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  • So, well, the simple version is just to tell you what the terms in the equation mean

  • which is that E means energy, and that's equal to m, mass, times c,

  • the speed of light, squared.

  • Energy can be measured in joules, mass of a particle could be measured in kilograms.

  • so if you've going to relate them, you have to relate them with some factor

  • and the factor that does it is this...

  • square of the speed of light.

  • Taken at face value, it means that energy is equivalent to mass

  • so that if you were to look at Newton's laws of motion and say that masses attract

  • this now implies that energy is attracted by another mass.

  • So, if a light wave with energy goes near a planet or the sun, it's actually bent by it

  • because it's attracted. So it's saying that energy is equivalent to mass.

  • The consequence of it is quite dramatic, because the speed of light squared is a huge number.

  • The speed of light in meters per second is...

  • ... Uh... three times ten to the eight (power). Three hundred million meters per second.

  • You square that, and you've got...

  • ... Uh...

  • ... Oh, rubbish...

  • ... nine times ten to the sixteenth. So, you've got an order of ten to the seventeeth as a conversion factor.

  • So, a very small amount of mass

  • is equivalent to a hugh amount of energy.

  • In physical terms, what it means is that there's actually an energy associated with mass.

  • It's something that just sort of falls out, sort of almost automatically from special relativity.

  • That is just something that comes out of the equations.

  • But, obviously, it's an incredibly powerful result, because it basically means that whenever you've got a mass

  • you have a source of energy.

  • And, so, you know, if you...

  • have a... fusion bomb, for example, you actually convert some of that mass directly into energy.

  • But it basically is another way of saying that mass is just a way of storing energy.

  • But it's not even the right equation!

  • The proper equation is E squared equals m squared (times) c to the fourth

  • plus another term involving the momentum, which is an extra p squared (times) c squared.

  • The mass in E equals m (times) c squared can either be the rest mass,

  • and that's what is usually thought of, that's where the object isn't moving,

  • and so it's actually just got an intrinsic mass, and so it's got an intrinsic energy associated with it,

  • or, it could be what's known as the relativistic mass.

  • And if it's the relativistic mass, then it's including the momentum

  • and I think I'm probably agreeing with Roger.

  • In the textbooks you often see the bare masses; m with a little subscript zero beside it

  • just to make it clear that that's not including the momentum of the particle.

  • The whole equation is never explained because people like you don't want us to write down equations

  • 'cause they're boring *pretends to yawn*.

  • But if you do it properly, that's what it is. And if you don't do it properly

  • then you can't explain why energy is attracted to (mass), gravitating to objects,

  • nor can you explain how a photon, which doesn't have any mass, behaves the way it does.

  • I think an interesting aspect is, why is it the squared speed of light?

  • Why isn't it the square of the speed of sound, which is a much lower number?

  • For that you have to look at what Einstein did

  • when he was coming up with this theory of special relativity.

  • Without any extra work, it sorta falls out of the analysis of special relativity,

  • that's just a result that comes along.

  • And, it's very nice when you just get a result that just sort of falls out without any extra work

  • but actually, on its own, has huge, amazing implications for the laws of physics.

  • The people I have spoken to, and when I gave public talks, the people who attended,

  • certainly have an idea that you've got energy and mass.

  • I don't think they often realized quite how significant it is, and quite how broad that equation is

  • at explaining phenomena that we experience.

  • They just tend to think of it in the world of particle physics, or something rather extreme.

  • But, in fact, it accounts for the binding of atoms.

  • If you've got the constituents of atoms, and you just measure that mass

  • then you put them together, the mass drops.

  • And the mass drops because of the binding energy, and the thing that explains that binding energy

  • is E equals m (times) c squared.

  • The correct equation, even if the momentum is zero,

  • is E squared equals m squared (times) c to the fourth.

  • And if you take the square root of that, you can get negative energies coming out.

  • And Dirac noticed this, and interpreted the negative energy states as the antiparticles.

  • So you now get something for nothing. If you use the correct equation, you can take the square root,

  • come out with a negative energy solution, and then interpret it in quantum mechanics as the antiparticle.

  • And he predicted this well before anybody did the experiment that discovered the positron.

  • So, the proper equation is much richer.

  • The public can't cope with anything more complicated than E equals m (times) c squared

  • and even that's so full of meaning.

So, well, the simple version is just to tell you what the terms in the equation mean

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B1 squared energy equation special relativity momentum speed

E=mc² is wrong? - Sixty Symbols

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    林宜悉 posted on 2020/03/30
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