Are the directions of electric fields lines affected by Gravity?

[Q-reeus]

Q-reeus: "a reduced force is experienced 'out here' when moving those cap plates located 'down there' within the shell, against a locally determined field E. It needs explaining somehow. A fully self-consistent one at that."
I've already given the self-consistent explanation, here and in other threads, but to recap briefly: the reduced force at infinity is due to the effect of the spacetime in between infinity and the region within the shell. The force transmitted down the linkage is "blueshifted" because of the change in potential, and energy transmitted back up is "redshifted" for the same reason. So if you measured the force exerted at the *bottom* end of the linkage, right where it hooks to the capacitor, it would *not* be "redshifted"--it would be the *same* force that would be measured at the same point if everything were being done locally. Sorry if this part wasn't clear from my previous posts.

We're not quite finished here yet it seems. Everything you say above is and has been agreed on before as far as redshift/blueshift of force and energy. Our understanding of it's significance and interpretation is another matter. Avoided above is the implications, given our prior agreement on 1:1 motion linkage, for the necessary equating of redshifted coordinate determined force F = sqrt(J)F'= sqrt(J)q'E', where primed quantities are those locally measured within shell. One either declares it illegal/meaningless to face that sqrt(J) must operate on either q' or E' or some combination, or it is done. I chose the latter path.

Q-reeus: "You may have missed reading this passage in #102: "No suggestion any of that is locally observed within the shell of course!""
But the permittivity/permeability are local quantities--they appear in the local formulation of Maxwell's Equations. Saying that they "look different" when viewed from infinity makes no sense to me, at least not in the context of standard GR + EM; nothing corresponding to them is "transmitted" anywhere.

But my consistent position is there *is* something correspondingly transmitted - a reduced E at 'infinity'.
[Edit: need I mention this 'redshifted' E is owing to any general distribution of charge lying at the reduced potential - the obvious choice is a charged spherical shell owing to symmetry. This should cut off at the pass any talk of 'oh, but there is no external E field from that ideally thin parallel-plate capacitor.' Quite. And quite irrelevant to the issue. ]
And why so is, once again, summarized partly above. I take it you accept that slowed ticking of a light clock (laser etc.) when viewed from infinity is not without sense - unless of course one subscribes to the view that all we can say is energy 'tires' on the way out, and that it is futile to speculate about time 'really' running slower down there wrt us out here. A philosophical position easily shot down imo.

But the word "vacuum" in quantum physics means something different than it does in classical GR. If we're talking about classical GR, then saying "there is physically real structure" present means there *can't* be a "vacuum" in the GR sense; there *has* to be some nonzero SET corresponding to the "physically real structure", otherwise your model, at the GR level, is incomplete. One could say that the SET is "approximately" zero, but then the model won't include any effects from the "physically real structure of the vacuum".

Then pray tell sir how one explains gravitational waves as undulations of 'nothing' or how indeed even a static gravitational field is owing to curvature of - what - 'nothing'!?

Q-reeus: "(need I remind - not as locally observed!)"
This part is *not* fine--Maxwell's Equations are local. If the local values are the normal "vacuum" values, then there's no room in our standard theories to have them "look any different" from infinity. So in this case we're back to "too speculative to discuss further here".

As you wish.

 

[PeterDonis]

the implications, given our prior agreement on 1:1 motion linkage, for the necessary equating of redshifted coordinate determined force F = sqrt(J)F'= sqrt(J)q'E', where primed quantities are those locally measured within shell.

What physical observable does this "coordinate determined force" correspond to? I'm not the only one who has pointed out that your insistence on looking at coordinate-dependent quantities instead of invariant observables leads you astray. As far as I can see, the "coordinate determined force" here is simply a roundabout way of referring to the force exerted at infinity. The force measured locally, at the point where the linkage connects to the capacitor, is just F' = q'E' according to GR. The 1:1 motion linkage doesn't affect that at all; the 1:1 linkage is just a way of physically realizing the condition that the proper distance between the capacitor plates is the same for the two capacitors (the one inside the shell and the one at infinity), in order to remove variation in plate separation as a possible source of variation in the measurements.

So maybe we need another question here to make our positions clear: if a strain gauge were put on the linkage at the point where it connects to the capacitor inside the shell, what force do you think the gauge would actually measure?

