|Jan28-13, 10:39 PM||#52|
A SR experiment in which an entity exists in frame A but not frame B
|Jan29-13, 05:38 AM||#53|
Also known as the "retarded potential"
To get the potential, you need to add up the contributing potentials for all charges. Initially, all the charges should be in the battery, so at the start the LW potetial is determined by the battery.
The electric part of it varioulsy called E or [itex]\varphi[/itex] is basically a voltage. You can measure it with a voltmeter except for an additive constant.
If you'll look at the definition, you'll see that because of the retarded time, the L.W. potential of a charge incorporates lightspeed propagation delays. So the position of a charge now doesn't add to the potential until "later", later being determined by the lightspeed delay in the frame you choose to do the analysis.
The magnetic part of it is usually called A. I'm not sure how much to say about A,perhaps it's best to read the wiki article and see if you have any questions about it. Failing that (i.e. if the wiki is so much goobley gook as far as you're concerned) you can tell us if you know what div, grad, and curl are. If you do, we might be able to say a bit more about A.
(E,A) forms a perfectly valid 4-vector (i.e. a tensor). If you regard tensors as "existing", then it "exists". But I'm not sure of your philosophy here.
|Jan29-13, 07:17 AM||#54|
However, if someone did propose such a scenario then the charges for a) and b) are not related by a boost so we wouldn't expect the resulting EM fields or any other aspect of the scenarios to be related by a boost. That doesn't contradict my assertion above, it is just not relevant to such a scenario.
|Jan29-13, 04:51 PM||#55|
|Jan29-13, 05:38 PM||#56|
Honestly, I've never had an experience like this in my life. I've been working at understanding relativity for over five years--not full time, and not to the exclusion of other spare time interests, but five years just the same. I've been confused by other subjects, certainly. But in those cases, I never got it, I knew hadn't gotten it, and I moved on. With relativity, I read, I think I get it, I open my mouth, and I find that I am just plain wrong. That scenario has played out more times than I care to recall.
I have made genuine progress while actively working problems. I left off working problems for a while due to certain circumstances. I'm back at it, and, in spite of this most recent stumble, I believe that I will get this figured out.
I have not been able to form a mental picture of what happens in a relativistic episode that involves anything more than isolated particles. I can see the progression in either frame separately, but I cannot fuse the two into one process. It's the mix-up of time that gets me. I accept that the two seemingly contradictory narratives do not actually contradict each other, but until I can get a sense of the one reality that the two narratives express, I will continue to make dumb mistakes.
|Jan30-13, 09:45 PM||#57|
I spent some time studying the spacetime diagram for this plate and battery setup. To help me see it better, I doubled the rest lengths, shifted the start position and time to put the "middle" of the process at the origin, and added some time projection lines. The improved diagram is below. (I also found that saving the screenshot as a png avoids the smearing effect that I had with jpg.)
I'll make two observations now.
1. By what I consider the most natural reading of the referenced paper, the authors are saying that, in a given frame, an electrical signal will come into existence only when both terminals are in contact with the plate. In this scenario, that happens only in the rest frame of the plate. Therefore, an electrical signal exists in one frame but not the other. That cannot happen. In the OP, I called this a paradox. Now, I'll just call it incorrect. Perhaps the authors meant something else; then my complaint does not apply. As to whether they were thinking of retarded potential, perhaps they were. I don't think that changes the outcome of an em wave in one frame but not the other, based on what they actually said in the paper.
2. I was clearly wrong when I said that a terminal could be in contact with the plate in one frame but not the other. I saw that two days ago as I prepared my response to PeterDonis. What I was not able to do at that time was visualize the "combined" process, as opposed to two separate and independent processes. That's not a very good way to say what I have in mind, but that will have to do for now.
Looking at a specific event on the spacetime diagram, I can give you an idea of what I meant about one reality for the two frames, down to the particle level. (I don't refer to QED; I have a big enough headache already--and no desire to put my foot deeper into my mouth.)
At the origin of the spacetime diagram:
a) In the rest frame of the plate, both terminals have been in contact with the plate for some time.
b) In the rest frame of the battery, neither terminal has been in contact with the plate for some time.
Given the complexity of the problem, I am not going to say that current is flowing in the rest frame of the plate, but no current is flowing in the rest frame of the battery. Indeed, I am not going to make any prediction at all about the state of the plate.
What I will do is point out that in both frames the positive terminal (only) was in contact with the plate for some time, and thus some amount of charge passed into the plate. In the rest frame of the plate, when the second terminal comes into contact, the plate is already "primed" with charge, and thus the flow of charge would tend to increase. On the other hand, in the rest frame of the battery, when the terminal loses contact with the plate the flow of charge would tend to decrease.
I understand enough about inductance to know that sudden changes in current are resisted; not to mention the other complexities that have been talked about. So I am not making any disparaging remarks about relativity. What I am pointing out is that it is not at all obvious to someone who is not on the "inside" that everything will work out in practice so that when the state of the field in the plate is calculated from the perspective of the rest frame of the plate, it will match (after transformation) the state calculated from the perspective of the rest frame of the battery.
On the other hand, there is not much in this hypothetical case that is practical. So there is no point in getting too worked up about it. The only comment I can make of practical value is to suggest that physics textbooks for beginners would do better not to gloss over obvious difficulties. At the least, simplifications should be stated as assumptions.
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