What is the significance of the classical electron radius?

[seattle.truth]

I understand how the formulas for classical electron radius are derived.. but what significance does the classical radius really carry?

Obviously it's not really the size of the electron. So what does it mean?? Thank you for any help... Sorry, I'm new to this stuff.

 

[lugita15]

It is harder to accelerate a charged particle compared to an uncharged particle. That's because an accelerating charged particle releases electromagnetic radiation. So you need to supply more energy to accelerate a charged particle: you need to give it enough energy to reach the acceleration you want, and enough energy to fuel its electromagnetic radiation.

So you need to apply a greater force to give the same acceleration to a charged particle. Another way of looking at it is that charged particles have greater mass than uncharted particles, because they have special "electromagnetic mass.". In the late 1800's people were very excited by this, because they speculated that maybe all mass comes from the electromagnetic field. Among other things, they calculated how big an electron would have to be if its mass is entirely electromagnetic. This is the classical electron radius.

Nowadays we know that the electron, if it has any size at all, is much smaller than the classical electron radius, and we also know that not all of an electron's mass is electromagnetic in origin.

P.S. In classical physics, the nonelectromagnetic portion of an electron's mass comes from the so-called Poincare stresses. You see, according to classical theory an electron would exert an infinite repulsive force on itself. So there have to be some "rubber bands", or Poincare stresses, to keep an electron together. In quantum physics, this issue was much more serious and led to infinity appearing in a lot of problems. The famous physicist Richard Feynman resolved this problem, for which he was awarded a Nobel prize.