Are the directions of electric fields lines affected by Gravity?

[Q-reeus]

Ok, so you agree that the charge on both capacitor 1 (inside the shell where J(r) < 1) and capacitor 2 (at infinity) will be q, and you agree that GR predicts this (and I agree with that as well). Since q is an invariant number, calculated by taking a simple Gauss's Law surface that encloses one plate of each capacitor, all observers must agree on it; i.e., it doesn't matter whether you evaluate the integral, say for capacitor 1, in a local inertial frame or in the global Schwarzschild coordinates. So now I have some further questions:

Firstly, recall our relative stances here. I agree with the above *only insofar as it represents the GR (your) perspective*. Take note! My own perspective was given in that prior posting's link to #248 in that other thread. Which means imo q *in effect* is reduced in coordinate measure - as consistently maintained. Which means - forget about 'line counting'. Let's not confuse the two! No clever lawyer tactics!

Assume that the E field between the plates of capacitor 2 (at infinity) is E, and the plate separation (proper distance) is d. Since capacitor 2 is at infinity, it doesn't matter whether we evaluate these quantities in a local inertial frame or in the global Schwarzschild coordinates; in both cases the relevant metric coefficients are just +/- 1 (-1 for g_tt, +1 for g_rr_). By hypothesis, the plate separation of capacitor 1 (inside the shell) is also d, in terms of proper distance.

Now for the questions:

(1a) What is the E field between the plates of capacitor 1, as evaluated in a local inertial frame (where g_tt = -1 and g_rr = 1)?

E - on my or your (standard RN/GR) perspective.

(1b) What is the energy stored in capacitor 1, as evaluated in a local inertial frame?

Logically can only be that inferred by extrapolation in #69: dW = 1/2ε₀E²Adx, so total = 1/2ε₀E²Ad, where d = plate separation. We all agree on this.

(2a) What is the E field between the plates of capacitor 1, as evaluated in the global Schwarzschild coordinates (where g_tt = - J(r), and J(r) < 1; and g_rr = 1)?

Depends on one's perspective. On your (standard RN/GR) perspective, it has to be E, which follows directly from assuming global validity of Gauss's law, as evidenced in e.g. #34. My own perspective entails a reduced *coordinate evaluated* q' = √-g_ttq, as per #248 in thread previously linked.

(2b) What is the energy stored in capacitor 1, as evaluated in the global Schwarzschild coordinates?

If one follows the logic of RN/GR, it is unaltered from the local value. As shown in #10 and various postings subsequently (note carefully here - this entails that one either assumes an undifferentiated q in F = qE, or one attempts a split into 'active/'passive' charge as per #10) . You should have by now no doubt of my view - Schwarzschild = coordinate value is redshifted by factor √(-g_tt), in accordance with experience and the logic of applying potential modified permittivity, permeability, as per #10, and #248 in that other thread referenced above.

Not wishing to be too melodramatic about this saga, I nonetheless feel somewhat like a hapless defendent way back in a Stalinist show trial. Guilty is guaranteed outcome! But hey, this is 2012, and things are very different, right?

 

[Dale]

Not wishing to be too melodramatic about this saga, I nonetheless feel somewhat like a hapless defendent way back in a Stalinist show trial. Guilty is guaranteed outcome! But hey, this is 2012, and things are very different, right?

Then perhaps you should consider following the rules of evidence when presenting your arguments. Even in non-show trials the outcome is guaranteed if one of the lawyers is unfamiliar with large parts of the law and refuses to follow the rules of the court.

 

[Q-reeus]

Then perhaps you should consider following the rules of evidence when presenting your arguments. Even in non-show trials the outcome is guaranteed if one of the lawyers is unfamiliar with large parts of the law and refuses to follow the rules of the court.

Fair comment DS - but then what exactly are the rules here?
[PS: only recently got involved with Classical Physics section. Amazed quite frankly with how long it took you to come to a 'final decision' here: https://www.physicsforums.com/showpost.php?p=4024036&postcount=348]

 

[Dale]

Fair comment DS - but then what exactly are the rules here?

The EFE, Maxwells equations, and the corresponding mathematical frameworks of Riemannian geometry and classical mechanics.

Amazed quite frankly with how long it took you to come to a 'final decision' here

That is a good example of a thread where I did in fact change my mind based on the evidence presented. Regarding the amount of time, I thought it was reasonable, I certainly haven't seen you change your mind over that timeframe.

