B Length contraction of a pair of electrons

[DaveC426913]

This thread has left me shaken and humbled.

... you shouldn't expect to immediately understand.

I thought I already knew.

I sincerely thought I understood this subject better than I actually do. Bell's Spaceship Paradox, relativity of simultaneity, Lorentz contraction were all things I was comfortable with ...

It might be that I understood it a lot better 10-20 years ago, when I read up on physics heavily, but that, over time, my knowledge has rotted from the inside out. One would think, once you've learned how to ride a bike, you never "unlearn" it, but I guess use it or lose it.

Dunning-Kruger, ftw. Or onset of senility...

Thanks for being so patient, everyone.

 

[1977ub]

A stick might have clocks sitting at each end - initially synchronized. As it moves along its axis, and shortens in the lab frame, the clocks are no longer found to be synchronized by lab observers, though they are still found to be synchronized by observers at each end of the stick. "Shortening" can just be restated as desynchronization.

 

[metastable]

If we fire two electrons at the same time, one metre apart, should they length contract till they're less than a metre apart?

If you force the electron acceleration profiles fo be simultaneous in the lab frame, the the string will have been stretched

I'm confused on this point. How is the electrons being "fired" in the lab frame any different than an observer being fired away from the electrons? If the 2 scenarios are equivalent, why would the string between the electrons have any tension (ignoring the electric repulsion)?

 

[Ibix]

If the 2 scenarios are equivalent

They aren't. Who/what is being acted on by a force is different.

 

[Nugatory]

I'm confused on this point. How is the electrons being "fired" in the lab frame any different than an observer being fired away from the electrons? If the 2 scenarios are equivalent, why would the string between the electrons have any tension (ignoring the electric repulsion)?

They aren’t equivalent.

In one case there are inertial frames in which the lab, observer, and electron guns are moving with constant velocity throughout (the frame in which they are at rest is one of these, with the “constant velocity” being zero). There is no inertial frame in which the electrons move at constant velocity throughout.

The other case is the exact opposite. If we fire the lab and observers away from the electrons, then there are inertial frames in which the electrons are moving with a constant velocity (possibly zero) throughout there is no inertial frame in which the lab moves with constant velocity throughout.