SR, LET, FTL & Causality Violation

[PeterDonis]

Agreed that if we define LET such as to always make identical predictions to SR, it is nonsensical to argue one over the other. As both make strict use of the Lorentz transformation that seems settled.

Ok, good, we have agreement that far.

But the crux of my argument is the very existence of the phenomenon of vacuum breakdown implies a situation specific breakdown of LT's which is a dilemma for both.

And the crux of *my* argument is that this is incorrect. The phenomenon of vacuum breakdown can be described entirely by Lorentz-invariant quantities. Specifically: the EM field that causes the breakdown is described by the EM field tensor, which is a covariant geometric object; the breakdown threshold E field vector is described by contracting that tensor with the 4-velocity of the field source, which is also a covariant geometric object. The phenomenon is perfectly consistent with Lorentz invariance.

'Pumping energy in' = application of an E_crit for some minimum duration - by whatever means.

"Minimum duration" implies a frame has been specified. What frame? Obviously the rest frame of the source. If you rephrase this in properly covariant terms, it will read: "the EM field tensor has a particular form in the rest frame of the source, for a minimum interval of the source's proper time." And this is expressed, as above, by contracting the EM field tensor with the 4-velocity of the source.

You keep saying breakdown is defined in the apparatus/source rest frame. But on what basis other than sheer assertion?

On the basis that the breakdown is determined by contracting the EM field tensor with the source's 4-velocity. IIRC this was described in the paper you linked to, but not in precisely those terms, so the point may not have been clear from the paper.

In what way can the vacuum 'know' that a field of given strength E is owing to a source that is moving or static wrt any given lab frame (apart from B field which is not germane to vacuum breakdown issue)?

Because it's not anything associated with the "vacuum" that determines the breakdown; it's the contraction of the EM field tensor and the source's 4-velocity, both of which are perfectly well defined in terms of actual physical objects that can be observed.

If you can't see any issue by now then I guess it's quits from me. No point bashing ones head against a brick wall.

I see the "issue" perfectly well, and I've described in more detail above why it's not actually an issue.

 

[Dale]

If you have a source please post. Inspired by that claim, I did some searching and it seems there is much expert controversy in this area: e.g. arxiv.org/pdf/1102.2974

Although your own source does describe a controversy regarding the proper renormalization it uses $\Pi^{\mu\nu}$ for the vacuum polarization tensor throughout the paper. There is also http://arxiv.org/abs/1107.0286 and even http://en.wikipedia.org/wiki/Vacuum_polarization.

 

[ghwellsjr]

OK perhaps it's best to recast the issue somewhat. Agreed that if we define LET such as to always make identical predictions to SR, it is nonsensical to argue one over the other. As both make strict use of the Lorentz transformation that seems settled.

You've got it backwards: SR is defined such as to always make identical predictions to LET. The Lorentz Transform of LET came first. Einstein simply said that the elusive aether frame is any frame you want to pick.

 

[harrylin]

What do you think Einstein meant by "is" when he stated his second postulate as
[..]
Why do you link to the German and provide your own English translation when the full text of the paper is already available in English:
http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1907_Jahrbuch.pdf

I find his 1905 paper ambiguous on some points, but happily his 1907 paper is much clearer (see next). There exist several unofficial translations of his 1907 paper and the best one I know (to which my own translation closely corresponds) is not online. Anyway, I don't need to rely on others to read German.

[..] Your statement that SR "only refers to measurements, without reference to hidden reality" is very curious to me, not just because you say it "only refers to measurements" but because you think that the alternative is a "hidden reality". [..] I fail to see how you can claim that SR only refers to measurements when Einstein clearly pointed out that we cannot make any measurements with regard to time until we create our definition of time.

He stressed that it is an operational theory in both papers, as well as in some later ones that I don't have at hand now. In his 1905 paper he immediately refers to "the observable phenomenon" and "laws" and by the introduction of purely operational definitions. Such things as "time", "distance" and "speed of light" are defined without referral to hidden reality - they are operational definitions, so that what any of those "is" can only have an operational meaning. And in his 1907 paper he clarifies that the (one-way) speed of every light ray in vacuum can be made to become c with respect to an inertial coordinate system by means of an appropriate adjustment of clocks. Again: the adjustment of clocks by an operator is not an assumption of hidden reality! :tongue2:

Note: a definition (such as the definition that current flows from plus to minus) only has operational meaning for making measurements; that's not the issue here. Sorry if I was not clear about that.

 

[Q-reeus]

nd the crux of *my* argument is that this is incorrect. The phenomenon of vacuum breakdown can be described entirely by Lorentz-invariant quantities. Specifically: the EM field that causes the breakdown is described by the EM field tensor, which is a covariant geometric object; the breakdown threshold E field vector is described by contracting that tensor with the 4-velocity of the field source, which is also a covariant geometric object. The phenomenon is perfectly consistent with Lorentz invariance.

