Why is the speed of light squared the multiplier in E=mc²?

[Dale]

Piggybacking off Ted's question, why not just say that the equation is E=ML? [ Where L = kinetic energy in light MV^2 with no M]

Your units don't work out, E is in units of Joules, M is in units of kg, and if L is kinetic energy then L is in units of Joules. So for units you have J = kg J, which doesn't match.

 

[Dale]

Is the entire theory not a mathematical proof of the postulate for c? I don't know math, but it seems like the postulate for c is a bit of a keystone to the theory.

Of course it is a keystone, but it is a key assumption, not a key proof. In SR there is no proof of the postulate for c, it simply assumes it and goes from there.

 

[Drakkith]

Maybe I'm math illiterate, how else could that equation be "read"?

energy is equivalent to matter.

So why does that statement make no sense?

I see E=mc2 as another example of the symmetry in classical physics, a bit of a truism.

Mathematically the equation simply means that the energy in joules is equal to the mass of something in kilograms times the speed of light squared. It doesn't mean energy is equivalent to matter, it's just a formula to convert mass to energy. Given the definitions of energy and matter the two cannot be "equivalent", as they are totally different things.

 

[Matterwave]

Maybe I'm math illiterate, how else could that equation be "read"?

energy is equivalent to matter.

So why does that statement make no sense?

I see E=mc2 as another example of the symmetry in classical physics, a bit of a truism.

A statement like the one I made makes no sense at all (you can go back and read it and tell me if you think it makes any sense). The equation is a mathematical equation, and not a verbal one. What I was trying to get at with my statement, was that I see a whole lot of people posting things like "Does E=mc2 mean that if matter moves at the speed of light, it turns into energy?" or "does E=mc2 mean that energy is just matter moving at the speed of light squared?" or other non-nonsensical questions like this.

Like Drakkith says, E=mc^2 is simply a way of knowing how much energy is contained within one kilogram of mass at rest.

Also, like Dalespam (lol, I almost wrote that as Dalesperm) says, Special relativity takes the constant c as a postulate. The proof of the postulate can either come from direct tests of the postulate (e.g. the Michelson-Morley experiment), or from testing SR itself (and thereby testing both of its postulates indirectly at the same time), such as with time dilation experiments or particle beam experiments.

 

[nitsuj]

Mathematically the equation simply means that the energy in joules is equal to the mass of something in kilograms times the speed of light squared. It doesn't mean energy is equivalent to matter, it's just a formula to convert mass to energy.

Given the definitions of energy and matter the two cannot be "equivalent", as they are totally different things.

Just a formula? it describes what's observed in physics.

Yes there is a relationship between the two, yes they are "totally different things". The fact they are two "totally different things" and the fact the two are "interchangeable" according to c^2 is a pretty remarkable equivalence.

As if I have to quote wiki for more authority lol here it is
[/PLAIN]
"In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant"

I like physics, any definition of mass & energy that excludes mentioning the equivalence between the two is an incomplete definition in my opinion, and would absolutely be two "incomplete" "concepts" from a physics perspective.

 

[nitsuj]

A statement like the one I made makes no sense at all (you can go back and read it and tell me if you think it makes any sense). The equation is a mathematical equation, and not a verbal one.

What I was trying to get at with my statement, was that I see a whole lot of people posting things like "Does E=mc2 mean that if matter moves at the speed of light, it turns into energy?" or "does E=mc2 mean that energy is just matter moving at the speed of light squared?" or other non-nonsensical questions like this.

Like Drakkith says, E=mc^2 is simply a way of knowing how much energy is contained within one kilogram of mass at rest.

Also, like Dalespam (lol, I almost wrote that as Dalesperm) says, Special relativity takes the constant c as a postulate. The proof of the postulate can either come from direct tests of the postulate (e.g. the Michelson-Morley experiment), or from testing SR itself (and thereby testing both of its postulates indirectly at the same time), such as with time dilation experiments or particle beam experiments.

