e=mc^2

**blackbird86** · Nov15-09, 05:27 AM

So energy apparently equals mass times the speed of light squared. According to Einstein anyway. I was taking an objective look at this theory or whatever it's called just now and I got to wondering...what exactly does Einstein mean by "energy" and what does the speed of light have to do with it? I'm no physicist, but it seems to me that the speed of light is just some random number and I'm hazy on what how he defines "energy." Does he mean total potential work possible from a piece of matter? If so, how does he know it's not infinite? I mean, aren't there physics theories out there that say that this sort of pattern of things revolving around things goes infinitely small. By that I essentially mean, there are particles within an atom's components acting in the same way that the earth does in the relation to the Sun in the solar system, to the center of the galaxy, and then the universe and all that. Yeah, please forgive my lack of physics knowledge, but I just thought I'd try a skeptics view at this stuff for kicks. Thanks in advance for your patience and replies.

I was sitting on the toilet just a minute ago thinking that perhaps nuclear fission isn't a result of an immense amount of energy existing within a single atom, rather just due to the contagiousness of a single loose proton. by that i mean a single atom might not have an unbelievable amount of energy, rather a loose proton has the ability to cause a massive domino effect in the same way an army of trillions red ants would be more potent a weapon than one bear, but that doesn't make a single ant more deadly than a bear. i hope that makes sense...and again, please excuse my ignorance.

another way to look at it: while an atom involved in a fission reaction can cause an immense impact on the atoms around it, that same single atom, if it is completely isolated from any other atom and was split the same way, would be unable to affect the surrounding atoms. it seems to me that the energy within a single atom is dependent on its surrounding environment which it can effect and it seems to me that there is always a way to increase the impact the same atom can have on its surroundings, whether that be by placing atoms around it in a certain way or varying temperature or whatnot. maybe not infinite with there being certain physical constraints, but the energy is certainly varied based on the atom's environment. this is based off the definition of energy i found off another website and stated two paragraphs up. the potential amount of work capable of a whatever.

following the same logic, the amount of work that can be done by a single carpenter can be varied based on giving him manual tools vs power tools. increasing the usefulness of the supplies. is the energy of this carpenter changing here? i mean, it seems to me that in this case, there is no maximum limit to his "energy" as there are probably an infinite number of ways utilizing technology and more efficient ways of working to increase his productivity. but in the end it's the same guy. i dunno. it just doesn't make much sense to me that the potential energy of anything is finite.

**HallsofIvy** · Nov15-09, 09:18 AM

Originally Posted by blackbird86

So energy apparently equals mass times the speed of light squared. According to Einstein anyway. I was taking an objective look at this theory or whatever it's called just now and I got to wondering...what exactly does Einstein mean by "energy" and what does the speed of light have to do with it? I'm no physicist, but it seems to me that the speed of light is just some random number and I'm hazy on what how he defines "energy."

No, the speed of light is not "just some random number". Any good text on advanced physics should have a proof of

and show exactly why "c" enters into it.

Does he mean total potential work possible from a piece of matter? If so, how does he know it's not infinite? I mean, aren't there physics theories out there that say that this sort of pattern of things revolving around things goes infinitely small. By that I essentially mean, there are particles within an atom's components acting in the same way that the earth does in the relation to the Sun in the solar system, to the center of the galaxy, and then the universe and all that. Yeah, please forgive my lack of physics knowledge, but I just thought I'd try a skeptics view at this stuff for kicks. Thanks in advance for your patience and replies.

How can you "take a skeptics view" of things you do not understand?

I was sitting on the toilet just a minute ago thinking that perhaps nuclear fission isn't a result of an immense amount of energy existing within a single atom,

Ah, sitting on the toilet. Well, that explains a lot. For one thing, no one has said there is " immense amount of energy existing within a single atom". A single atom has very small mass and it is not at all difficult to calculate how much "energy" would be produced if all that mass could be converted to energy. And it isn't. A uranium atom typically fissions into Thorium and Cesium- and there combined mass is slightly less than the mass of the uranium atom. It is that "missing" mass that is converted into energy.

rather just due to the contagiousness of a single loose proton. by that i mean a single atom might not have an unbelievable amount of energy, rather a loose proton has the ability to cause a massive domino effect in the same way an army of trillions red ants would be more potent a weapon than one bear, but that doesn't make a single ant more deadly than a bear. i hope that makes sense...and again, please excuse my ignorance.

