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Thread: E = mc²

  1. #1 E = mc² 
    WYSIWYG Moderator marnixR's Avatar
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    the well-known equation indicating that energy is liberated mass and mass frozen energy + showing that you get a lot of energy per unit of mass if you liberate it

    but why should the constant be the speed of light squared (rather than some other large number) + what is its meaning in physical terms ?


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    Forum Freshman StarMountainKid's Avatar
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    I think one reason is because when we use c in the equation the results are correct. Sounds kind of silly but I guess go with what works. We must remember that the speed of light is a definition and not a measurement. 'c' is mearly a conversion factor telling you how mass and energy relate to each other. 'c^2' is used because if you accelerate a ball twice as fast as before it's energy is not twice as much but four times as much. So 'c' must be squared in the equation.

    I don't think this really answers your question, though.


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    WYSIWYG Moderator marnixR's Avatar
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    Quote Originally Posted by StarMountainKid
    ... We must remember that the speed of light is a definition and not a measurement. ...
    are you sure about this ? i was under the impression that the speed of light had been measured, even before Einstein developed his famous formula
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    I think it refers to the absoluteness of light.
    Something about if a box moves and you send a photon of light from one to the other end, then it's still lightspeed, but not more or something like that...
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    Quote Originally Posted by StarMountainKid
    I think one reason is because when we use c in the equation the results are correct. Sounds kind of silly....
    It does, doesn't it? That's because that is not how E = mc<sup>2</sup> is arrived at. Einstein starts by calculating the energy loss L of a light-emitting body in constant motion as observed by a relatively "stationary" observer i.e. subject to the Lorentz transform. Then, taking that result to 2nd order in v<sup>2</sup>/c<sup>2</sup> i.e. considering only the first two terms of the Taylor expansion, arrives at DeltaE = ½(L/c<sup>2</sup>)v<sup>2</sup>. Noticing this is identical in form to another "energy in motion" equation KE = ½mv<sup>2</sup> concludes that, up to an irrelevant scale factor E = ½(L/c<sup>2</sup>)v<sup>2</sup> = ½mv<sup>2</sup>, whereby L/c<sup>2</sup> = m. But L is light energy and represents the change in energy of the emitting body, hence E = mc<sup>2</sup>.

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    Also, by squaring c and multiplying it by m we get the correct units... that of energy.

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  8. #7  
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    It was by no means pulled out of his ear
    No he didn't. What he did pull out of some magical place, though, was his postulate that the speed of light be the same for all observers, regardless of their relative motions. Everything that follows with little more than algebra (including E=mc^2) is hinged on that assumption. And that wasn't proven at the time he wrote it down.
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    Well then, you might take a microsecond to mull over the word "postulate". If you're having trouble, let's say it is an heuristic assumption. If a postulate can be used to a) derive a self-consistent theory and b) that theory, standing or falling on that postulate, can be verified experimentally to some arbitrary degree of precision, it is customary to assume the postulate was, at worst, reasonable, and at best correct.

    This is how science works.
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    ...it is customary to assume the postulate was, at worst, reasonable, and at best correct.
    Correct, maybe.

    Reasonable is a different matter... a little harder to grasp. If I proclaim today that the moon will break into two half's tonight, it will seem unreasonable, even to myself. However, let's hypothesize the moon really does break into pieces after I say so. Does that make my conjecture any more reasonable? No, it doesn't. It may make it a correct prediction, but it was still an unreasonable wild guess that just happened to turn out right against all odds. Correctness can always be estalished with hindsight, but reason is established in the process of making a decision.

    There is of course a correlation between reason and correctness with postulates in physics: Reasonable assumptions are more likely to be correct. Whether Einstein's postulate was reasonable will not be answered by "correctness" but by the way he arrived at it.
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  11. #10  
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    Quote Originally Posted by M
    It may make it a correct prediction, but it was still an unreasonable wild guess that just happened to turn out right against all odds. Correctness can always be established with hindsight, but reason is established in the process of making a decision.
    Sorry to be rude, but this makes no sense. If what you call a "guess" turns out to be correct, was it not a "correct guess"? And who, by the way, established what you call "the odds", in the absence of a pre-existing theory?
    Reasonable assumptions are more likely to be correct.
    You're in a circle here, my friend. Explain your criteria for what you call a "reasonable assumption" - I demand precision!
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  12. #11  
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    Sorry to be rude, but this makes no sense. If what you call a "guess" turns out to be correct, was it not a "correct guess"?
    I don't mind your being rude. Just kindly go back and read my post again. You are absolutely right about "correctness", and if you read carefully you'll see that I already said this: Correctness can and will be established in hindsight. Any wild guess can turn out to be correct.

