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Energy apparently equals mass times the speed of light squared

  1. Nov 15, 2009 #1
    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.
    Last edited: Nov 15, 2009
  2. jcsd
  3. Nov 15, 2009 #2


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    Re: e=mc^2

    No, the speed of light is not "just some random number". Any good text on advanced physics should have a proof of [itex]E= mc^2[/itex] and show exactly why "c" enters into it.
    How can you "take a skeptics view" of things you do not understand?

    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.

    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?

    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.
    Last edited by a moderator: Nov 15, 2009
  4. Nov 15, 2009 #3
    Re: e=mc^2

    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."
  5. Nov 19, 2009 #4
    Re: e=mc^2

    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"
    Last edited: Nov 19, 2009
  6. Nov 19, 2009 #5
    Re: e=mc^2

    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.
  7. Nov 19, 2009 #6
    Re: e=mc^2

    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 :)
  8. Nov 19, 2009 #7
    Re: e=mc^2

    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.
  9. Nov 19, 2009 #8


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    Re: e=mc^2

    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.
  10. Nov 19, 2009 #9


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    Re: e=mc^2

    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.
  11. Nov 20, 2009 #10
    Re: e=mc^2

    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...
  12. Nov 20, 2009 #11


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    Re: e=mc^2

    Welcome to PF!

    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.
  13. Nov 20, 2009 #12
    Re: e=mc^2

    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?
  14. Nov 20, 2009 #13
    Re: e=mc^2

    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).
  15. Nov 22, 2009 #14
    Re: e=mc^2

    Sorry edited your words to what I think you might have meant....

    But if you get it so often then that makes it a frequent question.
    A questions validity isn't based on the persons ability to see the answer themselves otherwise they would not ask the question would they???
    Just because someone is stupid doesnt mean they cant learn. At one time everything was a question for everyone.
    The question is valid if many people ask it, and no one has managed to explain it in a simply enough manner satisfy the many who question it.
    So it is therefore by your rating on it A VERY GOOD question.

    And to be honest although you pointed out the units of measurement dont matter .... I supose its just a number name to refer to an energy output.... But how a random number can tell you the energy based on another multiplying by another (random type) number, the mass, can actually calculate the energy. All the answers dont focus on the question


    why does it work????????????

    Or does it just give you a random answer to use as a random number name for a big explosion a big bang and a noise that we shall call say 4million bits of energy.......????

    No one has focused on the question WHY?

    WHY does the equation work.
    I dont think anyone can deny that it does, it's tested and proven
    but WHY?
  16. Nov 22, 2009 #15


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    Re: e=mc^2

    Perhaps - I was struggling to decide if it was only a mediocre question or really just a bad one.
    No, my criteria (my "rating") doesn't have anything to do with the frequency with which a question is asked. To me a "good" question is a question that has a good thought process behind it. Anyway, that's not really relevant....

    Lets simplify. You have three units of distance: a meter, a Russ and a foot. Here's how they were decided on:

    -The "meter" was designed to be approximately one ten millionth of the distance between earth's equator and earth's north pole.
    -A "Russ" is equal to my height.
    -A "foot" is an ancient distance unit that was often recalibrated to the length of a king's foot. Our current standard may be the length of King Henry I's foot.

    I am 1 "Russ" tall or 5.583 feet tall or 1.7 meters tall.

    Do you understand that I am a physically real object with a physically real height and the choice of units used to describe my height is completely arbitrary and has no real bearing on the physical reality which is my height?
    Last edited: Nov 22, 2009
  17. Nov 23, 2009 #16
    Re: e=mc^2

    It shouldn't be that surprising that energy is mc2 after all what are the units of energy? Kinetic energy is [tex]\frac{1}{2}[/tex]mv2. There we have a mass multiplying the square of a velocity. mc2 differs only by a factor of [tex]\frac{1}{2}[/tex].

    In Newtonian mechanics velocity is a three component vector. It has components [tex]\frac{dx}{dt}[/tex] [tex]\frac{dy}{dt}[/tex] [tex]\frac{dz}{dt}[/tex]. In relativity you need four component vectors, things with an x,y,z and t component. Also you differentiate with respect to proper time [tex]\tau[/tex], so you now have [tex]\frac{dx}{d\tau}[/tex] ect. This is the four velocity. If you multiply this by mass, you end up with three components like regular momentum (they are not the same as regular momentum) and one component the mc2 + [tex]\frac{1}{2}[/tex] mv2.
    This is just an idea of how this is worked out, and why the mc2 turns up as energy. It is by no means meant to be complete.
    you can find a very good explanation here
    http://www.youtube.com/profile?user=StanfordUniversity#p/c/5F9D6DB4231291BE/3/niHEq9i3B-4" at about 1:43:00 into the lecture.

    These lectures by Susskind are unfortunately miss titled Quantum Entanglements Part 3 but are really about special Relativity. Please note Quantum Entanglements part 1 are really about quantum mechanics (go figure).

    I hope this is somewhat helpful. Relativity is mainly about rewriting things with three components as things with four components.
    Last edited by a moderator: Apr 24, 2017
  18. Nov 24, 2009 #17
    Re: e=mc^2

    That's the easy part. And I assume is a light hearted attempt at humour ha ha :)
    In fact that is exactly my point "units or numbers ....completely arbitrary and has no real bearing on the physical reality...!!" in your words
    So change height in to a number then we have a different numbetr depending on the choice of measurement.
    BUT... the actual question is still totally un-adressed

    Why does light speed times itself effect or relate to mass and help calculate energy?

