When electrons move at high speeds, why is their mass LARGER than their rest mass? Why isn't it the opposite?

Question

When an electron moves at a high speed, it has a large kinetic energy.

I know that E = mc^2 and so if an electron was travelling at a high speed, wouldn't the mass decrease in order to increase the kinetic energy (as smaller masses travel faster)?
Where does the energy come from to increase the mass; if the energy came from the kinetic energy of the electron, this would cause the electron to travel slower?

Does this answer your question? Why does the (relativistic) mass of an object increase when its speed approaches that of light? In particular, I would recommend looking at the answer below the accepted answer, which explains how relativistic mass is an outdated concept. — Sandejo, Sep 27 '20 at 16:12
@Sandejo By "the answer below the accepted answer," do you mean Igor Ivanov's answer posted Dec 6 '10 at 19:40? — Tanner Swett, Sep 27 '20 at 16:23

score 2 · Accepted Answer · answered Sep 27 '20 at 16:17

The mass of an electron does not increase with speed! The invariant mass (the true mass!) of a particle does not depend on how fast it is going. What does change is the energy of the particle. $E=mc^2$ is not the full picture; the real relation is $$E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}$$ As you can see, when $v=0$, $E=mc^2$; this is Einstein's famous relation, which relates the mass of a particle to the energy it innately possesses, called the rest energy. But unless $v=0$, the above, more general, relation holds. Thus, as you can see, when $v$ increases, the particle's energy increases, not decreases.

Ok! Thanks I understand it now! – Phoooebe Sep 28 '20 at 12:48 — Phoooebe, Sep 28 '20 at 12:48

score 1 · Answer 2 · answered Sep 27 '20 at 16:13

The energy comes from whatever accelerated the electron. There is no need for the mass to decrease to “compensate” for an increase in kinetic energy. An electron with higher velocity has more energy overall. The increased mass for this electron is simply a reflection of its greater total energy.

When electrons move at high speeds, why is their mass LARGER than their rest mass? Why isn't it the opposite?

2 Answers2