Explanation of EM-fields using SR

[universal_101]

See my reply to you in post #63. Length contraction does imply contraction of the repulsive Coulomb field between the electrons (although extremely small, in view of the extremely small drift speeds); for an induced current in a closed wire loop that is irrelevant, but it may be of relevance in a wire that is fed by a battery, at least in theory. In practice (in view of an experimental paper of 1985) it appears that other, unknown effects may play a greater role.

Thanks harrylin, for addressing the issue in this, and in your post #63, but I think the problem here is unknown effects, because even if you consider any test charge moving w.r.t the wire at the drift speed of electrons in the direction of moving electrons the test charge feels a force(i.e test charge is co-moving with current producing electrons and moving w.r.t the cations). Whereas, nothing of the sort happens when the test charge is at rest w.r.t the wire and all the current electrons are moving w.r.t the test charge. Even though the situation is symmetric there are different results.

 

[A.T.]

even if you consider any test charge moving w.r.t the wire at the drift speed of electrons in the direction of moving electrons the test charge feels a force(i.e test charge is co-moving with current producing electrons and moving w.r.t the cations). Whereas, nothing of the sort happens when the test charge is at rest w.r.t the wire and all the current electrons are moving w.r.t the test charge. Even though the situation is symmetric there are different results.

The situation is not symetric because the spacing of electrons in the electron's rest frame is different than the spacing of cations in the cation's rest frame.

 

[yuiop]

See my reply to you in post #63. Length contraction does imply contraction of the repulsive Coulomb field between the electrons (although extremely small, in view of the extremely small drift speeds); for an induced current in a closed wire loop that is irrelevant, but it may be of relevance in a wire that is fed by a battery, at least in theory. In practice (in view of an experimental paper of 1985) it appears that other, unknown effects may play a greater role.

In order for a current to flow in the wire, there has to be a potential difference across the length of the wire, so the Voltage at one end has to be higher than at the other so their is slight increase in the density of electrons at one end compared to the other. I think the effect is small and averages out over the length of the wire and can probably be ignored for the purposes of this thread, but it might show up in very precise practical experiments.

 

[harrylin]

The situation is not symetric [between the wire's rest frame and the electron's rest frame] because the spacing of electrons in the electron's rest frame is different than the spacing of cations in the cation's rest frame.

Indeed - for a reason that may still need a little more discussion, the electron density in the wire's rest frame is approximately equal to the metal ion density (see also below). I guess that the nearly perfect equilibrium of positive and negative charges in a stationary wire can be explained by the Coulomb force of the metal ions on the electrons. But then how about the cat's rest frame? There is an asymmetry because the metal wire's ions are strongly bound, but .. I'll have to refresh my memory about the different force and field transformations. Meanwhile, perhaps someone else can provide that "missing piece" (WannabeNewton, what does Purcell say about that?).

In order for a current to flow in the wire, there has to be a potential difference across the length of the wire, so the Voltage at one end has to be higher than at the other so their is slight increase in the density of electrons at one end compared to the other. I think the effect is small and averages out over the length of the wire and can probably be ignored for the purposes of this thread, but it might show up in very precise practical experiments.

Yes, there is a number of Coulomb effects involved with a current in a wire, but obviously they are all very small compared to the magnetic force - else the definition of the Ampere would have been messed up.

Still, this discussion gives me the feeling -and perhaps I'm not the only one - that I am "missing" something. Hopefully that feeling will disappear in the course of this thread which by now has become truly interesting for me.

 

[WannabeNewton]

Purcell doesn't address that issue verbatim unfortunately (as far as I can tell) but in the meantime, see if this piques your interest: http://www.chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf

 

[Dale]

unknown effects may play a greater role.

I think the problem here is unknown effects

As far as I know there are no known EM experimental results which are in conflict with standard EM theory. Perhaps there are some unknown influences in a given experiment where some particular condition was not sufficiently controllable to be known, but in well-controlled experiments I am not aware of anything unknown.

universal_101, certainly, your confusion on the topic at hand is not indicative of a fundamental unknown.

 

[Dale]

I think the effect is small and averages out over the length of the wire and can probably be ignored for the purposes of this thread, but it might show up in very precise practical experiments.

I agree. Typical self-capacitances are on the order of pF or even less, so you would need extremely high voltages to get any appreciable charge. And, as you said, you would need to raise both ends of the wire to a high voltage to get a net charge that isn't balanced out over the length.