Which is a technical way of saying that only the E field in the source rest frame is deemed to count. Again, where is the underlying justification? The invariant tensor doesn't induce breakdown - just the E field, which undeniably varies from frame to frame. But somehow the vacuum makes a choice.

Originally Posted by Q-reeus: 'Pumping energy in' = application of an Ecrit for some minimum duration - by whatever means.

"Minimum duration" implies a frame has been specified. What frame? Obviously the rest frame of the source.

Why obviously? How is that not merely an arbitrary choice?

If you rephrase this in properly covariant terms, it will read: "the EM field tensor has a particular form in the rest frame of the source, for a minimum interval of the source's proper time." And this is expressed, as above, by contracting the EM field tensor with the 4-velocity of the source.

Reapplying a neat definition but one that fails to tackle how an empty vacuum makes it's breakdown choice from an infinity of possible E's. Again, your formal definition implies it is the source charges rest frame, but without justifying it otherwise.

Originally Posted by Q-reeus: "You keep saying breakdown is defined in the apparatus/source rest frame. But on what basis other than sheer assertion?"

On the basis that the breakdown is determined by contracting the EM field tensor with the source's 4-velocity. IIRC this was described in the paper you linked to, but not in precisely those terms, so the point may not have been clear from the paper.

And again - imo assertion clothed in a formal definition. But re being in paper - as layman I probably wouldn't have recognized it as such.

Because it's not anything associated with the "vacuum" that determines the breakdown; it's the contraction of the EM field tensor and the source's 4-velocity, both of which are perfectly well defined in terms of actual physical objects that can be observed.

And yet again, formal definition. An astonishing viewpoint imo - vacuum breakdown that has nothing to do with the vacuum. What this really repeats is the above claim that only E in the source rest frame counts. Sorry but it doesn't satisfy my idea of explanation. Unfortunately for the forseeable future there is no chance of experimental test.

 

[Q-reeus]

Although your own source does describe a controversy regarding the proper renormalization it uses $\Pi^{\mu\nu}$ for the vacuum polarization tensor throughout the paper. There is also http://arxiv.org/abs/1107.0286 and even http://en.wikipedia.org/wiki/Vacuum_polarization.

First link is highly technical and deals with magnetic fields, the last makes no reference to the central issue of vacuum breakdown.

 

[Q-reeus]

You've got it backwards: SR is defined such as to always make identical predictions to LET. The Lorentz Transform of LET came first. Einstein simply said that the elusive aether frame is any frame you want to pick.

See first part of #281. There was no even implied claim of priority being discussed.

 

[ghwellsjr]

I find his 1905 paper ambiguous on some points, but happily his 1907 paper is much clearer (see next). There exist several unofficial translations of his 1907 paper and the best one I know (to which my own translation closely corresponds) is not online. Anyway, I don't need to rely on others to read German.


He stressed that it is an operational theory in both papers, as well as in some later ones that I don't have at hand now. In his 1905 paper he immediately refers to "the observable phenomenon" and "laws" and by the introduction of purely operational definitions. Such things as "time", "distance" and "speed of light" are defined without referral to hidden reality - they are operational definitions, so that what any of those "is" can only have an operational meaning. And in his 1907 paper he clarifies that the (one-way) speed of every light ray in vacuum can be made to become c with respect to an inertial coordinate system by means of an appropriate adjustment of clocks. Again: the adjustment of clocks by an operator is not an assumption of hidden reality! :tongue2:

Note: a definition (such as the definition that current flows from plus to minus) only has operational meaning for making measurements; that's not the issue here. Sorry if I was not clear about that.

After my last paragraph in post #275, which you only partially quoted, I don't know why you continue to argue as if I am claiming that there exists a hidden reality or that Einstein is claiming this. That would be a claim that a LET theorist would believe.

But if your point is that Einstein's second postulate/definition, along with his other definitions, especially of time, are based on things that can be observed (the hands on a clock, the elapsed time on a clock, the distance defined by a rigid rod, etc) and that is what you are calling an operational theory/definition/meaning, then I totally agree with you. I just don't know why you thought my explanations weren't already clear enough and needed to have the word "operational" attached to them. Did Einstein ever use that word?

 

[PeterDonis]

Which is a technical way of saying that only the E field in the source rest frame is deemed to count.

No, it's a physical description of the conditions of the problem. In the paper you referenced, they say explicitly the following (p. 3):

"We choose a coordinate frame where pairs are created at rest. Electric field in
this frame is directed along x-axis"

In other words, they are *specifying* an electromagnetic field tensor in which the only nonzero component, in the frame they specify, is F_01 = -F_10 = E. (They don't explicitly say there is no magnetic field component in this frame, but there can't be or the rest of their equations would not be correct. So this has to be the only nonzero component.) That specifies the entire EM field tensor, which in turn fixes what its components are in *any* Lorentz frame.