    And why is it so easy to address everything about my question but the actual question itself? What relationship does C have to mass and energy in real terms and not in terms of a random number picked to represent it?

    Is it so hard to see the question and why it is in fact a VERY VERY good question??
  19. Nov 24, 2009 #18


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    Re: e=mc^2

    No, that is a very good question. But the only good answer would be to derive the equation just like Einstein orginally did and posters gave references to that.
  20. Nov 24, 2009 #19
    Re: e=mc^2

    You can't really give a good answer to that question without referring to the fact that c is an "arbitrary" number. As someone said before, Einstein showed in 1905 that c is more than just the speed of light, it's an important universal constant, which shows up in many other equations as well. You pretty much need to know the math for it to make any real sense to you.

    Here's one simple way of looking at it. E is measured in joules, or (kg*m^2)/s^2. Mass is measured in kg. By looking at the units, you see that to obtain a value for E, you need to multiply m by something with units m^2/s^2. Since velocity, v, is measured in m/s, the component we are looking for here is v^2, and in this case, v = c.

    Obviously this isn't an in depth look at relativity. I'm just trying to show you why m must be multiplied by a velocity to get energy. I know what you're asking is, "why is this velocity the same as the speed of light?" but like I said, you need to know the math before it will start to make any real sense.
  21. Nov 24, 2009 #20


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    Re: e=mc^2

    Being that I have no background whatsoever in physics myself, I really have no way of knowing if this is correct, or complete nonsense; but I do have a way that I have always thought of this problem.

    As other posted have mentioned, the speed of light is constant. Well I consider it the only constant, and everything else is relative to it. So the number is arbitrary, as has been said... It's like measuring a pond that rises and falls. The depth of the pond may change, but the measuring stick stays the same. So we always have to include this measuring stick in our calculations...

    Blah, I don't understand well enough to describe it, but I would like to know if I am on the right track.
  22. Nov 24, 2009 #21
  23. Nov 24, 2009 #22


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    Re: e=mc^2

    No, I picked it because it is an easy example for people to get their arms around.
    There were actually two separate questions being asked.

    The first question, by the OP, is essentially 'why does e=m^2 work?' and that's a question about its derivation and meaning. And that's what you appear to be asking here. That question has been answered several times with links to the derivation and how it is related to the kinetic energy equation.

    The second question was essentially 'how do units work?' (or, 'why does an equation still work when you change its units?') and that's the question you asked in several different ways in post #10.
    C is a speed. Kinetic energy is a measure of the energy a particle has due to its speed. Obviously, there is more to it than that - that should get you started thinking in the right direction, but here's the wiki on the concept of mass-energy equivalence: http://en.wikipedia.org/wiki/Mass-energy_equivalence
    Last edited: Nov 24, 2009
  24. Nov 25, 2009 #23
    Re: e=mc^2

    I have read through ths post and am still asking the question I didnt see or understand anything that even seemed to remotely address my question.
    No mass being measured ever travels at the speed of light so the relationship of C to kinetic energy in any mass isnt relavent to C but instead to it's OWN speed which is much slower MUCH slower. Last I knew only light goes that fast and they are not sure if it s a particle or wave. How does the speed of light coming off a peice of cheese help us measure the energy of that cheese?
    Im begining to assume there either is no "answer" or that the answer is so complicated that you have to learn a new langauge to understand it.
    My real query is speed is not a number its an energy a movement it has no fixed number until we give it one with created units and as I think it was you that pointed out that number could be 1 (1 light year per year) E=M12?? not quite the same
    Where do you even begin to think that the speed at which an obect gives off light might be a way to calculate the energy ...not of the light coming off the object... but the energy stored inside the object? And basing that on its substance its consistancy it raw material or mass each object being made of different materials ...or all made of atoms. If an object with mass is in complete darkness with no light at all does it still have energy? Why is lights speed so special? And what really gets me why CxC ?? 1x 1 = 1 light speed has no number until we choose one.
    Wasnt there a fear that the first atomic bomb might cause a chain reaction and trigger off each and every atom near to it, to also explode and destroying the entire planet into a small sun? They didn't know for sure rght. When energy gets past the point of being able to measure it how can it be confirmed you are truly measuring it... a bright flash a big noise lots of heat all the measuring equipment melted in to radiation and a big hole left which may or may not have been effected by the chain reacton theory... That a different question but slightly relavent.
  25. Nov 25, 2009 #24


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    Re: e=mc^2

    Have you read any of the linked information sources? They go deeper than we can in a post on an internet forum.
    Well that's going back to question #2, which you said you understand, but clearly you don't and you've dropped the explanation given to you and started over from scratch! 1x1=1 still has units associated with it! You need to get your arms around that. Try this. Is the following statement true?:
    300,000x300,000 = 186,000x186,000
    Last edited: Nov 25, 2009
  26. Nov 25, 2009 #25
    Re: e=mc^2


    You are missing the point that "c" is the speed of light, but "300 000 000" is not. When you replace "c" with a number, that number includes a unit of measure (though that can be, for people who are very good in math, implied). There is no such thing as a speed of 186 000, or 1; there must be a unit.
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