It is found that the e/m ratio of an electron varies with velocity. Current physics assumes that it is mass that is variable with speed. Is there any fundamental reason why it cannot be assumed that it is electric charge that varies with velocity while mass is constant.
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1$\begingroup$ We can measure the charge in relativistic beams (e.g. by beam current measurement) and it's the same at any velocity. If charge was velocity dependent we would be seeing enormous (and catastrophic) changes in metals and in plasmas, where the electrons are moving at a very different velocity from the nuclei. $\endgroup$– CuriousOneCommented Mar 3, 2016 at 8:09
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2 Answers
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You say:
Current physics assumes that it is mass that is variable with speed.
but this is not true. The momentum of an electron is given by:
$$ p = \gamma m v $$
where $\gamma$ is the Lorentz factor and $m$ is the rest mass. The rest mass is constant just like the charge so there is no need to discuss which of the two is changing and which is constant.
Historically there has been a tendancy to group the two factors $\gamma$ and $m$ together to form a relativistic mass $\gamma m$, and historically this has led to vast amounts of confusion amongst physics students. If you mention relativistic mass these days physicists will reach for the tar and feathers.
tl;dr the trajectory of the relativistic electron in a magnetic field is described by taking into account the velocity dependance of $\gamma$. Both the mass and charge are constant.
answered Mar 3, 2016 at 8:09
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1$\begingroup$ Can I throw some rotting tomatoes and eggs, too? :-) $\endgroup$ Commented Mar 3, 2016 at 8:11
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$\begingroup$ actually the OP is asking whether charge depends on velocity, which can be disproved by the virtue of many experiments performed till date.. $\endgroup$ Commented Mar 3, 2016 at 8:11
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$\begingroup$ but the "gravitating mass" does increase with velocity in general relativity. In other words if you fill a box with gas and heat it to relativistic velocities, it will gravitationally attract a test particle outside of the box more, doesn't it? $\endgroup$– bkocsisCommented Mar 11, 2021 at 2:55
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At the time of the mentioned experiment, it was difficult to measure the charge of electron, and what was actually measured was the $e/m$ ratio. But afterwards there have been many experiments till date, which show that charge is not velocity dependent. For example the potentials produced by a relativistic electron don't behave anomalously from what is given by Lienard-Wiechert potentials at high velocities. Another example is given by studying scattering cross sections of electron-electron collisions at high energies, as is predicted to go to zero if the velocity dependence of charge is taken into account. And of course, as is pointed by John, mass doesn't change, his explanation is sufficient.
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$\begingroup$ For scattering experiments we use bare charge and effective charge renormalization, so that seems question begging to cite high energy scattering experiments. And you seem to imply a specific velocity dependent charge theory made predictions that turned out wrong. Which sounds quite radical. The point is that electrons and positrons have opposite charges and have three times the charge as some quarks and 3/2 the charge of some others and the same as W bosons. We use charge to distinguish those strengths. $\endgroup$– TimaeusCommented Mar 6, 2016 at 4:48