Well, not a "single loose proton"- more like a "single loose neutron". That's exactly what a "chain reaction" is. Surely you have heard that phrase before?

another way to look at it: while an atom involved in a fission reaction can cause an immense impact on the atoms around it, that same single atom, if it is completely isolated from any other atom and was split the same way, would be unable to affect the surrounding atoms. it seems to me that the energy within a single atom is dependent on its surrounding environment which it can effect and it seems to me that there is always a way to increase the impact the same atom can have on its surroundings, whether that be by placing atoms around it in a certain way or varying temperature or whatnot. maybe not infinite with there being certain physical constraints, but the energy is certainly varied based on the atom's environment. this is based off the definition of energy i found off another website and stated two paragraphs up. the potential amount of work capable of a whatever.

following the same logic, the amount of work that can be done by a single carpenter can be varied based on giving him manual tools vs power tools. increasing the usefulness of the supplies. is the energy of this carpenter changing here? i mean, it seems to me that in this case, there is no maximum limit to his "energy" as there are probably an infinite number of ways utilizing technology and more efficient ways of working to increase his productivity. but in the end it's the same guy. i dunno. it just doesn't make much sense to me that the potential energy of anything is finite.

Yes, that's why you need a certain "critical mass" to set off an atomic bomb.

And I don't see why you would expect anything about "potential energy" to make sense to you when you tell us you do not understand what "potential energy" is, anyway.

**robert Ihnot** · Nov15-09, 05:53 PM

HallsofIvy: No, the speed of light is not "just some random number". Any good text on advanced physics should have a proof of and show exactly why "c" enters into it.

There is a fairly simple proof of E=mc^2 in Max Born's "Einstein's Theory of Relativity, " page 283. Here it is stated that the momentum transferred to an absorbing surface by a short flash of light is equal to E/c.

"This fact was confirmed experimentally by Lebedew (1890) and again later with greater accuracy by Nichols and Hull (1901) and others."

**blackbird86** · Y, 10:02 PM

while i appreciate the patronization, i still don't understand what the speed of light has to do with energy. i mean, sure there's proofs out there and all. but i mean, the speed of light seems to me like an arbitrary number when you're talking about the amount of energy in a chunk of matter that might not be producing any light at all. if anyone has any idea of the logic behind this, rather than just reiterating some mathematical proof they once learned, i'd like to hear it. i'll have a look at this proof you're talking about robert later.

i did a quick google search and apparently i'm not alone in this notion that e=mc^2 is wrong. honestly i'm too oblivious on the subject to concretely say it's wrong, but the theory really seems illogical to me.

it seems to me that energy being solely dependent on mass, rather than type of element or isotope or whatever factor would mean that the energy in an electron / its mass would equal the energy in a proton / its mass which would also equal the energy in a neutron / its mass regardless of the element or the circumstances in which that element is...temperature and velocity to name two. if there's a finite number of particles in a given amount of mass, then it is feasible i guess that there's a finite amount of energy...or at least more easily comprehensible than there being and infinite number of particles.

i mean....for 1 gram of a supernova to have the same amount of energy as 1 gram of ice seems pretty wild to me.

essentially, i'm asking "why"

**Count Iblis** · Y, 10:32 PM

Originally Posted by blackbird86

while i appreciate the patronization, i still don't understand what the speed of light has to do with energy. i mean, sure there's proofs out there and all. but i mean, the speed of light seems to me like an arbitrary number when you're talking about the amount of energy in a chunk of matter that might not be producing any light at all. if anyone has any idea of the logic behind this, rather than just reiterating some mathematical proof they once learned, i'd like to hear it. i'll have a look at this proof you're talking about robert later.

i did a quick google search and apparently i'm not alone in this notion that e=mc^2 isn't wrong. honestly i'm too oblivious on the subject to concretely say it's wrong, but the theory really seems illogical to me.

Relativity unites space with time. According to relativity, there exists a unified spacetime. Before relativity we did not know how to compare lengths to time intervals and we used different units for space and time. To this day we use the pre-relativistic units for space and time that are mutually inconsistent (although we now have fixed the ratio between the meter and the second). If we insist on using inconsistent units for lengths and time intevals, then we need to do the conversion between the two by inserting a conversion factor in the equations.

This conversion factor is the speed of light. Its value is indeed arbitrary, as it is of the way we chose our unit of length and our unit of time. If we measure time intevals and distances in the same units then the speed of light is equal to 1.

The equation E = m c^2 says nothing more than that what we call mass, is nothing more than the total energy of an object at rest. The c^2 only appears in here because we want to use inconsistent units. The physical meaning of E = m c^2 is thus completely trivial, nothing more than saying that one mile is 1.609344 kilometers.

**T.O.E Dream** · Y, 10:38 PM

The most amazing thing about E=mc^2 is that it means that a tiny mass has a huge amount of energy, an unbelievable number. And just because the number is too big for you to believe it doesn't mean that it's wrong.

I don't know how to break it to you but a google search isn't a reliable source. A person of your ignorance cannot disprove a man of one of the highest intellects (other than me of course :)

**blackbird86** · Y, 10:45 PM

einstein was actually supposed to only have a 165 iq...still in the 99.9th percentile but nothing compared to hawking who's way above 200...and edison too from what i hear. he apparently just had a knack for transcendental thought.

i'm not really trying to prove or disprove it. just to understand the logic behind it.

