tricky part) two observers can measure the same thing as having a different mass. Suppose Yolanda is stationary with respect to the Earth. Just standing there in space, I guess. Now suppose Zelda is zipping by at 90% of c. They both somehow measure Earth’s mass. Yolanda measures it as being the rest mass, but Zelda measures it as being much more massive, because to her, it’s moving at .9c.
And by the way, if you want to sound impressively smart, don’t admit to not getting Relativity, even if you don’t. The truth is, nobody gets Relativity. But if you can explain that photon paradox as well as you did, you can say that you get it, and everyone (except possibly Einstein himself, who would be far too decorous to point it out) will believe you.
No, it is NOT possible to tell what is moving. As the name implies motion is relative to the observer. Each point you mentioned (A, B & C) will view themselves as motionless and the other two as moving. While you might say, “I know I’m moving…my rocket ship pushed me out here,” it doesn’t matter. Let’s say you kidnapped someone, put them on your spaceship in deep freeze and then thawed them out later and told them to look out the window. Once they get over their surprise they will view themselves as motionless and everything else as moving in relation to them.
The proof of this is that you will always measure the speed of light as the same speed regardless of how fast you are moving. This trick is caused by two things. When reaching relativistic speeds time slows down for you and your rulers (measuring tape) get shorter. As you approach another spaceship at 0.999999C you would see the ship scrunched up. From the other ship the people looking at you would see you as scrunched up. Both are correct. And both could claim the other is the one who is moving. All measurments they take will verify that they are standing still and it’s the other one who is moving.
Until someone finds a rock somewhere in the Universe with a plaque on it that says, “This Rock Is Not Moving – GOD” we’ll have to deal with this brain melting stuff.
I think I did see that rock, but it was moving so fast, I could’t get a good look.