But my consistent position is there *is* something correspondingly transmitted - a reduced E at 'infinity'.

How do you "transmit" a "reduced E"? In the other cases we've discussed, there's something tangible covering the spacetime in between: a photon travels up or down, or a linkage connects the two points. Are you saying a "reduced E" somehow gets "transmitted" through the linkage? I don't understand.

[Edit: need I mention this 'redshifted' E is owing to any general distribution of charge lying at the reduced potential - the obvious choice is a charged spherical shell owing to symmetry.

If there is charge density anywhere except on the capacitor plates, then we are talking about a different model than the one I have done the math for, and that I thought we were talking about. The model I thought we were discussing had a neutral shell by definition, and a vacuum inside and outside the shell. There's no charge distribution anywhere, except on the capacitor plates themselves. I suppose I should have commented on this before, but I missed your claim about charge density among everything else.

I take it you accept that slowed ticking of a light clock (laser etc.) when viewed from infinity is not without sense

If you appropriately define how you are going to measure the slowed ticking, sure. For example: a light clock is at infinity, and a second, identically constructed light clock is down in a potential well. The clock down in the potential well starts emitting light signals once every tick. The signals arrive at the clock at infinity with a larger spacing--i.e., the time between each signal's arrival spans more than one tick of the clock at infinity.

Then pray tell sir how one explains gravitational waves as undulations of 'nothing' or how indeed even a static gravitational field is owing to curvature of - what - 'nothing'!?

Gravitational waves are fluctuations in spacetime curvature. Spacetime curvature can be present when the SET is zero. If you don't like the word "nothing" to refer to such a state, then fine, just say "SET is zero" instead. The physics is the same; there still won't be any quantum vacuum effects. To get those you need a nonzero SET.

[Edit: similar comments for a static gravitational field in vacuum--there is spacetime curvature present, even though the SET is zero.]

 

[Q-reeus]

What physical observable does this "coordinate determined force" correspond to? I'm not the only one who has pointed out that your insistence on looking at coordinate-dependent quantities instead of invariant observables leads you astray. As far as I can see, the "coordinate determined force" here is simply a roundabout way of referring to the force exerted at infinity.

There is still some doubt about that after it being stated explicitly many times by now?

The force measured locally, at the point where the linkage connects to the capacitor, is just F' = q'E' according to GR. The 1:1 motion linkage doesn't affect that at all; the 1:1 linkage is just a way of physically realizing the condition that the proper distance between the capacitor plates is the same for the two capacitors (the one inside the shell and the one at infinity), in order to remove variation in plate separation as a possible source of variation in the measurements.

Does this mean you disagree with my oft stated, bleeding obvious statements that it also means F = sqrt(J)F', given we agree energy redshift by sqrt(J), and dW = Fdx = sqrt(J)F'dx' = sqrt(J)q'E'dx? Moral - go back and actually study #10.

So maybe we need another question here to make our positions clear: if a strain gauge were put on the linkage at the point where it connects to the capacitor inside the shell, what force do you think the gauge would actually measure?

Do you actually think I could disagree that F' = F'?

Q-reeus: "But my consistent position is there *is* something correspondingly transmitted - a reduced E at 'infinity'."
How do you "transmit" a "reduced E"? In the other cases we've discussed, there's something tangible covering the spacetime in between: a photon travels up or down, or a linkage connects the two points. Are you saying a "reduced E" somehow gets "transmitted" through the linkage? I don't understand.

More endless repetition - is there some point to it? Go back to #10, and just think about it. Everything we endlessly circle around till now is set out quite clearly enough there - way back there. If you really can't fathom that, as I claim is logically required, Gauss's law fails = potential reduced effective charge by factor sqrt(J) = distantly observed E is like wise potential depressed by factor sqrt(J), then this truly has been a futile engagement.

Q-reeus: "[Edit: need I mention this 'redshifted' E is owing to any general distribution of charge lying at the reduced potential - the obvious choice is a charged spherical shell owing to symmetry."

If there is charge density anywhere except on the capacitor plates, then we are talking about a different model than the one I have done the math for, and that I thought we were talking about. The model I thought we were discussing had a neutral shell by definition, and a vacuum inside and outside the shell. There's no charge distribution anywhere, except on the capacitor plates themselves. I suppose I should have commented on this before, but I missed your claim about charge density among everything else.