 

[PeterDonis]

Firstly, recall our relative stances here. I agree with the above *only insofar as it represents the GR (your) perspective*. Take note! My own perspective was given in that prior posting's link to #248 in that other thread. Which means imo q *in effect* is reduced in coordinate measure - as consistently maintained. Which means - forget about 'line counting'. Let's not confuse the two! No clever lawyer tactics!

I'm not sure what you mean by that last comment, but you appear to me to have changed your answer. I asked you specifically what *your* answer was, in addition to asking what you thought the GR answer was. I also asked it with respect to a specific, well-defined question about the number that results from the Gauss's Law integral over a surface enclosing one plate of the capacitor. I didn't say anything about "line counting", or about any other "interpretation" of what the integral "means". I just asked about the actual, numerical value you get when you do the integral.

From your previous post I understood that your answers to both questions were the same: you thought the correct value of the integral was q, and you thought that GR says that the value of the integral is q. Now you appear to be saying that your answers to the two questions are different, but I can't tell for sure what the difference is. I *think* what the above quote means is: your correct value for the integral is q, you think that I think the GR value for the integral is q, but you think the "real" GR value for the integral is q sqrt(J), which is less than q--in other words, you think I have incorrectly stated what the "real" GR value for the integral is, so that I think the GR value is correct, but actually it is wrong. But the above quote could also mean: your value for the integral is q sqrt(J), but the GR value for the integral is q (which is what I think it is), and so you think the GR value for the integral is wrong, period. Which is it?

I can't respond to the rest of your post since I'm not sure now what your answer is on the previous questions about charge.

 

[Q-reeus]

The EFE, Maxwells equations, and the corresponding mathematical frameworks of Riemannian geometry and classical mechanics.

OK but my rule here is: no paradoxes when applied to any specific situation. And you know what I have been arguing on that.

That is a good example of a thread where I did in fact change my mind based on the evidence presented. Regarding the amount of time, I thought it was reasonable, I certainly haven't seen you change your mind over that timeframe.

Fair enough about taking your time - I'm not always above a little tit-for-tat. Maybe wrongly perceived the intent of your comments. And true I haven't changed my mind.

 

[Q-reeus]

I'm not sure what you mean by that last comment,

Sorry; I did get a little testy there, and maybe there is mutual misunderstanding as to what we both were meaning.

but you appear to me to have changed your answer.

No. Will clear that up below.

I asked you specifically what *your* answer was, in addition to asking what you thought the GR answer was. I also asked it with respect to a specific, well-defined question about the number that results from the Gauss's Law integral over a surface enclosing one plate of the capacitor. I didn't say anything about "line counting", or about any other "interpretation" of what the integral "means". I just asked about the actual, numerical value you get when you do the integral.

From your previous post I understood that your answers to both questions were the same: you thought the correct value of the integral was q,

No. I have said the correct value is q *if one accepts global validity of Gauss's law*, and that's not my view of how it actually goes.

and you thought that GR says that the value of the integral is q.

If ever I may have expressed it as 'What GR says', it referred to the RN incorporation of Gauss's law into GR as globally valid. GR per se doesn't afaik say anything itself about the matter. But given the seemingly complete acceptance of RN solution within GR community, one could loosely say 'GR says' by association.

Now you appear to be saying that your answers to the two questions are different, but I can't tell for sure what the difference is. I *think* what the above quote means is: your correct value for the integral is q,

No. Have been at pains to state numerous times my view is we obtain an effective q = sqrt(J)q by way of effective dielectric shielding when factor 1/sqrt(J) operates to increase the vacuum permittivity and permeability. See for instance, among many subsequently, #10 this thread, and 248# and later in that other thread.

you think that I think the GR value for the integral is q,

Correct.

but you think the "real" GR value for the integral is q sqrt(J), which is less than q--in other words, you think I have incorrectly stated what the "real" GR value for the integral is, so that I think the GR value is correct, but actually it is wrong.

No, we both agree (I think) the real GR value is just q - by 'real' meaning the one in accord with global Gauss's law holding and incorporated in RN sol'n.

But the above quote could also mean: your value for the integral is q sqrt(J), but the GR value for the integral is q (which is what I think it is), and so you think the GR value for the integral is wrong, period. Which is it?

That passage is correct as representing my view.

I can't respond to the rest of your post since I'm not sure now what your answer is on the previous questions about charge. Sorry

No need to be. Hope that is all now clear - and again my sorry for the 'lawyer references'. :shy::zzz:

 

[Dale]

OK but my rule here is: no paradoxes when applied to any specific situation.

Agreed. Part of the reason for "the rules of evidence" is to prevent paradoxes.

