I've asked before, but I'm still confused as to what the mass energy equivalence implies. I've taken an introductory course in relativity, so I only covered special relativity. From what I gather, all things have a rest mass. As you increase your energy, your mass increases as well, and the rest mass behaves as some potential. But then when we talk about fusion and fission, we are splitting the atoms to generate energy-breaking apart the potential stored in forces between atomic components. This kind of makes sense to me. But then are all energies and masses equivalent? An electron has a rest mass, is this considered energy as well? Is the mass stored in objects I hold due to the gravitational field simply too small for me to notice? Furthermore, if mass is energy, then why do nuclei weigh less? Is some of their mass going into the bonds? The fission and fusion also confuse me, both are building towards a more stable atom (32?) but somehow both paths generate energy.
3 Answers
It all depends on the scale at which you examine things. Just like thermal energy being resolved as the randomized kinetic energy of the parts if examined closely enough, so mass can be resolved into binding and kinetic energies plus some intrinsic masses of the bits if examined at the right scale.
As you increase your energy, your mass increases as well, and the rest mass behaves as some potential.
I assume you mean "as you increase your velocity"; correct me if I'm wrong. Rest mass does not depend on velocity. Be careful to distinguish between rest mass and relativistic mass. Rest mass, denoted as $m_0$, is the one that is equivalent to energy via $E_0 = m_0 c^2$. Relativistic mass is something like the resistance of the object to acceleration, but as a concept it's not used today. To quote einstein,
It is not good to introduce the concept of the mass $M = m_0/\sqrt{1 - v^2/c^2}$ of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.
Next,
But then are all energies and masses equivalent? An electron has a rest mass, is this considered energy as well?
Yes. In order to measure that energy, simply annihilate that electron with a positron. Without doing so, you can't "feel" the energy.
Edit
Here is how energy works in nuclear fission. Let's take the reaction
$$ n + _{92}^{235}\textrm{U} \to _{56}^{141}\textrm{Ba} + _{36}^{92}\textrm{Kr} + 3n $$
The total mass on the left hand side is
$$ (92 m_p + 143 m_n + E_U/c^2) + (m_n) $$
where $E_U$ is the binding energy of Uranium, or about -1783870 keV. The total mass on the right hand side is
$$ (56 m_p + 85 m_n + E_{Ba}/c^2) + (36 m_p + 56 m_n + E_{Kr}/c^2) + 3 m_n $$
comparing, the $m_n$ and $m_p$ cancel, as they should. The mass difference is $\frac{1}{c^2} (E_{Kr} + E_{Ba} - E_{U})$ which you can look up if you wish. This is the energy liberated by fission.
- 1,092
Well I'm not up on current practice, but when I studied such things, some particle physicists used a system of units where c = hbar = 1
So in that system of units you simply have E = m and also E = (nu)
When accelerated particles approach the speed of light (c) , they don't add much in the way of speed, but their mass increases.
And in any radioactive decays, or Nuclear fission or fusion, the mass balance has to involve the energies of the various components, treating mass and energy as identical.