    And who, by the way, established what you call "the odds", in the absence of a pre-existing theory?
    Very central question. Essential to my point on "reason". Whether an assumption is reasonable or not is not established by whether it ultimately turns out to be correct. It depends merely on how (or whether) you apply logical reasoning to arrive at your assumption.

    Let me give you another example and see if you can agree on that. If I want to decide whether there is a good chance of rain tomorrow, I will consult a meteorologist who is in charge of prediction for my region and pick her brain for all the data and advice she has available at this time. It would be reasonable to consider all data and theories that are available at the time to make a sound decision on probability. Let's say I do that and we determine that it will most likely rain tomorrow afternoon. Now, whether it turns out to be correct or not (it might not rain after all) has absolutely no impact on the fact that this was a reasonably assumption. It was reasonable, from a scientist point of view, because of the way we arrived at it, taking into account all data and theory at hand.

    Conversely, I might choose to ignore any scientific data (or maybe they don't exist) and rely on my psychic. Some people would call this reasonable, but most scientists would certainly not, and we're talking science, here. This would be unreasonable, regardless if the psychic's prediction this time turns out to be correct.

    Whether a decision is reasonable is established by the methods, not by correctness. Thus, whether an assumption was reasonable does not depend on whether it turns out to be right or not. An irrational assumption doesn't suddenly become reasonable, just because it happens to be right this one time. Correctness can be established in hindsight,... not so rationality of an approach.
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    OK, M, this is getting a bit too philosophical for both my taste and for this sub-forum. So let me be brief. You regard an assumption as "reasonable" if it was arrived at through some sort of "reasoning process"? I confess this is not how I was using the word, but maybe I'm guilty of abusing my Mother tongue. If this is what you meant, I apologize, but let me just say this.

    A postulate, an heuristic assumption I called it, is easily seen to be madness (i.e. unreasonable) if it already conflicts with pre-existing data, which by both our definitions of "reasonable" we agree on, more or less.

    I was making the additional stipulation, perhaps wrongly, in purely linguistic terms, that a postulate can be proved to be reasonable if one and only one experiment (or equation, I'm guessing) confirms that it might be true.
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  14. #13  
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    Sounds good.
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  15. #14  
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    I somehow dont like the squareness in the formula (more of an intuition I admit and I risk to be laughed away here for this). Maybe the topic starter is hinting towards this also?
    Couldn't it be possible (somehow) to distinguish a C factor in the way of spreading and a C' factor in a directional way or the other way around. C*C' would then still be constant while C and C' can diver.
    I could imagine then that when we see colours of a prism. that the material of the prism decreases the directional factor and increases the spreading factor resulting in both the prismatic colours (cause the trajectory legth through the prism differs) and a different C (directional). Put it this way "ordinary waves of water show some behaviour that show the principles underlying.
    For instance waves of water going between two iles, you see the iles and the shallow water decreases c directional and increases the spreading of the wave. Looking at the waves going along a shore you see the small breaking lines (where the water is mostly flat). In between the waves are bended cause the directional speed is higher in deep water. Within two breaking lines the frecquency is constant but C directional divers in direction(bended and always orthogonal to the waves)
    Its not that I want to make it sound like completely analogous (every phenomenon is a phenomenon by itself but there are underlying laws that connect the phenomena.
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  16. #15  
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    Quote Originally Posted by Ghrasp
    Maybe the topic starter is hinting towards this also?
    not really - i was just curious how c (squared or otherwise) got into the picture
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    Yes, and you were told by William and me. Gratitude is not expected, however!
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  18. #17  
    WYSIWYG Moderator marnixR's Avatar
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    i was just replying to the earlier post which seemed to imply i had some weird ulterior motive for my question

    but yes, i did get my answer, so thanks for that - a bit shoddy of me not to have thanked you before, it just slipped my mind
    "Reality is that which, when you stop believing in it, doesn't go away." (Philip K. Dick)
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    Just to add another view to the e = mc(squared) thing, I have been working on an alternative science that actually arrives at the same formula. The thing that the alternative science I use is that it suggests "c" as the speed of light propagates in two distinct dimensions, and it's propagation cannot be surpassed, it is the limit. So, c-squared represents the canvass, the surface area of energy conversion. Mass, that which is applied to that dual propagation, represents a basic factor associated to that c squared. Think of mass being the speed boat and the wake of water as c squared. Together they represent, ultimately, the energy of that system. I know it doesn;t sound very formula-orientated, but a theory I have been working on arrives at the equation e = m(squared). It's easier to conceptualize, as well. But, the point is, "c" is an envelope that propagates in two dimensions-axes. It can't be surpassed.
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