 

[PeterDonis]

Hope that is all now clear

I think so, but just to recap:

* You believe the charge on the capacitor inside the shell should be q sqrt(J).

* You believe that GR says the charge on the capacitor inside the shell is q.

* You believe the E field inside the capacitor, evaluated in a local inertial frame, is E, and you believe GR agrees with that.

* You believe the E field inside the capacitor, evaluated in global Schwarzschild coordinates, should be E sqrt(J), by consistency with your answer on charge above.

* You believe that GR says the E field inside the capacitor, evaluated in global Schwarzschild coordinates, is E, because that's the only way it can be consistent with GR's answer above on charge.

* You believe that the energy stored in the capacitor, evaluated in a local inertial frame, is W = E^2 d A (modulo some factors of epsilon_0 or 4 pi, depending on which units we're using, and which don't affect any of our discussion here), and you believe GR agrees with that.

* You believe the energy stored in the capacitor, evaluated in global Schwarzschild coordinates, should be W sqrt(J), by consistency with your answers above, and by the fact that the energy has to "redshift" as it climbs out of the gravity well (to speak somewhat loosely).

* You believe that GR says the energy stored in the capacitor, evaluated in global Schwarzschild coordinates, is W, because that's the only way it can be consistent with GR's answers above on charge and the E field.

I will follow up with a separate post on my analysis of the scenario.

my sorry for the 'lawyer references'. :shy::zzz:

No offense taken.

 

[PeterDonis]

I will follow up with a separate post on my analysis of the scenario.

This is the quick version, without math; I'll post the math separately (and may not get a chance to do so for a bit).

First, a key difference between the charge q and the other variables (E field and energy). The charge q is a Lorentz scalar; it is the result of an integral that can be written as an invariant contraction of vectors and tensors with no "free" indices, meaning that its value must be the same in *any* coordinate chart. The E field and energy are *not* scalars; in full generality, they are components of tensors (the EM field tensor and the stress-energy tensor, respectively), though they can be modeled more simply (energy, for example, for a "test object" can be modeled as the time component of the 4-momentum). So there is nothing a priori inconsistent about claiming that the E field and the energy can "redshift" (meaning, can have "metric coefficient factors" in them in global coordinates), while the charge q can't; they are different kinds of things. I believe DaleSpam commented a while back about this same issue.

Second, a bit of stage-setting. Since by hypothesis the plate separation (and area, though we haven't talked about that explicitly) d of the capacitors is constant, in terms of proper distance, we can talk about the voltage on the capacitors instead of the E field, since voltage V is just E * d (again modulo a factor of epsilon_0 or 4 pi depending on the units). So "the E field redshifts" is the equivalent of "the voltage redshifts", and since voltage is just energy per unit charge, this is also the equivalent of saying "the energy redshifts", which is why it's easier to talk about voltage in this scenario, since it makes clear the direct relationship between the field and the energy.

Now, the quick summary of what I think GR actually says about this scenario:

The charge on the capacitor inside the shell is q; since, as above, this is a Lorentz scalar, it has the same value in *any* coordinate chart, including the global Schwarzschild chart. The capacitor charge does not "redshift" in this scenario.

In a local inertial frame, the voltage on the capacitor inside the shell is V (the same as the voltage on the capacitor at infinity), and its energy is just W = V * q, since energy is voltage times charge. This is obvious just from the equivalence principle: the local observer next to the capacitor has no way of knowing, just from local observations, that he is inside a potential well where the "redshift factor" is less than 1. In the local inertial frame, physics looks just like it does in SR, where the voltage is obviously V, with no "redshift". But it can be derived rigorously from the math in a local inertial frame.

In the global Schwarzschild coordinates, the voltage on the capacitor inside the shell is V sqrt(J), and its energy is W sqrt(J) = V sqrt(J) * q, since the charge q is an invariant Lorentz scalar. This tells us that an observer "at infinity" will only be able to extract the "redshifted" energy from the capacitor, so global energy conservation (in the form suitable for a static spacetime) is preserved. This result can be derived by taking the result in a local inertial frame, above, and transforming it to the global Schwarzschild coordinates.

 

[PeterDonis]

Now, the quick summary of what I think GR actually says about this scenario

On re-reading, it may be confusing to state things in terms of coordinates and frames as I did. So in case it's needed to improve clarity, let me re-state everything in terms of how it would actually be measured in the scenario we are considering.