Isn't there entire books written on e=mc^2.

I don't disagree with you or Dalespam regarding the theory not proving the postulate of c experimentally. You kinda raised my point, that because c is a "keystone" to the theory, it can be tested indirectly, if results match predictions, pretty safe to start having confidence in the postulate. So much so most scoff at contradictory results, cerntainly there are even recent examples.

Ah, any test of SR is a test of the postulate, right?

 

[nitsuj]

A statement like the one I made makes no sense at all (you can go back and read it and tell me if you think it makes any sense).

Wait, no pun intended but is; equivalence = equivalent = equal = "=" not true?

Here is the comment and I re read it and yea I still makes sense of it.

"energy is equal to matter times light squared"

Rephrased to "there is an equivalence between energy and mass by a factor of c^2." anymore palatable?

 

[Matterwave]

You can't use an arithmetic operation (multiplication) on non-arithmetic objects (physical objects like matter and light).

You can only use them on numbers. Quantities. Mass, measured in some units, and the speed of light, measured in compatible units.

If you want to interpret my sentence semantically as a mathematical statement, you can, but it just leads to needless confusion, and you'll get people asking the type of nonsensical questions I raised in my last post.

 

[nitsuj]

You can't use an arithmetic operation (multiplication) on non-arithmetic objects (physical objects like matter and light).

You can only use them on numbers. Quantities. Mass, measured in some units, and the speed of light, measured in compatible units.

If you want to interpret my sentence semantically as a mathematical statement, you can, but it just leads to needless confusion, and you'll get people asking the type of nonsensical questions I raised in my last post.

I disagree, understanding the concepts is what is important in discussing (understanding) physics, and in turn the math. Otherwise it's just numbers and arithmetic operators.

 

[Drakkith]

Just a formula? it describes what's observed in physics.

Yes there is a relationship between the two, yes they are "totally different things". The fact they are two "totally different things" and the fact the two are "interchangeable" according to c^2 is a pretty remarkable equivalence.

As if I have to quote wiki for more authority lol here it is
[/PLAIN]
"In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant"

I like physics, any definition of mass & energy that excludes mentioning the equivalence between the two is an incomplete definition in my opinion, and would absolutely be two "incomplete" "concepts" from a physics perspective.

You have been using "Matter" in place of "Mass" in your posts. Perhaps this is the source of the confusion. My post you quoted was specifically talking about matter not being equal to energy, as it is not. E=MC^2 requires mass, not matter.

Here is the comment and I re read it and yea I still makes sense of it.

"energy is equal to matter times light squared"

See, here it is again. Please use Mass instead or you will confuse people.

 

[meBigGuy]

Seems like everyone here missed the whole point of the OP. What is it about the speed of light that make *IT* (well, IT squared, anyway) the constant for the relationship between mass and energy? Does it stem from the basic postulate that the speed of light is a universal maximum, a constant, and is independent of the reference frame?

 

[Drakkith]

Seems like everyone here missed the whole point of the OP. What is it about the speed of light that make *IT* (well, IT squared, anyway) the constant for the relationship between mass and energy? Does it stem from the basic postulate that the speed of light is a universal maximum, a constant, and is independent of the reference frame?

See post #26.

 

[nitsuj]

You have been using "Matter" in place of "Mass" in your posts. Perhaps this is the source of the confusion. My post you quoted was specifically talking about matter not being equal to energy, as it is not. E=MC^2 requires mass, not matter.
See, here it is again. Please use Mass instead or you will confuse people.

I had quoted someone else there, but it was in defense of the comment.

So yes I did read Matter as Mass, drakkith, you are absolutely right. Sorry for my confusion. If I had realized that, we wouldn't have had this back 'n forth.

And thanks for your attention.

I agree with you guys that matter is not equivalent to energy...or mass, for that matter.

