Absolute velocity measurements

[Weston]

Hi all, this is my first post to the forum.

I've been thinking about a mechanism that can't work, but I can't figure out why not. Here is the idea:

1) If I have two wires parallel to each other on a table and I run a current through them, they will be attracted to each other. I believe this will happen even if the current in the two wires is the same (same speed and direction).

2) Now imagine putting the wires on a train. If I run the train at the drift velocity of the current, then I could imagine the charge in the wires standing still (from the reference point of the train) while the wires zip by. That is, my train keeps pace with the electrons so that they are standing still in the "train frame".

3) Now, as long as the electrons aren't moving in the train's reference frame, let's replace them with statically charged marbles. Two negatively charged marbles sitting on the train should look a lot like a little piece of the current in the wires.

Here's the problem. From the "ground" reference frame, the marbles have a velocity and a charge, so they represent a current and the marbles should be attracted to each other. But from the reference frame of the train, the marbles are not moving, so they should not be attracted to each other.

Shouldn't I be able to measure the attraction between the marbles (or just watch whether they roll towards each other), and deduce some kind of "absolute velocity"? I know that isn't possible, but I'm not sure where my reasoning breaks down.

Thanks in advance for any thoughts.

Weston

 

[Bob S]

Hello Weston-
There are several problems:
1) If the two wires were on the train, the electron signal velocity will be the same on the train as it was at rest (wires at the railroad station).
2) The electron "velocity" is of the order of half or more times the speed of light (3 x 10^8 meters/sec) in any coordinate system.
3) Any field "at the station" that is orthogonal to the train velocity is transformed by relativistic transforms, which will transform transverse electric fields to magnetic fields, and vice versa. See the last four lines in
http://pdg.lbl.gov/2002/elecrelarpp.pdf
For example, if there were a charged parallel plate capacitor at the station with the field lines orthogonal to the train velocity, a rider on the train (at relativistic velocities) would see the transverse electric field converted to a magnetic field. Also, if the "electrons were at rest" in a similar capacitor on the train, an observer at the station would see a magnetic field.
Bob S

 

[Weston]

Hi Bob S, thanks for your response.
I want to make sure I understand. Using your numbering:
1) I probably should have said that the wires are next to the train, but fixed to the ground. From the ground frame, the wires are stationary and the current is moving. From the train perspective, the wires are passing by. Are you saying that the electrons move at the same velocity relative to the train and the ground, because of relativity?

2) My thought was that the electrons are moving very fast, but largely randomly. So their speed is fast, but their net movement along the wire is slow (like a drifting swarm of gnats). Does their instantaneous speed matter more than the overall drift velocity, or am I misunderstanding the idea of drift velocity?

3) That makes sense that there is a trade-off between electric and magnetic forces, depending on the observer. Part of what bugs me is the direction of the resulting force. It seems to me that in a frame in which the charges are static, they repel (they have the same sign). But in the frame in which they are moving, they attract (the currents have the same direction). Shouldn't the movement seen by both observers be the same, even if they attribute it to different forces?

I should say, I'm taking undergraduate-level classes and haven't studied relativity yet. If this is an elementary question regarding relativity, I don't want to ask you to explain what I could find a text on. :) Just let me know if that's the case, and I'll hit the books.

Thanks again.

Weston

 

[Doc Al]

1) If I have two wires parallel to each other on a table and I run a current through them, they will be attracted to each other. I believe this will happen even if the current in the two wires is the same (same speed and direction).

OK.

2) Now imagine putting the wires on a train. If I run the train at the drift velocity of the current, then I could imagine the charge in the wires standing still (from the reference point of the train) while the wires zip by. That is, my train keeps pace with the electrons so that they are standing still in the "train frame".

I assume that you mean that the wires remain on the table on the ground while the train travels past at the drift speed of the electrons. From the view of the train the electrons are at rest. (Of course the wires, and their positive charges, are now seen to be moving.)

3) Now, as long as the electrons aren't moving in the train's reference frame, let's replace them with statically charged marbles. Two negatively charged marbles sitting on the train should look a lot like a little piece of the current in the wires.

Here's the problem. From the "ground" reference frame, the marbles have a velocity and a charge, so they represent a current and the marbles should be attracted to each other. But from the reference frame of the train, the marbles are not moving, so they should not be attracted to each other.

Shouldn't I be able to measure the attraction between the marbles (or just watch whether they roll towards each other), and deduce some kind of "absolute velocity"? I know that isn't possible, but I'm not sure where my reasoning breaks down.

What are you missing is that in the frame of the moving train the positive charges in the wires are closer together (due to relativistic length contraction) and thus there's a net positive charge on the wire. That positive charge attracts the electrons.

What was a magnetic force in the ground frame becomes an electrostatic force in the train frame.