Is Net Charge Conserved in Special Relativity with Current Flowing in a Wire?

[DrGreg]

8/2=4

The eight electrons on the left are in a wire segment that is double the length of the contracted wire segment on the right that has two electrons.

Try measuring the distances between the electrons; the ratio is 1:2 not 1:4.

(NOTE: the length contraction is between the left and right diagrams as shown by the arrows. Comparing the top diagram with the bottom is not length contraction.)

 

[Fantasist]

The eight electrons on the left are in a wire segment that is double the length of the contracted wire segment on the right that has two electrons.

Try measuring the distances between the electrons; the ratio is 1:2 not 1:4.

I was referring to the 8 red charges and 2 blue charges in the segment in the bottom right corner. I make this a charge density ratio 1/4 electrons/ions.

 

[DrGreg]

I was referring to the 8 red charges and 2 blue charges in the segment in the bottom right corner. I make this a charge density ratio 1/4 electrons/ions.

Yes it is. But I thought you were talking about length contraction between two frames of reference, not charge density ratio within a single frame.

 

[A.T.]

If we're talking about a loop, instead of infinitely long wires, then presumably it works like the spokes on a wheel.

http://casa.colorado.edu/%7Eajsh/sr/wheel.html:

http://casa.colorado.edu/%7Eajsh/sr/contraction.html:

(Notice that it satisfies conservation-of-spokes.)

It's similar but not quite the same:
- The proper distance between the spokes doesn't change between rolling and not rolling.
- The proper distance between the electrons does change between current and no current.

ETA : The above is not correct as pervect noted. The proper distance between the spokes does change.

 

[A.T.]

Yes it is. But I thought you were talking about length contraction between two frames of reference, not charge density ratio within a single frame.

That's what I tried to clarify in post #22: Using the term "contraction" for different things leads to the most confusion here.

 

[pervect]

It's similar but not quite the same:
- The proper distance between the spokes doesn't change between rolling and not rolling.
- The proper distance between the electrons does change between current and no current.

If the circumference changes, and the number of spokes around the circumference doesn't change, how can you think that the proper distance between the spokes stays constant?

 

[A.T.]

If the circumference changes, and the number of spokes around the circumference doesn't change, how can you think that the proper distance between the spokes stays constant?

You are right. The proper spoke distance changes, so it is very similar to the current loop.

 

[Histspec]

That's what I tried to clarify in post #22: Using the term "contraction" for different things leads to the most confusion here.

In the following page, length contraction in terms of measurements in different frames is called "passive", and length contraction in terms of measurements in one inertial frame is called "active"
http://www.mathpages.com/home/kmath699/kmath699.htm
It seems to me that many misunderstandings concerning the "wire-current" scenario, Bell's spaceship paradox etc. can easily be avoided by using such a terminology.

 

[DrGreg]

In the following page, length contraction in terms of measurements in different frames is called "passive", and length contraction in terms of measurements in one inertial frame is called "active"
http://www.mathpages.com/home/kmath699/kmath699.htm
It seems to me that many misunderstandings concerning the "wire-current" scenario, Bell's spaceship paradox etc. can easily be avoided by using such a terminology.

Indeed. In my diagram of post #25, "Lorentz contraction" means "passive Lorentz contraction", between left & right diagrams. There is no "active Lorentz contraction", for the electrons between top & bottom diagrams, because the electrons are not rigidly separated from each other i.e. there's nothing forcing their separation, in their own rest frame, to remain constant.

 

[DarioC]

This reminds me of a discussion we had here some time ago about current flow in a wire. I actually sat down and computed the "free" electrons in a one millimeter square wire in the first atom wide right angle sheet at the beginning of the wire. Made the wire one meter long. The number was amazingly large to me. For a guy who worked as an electronics technician all his life it shed and entirely new light on my thought process concerning current flow.

Anyway the calculations, using a current of one ampere, which is quite a bit of current for this wire, indicate that it would take a really long time for a given electron to get to the other end of the wire. I had proposed that the wire was like a long pipe full of ping-pong balls, except that the pipe is huge and the number of balls is equally huge.

That is to say you push some balls in one end and they produce and interaction between balls all the way down the wire and pop some balls out the other end.

The analogy gets really interesting when you put in a very short pulse. In the real wire the interaction must travel down the wire at close to the speed of light but the electrons don't really have to move at a very fast average speed, especially when compared to the random thermal motion, which I understand to be much larger.

I believe the number I came up with for a given electron to travel down the one meter wire, at one ampere, could be as much as 23 hours. It sounds pretty insane and I have never seen anything in print that even mentioned such a calculation. One just has to compare the number of electrons supplied by one ampere with the available number of electrons in each atom-wide sheet of a meter long wire (and how many "sheets" there are) to see that the calculation might be reasonable.

DC

 

[Orodruin]

That is to say you push some balls in one end and they produce and interaction between balls all the way down the wire and pop some balls out the other end.

This is not a good analogy. Electric current works mainly by the application of an external electric field, not through the electrons pushing each other (electrons pushing each other makes sure the conductor is electrically neutral).

One just has to compare the number of electrons supplied by one ampere with the available number of electrons in each atom-wide sheet of a meter long wire (and how many "sheets" there are) to see that the calculation might be reasonable.

All electrons are not available for conduction so the actual average electron velocity is going to be larger than what is given by this assumption.

 

[DarioC]

You might want to look at what it is that generates that electric field, say in the example of an electric cell (battery), before you disagree that the electrons are pushing against each other. Obviously the charge of each electron is what does the pushing against the charge of the other electrons, I figured everyone here would know that.

I, of course, left out a few things, like that I am talking about the number of conduction band electrons available in a copper wire, not the total quantity of electrons possessed by all the atoms.

I guess that the way I put it did leave it open for that interpretation, if you make the assumption that I am ignorant enough to think that all the electrons in an atom are involved in electrical current flow.

My point is that there is a massive amount of conduction electrons in even a small wire compared to the number of electrons supplied by what would be considered a typical flow of current in an "everyday" situation.

DC