The difference is trivial - cap plates merely made it easier to connect reduced coordinate received force with reduced coordinate determined E field on plates. It follows quite obviously I would have thought that rearranging charge dist'n into say a charged spherical shell cannot then alter that, by the same reasoning coordinate determined cap E is reduced, so also we will have (*coordinate* evaluated) charged shell reduced E down there -> reduced E out here (that's the mysterious 'transmission' bit you seem to have so much trouble grasping). We have kind of gone over this before: If source charge is potential depressed, then so also the resulting E 'transmitted' out to here. Hard to figure is it?

As far as the implication of say spherically arranged charge 'disrupting' the assumed Schwarzschild geometry, have you actually forgotten we agreed this is a case of perturbatively small test charges? And even if not - so what? The aim is to establish whether gravity acts back on charge in the manner I claim. It matters not a whit in that respect even if there were significant E field energy density contribution to a finite SET exterior to the matter/charge dist'n. Keeping any charge present at a perturbative level simply makes the task easier.

Gravitational waves are fluctuations in spacetime curvature. Spacetime curvature can be present when the SET is zero. If you don't like the word "nothing" to refer to such a state, then fine, just say "SET is zero" instead. The physics is the same; there still won't be any quantum vacuum effects. To get those you need a nonzero SET.

On that issue at least I'm far from alone here at PF in questioning the physical/logical sense of a truly empty, structureless void curving, conveying energy/momentum etc.

 

[PeterDonis]

If you really can't fathom that, as I claim is logically required, Gauss's law fails = potential reduced effective charge by factor sqrt(J) = distantly observed E is like wise potential depressed by factor sqrt(J), then this truly has been a futile engagement.

Then I think it has been a futile engagement. Only I would say that it's futile because, after all this discussion, you really can't fathom that my simple, self-consistent explanation given in #105 is, in fact, simple, self-consistent, and correct. For example, you say:

F = sqrt(J)F'

Which to me means that the force measured at infinity, F, is "redshifted" relative to the force measured at the capacitor, F'. Which *I agree with*. And which is perfectly consistent with what I said in #105. And yet we are still arguing. :sigh:

 

[PeterDonis]

On that issue at least I'm far from alone here at PF in questioning the physical/logical sense of a truly empty, structureless void curving, conveying energy/momentum etc.

And if you want to question it again, by all means start a new thread. It's off topic in this one.

 

[Q-reeus]

Which to me means that the force measured at infinity, F, is "redshifted" relative to the force measured at the capacitor, F'. Which *I agree with*. And which is perfectly consistent with what I said in #105. And yet we are still arguing. :sigh:

Sure, because we continue to be at odds over the follow-on consequences. Anyway as of just now the game has changed for me:

Update! Something has finally sunk in, after brushing it aside as unimportant. If consistently extended to all of space, modelling things in terms of ε, μ = 1/sqrt(J)(ε₀, μ₀), there is a steady change back to 1/sqrt(J) = 1 values ε₀,μ₀ as r-> ∞. Which means depressed source charge q = sqrt(J)q' is supplemented, between down there to out here, by an effective dielectric bound charge volume density of the same sign as q' and net magnitude (1-sqrt(J))q'. So one finishes up with net enclosed charge = potential unaltered source charge q', which means Gauss's law will hold in that limit. This revised outlook does seem to allow having it both ways without the violation of Newton's 3rd law, which the 'active'/'passive' charge split cannot offer. Clashes though with arguments touched on way back here: https://www.physicsforums.com/showpost.php?p=3946413&postcount=1

If modified ε, μ = 1/sqrt(J)(ε₀, μ₀) really works, it has to work for a magnetic circuit. In #11 I found it did, but that was, as for charge, only when applied to a small or equipotential region. When extended to all space, it wrongly predicts a B field decline by factor J at large r. Consequently I am from this point dropping modified ε, μ = 1/sqrt(J)(ε₀, μ₀) as valid explanation.

So what to replace it with? Still thinking about that - just thought you should know where's it now at for me. And yes I agree with your #110.

 

[PeterDonis]

Sure, because we continue to be at odds over the follow-on consequences.

