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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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