 

[Noyhcat]

Lets say the loop of wire consists of 2 parallel wires (A and B), each 600m long and ignore the length of the connecting sections at each end. Let's also say there are 200 electrons in the entire circuit so they are 6m apart from each other, when equally spaced out and at rest with the wire in the wire/lab rest frame. (Yes, I know that is unrealistic but stick with me ;)

When the current is moving relative to the wire/lab, there are still 200 electrons distributed around 1200 m of wire as measured in the lab so the gap between electrons is still 6m as measured in the lab.

Now let's say the cat and the current are moving to the right at 0.8c relative to the wire/lab and the cat is at rest wrt to the electrons in wire A. (Again unrealistic, the electrons only move at something like walking pace). The gamma factor is 10/6 at 0.8c so the wire A is 360m long according to the cat. The gap between the stationary electrons in wire A is 6m*10/6 = 10m according to the cat. The number of electrons in wire A is 360/10 = 36 (according to the cat).

Now we have to find room for the other 164 electrons. To the cat the length of wire B is 360m (same as the length of A to the cat). The electrons are moving at 0.8c relative to the wire and the wire is moving at 0.8c relative to the cat, so using relativistic velocity addition the electrons in wire B are moving at (0.8+0.8))/(1+0.8*0.8) = 0.97561c relative to the cat. The gamma factor at that velocity is 4.5555 recurring. The gap between the electrons in section B is 10m/4.5555 = 2.19512195m (according to the cat).

The 360m of wire B, divided by the inter electron length 2.19512195 equals 164, so our remainder of electrons fits nicely into the return length of wire (from the cats point of view).

To summarise the case when the electrons are moving relative to the wire, from the point of view of the cat co-moving with the electrons in wire A, there are 100 positive charges and 36 negative charges in wire A and 100 positive charges and 164 negative charges in wire B, so the cat is repelled from A and attracted to wire B.

Yeah, see the video does leave a lot out, doesn't it. Which makes sense, as it's meant to maybe peak the interest in science of folks in general, rather than take them through a specific example like this or provide diagrams like DrGreg's to show exactly what's going on, etc. Thanks...

 

[yuiop]

Purcell doesn't address that issue verbatim unfortunately (as far as I can tell) but in the meantime, see if this piques your interest: http://www.chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf

Thanks for the link which is very interesting. I follow how they derive $Q_L = Iv/c^2$ but I cannot fathom how they conclude that the change in charge potential is due to the relativity of simultaneity. Here is the meat of their argument quoted.

We need an understanding of what is happening as a result of non-simultaneity:
An observer in the moving test-charge frame, who moves along with the wire (say in the same direction as the electrons in the wire) will, due to non-simultaneity, 'see' into the future of the wire downstream of the electrons, and into the past at the side where the electrons enter the wire. 'Seeing' is of course the wrong word. We just redefine simultaneity different in a different reference frame. We however have to adopt our calculations as if these events in the past and future are simultaneous to our time when we are observing from the test charge's rest-frame. The future at the downstream side of the electrons means that they did stream further out of the wire there. At the other hand, the past, at the side where the electrons enter the wire, means that less electrons have streamed into the wire there. The overall result is thus that we must calculate with less electrons in the wire per unit of length as positive ions. More electrons have streamed out while less of them have streamed in.

Surely if the current is constant over time, then the amount of electrons leaving (or entering) the section of wire per second is the same in the past as it is in the future?

I can see the temptation to assume there is a connection with the RoS, because the RoS is proportional to $L v/c^2$ (where L where is the length of the section of wire as measured in the rest frame of the positive test charge) and the expression for charge density above can be rearranged to $Q/I =Lv/c^2$, ( Where $Q_L = Q/L$). but I think that is coincidental and the link is more to do with link between length contraction and RoS as in this Wikipedia section.

 

[STEMucator]

I actually give this video a thumbs up. The "cation" pun was hilarious.

 

[jartsa]

I wonder what kind of understanding could be gained by considering a charged object that is being swung around in a circle on a deck of a ship that is moving linearly?

 

[A.T.]

Surely if the current is constant over time, then the amount of electrons leaving (or entering) the section of wire per second is the same in the past as it is in the future?

In every inertial frame that is true. But when you accelerate from the inertial wire's frame to the inertial current's frame your line of simultaneity rotates. In this accelerating frame there are more electrons per second leaving the segment, than entering it. So when you arrive in the current's frame you end up with less electrons in the segment, than there were in the wire's frame.

So yes, the relativity of simultaneity can be used to explain why there a different counts of electrons in the wire segment, between the two frames: Two events (electron entering, electron leaving) that are simultaneous in the wire's frame, are not simultaneous in the current's frame (leaving comes first).

