it is impossible to accelerate a particle to a speed greater than c, no matter how much kinetic energy we give it

In an experiment published in 1964, electrons were accelerated to a large voltage difference (up to 15 million volts) and the speed of electrons was directly determined. no matter how much accelerating voltage is increased, the speed never quite reaches or exceeds _c_ enter image description here

find this image here in this link

So from the chart in this image $( \frac vc )_{obs}=1 $ at $15MeV$ , hence we may say that at 15 MeV the speed of electron (rounded off) was equal to c. or better to say that limit $ v → c $

We also know that $$m= \frac {m_0}{\sqrt{1-\frac{v^2}{c^2}}}$$ hence limit $m→ \infty$ so its mass should tends to infinity.

Am I right?

Extension of this question

We also know that $density=\frac{mass}{volume}$, whatever be its volume however we know its mass tends to infinity hence its density should be infinite.

Take the example of a black hole its density is infinite (please go to this link and read the accepted answer) hence it should press the space time so much... like a black hole.

We also know that light cannot escape the black hole.

So if we accelerate the electron with same speed but this is time in an large particle collider then it should absorb all the light or radiations emitted?

will this happen?


1 Answer 1


Unfortunately this:

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

... is a stubborn and common misconception.

In reality it's the momentum $p$ that is relativistic:

$\large{p= \frac {mv}{\sqrt{1-\frac{v^2}{c^2}}}}$

Or as Albert Einstein wrote in a letter to Lincoln Barnett on 19 June 1948:

It is not good to introduce the concept of the mass $M = m/\sqrt{1 - v^2/c^2}$ 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.



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