They also don't explicitly specify that the source is at rest in that frame, but it has to be, because the only way for a source to produce a pure electric field is for the source to be at rest in the frame in which the field is measured. So the source must be at rest in the frame they specify, meaning its 4-velocity in that frame is (1, 0, 0, 0). Contract that vector with the EM field tensor above and you get exactly what they specify for the electric field vector, a pure E field along the x axis.

So the electric field vector is identical with the contraction of the EM field tensor and the source's 4-velocity; but now we have stated it in a way that is manifestly Lorentz covariant. None of this is an arbitrary choice; it is specified by the statement of the problem and the physics required to realize the situation described. And it is sufficient to properly state the breakdown condition in *any* frame, not just the frame specified in the paper. In other words, it is a completely Lorentz covariant description of the breakdown condition, that does not involve attributing any special properties to the "vacuum".

 

[TrickyDicky]

Specifically: the EM field that causes the breakdown is described by the EM field tensor, which is a covariant geometric object; the breakdown threshold E field vector is described by contracting that tensor with the 4-velocity of the field source, which is also a covariant geometric object. The phenomenon is perfectly consistent with Lorentz invariance.

The 4-velocity vector is not a covariant geometric object in the sense the EM tensor is (is not an invariant, is frame dependent).
It is Lorentz covariant, I guessed you referred to this, but this property is always locally confined in realistic (gravitation included) scenarios.

So I don't think it can be used in the way you pretend here (that simply by contracting the EM tensor with it is determining the breakdown threshold) because the vacuum breakdown is a physically invariant event, it is a phenomenon whose observation is shared by all observers regardles their motion state. You'd need some other constraining factor IMO.

 

[Dale]

First link is highly technical and deals with magnetic fields, the last makes no reference to the central issue of vacuum breakdown.

Regarding the first, if you boost a pure E field then you will get both E and B fields, so you need to deal with magnetic fields.

You are correct that the last does not discuss vacuum breakdown, but that was not the point I was making. I don't know anything about vacuum breakdown so I would be reluctant to make any claims about it.

The point is that to my (very limited) knowledge the vacuum polarization itself is a tensor. If it is, then it is guaranteed to transform correctly and all the rest is moot.

 

[Q-reeus]

Originally Posted by Q-reeus: "Which is a technical way of saying that only the E field in the source rest frame is deemed to count."

No, it's a physical description of the conditions of the problem. In the paper you referenced, they say explicitly the following (p. 3):
"We choose a coordinate frame where pairs are created at rest. Electric field in
this frame is directed along x-axis"

In other words, they are *specifying* an electromagnetic field tensor in which the only nonzero component, in the frame they specify, is F_01 = -F_10 = E. (They don't explicitly say there is no magnetic field component in this frame, but there can't be or the rest of their equations would not be correct. So this has to be the only nonzero component.) That specifies the entire EM field tensor, which in turn fixes what its components are in *any* Lorentz frame.

They also don't explicitly specify that the source is at rest in that frame, but it has to be, because the only way for a source to produce a pure electric field is for the source to be at rest in the frame in which the field is measured. So the source must be at rest in the frame they specify, meaning its 4-velocity in that frame is (1, 0, 0, 0). Contract that vector with the EM field tensor above and you get exactly what they specify for the electric field vector, a pure E field along the x axis.

So the electric field vector is identical with the contraction of the EM field tensor and the source's 4-velocity; but now we have stated it in a way that is manifestly Lorentz covariant. None of this is an arbitrary choice; it is specified by the statement of the problem and the physics required to realize the situation described. And it is sufficient to properly state the breakdown condition in *any* frame, not just the frame specified in the paper. In other words, it is a completely Lorentz covariant description of the breakdown condition, that does not involve attributing any special properties to the "vacuum".

Hmmm. I grabbed just the bare minimal expressions from that article that seemed relevant to the setup I devised. The article focuses on relativistic plasma oscillations and the issue raised in my #255 is not covered at all best I can tell. I appreciate you are trying to be helpful here, but all I'm seeing is the same position restated in slightly different ways. And And no doubt you feel the same about my stance. Probably best to just agree to disagree and let it drop.

 

[Q-reeus]

Regarding the first, if you boost a pure E field then you will get both E and B fields, so you need to deal with magnetic fields.

Quite, and I covered that issue myself on numbers of occasions.

The point is that to my (very limited) knowledge the vacuum polarization itself is a tensor. If it is, then it is guaranteed to transform correctly and all the rest is moot.

No argument that as polarization tensor it transforms as expected, but I will maintain breakdown and what decides it is far from a moot issue. However, as per my last entry, clearly no-one is going to shift ground on this, so let's just move on.

 

[Dale]

No argument that as polarization tensor it transforms as expected, but I will maintain breakdown and what decides it is far from a moot issue. However, as per my last entry, clearly no-one is going to shift ground on this, so let's just move on.

I really don't know enough about breakdown to make a more sophisticated argument nor to evaluate yours, so moving on is OK from my perspective too.

