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In the equation E=mc^2 (that's meant to say squared), what does the speed of light have anything to do with the energy in something?
Question
#57362. Asked by TheAlphaWolf. (May 24 05 6:17 PM)
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lanfranco
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It's been a long time since I took Physics, but:
Energy=Mass x the Square of the Speed of Light (being 300,000,000(?) meters per second).
I've probably got that wrong, but it might give someone else a starting point.
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TheAlphaWolf
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yeah that's right, but my question is about why the speed of light is in there in the first place. I see no connection between the speed at which light travels and the amount of energy to which matter can be converted.
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peasypod
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The speed of light being a constant is what flabbergasted Einstein into realizing that energy and matter must be one and the same...
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gmackematix
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Well, the speed of light (in a vacuum) is theoretically the maximum velocity at which any mass can travel. Is it that surprising to find that the amount of energy locked up in a given mass is related to the greatest velocity at which that mass can travel?
Especially given that an object's kinetic energy is proportional both to its mass and the square of its velocity.
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TheAlphaWolf
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yes. very surprising :P
so... light has mass?
I thought only electromagnetic radiation could travel at that speed because it has no mass. if mass could travel that fast it would be infinately ... dense?
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gmackematix
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I said it was a maximum but didn't say it was an attainable maximum! Also I didn't say light itself had mass although there have been experiments that suggest it might.
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TheAlphaWolf
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I'd say that the fact that it is bent by gravity suggests it has mass.
lol... how can it be a maximum if you can't attain it? if that's the case... my maximum running speed is 120 miles per hour and what's more, I can run for five months straight without eating or drinking. :P
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gmackematix
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I'll admit that to be more precise I should probably have said it was the limiting velocity of mass, rather than saying it was the "maximum velocty" at which "mass can travel".
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TheAlphaWolf
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ah... so mass can travel at 299, 999, 999.999999999999999999.... meters per sec. but not at the speed of light. gotcha.
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gmackematix
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Which way are you arguing here? That light can only travel at light speed because it has no mass or that it has mass because it is bent by gravity? You seem to be trying to argue both!
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TheAlphaWolf
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I'm arguing that I don't get it :P
so I guess yeah, I'm arguing both.
If light has mass, then it can't go at the speed of light. If it doesn't have mass, then the experiments should be re-thought and apparently gravity doesn't only affect mass.
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gmackematix
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Yeah, and the year after the dinosaurs died was 64,999,999 years ago!!
The amount of force needed to accelerate a mass to a given velocity starts to go up exponentially as the speed of light is approached but yes, theoretically, you can get to within 99.999% of light speed if you have enough force available.
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gmackematix
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Well we know that while special relativity is a good workable theory for most purposes, it isn't a grand unified theory and does break down at quantum level. Maybe this is just one example of that.
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TheAlphaWolf
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lol! you know what I meant.
so you'r saying that say I have a ball and I throw it with X force and it goes 1 mile per hour... then if I take the same ball and want to make it go at 2 miles per hour (wait... no... well, I want to make it go twice as fast... whatever that speed would be) I will have to use X squared and not 2X?
that's wicked. lol
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TheAlphaWolf
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oh that's right I forgot about that little quirck about it. That's why there is that string theory hypothesis (it is NOT a theory people!)
physics is so confusing.
and by X squared I meant any other exponent... not just SQUARED if you know what I mean :P
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gmackematix
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Of course, good old Newton's second law of motion F=ma is a good description of things until you get very near the speed of light. This is why particle accelerators are so huge and costly.
Note that many scientists these days rely less on the old theory/hypothesis/law definitions and prefer the word "model" if possible.
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peasypod
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Where was I when all this was going on?
An object that has "rest mass" can never be accelerated to the speed of light. To do that would require an infinite force since it's mass appears to increase as its speed increases. This "relativistic mass" becomes infinite in the limit of the speed of light. Hence particles that can move at the speed of light (photons , neutrinos...) have no rest mass. However they do have an apparent mass associated with their motion. (It is very old fashioned to talk about relativity in this way but it is the easiest way to explain it).
Under this idea of relativistic mass, The true energy of a particle is given by.
E = m c^2 / sqrt(1 - v^2/c^2)
or
E^2 = m^2 c^4 + p^2 c^2
In the limit of small velocities this looks like
E = m c^2 + 1/2 mv^2
or E = rest energy + kinetic energy
So the particle has a kinetic energy due to its motion (nothing to raise a Newtonian eyebrow there) and a rest energy associated with its mass (cue Newton to fall off chair).
The rest energy "falls out" to be proportianal to mass, with the constant of proportionality being the speed of light squared.
OK, so in a sound byte, why is the constant c^2? Well, its the only way to make the relativistic energy to be invariant under transformations. It comes out squared becuase the increase in relativistic mass is determined by the square of the velocity ratio.
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gmackematix
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Oh Peasy. I had imagined you were looking on and grinning while all this was going on. ;)
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peasypod
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Of course I was.....
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