>E=mc^2 does this mean that if you took 1kg of matter and

c^2 is a proportionality constant

>>8637169
No. First of all, a more accurate form of that equation would be
[math]E^2= p^2 c^2 + m^2 c^2[/math], where [math]p[/math] is the momentum of a particle.
It means that in the frame of reference of the particle, the particle would have a mass of [math]m_0[/math] and a momentum equal to [math]0[/math], while in the frame of reference of the laboratory (which would see the particle in motion), the particle has a momentum of [math]p[/math] and a squared mass equal to [math]m^2= E^2 - p^2[/math] (here I've posed c=1 for simplicity), where the Energy [math]E=mc^2[/math] is a costant across all frames of reference.

>>8638646

So it's just a coincidence that it's c^2, or were joules defined so that c^2 would be the value of the constant, and why would defining it in that way be of any benefit over the constant just being some number called zeta or something?

>>8637169
E^2 = P^2 C^2 + M^2 C^2
where E is energy, P is momentum, C speed of light and M mass

Photon has zero mass so

E^2 = P^2 C^2
E = PC
E = MCC
E = MC^2

[E] = [kg][m/s][m/s]
[E] = [kg m2 s-2]

Don't think about dimensions too much.
It just means "energy = mass*constant" or "if you have X energy, you get Y mass"

>>8637169
When two atoms fuse, the mass of the combined atom is less than the mass of the original atoms that fused to form it. That tiny difference in mass in converted into energy.

And yes, you literally can just plug in the amount of mass lost in the fusion, multiply it by the square of the speed of light and you get an approximation of the amount of energy released.

Of course, in fusion, the amount of mass lost is miniscule. But when you remember that just 1kg of matter has so fucking many Avogadro's of atoms in it, and then you multiply that by the square of the speed of light which is a very large number, the energy obtained can be quite substantial.

>>8638863
J=kg*m^2/s^2
J=kgc^2
kgc^2=kg*m^2/s^2
c^2=m^2/s^2
c^2=v^2
c=v
basically it's saying the work needed to accelerate a mass to the speed of light=energy of the mass

>>8638863
>it's just a coincidence that it's c^2
It's not. [math]c^2[/math] comes out because it is the maximum velocity achievable, and because of that it appears in the Lorentz transformations, and thus in the relation between energy, mass and momentum
>were joules defined so that c^2 would be the value of the constant
It doesn't really have anything to do with the definition of measurement units. In fact, the set of units of measurement used in particle physics has [math]c=1[/math] in order to simplify calculations.

>>8637169
>another stupid thread

All the equation means is that for any relevant circumstance (like fusion) the equivalent of mass*c^2 is the energy.

Fusion is the best example, any excess mass from fusion is released in energy where the amount of energy abides to the equation.