 

[PeterDonis]

The article focuses on relativistic plasma oscillations

Yes, but the only real complication that adds is that the E field prior to the breakdown threshold being reached is slowly varying in time instead of constant; that's because the apparatus prior to breakdown is not a perfect vacuum, but has some plasma present, and that plasma responds to the applied electric field by polarizing, which gives rise to a current the paper calls "conduction current" $J^{\mu}_{cond}$. In other words, even before breakdown occurs and electron-positron pairs are produced, there is an electric current induced by the applied field, which has to be corrected for in order to measure the current that's actually due to the breakdown itself. The case we have been discussing here is simply the idealized version where $J^{\mu}_{cond} = 0$, i.e., no plasma present, perfect vacuum, and the E field is constant until breakdown occurs.

and the issue raised in my #255 is not covered at all best I can tell.

If you mean they don't talk about what would happen if the experimental apparatus were in motion, you're correct, they don't. They don't need to, because they've already given enough information to transform their equations into any frame you like, as I explained in my last post.

They also don't discuss LET, of course.

all I'm seeing is the same position restated in slightly different ways.

If by "the same position" you mean I'm continuing to assert that this entire experiment is describable in purely Lorentz invariant terms, that's correct. Do you disagree? Bear in mind that that statement, in itself, is not a statement about whether SR or "LET" is correct; it's a simple question of mathematics and assigning clear operational meanings to the mathematical symbols. It's also not asserting that the Lorentz invariant description is the *only* possible description, or that there is only one possible interpretation of that description.

In particular, I am not trying to take a position on what "LET" would say, because, as I've said, I don't think the term "LET" is well defined enough. In so far as "LET" is a theory that makes the exact same experimental predictions as SR, it would obviously do so for this experiment. If there is a version of "LET" that doesn't, I would need to see a formulation of such a theory that is clear and precise enough to allow predictions to be made.

 

[PeterDonis]

That is surely inconsistent with the notion that the vacuum should not distinguish between an E field generated by a source at rest or moving

On re-reading your post #255 I saw the part quoted above; this may be part of the issue that you're still seeing as unresolved. Remember the statement I quoted from the paper you linked to: part of it was that they work in a frame in which "pairs are created at rest", and in this frame the EM field is a pure E field so we know the source is also at rest in that frame.

Note the bolded phrase: if pairs are created at rest in that particular frame, the rest frame of the source, then they must be created in motion when viewed from another frame that's moving relative to that one, i.e., moving relative to the source. But if a pair is created in motion, then the pair will have kinetic energy as well as rest mass energy when it is created, so the E field has to be higher to supply the additional energy.

 

[stglyde]

I agree. The problem is that you keep on forgetting #2.

No, I am not.

We do not and cannot know that the cmb IS isotropic.

?

All we can know is that it is MEASURED to be isotropic. Because of #2,

If the CMB were associated with an external 'object' with which we 'could' move relative to then #2 would come into play, it is not. It literally fills the entire universe and we (and
everything else) are immersed within it. It does not matter to a submarine that Earth's ocean is moving wrt to the Sun, Moon, Stars, or CMB it either is or is not 'at rest' wrt to the local ocean medium.

Yes the entire universe 'could' be moving at an unknown speed wrt to some other external object but it matters not to our system.

that measurement provides no information about the speed of the cmb relative to the aether.

If and only if something is external and separate from its field.

All of your arguments are circular: you assume that the cmb is at rest wrt the aether,

No, I do not assume the CMB is 'at rest' wrt the aether. I assume that the aether provides the very 'source' for the existence of light just as air or water does for sound. IOW only aether actually has light isotropy.

use that fact to claim that the cmb is not just MEASURED to be isotropic but actually IS isotropic, and therefore conclude that the cmb is at rest wrt the aether.

The CMB is not 'at rest' wrt the aether. The CMB illuminates the actual aether making measurements of speed wrt it possible. Just the very same way as naturally occurring background white noise allows a sonar tech to passively determine the speed of his sub wrt to the local water medium. This is not a circular argument. Doppler shift is an ironclad way of making this determination for any immersed object in a medium.

 

[Dale]

If the CMB were associated with an external 'object' with which we 'could' move relative to ... Yes the entire universe 'could' be moving at an unknown speed wrt to some other external object

Such as the aether.

The CMB illuminates the actual aether making measurements of speed wrt it possible.

And what evidence do you have to support this claim? This is the key point that you are simply assuming without either any observational or theoretical justification.

Doppler shift is an ironclad way of making this determination for any immersed object in a medium.

Not for light in LET. Go ahead and work out the math. LET does not predict what you think that it does.

 

[Aether]

No, I do not assume the CMB is 'at rest' wrt the aether. I assume that the aether provides the very 'source' for the existence of light just as air or water does for sound. IOW only aether actually has light isotropy.

If you were at rest in the center of any black spherical shell of reasonably uniform temperature, you could measure a spectrum for the blackbody radiation that would be originating from any point on the inside surface of the shell and there would be no Doppler anisotropy regardless of what inertial frame you were in. That is what the CMB dipole anisotropy represents, our relative motion with respect to a big black spherical shell. This has nothing to do with the aether.

