Feynman: Relativity of Magnetic and Electric Fields

[Hetware]

The diagrams aren't coming through on my system, but the text is readable:

http://books.google.com/books?id=hlRhwGK40fgC&pg=SA13-PA6&lpg=SA13-PA6&#v=onepage&q&f=false

First off, I'm pretty sure he re-uses $\rho_\omicron$ to mean different things at different points in the discussion. That was very confusing to me. It gives the impression that $\rho_\omicron=\rho_+=\rho^{'}_{-}$ which is incorrect.

I do understand that the velocity of attributed to the electrons is an average "drift" velocity.

I believe I finally figured this out. To an extent. Eq. 13.24 and eq 13.26 tell us that the conduction electron density is lower in the frame moving along with the electrons than it is in the rest frame of the wire. At the same time the positive charge density at rest relative to the wire becomes greater when transformed to the electron rest frame.

That means the proportion of electrons to protons in the wire is different when measured in relatively moving reference frames. Does this depend on the relativity of simultaneity?

Could this be demonstrated by placing a uniformly negatively charge moving train in a uniformly positively charged tunnel and adjusting the relative charge so that the electric field at rest with respect to the tunnel vanishes.

Assume at a given instant the entire train is just inside the tunnel as viewed from the tunnel rest frame. So the train appears Lorentz contracted. Now if we run along with the train, the tunnel will appear Lorentz contracted, and there will never be a time in the train's inertial frame when the entire train is in the tunnel. The event of the front for the train reaching the end of the tunnel will precede the event of the end of the train passing the beginning of the tunnel.

In the tunnel rest frame both events occur at the same time.

I recall reading something that discouraged that line of reasoning, but I don't see how it's wrong.

 

[pervect]

The diagrams aren't coming through on my system, but the text is readable:

http://books.google.com/books?id=hlRhwGK40fgC&pg=SA13-PA6&lpg=SA13-PA6&#v=onepage&q&f=false

First off, I'm pretty sure he re-uses $\rho_\omicron$ to mean different things at different points in the discussion. That was very confusing to me. It gives the impression that $\rho_\omicron=\rho_+=\rho^{'}_{-}$ which is incorrect.

I'm pretty sure that \rho_\omicron is the charge density in the rest frame of the charges. The only confusion here is that this will be a different frame for the electrons than the protons, because they have different rest frames.

I do understand that the velocity of attributed to the electrons is an average "drift" velocity.

I believe I finally figured this out. To an extent. Eq. 13.24 and eq 13.26 tell us that the conduction electron density is lower in the frame moving along with the electrons than it is in the rest frame of the wire. At the same time the positive charge density at rest relative to the wire becomes greater when transformed to the electron rest frame.

That means the proportion of electrons to protons in the wire is different when measured in relatively moving reference frames. Does this depend on the relativity of simultaneity?

Yes, indeed it does.

Could this be demonstrated by placing a uniformly negatively charge moving train in a uniformly positively charged tunnel and adjusting the relative charge so that the electric field at rest with respect to the tunnel vanishes.

That's a good informal summary of what Feynman just did, don't you think?

Assume at a given instant the entire train is just inside the tunnel as viewed from the tunnel rest frame. So the train appears Lorentz contracted. Now if we run along with the train, the tunnel will appear Lorentz contracted, and there will never be a time in the train's inertial frame when the entire train is in the tunnel. The event of the front for the train reaching the end of the tunnel will precede the event of the end of the train passing the beginning of the tunnel.

In the tunnel rest frame both events occur at the same time.

I recall reading something that discouraged that line of reasoning, but I don't see how it's wrong.

Offhand, I don't see anything wrong with it either.

 

[bcrowell]

Here is a more lowbrow treatment of the same topic: http://www.lightandmatter.com/html_books/0sn/ch11/ch11.html

The classic presentation of these ideas for undergraduates is in Purcell, Electricity and Magnetism.

It can also be done by boosting a loop rather than a straight wire: https://www.physicsforums.com/showthread.php?t=631446

 

[Hetware]

Here is a more lowbrow treatment of the same topic: http://www.lightandmatter.com/html_books/0sn/ch11/ch11.html

The classic presentation of these ideas for undergraduates is in Purcell, Electricity and Magnetism.

It can also be done by boosting a loop rather than a straight wire: https://www.physicsforums.com/showthread.php?t=631446

Bookmarked.