Which I have also given self-consistent descriptions of, multiple times. But you continue to disagree, and it doesn't seem like there will be any movement on either side at this point.

 

[Q-reeus]

Which I have also given self-consistent descriptions of, multiple times. But you continue to disagree, and it doesn't seem like there will be any movement on either side at this point.

The last two paragraphs of #101 gave some indication you were getting it. I dared not hope too much and just as well because it seems clear cold-feet-itis set in soon after. Let's face it, by following through with and adopting the logical consequences of the realization you were seemingly arriving at there, it sort of places one in an unorthodox position.

As you are now aware, having now undermined and abandoned my own till now key resolution, things are in limbo. Concocting ad hoc patches isn't hard but a fully consistent picture - one that deals with the issues imo you got cold feet on - is a different matter. Just out of interest - wondering how you would explain the force interaction of two identical magnetic loop currents (co-axial alignment for ease) both within the shell - in terms of coordinate determined values for loop current etc.? :zzz:

 

[PeterDonis]

The last two paragraphs of #101 gave some indication you were getting it. I dared not hope too much and just as well because it seems clear cold-feet-itis set in soon after. Let's face it, by following through with and adopting the logical consequences of the realization you were seemingly arriving at there, it sort of places one in an unorthodox position.

Nothing I said in #101 casts the least doubt on the consistency of the "standard" position, the one I have been defending in this thread. I was merely considering an alternate possible interpretation, which, as I pointed out, was *not* the interpretation you have been proposing, and which I don't see any reason to adopt anyway since the standard interpretation works fine. Also, I noted that I could not see how to square any alternate interpretation with the requirement that W = V * q.

Just out of interest - wondering how you would explain the force interaction of two identical magnetic loop currents (co-axial alignment for ease) both within the shell

I haven't considered the magnetic case in any detail, but I don't see why it would work any differently than the capacitor case. The local measurements inside the shell would all look just like they do in flat spacetime. If work were done on, or extracted from, the magnetic system and transmitted to/from infinity, the work measured at infinity would be "redshifted".

 

[Q-reeus]

Nothing I said in #101 casts the least doubt on the consistency of the "standard" position, the one I have been defending in this thread. I was merely considering an alternate possible interpretation, which, as I pointed out, was *not* the interpretation you have been proposing, and which I don't see any reason to adopt anyway since the standard interpretation works fine. Also, I noted that I could not see how to square any alternate interpretation with the requirement that W = V * q.

The standard position on this issue has imo much in common with say typical M.C.Escher illusions (e.g. http://trese.cs.utwente.nl/taosad/escher.htm). He even made one titled
'Relativity' - not that I'm suggesting relativity per se is an illusion. Thing is, by just concentrating on anyone part of the standard position re RN BH, nothing seems out of place. Just don't try and actually put it all together and expect a fit.

I haven't considered the magnetic case in any detail, but I don't see why it would work any differently than the capacitor case. The local measurements inside the shell would all look just like they do in flat spacetime. If work were done on, or extracted from, the magnetic system and transmitted to/from infinity, the work measured at infinity would be "redshifted".

Another nice safe answer. Can't disagree with it, but that's because it avoids certain things - as indicated by your excising the last part of my question on that.

Not to leave it here on a sour note, here's my tentative fix - for 'house plans a builder can actually construct'. Not one I expect you will give any time to. May have abandoned the permittivity/permeability mod idea too hastily. My as I say tentative conclusion is it can't work as is, owing to the nature of Schwarzschild geometry. There is a rival one that if applied, looks to completely remedy the magnetic dipole problem I identified in #111, without introducing additional ones in the process. Saying no more. Enjoy your day!

 

[PeterDonis]

Just don't try and actually put it all together and expect a fit.

No, this is not correct. I, and others, *have* put it all together and it fits fine. It just doesn't fit in a way that matches your intuitions. But it is self-consistent and it matches experiment, where experiments have been done. (Nobody has done experiments with capacitors inside vacuum-filled shells whose self-gravitation is measurable, so there's no direct test there.)

Can't disagree with it, but that's because it avoids certain things - as indicated by your excising the last part of my question on that.

Because the last part was about coordinate-dependent quantities, which I and others have told you many times are the wrong things to focus on. If you're really interested in them, you should be able to figure out what they would be from what I said.