 

[universal_101]

As far as I know there are no known EM experimental results which are in conflict with standard EM theory. Perhaps there are some unknown influences in a given experiment where some particular condition was not sufficiently controllable to be known, but in well-controlled experiments I am not aware of anything unknown.

universal_101, certainly, your confusion on the topic at hand is not indicative of a fundamental unknown.

Just switching the current on and off is in conflict with the standard EM theory(i.e. SR).

 

[universal_101]

DrGreg doesn't drop length contraction at any point. See his image below. The flowing electrons (their E-fields) are contracted in the wire's frame. But since they are all contracted by the same amount, and their number is constant, they keep a constant spacing by distributing themselves uniformly.

He specifically mentions there is NO Length Contraction when switching the current on. To me it's a drop.

Length contraction is part of the situation. But Length contraction doesn't imply that the spacing in the wire's frame will decrease when the current starts flowing. If the spacing in the current's frame changes, the spacing in the wire's frame can stay constant.

What does the Length Contraction implies then ?, because standard theory says there should be length contraction and as a result closer spacing and higher density of electrons and as a result some negative charge.

 

[universal_101]

The situation is not symmetric because the spacing of electrons in the electron's rest frame is different than the spacing of cations in the cation's rest frame.

This should result in excess charge, since different spacing of electrons and cations means different density, which in turn means some net unbalanced charge.

 

[universal_101]

In order for a current to flow in the wire, there has to be a potential difference across the length of the wire, so the Voltage at one end has to be higher than at the other so their is slight increase in the density of electrons at one end compared to the other. I think the effect is small and averages out over the length of the wire and can probably be ignored for the purposes of this thread, but it might show up in very precise practical experiments.

Not always, Superconducting wire can easily contain the current for long time without needing any potential difference. But for ordinary wires the implications are correct, but again as you said they can be ignored safely.

 

[harrylin]

As far as I know there are no known EM experimental results which are in conflict with standard EM theory. Perhaps there are some unknown influences in a given experiment where some particular condition was not sufficiently controllable to be known, but in well-controlled experiments I am not aware of anything unknown.

Yes, I dug a little deeper and found that the results could not be reproduced.
- http://rsi.aip.org/resource/1/rsinak/v61/i10/p2637_s1

 

[A.T.]

The situation is not symetric because the spacing of electrons in the electron's rest frame is different than the spacing of cations in the cation's rest frame.

This should result in excess charge,...

It does, in all except one frame, where the differential length contraction makes the charge densities equal. That is the wire's frame.

...since different spacing of electrons and cations...

You seem to be comparing spacing of electrons and cations in different frame each. That doesn't make any sense except to check if the situation is symmetrical (as I did above). Read exactly what I wrote in the top quote and pay attention to reference frames. Try to be more precise in your language by always stating the reference frame (as I did above). This is the most common source of confusion.

 

[harrylin]

[..] I cannot fathom how they conclude that the change in charge potential is due to the relativity of simultaneity. [..] Surely if the current is constant over time, then the amount of electrons leaving (or entering) the section of wire per second is the same in the past as it is in the future? [..] I think that is coincidental and the link is more to do with link between length contraction and RoS [..].

Yes, exactly. The challenge that we face (if we don't satisfy ourselves with superficial arguments) is to explain the near-steady state force balance in the cat's rest frame. I have seen similar wrong explanations for other problems, and I think that you correctly nail down the cause of that misunderstanding. However already the next section, which I did not yet have time to study, looks very interesting - thanks WannabeNewton!

 

[universal_101]

It does, in all except one frame, where the differential length contraction makes the charge densities equal. That is the wire's frame.

i think you are considering the situation rather casually, I'm not questioning a regular Lorentz transform. Let me say it again then, the situation you should be considering is switching the current on and off all in the wire's frame. There is no need to transform the constant flowing current for different inertial frames, which you are describing and many others before you.

You seem to be comparing spacing of electrons and cations in different frame each. That doesn't make any sense except to check if the situation is symmetrical (as I did above). Read exactly what I wrote in the top quote and pay attention to reference frames. Try to be more precise in your language by always stating the reference frame (as I did above). This is the most common source of confusion.

Alright, let's consider a particle accelerator, and suppose there are highly energetic(fast moving) Muons in the tunnel, and there is a sample of them in a stationary lab w.r.t the accelerator. Now, my question is since the particles in the tunnel are length contracted, time dilated etc. compared to the samples in the stationary lab because of the relative motion(this is all in the lab's frame). Why does the same not follow for the case of switching the current on from off because of the relative motion between electrons and protons(this is all in the wire's frame).