**diazona** · Y, 10:51 PM

Originally Posted by T.O.E Dream

A person of your ignorance cannot disprove a man of one of the highest intellects (other than me of course :)

I wouldn't say that... I mean, there's nothing special about Einstein or his theory that makes him infalliable. If the theory of relativity is somehow incorrect, then it's conceivably possible that someone who doesn't understand it could come up with the evidence that shows how it's incorrect. But that evidence would need to be really solid, not just a feeling that something doesn't make sense.

**diazona** · Y, 10:58 PM

Originally Posted by blackbird86

einstein was actually supposed to only have a 165 iq...still in the 99.9th percentile but nothing compared to hawking who's way above 200...and edison too from what i hear. he apparently just had a knack for transcendental thought.

i'm not really trying to prove or disprove it. just to understand the logic behind it.

IQ doesn't really mean much :-/

You might like to think about this: the reason the speed of light is special is not because it's the speed of light. That speed is special because it's the fastest speed that any two things (objects, particles, whatever) can pass each other at. It's been called a "universal speed limit" by some people. It just so happens that light, like a careful driver, always goes at the speed limit.

We only call it the speed of light because that's the first way anyone measured this speed, by measuring how fast light traveled. And at that time, many people thought as you did: that it was just the speed that light happened to travel at, nothing special. It wasn't until much later (1905, when Einstein published his theory) that everybody realized that the speed was actually some sort of important universal constant.

**dailyplanit** · T, 03:28 PM

Originally Posted by blackbird86

what does the speed of light have to do with it? I'm no physicist, but it seems to me that the speed of light is just some random number

If light travels as far as it does in a given time, how do you decide how to put a number on that speed? In 1 second it travels 1 light second. Its speed is measured as.... miles per hour or kilometers per hour or seconds per inch or cubits per century ALL different numbers all are very much THE actual speed of light.....? So any random number you decide to choose can equal the speed of light given the method of mesurement you choose.
So how does choosing one of those numbers make that number in any way related to the equasion being calculated? I think that is the question being asked.

How does a speed times a speed work?
does multiplying it by speed make the speed that much faster?
Or is it just a number related loosely to an idea of the speed multiplied as a number not as a faster speed.......

I do agree this question is a very good one and so far havent seen anyone that has even understood the question never mind tackled answering it...

**russ_watters** · T, 04:44 PM

Welcome to PF!

Originally Posted by dailyplanit

So any random number you decide to choose can equal the speed of light given the method of mesurement you choose.

Yes.

The speed of light is also about 175 million Russ's per second (a unit of length I just made up, which is equal to my height).

So how does choosing one of those numbers make that number in any way related to the equasion being calculated? I think that is the question being asked.

The choice of units has no effect whatsoever on how the equations work. As long as you keep your equations consistent, the physical reality of the results is always the same.

How does a speed times a speed work?
does multiplying it by speed make the speed that much faster?

No. Check the units. The units of speed are distance/time so if you square that and get distance^2/time^2, that's not the units of speed anymore, is it?

You can't cherry-pick a piece of an equation and always expect it to have meaning on its own. The meaning of the equation is in the full equation (and it isn't a very big one anyway). Note, though, that the equation is very similar to the equation for kinetic energy...

I do agree this question is a very good one and so far havent seen anyone that has even understood the question never mind tackled answering it...

Ehh, it isn't a terrible question and it is one we get often, but it is one borne of wrong thinking about how equations work. For some reason, people have a problem with this particular equation and try to dissect it in a way that makes no sense. I don't know what it is about this equation that makes people forget how math works or why we never get this question asked about other equations.

**TVP45** · T, 05:25 PM

Originally Posted by russ_watters

Welcome to PF! Yes.

The speed of light is also about 175 million Russ's per second (a unit of length I just made up, which is equal to my height). The choice of units has no effect whatsoever on how the equations work. As long as you keep your equations consistent, the physical reality of the results is always the same. No. Check the units. The units of speed are distance/time so if you square that and get distance^2/time^2, that's not the units of speed anymore, is it?

You can't cherry-pick a piece of an equation and always expect it to have meaning on its own. The meaning of the equation is in the full equation (and it isn't a very big one anyway). Note, though, that the equation is very similar to the equation for kinetic energy... Ehh, it isn't a terrible question and it is one we get often, but it is one borne of wrong thinking about how equations work. For some reason, people have a problem with this particular equation and try to dissect it in a way that makes no sense. I don't know what it is about this equation that makes people forget how math works or why we never get this question asked about other equations.

Russ, that's a really good question that's mystified me for a long time. It's sort of like watching moths drawn to a candle. Why E=mc^2 (which it doesn't) and not Poiseuille's Equation. Why the Twin Paradox and not the speed variation in rolling friction? Why black holes and not zero-work forces? What is it about Einstein, Hawking, Tesla, etc that draws so much attention?

**T.O.E Dream** · T, 05:32 PM

Remember that the speed of light always stays constant no matter how fast an observer is going. That's what makes it so special.

Space and time are variables so really every other constant other than c changes (for example pi).