Science Forums 2

[CraigD]

Originally Posted by martillo

… Now, Classical Physics determines two different behaviors because it considers that if a new absolute velocity is given to the isolated electron and the beam then this actually is a new phenomenon, a new system whith justified different behavior.
Now how Relativity consider and justify the two cases? The relative initial velocity of the two cases is the same so they would represent the same phenomenon, the same system for Relativity, then, how two different behaviors (to match with the classical prediction) are justified? Remember that just a change in the freference frame have been done. Then how?
I don't understand. …

I think you confusion arises, martillo, in a faulty understanding of classical electromagnetism.

In the equation for the force acting upon a particle with charge and velocity by magnetic field ,
, (the Lorentz force)
which is the starting point of your page “absolute magnetic force”, the vector quantities and must be in the same coordinate frame.

So, in both of your examples, , and you conclusion that is different for the 2 cases is incorrect.

Note that, except for cases where the magnitude of in a large fraction of the speed of light, classical electromagnetism provides an adequate approximation of the more general relativistic electromagnetism. The Lorentz force formula remains usable in either case, because it describes only force, not the acceleration. All that’s necessary to calculate acceleration due to Lorentz force relativistically is to include the term for mass dilation,

in the classical equation for acceleration,
.

Because the motion of charged particles such as electrons and protons are routinely and precisely observed, in devices from the most humble mass spectrometers to the most advanced cyclotron particle accelerators, relativity is very well confirmed by it.

I noticed another troubling sentence in your page (bolding mine):

Relativity applies Lorentz Transform with length and charge contraction in the beam of electrons.

Although you may not intend to apply otherwise, relativity describes mass dilation, and length contraction, but not any change in charge. For example, regardless of its velocity relative to an observer, the charge of an electron remains constant.