 

[stglyde]

And what evidence do you have to support this claim? This is the key point that you are simply assuming without either any observational or theoretical justification.

I have given you the physical explanation and used clear direct examples. This is not a aberrant position, many have realized this. Here are three recent examples,

http://arxiv.org/PS_cache/gr-qc/pdf/0210/0210049v2.pdf
(http://prl.aps.org/abstract/PRL/v90/i6/e060402)


"Generally, the best candidate for is taken to be the frame of the cosmic microwave background (CMB) [15, 16] with the velocity of the solar system in that frame taken as v? 377 km/s, decl. -6.4?, RA 11.2h."


http://arxiv.org/ftp/arxiv/papers/1011/1011.1318.pdf


"The preferred frame of reference is identified with the CMB frame in the modern version of experiments to test the isotropy of the speed of light. Therefore, the moving frame of reference attached with the Earth Which represents our laboratory system is moving with a velocity relative to CMB [27, 29 - 33]. This would lead to an improved limit of the verification of the
isotropy of the speed of light."


http://www.tapir.caltech.edu/~kamion/CFP/Byer_Space_Time_Asymmetry_Research_CFP.pdf...


"For most of the 20th century there was no reason to believe that there is a special universal frame of reference. The postulate that all inertial frames are equivalent, never contradicted empirically, has led to many great advances -- especially in general Relativity. However, we now know of a unique rest frame: that defined by the cosmic microwave background (CMB) (see experiment foldouts), with respect to which the solar system is moving at a velocity of ~370 km/s."


Think of each photon as a ray, then for every cc of space these rays are traversing from all directions evenly (this is the meaning of isotropic). You cannot possibly choose any frame except one where there exist no discenable Doppler shift. This is uniquely when the particular object has not motion net wrt this flux. This is the 'rest frame' of the CMB. Since this background is global it provides the common frame by which all such motion can be measured.

Not for light in LET. Go ahead and work out the math. LET does not predict what you think that it does.

I have no clue as to what you are thinking?

 

[harrylin]

After my last paragraph in post #275, which you only partially quoted, I don't know why you continue to argue as if I am claiming that there exists a hidden reality or that Einstein is claiming this. That would be a claim that a LET theorist would believe.

But if your point is that Einstein's second postulate/definition, along with his other definitions, especially of time, are based on things that can be observed (the hands on a clock, the elapsed time on a clock, the distance defined by a rigid rod, etc) and that is what you are calling an operational theory/definition/meaning, then I totally agree with you. I just don't know why you thought my explanations weren't already clear enough and needed to have the word "operational" attached to them. Did Einstein ever use that word?

You appeared to suggest that SR makes a claim about hidden reality by writing "is" in capitals, in contrast with "measurements" - as if Einstein attached substantialist meaning to the speed of light. I therefore added that SR is a theory about measurements of phenomena, complete with pragmatic definitions to enable such measurements. The term "operational definition" is the usual label for the kind of definitions as found in Einstein's 1905 and 1907 papers.
- http://en.wikipedia.org/wiki/Operational_definition

PS. perhaps the essential point here is this: Einstein's postulates only refer to observables; that was his main purpose. This is the contrary of what you stated in post #271

 

[Aether]

Think of each photon as a ray, then for every cc of space these rays are traversing from all directions evenly (this is the meaning of isotropic). You cannot possibly choose any frame except one where there exist no discenable Doppler shift. This is uniquely when the particular object has not motion net wrt this flux. This is the 'rest frame' of the CMB. Since this background is global it provides the common frame by which all such motion can be measured.

The CMB frame is an interesting landmark, but the CMB photons are not randomly distributed photons. They represent the temperature of a surface that is visible from every direction; a spherical surface (of last scattering). Every enclosed room has a similar field of photons that can be measured using an infrared thermometer.

 

[TrickyDicky]

No, it's a physical description of the conditions of the problem. In the paper you referenced, they say explicitly the following (p. 3):

"We choose a coordinate frame where pairs are created at rest. Electric field in
this frame is directed along x-axis"

In other words, they are *specifying* an electromagnetic field tensor in which the only nonzero component, in the frame they specify, is F_01 = -F_10 = E. (They don't explicitly say there is no magnetic field component in this frame, but there can't be or the rest of their equations would not be correct. So this has to be the only nonzero component.) That specifies the entire EM field tensor, which in turn fixes what its components are in *any* Lorentz frame.

They also don't explicitly specify that the source is at rest in that frame, but it has to be, because the only way for a source to produce a pure electric field is for the source to be at rest in the frame in which the field is measured. So the source must be at rest in the frame they specify, meaning its 4-velocity in that frame is (1, 0, 0, 0). Contract that vector with the EM field tensor above and you get exactly what they specify for the electric field vector, a pure E field along the x axis.