 

[Naty1]

Mileman:

So why c?

no intuitive logic would necessarily reveal this value until you use Einstein's relativity as a model. Then it flows as in the post #26 derivation...so we start with a theory and many results flow from it. We confirm which of those match experimental observations...and if they do, voila we have a viable theory. If not, we have to change our theory...so 'ether' was a start, but 'relativity' better fit observations...so we use that.

It's akin to asking..."Why are Planck time, [or energy and length] what they are?"

Wikipedia says it this way:

The Planck time is the unique combination of the gravitational constant G, the relativity constant c, and the quantum constant h, to produce a constant with units of time.

Without such a framework, you could go on guessing from among an infinite variety of values for a long time. In fact it's quite likely that such a quantized view of things would never even be thought about without some experimental observations combined with some theory. It sure would not flow easily from relativity.

If you subscribe to the big bang model, apparently all these apparently disparate pieces [light,mass,energy,space,time,etc] somehow originated from a unified origin...So far we have a bunch of piecepart models that reveal some things we observe around us...but not all, not what caused the bang, for example. Hence dark matter and dark energy, for example, haven't unambiguously appeared in any 'logical theory'...we just discovered them experimentally in the 1990's! And we haven't yet figured out how relativity and quantum mechanics can be 'unified'...so pieces appear to be missing.

 

[Dale]

What is it about the speed of light that make *IT* (well, IT squared, anyway) the constant for the relationship between mass and energy?

What else could it be? There is no other way to get a constant with units of $L^2/T^2$ from any of the other universal constants. So it has to be some multiple of $c^2$. The only other possibility would be for there to be no conversion between mass and energy.

 

[harrylin]

Seems like everyone here missed the whole point of the OP. What is it about the speed of light that make *IT* (well, IT squared, anyway) the constant for the relationship between mass and energy? Does it stem from the basic postulate that the speed of light is a universal maximum, a constant, and is independent of the reference frame?

It may be related: c is a property of space, and thus c² the same.
Somehow, the inertial property of energy is determined by that constant - and it would be great if someone physically (not just mathematically) would understand the "somehow".

 

[-Physician]

That formula is wrong anyway, Einstein wasn't that smart than sciencists today, even though if Einstein wouldn't make this mistake sciencists wouldn't have work to do. So:
$E≠mc^2$,
$E^2=m^2 c^4 + p^2 c^2$.

 

[harrylin]

That formula is wrong anyway, Einstein wasn't that smart than sciencists today, even though if Einstein wouldn't make this mistake sciencists wouldn't have work to do. So:
$E≠mc^2$,
$E^2=m^2 c^4 + p^2 c^2$.

Formula's are never on themselves, they relate to certain conditions and definitions. Both equations are correct for their application.

 

[-Physician]

Formula's are never on themselves, they relate to certain conditions and definitions. Both equations are correct for their application.

Einstein defined:
The velocity of light is the fastest one. His formula says: $E=mc^2$, but that theory gone down, so that formula wouldn't stay for any application, if it would then it would be wrong.

 

[Doc Al]

That formula is wrong anyway, Einstein wasn't that smart than sciencists today, even though if Einstein wouldn't make this mistake sciencists wouldn't have work to do. So:
$E≠mc^2$,
$E^2=m^2 c^4 + p^2 c^2$.

Both equations are due to Einstein. The first reflects the rest energy of a massive particle. They are hardly 'wrong'.

 

[Agerhell]

What else could it be? There is no other way to get a constant with units of $L^2/T^2$ from any of the other universal constants. So it has to be some multiple of $c^2$. The only other possibility would be for there to be no conversion between mass and energy.

Have you ever heard of such a thing as a dimensionless constant? You could in principle have any dimensionless number k and E=mkc², but that would not not work with the definition of relativistic momenta as seen in the link posted in response #26. k must therefore be equal to one. Are you trying to confuse the kid?

 

[Agerhell]

Einstein defined:
The velocity of light is the fastest one. His formula says: $E=mc^2$, but that theory gone down, so that formula wouldn't stay for any application, if it would then it would be wrong.

