OK I get what e=mc squared means but I have one question about it that I have yet to find an answer on. why do we use the speed of light. why is E = to the mass of the object times the speed of light squared. I mean how does how fast light goes have to do with it all. why is it squared and not just the speed of light?
How about you change the formula around so that c is on it’s own?
C = square root of E/m
Does that make it any easier?
The equation E = mc[sup]2[/sup] simply says that the rest energy of a given object is equal to it’s mass times the constant squared. Of course Einstein didn’t pull this out of nowhere, this formula was derived from using relativistic lorentz transformations on stuff and Einstein found this equation. The importance of this equation is that the rest mass and rest energy of an object don’t change as velocity changes, and also helps in other various ways for calculating energy released by certain reactions.
In any case,
Because the equations the formula is derived from have C in them.
See above. It might help to read up a bit on special relativity if you haven’t already. That might help you understand where that equation fits in to the whole picture.
Enlightenment (har) will come when you stop thinking of c as a speed and start thinking of it as a conversion factor. 3 feet/yard = 1, so x yards is 3x feet. In exactly the same way, c meters/second = 1, so x seconds = cx meters. Time is a direction like any other, but we’ve historically measured it in radically different units. c is the conversion factor between those units. It’s an intrinsic property of the geometry of spacetime.
So how does e = mc[sup]2[/sup] come into it? Remember that energy has units kg*m[sup]2[/sup]*s[sup]-2[/sup]. Since a second is c meters, m[sup]2[/sup]*s[sup]-2[/sup] = c[sup]-2[/sup], reducing the units to those of mass with an appropriate conversion factor.
Oh, and incidentally: c is only incidentally the speed of light in a vacuum. c is defined geometrically, and it turns out that when interpreted as a speed disturbances in the electromagnetic field propagate at that rate.
Ok i think i didn’t explain myself very well as to what i was asking. still not sure if i can. why does light factor into it at all. what does light have to do with how much energy something has. in all other formulas i get what they all have to do with each other but why does the speed of light come in to play in this one at all.what relationship does the speed of light have to do with energy.
ok i looked up some more information on the web about this and still didn’t help me understand why the speed of light has to do with energy. i understand it works that when you have the energy and the mass that it comes out to the the speed of light squared but why or does anyone really know? but i did come up with another silly question. if the closer you get to the speed of light the heavier you are. so you will become infinitly heavy therefor you would need infinite force to go the speed of light. how does light particles go the speed of light? wouldn’t they need infinite force?(and be infinitly thin for that matter)
Try looking up my last post on the web, particularly the part and the end where I state that light is to the side of the discussion.
Once again: c is a conversion factor reflecting an underlying property of the geometry of spacetime. It relates distance and time. Since energy’s units involve those of distance and time, we can change the time units into distance units, which then cancel out. The remaining units are those of a mass, and a conversion factor of c[sup]-2[/sup] is involved. m = Ec[sup]-2[/sup], or E = mc[sup]2[/sup].
It also turns out that lines with “slope” (in a certain 4-d sense) c are the lines along which disturbances in the electromagnetic field (light) propagates in a vacuum. By a historical accident, this property was discovered before the geometric nature of spacetime, and ever since c has been unfortunately saddled with the name “speed of light”.
In short: for the third time now, light has nothing to do with E = mc[sup]2[/sup]. It’s a formula about the geometric structure of spacetime.
Remember that when we use that phrase, speed of light, it refers to the whole electromagnetic spectrum of which the visible light is only a small part. Radio waves, infrared (heat), ultraviolet and gamma rays are also part of that spectrum and thus moving on the speed of light. Multiply the wavelength and frequency of certain radiation and you’ll get c, for example the wavelength of typical FM radio transmission could be c / 93,2 MHz = 3,22 m. Anyway, you’re right in that moving on the speed of light in vacuum would be impossible for any object with even the slightest mass. Therefore, light particles, usually called fotons, are without mass and so can achieve c.
Again, it should be said that when light is moving through a medium (not vacuum) its speed is less than c. Similarly any other particle with zero mass moves at speed of c. Note that fotons are affected by gravity since they have energy, even though they don’t have mass.
And obviously, foton is photon in English language.
I think the answers so far are over the head of the OP – they’re over my head, and I know a little something about relativity.
toth, the short answer to your question is that “we” don’t use c in the equation. The Universe uses c. It simply happens to be true that E = mc[super]2[/super].
–Cliffy
I understand them, sorta, but I think Mathochist oughta try using simpler language with the OP (who, apparently, hasn’t even reached the part of his education where he learns about the question mark and capital letters. Such inquisitiveness in such a young mind ought to be encouraged.)
I’ve noticed, though, that math types tend not to be very good at explaining the things they know. They seem not to use a word more than they think necessary for their explanation. Each sentence seems to be something like a line in a mathematical proof - it advances the explanation in exactly one respect, and no extraneous sentences are used. In fact, they seem attached to the language used to describe things in the papers they read.
thot200 – I’ll give it a shot, if you want another try.