So the electric field vector is identical with the contraction of the EM field tensor and the source's 4-velocity; but now we have stated it in a way that is manifestly Lorentz covariant. None of this is an arbitrary choice; it is specified by the statement of the problem and the physics required to realize the situation described. And it is sufficient to properly state the breakdown condition in *any* frame, not just the frame specified in the paper. In other words, it is a completely Lorentz covariant description of the breakdown condition, that does not involve attributing any special properties to the "vacuum".

I don't think anyone is debating that this is Lorentz covariant, but the issue is whether it can be interpreted in other ways too.
My last post was admittedly confusing, let's see if I can make myself understood here.
If they talk about the frame where pairs are created at rest, and this is supposed to correspond to vacuum, then I think the fact the EM tensor F is antysymmetric gives us that the electric covector field obtained by contraction of F with 4-vector U:
$F_{\mu\nu} U^\nu=E_\mu$ so by the said antysymmetry of the EM tensor $E_\mu U^\nu=0$
We then have that the electric field regardless what 4-velocity vector we use is always going to have only three spatial components, that is even if it is formally a 4-covector it only has three degrees of freedom, a static (time independent) electric field , and this field corresponds to the vacuum frame where pairs are created and vacuum breakdown is produced. And this event is agreed by all observers no matter what their state of motion might be (Lorentz covariance respected), included of course the source rest frame. You've tried several times to dismiss the vacuum as a relevant frame in the experiment which is curious when the phenomenon involved is an intrinsic property of the vacuum, while at the same time linking the electric field to the state of motion of the source of the EM field which should be comoving with the vacuum frame. When you say that the source is not explicitly referred to be at rest (frame where "the pairs are created at rest") because it is not necessary since it is the only way a pure electric field can be produced, I think you are implicitly saying the vacuum is picking a very specific electric field's frame to produce the pairs, not *any* frame, even if all 4-velocity frames can be locally Lorentz transformed to get this particular frame.

I think the fact the electric field is purely spatial and the phenomenon of vacuum breakdown should be agreed by all observers could point to a possible interpretation of this vacuum frame being somewhat special. Independently of whether one wants to call it an aether frame or an absolute rest frame or else. Then again interpretations are subjective.

 

[Q-reeus]

Allright, given your thoughtful response in #295-296 I'll come out of retirement on this one and respond best I can.

...They also don't discuss LET, of course.

Naturally - their ugly anti-crackpot bias shows all to strongly.

Originally Posted by Q-reeus: "all I'm seeing is the same position restated in slightly different ways."
If by "the same position" you mean I'm continuing to assert that this entire experiment is describable in purely Lorentz invariant terms, that's correct. Do you disagree?

I will take 'disagree' here to be referring to what is my position on total applicability of LT's re experiment - I certainly agree that describes your position. On that understanding; yes and no. Yes insofar as whatever physics is transpiring in a given frame, LT's correctly predict the observed physics in any other inertial frame, whether SR or LET is assumed. No insofar as the phenomenon of vacuum breakdown itself has imo an arbitrariness re source of applied Ecrit. Will elaborate later here, where you refer to the matter of pair creation at rest in a given preferred frame.

In particular, I am not trying to take a position on what "LET" would say, because, as I've said, I don't think the term "LET" is well defined enough. In so far as "LET" is a theory that makes the exact same experimental predictions as SR, it would obviously do so for this experiment. If there is a version of "LET" that doesn't, I would need to see a formulation of such a theory that is clear and precise enough to allow predictions to be made.

All I can say to that is what was stated in #280:
"SR has by postulating the complete absense of any 'physical' vacuum, in principle no means of laying the groundwork for a resolution. LET however can at least suggest a resolution in that a 'true rest frame' would be the natural reference frame to define as having a maximal value for breakdown Ecrit."
Obviously that is a vacuous (pardon the pun) statement if there is no real issue. Which brings us to your entry #296:

Q-reeus: "That is surely inconsistent with the notion that the vacuum should not distinguish between an E field generated by a source at rest or moving"
On re-reading your post #255 I saw the part quoted above; this may be part of the issue that you're still seeing as unresolved. Remember the statement I quoted from the paper you linked to: part of it was that they work in a frame in which "pairs are created at rest", and in this frame the EM field is a pure E field so we know the source is also at rest in that frame.

Yes, no argument there.

Note the bolded phrase: if pairs are created at rest in that particular frame, the rest frame of the source, then they must be created in motion when viewed from another frame that's moving relative to that one, i.e., moving relative to the source. But if a pair is created in motion, then the pair will have kinetic energy as well as rest mass energy when it is created,...

True as far as it goes to this point, but one should ask how the pairs 'know' which frame is the one to be created at rest in - given that a quoted E_crit per se in the E field source rest-frame can, by the LT's, be arbitrarily exceeded in an infinity of other frames. Also, the pair initial KE argument only has use at all when relative motion is transverse to the applied E. You go on to add:

...so the E field has to be higher to supply the additional energy.

