First
Question :
Aberration effect :
Suppose
that you are in 1900. You are named Millikan and want to compute the
e/m ratio
for the electron.
You will make an experiment
with an glass tube without any air in it.
There will be two metal
pieces of rectangular shape in it, on which you will put various
electrical
potentials.
A small copper wire, while conducting
heavy current, emit electrons through a small hole.
You can
control it's speed with an accelerating electrode.
The electron
deviate on the effect of the electrical field.
The process
implies that you make measures of the electron deviation from the
center path.
With a lot of anger the electron does not
deviate as much as it must do with classical physics.
If you
assume that e is a constant, the term m must have increased.
(Millikan was opposite to Special Relativity and gave out only
after 20 years of experimentations.
His measures were finally a
strong support for SR)
But you suddenly realized that when
the electron enter in the electrical field, the perturbation
must
go at nearly the speed of light to the metal piece, then the power
source must give energy
to the electron to put it aside, with
also a travel time between the metal pieces at
the speed of
light.
So the electron is a shorter time in the field (OK
it's depend on geometry)
If the time is shorter in the field,
deviation is smaller at high speed that at lower.
There is no
more use for mass increase, even if the effect is the same.
You
imagine Albert Einstein "deconfiture", with a lot of
anticipated joy, there is so much time
you are waiting for this
event.
You make quick and dirty calculus and found that the
effect is the same with good approximation.

You have no doubts that with some refinements you will make
your result equal to Lorentz's one