The charge on the capacitor inside the shell is q. Since this charge is only "visible" between the plates, if we are going to measure it using Gauss's Law (which is the point at issue), we have to, as I said previously, use a closed surface that encloses just one plate, measure the electric field normal to each small segment of that surface, and integrate over the entire surface. The electric field is nonzero only between the plates, and (in the idealized case) is exactly uniform and exactly normal to the plates, so the measured charge will be q = E * A, where E is the electric field and A is the plate area (in "proper" units). Note that, as before, I am leaving out constant factors of epsilon_0 or 4 pi or whatever that depend only on the units we're using.

One could, I suppose, try to concoct a way of "remotely" measuring the charge, by "remotely" measuring either the electric field or the area. But how would you do that directly? You could measure the electric field indirectly, by measuring energy (we'll discuss that below), but that requires you to "interpret" what the energy measurement says about the electric field. The whole point here is to get down to the direct observables, eliminating all indirect "interpretation" steps. So one way of putting the fact that the charge is q "regardless of which coordinates you use" would be to say that there is only one way to *measure* q, which is locally; there is no way for an observer at infinity to directly measure q on the capacitor inside the shell.

The energy stored in the capacitor, as measured anywhere inside the shell, is W = E * d * q = E^2 * d * A, where d is the plate separation (again in "proper" units). As our direct measurement of energy, we will adopt Q-reeus' method of putting a known charge on the plates (measured using Gauss's Law as above), and then measuring the work required to separate the plates by a proper distance d, by means of a linkage between the "source" of the work and the capacitor itself. If we do this using a "source" of work anywhere inside the shell, we will get W as above.

The energy stored in the capacitor, as measured at infinity, is W sqrt(J). This is easy to see just by comparing the measurement at infinity with the measurement inside the shell, given above. The measurement at infinity requires a linkage extending from infinity to the capacitor inside the shell, and any work done through that linkage will be "redshifted" by a factor of sqrt(J). More precisely, it will be redshifted by a factor sqrt(ratio of g_tt inside shell to g_tt at infinity), but since g_tt at infinity is 1, the ratio is just sqrt(g_tt inside shell) = sqrt(J). (Btw, this analysis also shows us that the reason why the energy measurement gives W anywhere inside the shell, is that g_tt is *constant* inside the shell--if it varied there, the energy measurement would vary too, depending on where the "source" of the work was relative to the capacitor. Only in the limiting case of a truly local inertial frame, where g_tt can be considered constant throughout the "patch" of spacetime under consideration, will we always get W as the energy measurement.)

The voltage on the capacitor, measured anywhere inside the shell, is, as is obvious from the above, V = E * d. The obvious direct measurement of voltage would simply be to put a voltmeter across the capacitor plates, which amounts to measuring the work required to move a test charge from one plate to the other against the electric field. Note that this is *not* the same as the total energy stored in the capacitor; it is better viewed as a "cross check" of sorts. In other words, once all three measurements are taken (charge, energy, and voltage), we must have W = V * q, even though all three were measured using independent methods.

As with charge above, however, I do not see any way to *directly* measure the voltage on the capacitor "at infinity"; the only way I see to do it is indirectly, by measuring energy at infinity and then deducing, since W = V * q and q is the same, that V must "redshift" the same way W does. However, this does open up a question: since both V and q can't be measured directly "at infinity", could we adopt an interpretation of the energy "redshifting" that has q "redshifting" *instead* of V? In other words, we would say that V(at infinity) = V and q(at infinity) = q sqrt(J), so W(at infinity) = V(at infinity) * q(at infinity) = W sqrt(J) still holds.

I personally don't see any reason to adopt this interpretation, but I can't say on a quick look that it's actually inconsistent--although I haven't checked it with the math, it's quite possible that there would be an inconsistency (or more precisely, that there would be no way to consistently formulate the "q redshifting instead of V" interpretation mathematically). However, one thing I do want to note is that this is *not* what Q-reeus is proposing! Q-reeus is saying that q(at infinity) = q sqrt(J) *and* V(at infinity) = V sqrt(J) (because he says the E field "redshifts" *and* charge "redshifts"). I don't see how to fit this in with the fact that W = V * q should hold.

 

[Q-reeus]

One could, I suppose, try to concoct a way of "remotely" measuring the charge, by "remotely" measuring either the electric field or the area. But how would you do that directly? You could measure the electric field indirectly, by measuring energy (we'll discuss that below), but that requires you to "interpret" what the energy measurement says about the electric field. The whole point here is to get down to the direct observables, eliminating all indirect "interpretation" steps. So one way of putting the fact that the charge is q "regardless of which coordinates you use" would be to say that there is only one way to *measure* q, which is locally; there is no way for an observer at infinity to directly measure q on the capacitor inside the shell.