That may be standard argument, but it is spurious imo. Consider something analogous - a gas of ionically bonded diatomic molecules, tangentially flowing between the parallel plates of a charged capacitor. At a certain applied E = E_crit molecules will dissociate into ions that strike the plates with a tangent speed and momentum which has absolutely no effect on the concommitant discharge of capacitor voltage/stored energy (a path independent, quasi-static energy balance). However ionization followed by impact with the plates has effected the mechanical energy/momentum residing in the gas flow. Momentum, and energy (as heat) has been transferred from gas flow KE to capacitor plates. It is also here that magnetic interaction (as seen in the molecules frame) plays a part in that transverse mommentum/energy exchange. The analogy with vacuum pair production should be obvious - the 'extra energy' of pairs is supplied by the system KE of relative motion, not the electrical field energy associated with E_crit. And notice that E_crit for flowing gas molecules is *less* than if not flowing, as, by the LT's, they 'see' a larger E_crit in their rest frame. Ditto surely for vacuum pair production - or you can give some convincing reason why this analogy can be turned on it's head? I can supply one part critique of the above, but it won't help your argument. By definition, a vacuum (not undergoing breakdown) can have no sense of underlying flow - so in that sense the flowing gas analogy is wrong, but is relevant for breakdown condition discussion.

And this imo touches on the crunch issue. Vacuum, unlike ponderable media, is taken as possessing no property dependent on relative velocity - period. Vacuum breakdown should thus be quite unlike say electrostatic corona discharge which is necessarily anchored to ponderable media, and hence has an obvious frame linkage to a charged surface. I repeat, the tacit belief that vacuum breakdown is somehow anchored to the source charges rest frame assumes some almost mystical linkage that 'trumps' the very idea of electric field as sole reason for such breakdown. Except, as before discussed, modified by the matter of minimal field duration - hence the long coax (or equivalent) capacitor that deals with that out.

Now since vacuum polarization/breakdown is a QED concept foreign to SR/LET anyhow, we are dealing with a kind of hybrid phenomenon and just maybe it is here there is room for that mystical linkage - but imo it's not logically to be found in SR in particular. It appears the mini-saga continues!

 

[Dale]

I have given you the physical explanation and used clear direct examples.

No you haven't. You have posted random links to papers that fail to make the point that you are claiming.

Here are three recent examples,

All three of those recent examples explicitly consider the CMB as a Lorentz-violating aether frame. None of them are at all relevant (and none detected any Lorentz violations).

Don't you understand that the aether of Lorentz aether theory (LET) is not Lorentz-violating but rather obeys the Lorentz transform? Whenever you see "Lorentz violating" they are not discussing LET.

Think of each photon as a ray, then for every cc of space these rays are traversing from all directions evenly (this is the meaning of isotropic). You cannot possibly choose any frame except one where there exist no discenable Doppler shift. This is uniquely when the particular object has not motion net wrt this flux. This is the 'rest frame' of the CMB. Since this background is global it provides the common frame by which all such motion can be measured.

All of this is true, none of it implies that the rest frame of the CMB is Lorentz's aether.

I have no clue as to what you are thinking?

Clearly not. I will go ahead and work out the math for you.

In units where c=1 consider a set of 6 photons with the following four-momenta, p, in the aether frame:

$$\begin{array}{cccccc} \left( \begin{array}{c} 2. \\ 2. \\ 0. \\ 0. \end{array} \right) & \left( \begin{array}{c} 0.5 \\ -0.5 \\ 0. \\ 0. \end{array} \right) & \left( \begin{array}{c} 1.25 \\ 0.75 \\ 1. \\ 0. \end{array} \right) & \left( \begin{array}{c} 1.25 \\ 0.75 \\ -1. \\ 0. \end{array} \right) & \left( \begin{array}{c} 1.25 \\ 0.75 \\ 0. \\ 1. \end{array} \right) & \left( \begin{array}{c} 1.25 \\ 0.75 \\ 0. \\ -1. \end{array} \right) \end{array}$$Clearly, the photons are not isotropic in the aether frame.

Now, suppose that their frequency is measured by a detector which is not at rest in the aether frame, but is moving with four-velocity $v=(1.25,.75,0,0)$. For all six photons, the measured frequency is given by $p \cdot v = 1$ where the dot is the Minkowski dot product.

So due to the local-frame distortions of the measuring device, the photons are measured to be isotropic despite the fact that they are not isotropic in the aether frame. Therefore, isotropy of measured Doppler data does not imply that the detector is at rest wrt the aether.

 

[stglyde]

No you haven't. You have posted random links to papers that fail to make the point that you are claiming.

All three of those recent examples explicitly consider the CMB as a Lorentz-violating aether frame. None of them are at all relevant (and none detected any Lorentz violations).

Don't you understand that the aether of Lorentz aether theory (LET) is not Lorentz-violating but rather obeys the Lorentz transform? Whenever you see "Lorentz violating" they are not discussing LET.

All of this is true, none of it implies that the rest frame of the CMB is Lorentz's aether.

