Energy, Mass, and Velocity: Exploring E = mc^2

[cdux]

Why does popular science say that Energy is a form of Mass because of E = mc^2, when there's also 'c' in that equation? Isn't velocity energy in that train of thought? Or is it not at least part of the story?

 

[vanhees71]

The formula isn't even correct. It must read
$$E=\frac{m c^2}{\sqrt{1-\vec{v}^2/c^2}}.$$
The energy is the temporal component of the energy-momentum vector
$$p=\begin{pmatrix} E/c \\ \vec{p} \end{pmatrix}= \frac{m}{\sqrt{1-\vec{v}^2/c^2}}\begin{pmatrix} c \\ \vec{v} \end{pmatrix}.$$
The reason is that nowadays we clearly understand the mathematical structure of special relativity thanks to Minkowski's work from 1908. According to this modern point of view mass is a scalar and energy the temporal component of the above given four-vector. Why popular-science-book writers don't take up this much clearer convention but stick to the pre-Minkowskian mystification is an enigma to me!

 

[mfb]

c^2 in that equation is just a conversion factor, it is not the velocity of anything. You could give every mass in units of energy, and the equation (for particles at rest) would be E=m. In particle physics, this is quite common - particle masses are usually given in units of energy.

 

[haael]

That's right, and you can do similar conversions between the units of energy, mass and momentum and between the length and time. Going a bit outside relativity, you can convert between the units of energy and temperature. And in quantum mechanics you can convert between length/time and energy/mass/momentum, but it is an inverse proportionality.

 

[Parlyne]

Why does popular science say that Energy is a form of Mass because of E = mc^2, when there's also 'c' in that equation? Isn't velocity energy in that train of thought? Or is it not at least part of the story?

If they say that, then they have it exactly backwards. The correct statement is that mass is a type of energy; and that $E = mc^2$ states how much energy is associated with mass m. The statement needs to be made in this way specifically to be clear that energy due to motion is not in any way equivalent to mass.