This is true, but no more a problem imo than remotely measuring the surface temp of a star via it's received spectrum here on earth. Or of determining it's mass via Keplerian orbital dynamics of say a circling planet. We are free to accurately infer so long as there is an agreed set of physical relations to work from.

As with charge above, however, I do not see any way to *directly* measure the voltage on the capacitor "at infinity"; the only way I see to do it is indirectly, by measuring energy at infinity and then deducing, since W = V * q and q is the same, that V must "redshift" the same way W does. However, this does open up a question: since both V and q can't be measured directly "at infinity", could we adopt an interpretation of the energy "redshifting" that has q "redshifting" *instead* of V? In other words, we would say that V(at infinity) = V and q(at infinity) = q sqrt(J), so W(at infinity) = V(at infinity) * q(at infinity) = W sqrt(J) still holds.

It's possible to have it both ways here to an extent if, as I have looked at in #10, one does the split between 'active' charge q_a and 'passive' charge q_p. Work W will redshift as required, and Gauss's law holds good. One serious fly in the ointment is described in the second last para in #$10. Unfortunately, imo can't really have cake and eat it too! If there is some other solution apart from my own fix in #10, I'm 'all ears'.

I personally don't see any reason to adopt this interpretation, but I can't say on a quick look that it's actually inconsistent--although I haven't checked it with the math, it's quite possible that there would be an inconsistency (or more precisely, that there would be no way to consistently formulate the "q redshifting instead of V" interpretation mathematically). However, one thing I do want to note is that this is *not* what Q-reeus is proposing! Q-reeus is saying that q(at infinity) = q sqrt(J) *and* V(at infinity) = V sqrt(J) (because he says the E field "redshifts" *and* charge "redshifts").

Yes, but recall I have it as owing to modification of vacuum permittivity and permeability. When that is done, there is automatically an even split between reduced q and reduced V E, with the latter's reduction projecting out to a distant observer.[Edit: E owing to a charged sphere say - not of course the 'ideal very thin capacitor' discussed above] No suggestion any of that is locally observed within the shell of course! Using loose talk here, the idea of vacuum as more than nothing and having physical structure which includes dielectric and magnetic susceptibilities is in line with, to get it back to ME's, Maxwell displacement current concept. Or QED concept of vacuum polarization/breakdown, which there is considerable effort in testing with e.g. high power lasers. So to me it makes sense that gravity will alter these vacuum quantities in the way suggested.

I don't see how to fit this in with the fact that W = V * q should hold.

There is it seems an interesting situation here. :zzz:

 

[PeterDonis]

This is true, but no more a problem imo than remotely measuring the surface temp of a star via it's received spectrum here on earth.

You can measure the star's surface temp "remotely" by measuring the spectral lines in the radiation from it (and adjusting for the redshift due to the star's mass, if it's large enough to matter). In other words, you are making a direct measurement of something that traveled to you from the star. What corresponding measurement allows you to "remotely" measure the charge on the capacitor inside the shell? What can "travel to you" from the charge bearing information about it? Saying "energy" or "voltage" won't work because you would have to assume a relationship between those things and charge, and that's precisely the point at issue.

Yes, but recall I have it as owing to modification of vacuum permittivity and permeability.

But that's not a matter of interpretation--that's a change in the physics. You can independently measure the vacuum permittivity and permeability, for example by making measurements with a magnet inside the shell and also measuring the speed of light. GR predicts that all those measurements will yield the same vacuum values as they do at infinity--again, this is obvious by the equivalence principle. So if an experiment were actually done in a vacuum inside a spherical massive shell, and it was found that the electromagnetic constants were different, we would need to rework our entire structure of physical theories. (Which means that this particular subtopic is probably verging on being too speculative to take further here.)

(There is one possible way it could be somewhat simpler than that--see below.)

QED concept of vacuum polarization/breakdown, which there is considerable effort in testing with e.g. high power lasers.

It will definitely be interesting to see what those efforts turn up. Bringing up QED and vacuum polarization does raise a good point, though. If any kind of QED effect like this is involved, we would have to change the model we have been using; the "vacuum" inside the shell in the capacitor scenario will not actually be vacuum in the GR sense. A "vacuum" in the GR sense means an SET of *zero*, period. A "vacuum" in the QED sense means an SET which, in the simplest case, amounts in GR terms to a small positive cosmological constant--i.e., *not* zero.