Don’t think of ‘c’ as ‘the speed of light’ in the same way you think of the speed of sound, or the top speed of a Ferrari or unladed swallow or something.
Instead, think of ‘c’ as a universal constant, kind of like Pi (3.14159…) or something. (In fact, that’s why we use ‘c’, it’s short for ‘constant’) It shows up in a bunch of places when you describe the universe. One place it shows up is in converting energy to mass (E=mc squared). Another place it shows up is in looking at the sort of universal speed limit, which nothing can go faster than. It turns out this is ‘c’, exactly. Now it turns out that because of the physics of light, in a vacuum, it’s speed is the same as the universal speed limit, so the speed of light in vacuum happens to be ‘c’. But that’s not really how it’s defined, it’s just one of the places that ‘c’ shows up.
Now, if you ask 'But why does it show up in defining the speed of light?", then you have to get into serious relativity theory, which will take a little more than one paragraph to get across, and some serious mental effort to understand.
This page (and many others, I suspect) may be useful for those who prefer to consider these things in mathematical terms.
Now, the Lorentz transformation equation already has the (1 - v²/c²)[sup]1/2[/sup] term found in the relativistic time and mass equations. What was the original meaning of the c term? Did Lorentz foresee that the speed of light was a ‘speed limit’, or at least that there was some universal speed limit? (It shouldn’t be hard to see that the equation becomes undefined if v=c.)
It may be a bit easier to understand why light travels at the universal speed limit if you consider that photons don’t have mass. The relativistic mass of any object which does have mass approaches infinity as its speed approaches c, but the relativistic mass of a photon is still zero even at light speed. I’m not sure how well this explains why photons in a vacuum travel at the fastest possible speed, but at least it explains why they can.
My turn!
c represents the observed and demonstrated speed limit of the universe. Einsteinian relativity shows that no observer in any frame of reference ever observes anything travelling faster than c. The Lorentz equations mentioned by dakravel found c to be a necessary factor to include when figuring out velocities and such for objects travelling at very high speeds. Einstein further manipulated these equations to show what the total contained energy in any physical body was. As Mathochist pointed out, Energy is measured in terms of “mass x square of a velocity”. Einstien’s work shows that c is the velocity to be squared in the equation of how much energy each unit mass possesses.
Light enters into it because light travels faster than anythig else: at the speed lmit of the universe.
Why is the speed limit of the universe c and not some other number? Sorry, ask a real physicist.
In this format, yes, it’s difficult since I can’t get a back-and-forth like I could in a personal meeting at a board or something. As for the spare language, I tend to find that the more I say and the more nuanced I put it the more confused people get. Better to keep it simple, spare, and logical. Whether this is a side-effect of reading a lot of mathematics papers or that mathematics papers read like they do because the people who are good at thinking clearly think like this… that’s another thread entirely.
As others have said, it’s best not to think of c as “the speed of light”. Much better to think of it as just “The Speed”. It’s a fundamental constant of the Universe with the same units as a speed, and in fact it’s the only such constant with speed units. This means that anytime you have a fundamental statement about the Universe with a speed in it, that speed must be c.
Two examples of fundamental statements about the Universe are “A massive object inherently has energy equal to its mass times a speed squared” and “Light travels at a fixed speed”. In both cases, it remains only to say what that speed is. But in this universe, there’s only one speed to choose from, c. So the first statement becomes “E = mc[sup]2[/sup]”, and the second statement becomes “The speed of light is c”.
This is actually a trivial question. Given that we have an absolute speed limit in the Universe, we decided to call that speed limit c. If it were something else, why, we would have called that other number c, instead.
How does Energy relate to the structure of spacetime? (Honest question).
At the risk of hijacking, it’s got nothing to do with being a math type. Writing for a knowledgeable audience with a similar background and writing for a lay audience are two completely different types of writing, and experts in any jargon-heavy field will struggle to do the second clearly. The key to writing for a lay audience is starting with information they know and building on that to reach information they don’t know. For an expert in a given field, it can be quite difficult to remember what non-experts don’t know.
I have a question. Where, in non-relativistic terms does the “1/2” term come from for kinetic energy (E = 1/2 mv^2) and why is it not present in E = mc^2?
(I should know the answer, as I’m in my 3rd year of electrical engineering and my second year of a concurrent physics degree, but I can’t think of it at the moment.)
I know this is a bit distantly related to the OP, but I would encourage thoth200 to pick up a copy of The Fabric of the Cosmos by Brian Greene. It’s filled with far more interesting questions (and answers) about physics than simply why is the speed of light involved in the equivalence of matter and energy. I was a physics major in college (before switching to computer science), so some of what’s in the book is familiar to me, but a lot of it is new and it’s just a downright fascinating read. And written in a very accessible style for people both with and without any background in physics.