If you define $m=m_0\sqrt(1/(1-v^2/c^2))$ then the initial relation $E=mc^2$ would still be correct. Just replace the rest mass with the relativistic mass and you are OK.

 

[Dale]

Have you ever heard of such a thing as a dimensionless constant? You could in principle have any dimensionless number k and E=mkc²

Sure, that is why I said "some multiple of c²". You must have the c² term simply due to the units. IMO, the reason why k=1 is interesting, but the c² seems to get the questions instead for some reason.

 

[-Physician]

If you define $m=m_0\sqrt(1/(1-v^2/c^2))$ then the initial relation $E=mc^2$ would still be correct. Just replace the rest mass with the relativistic mass and you are OK.

WOULD be correct but it's not, and IF we define, we can't define if we shouldn't , we can't just define it.

 

[Agerhell]

WOULD be correct but it's not, and IF we define, we can't define if we shouldn't , we can't just define it.

If you replace the "rest mass" with the "relativistic mass" as suggested you get an expression for the energy that would work if you want to calculate for instance the amount of energy you get when you smash a proton and an antiproton togehter at a certain velocity in an accelerator for instance.

Right?

If you use the concept of "relativistic mass" the relation still holds when there are moving masses.

Right?

 

[harrylin]

If you replace the "rest mass" with the "relativistic mass" as suggested you get an expression for the energy that would work if you want to calculate for instance the amount of energy you get when you smash a proton and an antiproton togehter at a certain velocity in an accelerator for instance.

Right?

If you use the concept of "relativistic mass" the relation still holds when there are moving masses.

Right?

Certainly correct - and while it may be not exactly as originally intended by Einstein, it is how my textbook applied it when I was a student. Works perfect. But it has little to do with the topic I fear...

 

[DrStupid]

But it has little to do with the topic I fear...

Why not? The original question was why c² and not any other proportionality factor between energy and mass. Without other information this may refer to rest energy and rest mass or to total energy and relativistic mass. This question can be answered for both cases at once:

Assuming we know that energy is linear correlated with mass (as used in Newton's definition of momentum) but we do not know the proportionality factor k:

$E = k \cdot m$

Then the change of mechanic energy is

$dE = F \cdot ds = k \cdot dm$

According to Newton's second law the force is

$F = \frac{{dp}}{{dt}} = \frac{{d\left( {m \cdot v} \right)}}{{dt}} = m \cdot \frac{{dv}}{{dt}} + v \cdot \frac{{dm}}{{dt}}$

Integration of the resulting differential equation

$\frac{{dm}}{m} = \frac{{v \cdot dv}}{{k - v^2 }}$

results in

$m = \frac{{m_0 }}{{\sqrt {1 - \frac{{v^2 }}{k}} }}$

The constant of integration m₀ is the mass of the body at rest and as this equation gives rational results for k<v² only the unknown proportionality factor k must be the square of a maximum velocity that no body can reach or exceed. In relativity there is such a velocity: the speed of light in vacuum. Therefore there is only one possibility for a linear correlation of energy and mass:

$E = m \cdot c^2 = \frac{{m_0 \cdot c^2 }}{{\sqrt {1 - \frac{{v^2 }}{c^2}} }}$

 

[harrylin]

[..] The constant of integration m₀ is the mass of the body at rest and as this equation gives rational results for k<v² only the unknown proportionality factor k must be the square of a maximum velocity that no body can reach or exceed. In relativity there is such a velocity: the speed of light in vacuum. Therefore there is only one possibility for a linear correlation of energy and mass:

$E = m \cdot c^2 = \frac{{m_0 \cdot c^2 }}{{\sqrt {1 - \frac{{v^2 }}{c^2}} }}$

Very good, I had not thought of that - that mathematical insight also has physical suggestion: it tells us how and why the inertial property of energy is determined. Thanks!