Such a case could in principle be modeled in GR as we have it, without requiring a wholesale change in the theory, but I don't know that I'll have time any time soon to try to extend what I've already done in this thread to cover such a model.

 

[Q-reeus]

You can measure the star's surface temp "remotely" by measuring the spectral lines in the radiation from it (and adjusting for the redshift due to the star's mass, if it's large enough to matter). In other words, you are making a direct measurement of something that traveled to you from the star. What corresponding measurement allows you to "remotely" measure the charge on the capacitor inside the shell? What can "travel to you" from the charge bearing information about it? Saying "energy" or "voltage" won't work because you would have to assume a relationship between those things and charge, and that's precisely the point at issue.

Ideally one could directly check for any 'anomalous' E field owing to grav. potential of a central mass of a spherical capacitor. If my idea is correct, there will in fact be a net E external to the outer shell, owing to a relatively depressed effective charge on the inner shell surface. I could try some figures, but gut instinct says way too feeble for any terrestrial experiment to detect. So it gets back to argument based on self-consistency criteria. Issue remains that, using those ideal 1:1 remote-linkage rods, 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.

Q-reeus: "Yes, but recall I have it as owing to modification of vacuum permittivity and permeability."
But that's not a matter of interpretation--that's a change in the physics. You can independently measure the vacuum permittivity and permeability, for example by making measurements with a magnet inside the shell and also measuring the speed of light. GR predicts that all those measurements will yield the same vacuum values as they do at infinity--again, this is obvious by the equivalence principle. So if an experiment were actually done in a vacuum inside a spherical massive shell, and it was found that the electromagnetic constants were different, we would need to rework our entire structure of physical theories. (Which means that this particular subtopic is probably verging on being too speculative to take further here.)

You may have missed reading this passage in #102: "No suggestion any of that is locally observed within the shell of course!"
In principle one might detect a local, exceedingly small 'tidal polarization', similar to detecting 'tidal clock-rate' variation. [exterior to the shell interior of course]

It will definitely be interesting to see what those efforts turn up. Bringing up QED and vacuum polarization does raise a good point, though. If any kind of QED effect like this is involved, we would have to change the model we have been using; the "vacuum" inside the shell in the capacitor scenario will not actually be vacuum in the GR sense. A "vacuum" in the GR sense means an SET of *zero*, period. A "vacuum" in the QED sense means an SET which, in the simplest case, amounts in GR terms to a small positive cosmological constant--i.e., *not* zero.

Just to clarify comment in #102 re vac. pol. - the usual usage of vacuum polarization in QED context refers to highly non-linear effects. I merely drew on it as indicative of the view there is physically real structure to the vacuum. Have mentioned it briefly before, but worth bringing up again - if we posit physically real vacuum polarizability (classical context a la Maxwell), it could be seen as preserving Gauss's law 'in reality' though not 'in effect'. That's because vacuum permittivity and permeability modification by factor 1/sqrt(J) is clearly introducing non-linearity to those quantities (need I remind - not as locally observed!). Apply an E field to a non-linear dielectric medium and effective volume bound charge density ρ_p results according to ρ_p = -div P, which in the spherically symmetric cases we have been considering comes down to ~ d/dr (1/sqrt(J)), which is non-zero. If this ρ_p is physically real, lines always begin and end on charge, but some of that charge is of the fleeting vacuum kind. Take it or leave it.

Such a case could in principle be modeled in GR as we have it, without requiring a wholesale change in the theory, but I don't know that I'll have time any time soon to try to extend what I've already done in this thread to cover such a model.

I get the drift. Things have been going nowhere much and won't lose any sleep if above turns out to be my closing statement. Cheers, and thanks for sticking around awhile longer than others.

 

[PeterDonis]

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.

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. See further comments below.

Just to clarify comment in #102 re vac. pol. - the usual usage of vacuum polarization in QED context refers to highly non-linear effects. I merely drew on it as indicative of the view there is physically real structure to the vacuum.

Yes, I understand that view, and I agree with it, if we're talking about quantum physics. 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".

That's because vacuum permittivity and permeability modification by factor 1/sqrt(J) is clearly introducing non-linearity to those quantities

This part is fine, it just means that, in the Maxwell's Equations portion of the model, we are treating the region inside the shell as a material medium, where the permittivity and permeability can vary from their "vacuum" values. The word "vacuum" is not really appropriate in this case, though, at least not if we're using classical GR + EM, for the reason given above.

(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".

 

[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.