# Length contraction test in electrical circuits

1. Apr 16, 2015

### exmarine

As I am sure everyone is aware, there are still folks who don’t believe SRT and GRT. While 99.9% of them are nut-jobs, there is at least one that I respect – Tom Phipps specifically. I am not familiar with any of his writing before the advent of the GPS satellites. In any case, he now accepts “time dilation”, but not “length contraction”. The last I knew (~2006?) he claimed that it has never been proven empirically. I think he is wrong, and the most compelling evidence of length contraction for me is the explanation of magnetism / Ampere’s law given by Purcell. I assume that at least some of you are familiar with that? Briefly, the apparent length contraction of a passing line of charges enhances their influence on neighboring lines of charges. Thus “parallel currents attract”, i.e., Ampere’s law and magnetism, is so simply and elegantly understood as length contraction, or at least the apparent contraction of a line of charges.

Finally getting to my question: The only objection to Purcell’s interpretation that I can think of is the excess negative charge on a current carrying wire (in the lab frame) that should appear during the starting transient. Since all practical circuits are grounded, I don’t suppose that such would be apparent. But can anyone think of a way to test that – does an excess negative charge appear on a current carrying wire during the starting transient? Or has someone already tested that?

Thanks.

2. Apr 21, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Apr 21, 2015

### jartsa

Physicist J.S Bell thinks that a passing line of objects is not length-contracted.
"The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start"

On the other hand Purcell and other people think that a moving capacitor is length-contracted, and charge density is therefore increased.
http://en.wikipedia.org/wiki/Relativistic_electromagnetism

If we measure the current from a circuit to the ground, when a current is started in the circuit, we will notice that there is no current. I mean circuits don't become negatively charged when current is turned on.

Magnetism may be some kind of proof of contraction. People who understand how Lorentz-contraction explains magnetism understand the proof, the problem is that it's difficult to understand.

4. Apr 21, 2015

### PAllen

This misunderstands Bell, as well as the scenario Bell analyzed. In that scenario, by construction, the distance remains constant in the starting inertial frame. This is primarily because the accelerations start simultaneously in this frame. In the frame of one of the rockets, the accelerations do not start at the same time, and the distance between the rockets increases.

For a current loop, there are no accelerations (once equilibrium is reached). There are just two different inertial frames to compare. Bell would not dispute that if the distance between electrons in the frame comoving with them is L, then it is less than L in the frame in which the wire is at rest.

5. Apr 22, 2015

### wabbit

I agree with this. Now the op was precisely about the transient, i.e. the period when the electrons are accelerated as the potential applied between the ends of the wire is increased from 0 to its stationary value (assuming the wire itself is at rest in the lab frame). This does seem similar to the spaceship situation, in the lab frame all electrons simultaneously undergo the same acceleration, and they move apart in their own frames. At the end of the transient the length of the wire is greater in an electron frame than in the lab frame, so the moving line of electrons appears length contracted while the static line of atoms in the wire does not (as with the spaceships, the lab distance between electrons remains the same, it is length contracted relative only to their own frame).
Is this correct ?

Last edited: Apr 22, 2015
6. Apr 22, 2015

### PAllen

Transients in wires treated relativistically is surprisingly complex. I was not addressing this case. I looked for some reasonable write up on this available on the web and couldn't find one worth linking to. There have been several involved discussions over the years on this here on PF.

7. Apr 22, 2015

### wabbit

Thanks. There must also be something wrong in my analysis above since the electrons are always moving very slowly in the wire so relativistic effects can't really be of any significance.

8. Apr 22, 2015

### jartsa

Electron sees an accelerating wire, so electron sees a shortening wire.

As electron sees an expanding line of electrons and a shortening wire, electron concludes that electrons are spouting out of the end of the wire at high speed, if the wire is a straight wire.

If the wire is a loop, it's the same thing, except that electrons stay inside the wire.

Last edited: Apr 22, 2015
9. Apr 22, 2015

### jartsa

So in the frame where acceleration of spaceships is simultaneous, spaceship density, number of spaceships per meter, is constant. If spaceships are charged, charge density is constant.

While in the frame of spaceships the spaceship density decreases. If spaceships are charged, charge density is decreases.

10. Apr 22, 2015

### pervect

Staff Emeritus
I've missed the arguments / posts on this topic, apparently, but I think it's reasonable to point out to the OP that charge is conserved, so that any buildup of negative charge in one area will have a buildup of positive charge in another.

Additionally, while a full computation of transients in wires would be messy, a computation of what happens in a transmission line is very simple. I'm not feeling motivated to do such a treatment but I'd encourage the OP to look into it giving that they are trying to get a better understanding.

I'd also like to point out that conceptually it's better to think about testing the full Lorentz transform, rather than trying to chop it up into "time dilation" and "length contraction" and the often-neglected (by people who insist on chopping the transform into pieces) effect called "the relativity of simultaneity". If you believe that the whole transform "works", arguments based on chopping it up into pieces seem incoherent.

I believe I've already seen a proof on PF that shows that 3 key experiments experimentally determine all four possible coefficients of a general linear transform between frames, but I couldn't track the link down.

Other arguments (such as the homogeneity and isotropy) rule out nonlinear transforms, as first pointed out by Einstein. This may be a bit abstract, on the experimental side I'd like to point out that that fact that sine-waves in one frame transform to sine-waves in another frame (i.e. no effects of frequency doubling of light or electromagnetic radiation) rule out nonlinear transforms.

11. Apr 22, 2015

### wabbit

Yes you re right I misspoke, I was thinking of an "abstract wire" comoving with the electrons here. That one is longer in the electron frame than the physical wire, which is consistent with how you describe it.

Still these effects are truly tiny given the very low velocities concerned, I don't see how they could explain magnetism.

12. Apr 22, 2015

### bcrowell

Staff Emeritus
13. Apr 22, 2015

### Mentz114

Agree. I think it needs saying.