 

[universal_101]

Lets say the loop of wire consists of 2 parallel wires (A and B), each 600m long and ignore the length of the connecting sections at each end. Let's also say there are 200 electrons in the entire circuit so they are 6m apart from each other, when equally spaced out and at rest with the wire in the wire/lab rest frame. (Yes, I know that is unrealistic but stick with me ;)

When the current is moving relative to the wire/lab, there are still 200 electrons distributed around 1200 m of wire as measured in the lab so the gap between electrons is still 6m as measured in the lab.

Why do you need to measure it, I think it should be predicted(logically deduced) by the standard EM theory, that given a wire with NO current and NO excess charge should remain neutral NO matter how high the current through it.

 

[Dale]

Just switching the current on and off is in conflict with the standard EM theory(i.e. SR).

In what possible way could you think this statement is true? What possible conflict between Maxwells equations and an electrical switch could you think exists?

To make a claim like this you need a rigorous derivation showing exactly how closing a switch violates Maxwells equations. Otherwise it is just your personal speculation.

 

[A.T.]

There is no need to transform the constant flowing current for different inertial frames

You claimed that the situation was symmetrical from both frames, and I explained why this not the case. Of course you have to compare the frames to show that. And when you claim there is excess charge, you also have to specify in which frame. Otherwise it is meaningless.

Alright, let's consider a particle accelerator, and suppose there are highly energetic(fast moving) Muons in the tunnel, and there is a sample of them in a stationary lab w.r.t the accelerator. Now, my question is since the particles in the tunnel are length contracted, time dilated etc. compared to the samples in the stationary lab because of the relative motion(this is all in the lab's frame). Why does the same not follow for the case of switching the current on from off because of the relative motion between electrons and protons(this is all in the wire's frame).

The individual electrons are length contracted in the wire's frame. But their spacing doesn't decrease in the wire's frame, when the current starts flowing.

 

[Dale]

Why does the same not follow for the case of switching the current on from off because of the relative motion between electrons and protons(this is all in the wire's frame).

Length contraction does follow, always. If the current is on then different frames disagree about the distance between electrons. If the current is off then different frames disagree about the distance between electrons. Different frames always disagree about the distance between electrons. That is length contraction. It is always present.

The comparison of distances at different times in one frame is not length contraction. Length contraction is a disagreement between two frames, not a change over time in one frame. Because of that, your comment about length contraction all in one frame is a self-contradiction. There is no such thing as length contraction in one frame.

 

[harrylin]

[..] Length contraction is [..] not a change over time in one frame. [..] There is no such thing as length contraction in one frame.

On a side note: sorry, but No. Once more, please digest our earlier comments here:

https://www.physicsforums.com/showthread.php?p=4517568
https://www.physicsforums.com/showthread.php?p=4517685

Thus, length contraction is also the Lorentz contraction of a body that changed from rest to motion as determined in a single inertial reference system; as a matter of fact, historically it's even the first meaning of that expression.

 

[A.T.]

Thus, length contraction is also the Lorentz contraction of a rigid body that changed from rest to motion as determined in a single inertial reference system; as a matter of fact, historically it's even the first meaning of that expression.

Fixed it for you. This the key element that people often forget, when assuming "length contraction" in that historical sense. And it is a good reason to avoid that historical usage, because it is based on this often not explicitly stated assumption, that the proper length is constant which is not always true. This leads to confusion like we see here with universal_101, and generally in Bell-Spacehip-Paradox threads.

 

[yuiop]

In every inertial frame that is true. But when you accelerate from the inertial wire's frame to the inertial current's frame your line of simultaneity rotates. In this accelerating frame there are more electrons per second leaving the segment, than entering it. So when you arrive in the current's frame you end up with less electrons in the segment, than there were in the wire's frame.

So yes, the relativity of simultaneity can be used to explain why there a different counts of electrons in the wire segment, between the two frames: Two events (electron entering, electron leaving) that are simultaneous in the wire's frame, are not simultaneous in the current's frame (leaving comes first).

Get it now. Thanks A.T. Must have been tired last night. The initial loss of electrons from the section of wire is not recovered later in the steady state phase when the amount of electrons entering is the same as the amount of electrons leaving. As a side note, generally speaking the electrons do not all start moving simultaneously in the rest frame of the wire when the switch is closed. I am checking out the situation when the switch on event propagates down the wire at the speed of light which is probably faster than in reality. The end result is the same as far as charge density is concerned, but the explanation appears to be a little different.

 

[Dale]

Thus, length contraction is also the Lorentz contraction of a body that changed from rest to motion

This the key element that people often forget, when assuming "length contraction" in that historical sense. And it is a good reason to avoid that historical usage

As noted, this is a deprecated historical usage. Furthermore, even the deprecated historical usage is not relevant to the current discussion. For both reasons (historical and irrelevance) a further discussion of this usage would be off-topic.

Please do not hijack the thread.

 

[A.T.]

Furthermore, even the deprecated historical usage is not relevant to the current discussion.

The confusion of the two meanings of "length contraction", and the misapplication of the deprecated meaning might be the reason why there still a discussion. So maybe it's not bad to clarify it.

 

[Dale]

I think that your post clarifies why the historical usage is not relevant. The electrons are not a rigid body, so the only usage which is relevant to the current discussion is the standard modern usage. If universal_101 has questions about the modern usage then he can ask, but I don't want any historical apologists cluttering up the thread.

 

[harrylin]

Get it now. Thanks A.T. Must have been tired last night. The initial loss of electrons from the section of wire is not recovered later in the steady state phase when the amount of electrons entering is the same as the amount of electrons leaving. As a side note, generally speaking the electrons do not all start moving simultaneously in the rest frame of the wire when the switch is closed. I am checking out the situation when the switch on event propagates down the wire at the speed of light which is probably faster than in reality. The end result is the same as far as charge density is concerned, but the explanation appears to be a little different.

It appeared that you were not tired but lucid; see my earlier reply to you. If I'm not mistaken then RoS merely gives you in an indirect way the electron distance as transformed from the stationary frame, and which can be found directly. Isn't that what you meant? The transformation doesn't contain information about final force equilibrium according to the cat's reckoning, other than that according to PoR the cat should obtain that result.

 

[TrickyDicky]

I think the problem with the clip's explanation is that it doesn't clarify why(and I'm referring to the current switch on) for observers at rest wrt the protons(like the guy who explainss it) the electrons are not length contracted while for observers at rest wrt the electrons (like the cat moving along them) protons are length contracted.

 

[yuiop]

I think the problem with the clip's explanation is that it doesn't clarify why(and I'm referring to the current switch on) for observers at rest wrt the protons(like the guy who explainss it) the electrons are not length contracted while for observers at rest wrt the electrons (like the cat moving along them) protons are length contracted.

In DrGregs excellent diagram, the electrons are shown as length contracted in the rest frame of the wire when the current is on (bottom left drawing). It is just the gaps between the centres of the electrons that remains the same as when the current was off in the rest frame of the wire (top left drawing). I think it is also debatable whether electrons length contract if they are considered as quantum point particles and the length contraction of the electrons themselves is not important to the basic theme of this thread. It is only the inter electron gaps that has any significance.

I think a better question is why the battery (which is a store of excess electrons) does not take the opportunity to pack extra electron into the wire when the circuit is switched on. I am sure there is a good reason that does not happen, but it is just sort of assumed without explanation.On the other hand, it would be possible to construct a circuit with a coil at one end and induce a current, so that we are certain no additional electron are added to the circuit.

 

[Dale]

I think the problem with the clip's explanation is that it doesn't clarify why(and I'm referring to the current switch on) for observers at rest wrt the protons(like the guy who explainss it) the electrons are not length contracted while for observers at rest wrt the electrons (like the cat moving along them) protons are length contracted.

The video may not draw it correctly (not sure), but they are both length contracted in fact. The spacing between the electrons is greater in the electrons' frame than in the protons' frame. The spacing between the protons is greater in the protons' frame than in the electrons' frame. Length contraction occurs for both protons and electrons.

 

[Dale]

I think a better question is why the battery (which is a store of excess electrons) does not take the opportunity to pack extra electron into the wire when the circuit is switched on. I am sure there is a good reason that does not happen, but it is just sort of assumed without explanation.

It is not really an assumption, it is more like part of the specification of the problem. It is what I called earlier a boundary condition.

You could pack additional electrons on if you used a very high voltage battery (MV or more) and a big resistor in series with the wire so that very little voltage is dropped across the wire. But that would be a different problem.

If you were working a projectile problem and the problem description says that the projectile leaves the barrel at 45º angle and 1000 m/s then I wouldn't call the 1000 m/s an assumption, it is just part of the specification of the problem. Would you?