Clearly not. I will go ahead and work out the math for you.

In units where c=1 consider a set of 6 photons with the following four-momenta, p, in the aether frame:

$$\begin{array}{cccccc} \left( \begin{array}{c} 2. \\ 2. \\ 0. \\ 0. \end{array} \right) & \left( \begin{array}{c} 0.5 \\ -0.5 \\ 0. \\ 0. \end{array} \right) & \left( \begin{array}{c} 1.25 \\ 0.75 \\ 1. \\ 0. \end{array} \right) & \left( \begin{array}{c} 1.25 \\ 0.75 \\ -1. \\ 0. \end{array} \right) & \left( \begin{array}{c} 1.25 \\ 0.75 \\ 0. \\ 1. \end{array} \right) & \left( \begin{array}{c} 1.25 \\ 0.75 \\ 0. \\ -1. \end{array} \right) \end{array}$$Clearly, the photons are not isotropic in the aether frame.

Now, suppose that their frequency is measured by a detector which is not at rest in the aether frame, but is moving with four-velocity $v=(1.25,.75,0,0)$. For all six photons, the measured frequency is given by $p \cdot v = 1$ where the dot is the Minkowski dot product.

So due to the local-frame distortions of the measuring device, the photons are measured to be isotropic despite the fact that they are not isotropic in the aether frame. Therefore, isotropy of measured Doppler data does not imply that the detector is at rest wrt the aether.

Thanks for the illumination. Now I guess I'll just have to go to Quantum Gravity research (as it's more fruitful than search of the Aether rest frame).

 

[PeterDonis]

If they talk about the frame where pairs are created at rest, and this is supposed to correspond to vacuum,

The vacuum part has nothing to do with the frame; it just signals that we are considering the idealized case where there is absolutely zero density inside the experimental apparatus. In a real experiment, as I noted in an earlier post, you can't create a perfect vacuum, there will be some very low density plasma inside the apparatus. But if there is a vacuum inside the experiment, it is a vacuum regardless of which inertial frame we view it from; it is a vacuum in a frame in which the experimental apparatus is moving, just as much as it is in a frame in which the experimental apparatus is at rest.

then I think the fact the EM tensor F is antysymmetric gives us that the electric covector field obtained by contraction of F with 4-vector U:
$F_{\mu\nu} U^\nu=E_\mu$

Yes; in fact this would hold for any tensor, not just an antisymmetric one.

so by the said antysymmetry of the EM tensor $E_\mu U^\nu=0$

Yes. This part is what depends on the EM tensor being antisymmetric; that means the 0 component of $E_{\mu}$ must be zero, so contracting it again with the 4-velocity gives zero. So the E vector is purely spatial.

We then have that the electric field regardless what 4-velocity vector we use is always going to have only three spatial components, that is even if it is formally a 4-covector it only has three degrees of freedom

Yes, this is true; but note that, as above, if we transform into a different frame, the electric field will no longer be the only nonzero part of the EM field tensor; there will also be a magnetic field (which lives in the space-space components of the tensor; the electric field is the time-space components).

a static (time independent) electric field

For the idealized case of a perfect vacuum inside the apparatus, yes.

and this field corresponds to the vacuum frame where pairs are created and vacuum breakdown is produced.

See my remarks on the vacuum part above. Also, the vacuum breakdown can be observed from any frame, not just the frame in which the EM field is a pure electric field. As I noted in a previous post, what happens when this process is viewed in a frame in which the apparatus is moving is that, at the threshold of breakdown, pairs are not created at rest; they are created in motion (because they are created at rest with respect to the apparatus, since that is the minimum energy they can have in that frame, and at the threshold of breakdown only the minimum possible energy is available). That means that they have kinetic energy in a frame in which the apparatus is moving. The electric field required to induce breakdown is also observed to be higher in a frame in which the apparatus is moving, and this is explained by an observer in that frame as being due to the need to have enough extra energy in the field to supply the kinetic energy of the created pairs, as well as their rest mass energy.

And this event is agreed by all observers no matter what their state of motion might be (Lorentz covariance respected), included of course the source rest frame.

It is "agreed" in the sense that everybody agrees on the physical law involved: that the electric field required to induce breakdown is given by the contraction of the EM field tensor with the *source's* 4-velocity.

You've tried several times to dismiss the vacuum as a relevant frame in the experiment which is curious when the phenomenon involved is an intrinsic property of the vacuum

No, it isn't. Don't be misled by the term "vacuum polarization". A vacuum left to itself doesn't create any real electron-positron pairs, only virtual ones, which can exist only for a very short time, within the constraints of the uncertainty principle. The pairs created in this experiment are real ones, whose existence is not limited by the uncertainty principle. Such pairs require an applied field, and they are created from the energy in the applied field. That's why the rest frame of the field source is picked out as being "special". The term "vacuum polarization" applied to this phenomenon is probably unfortunate; it is used because that particular quantum field mode is where the energy in the electric field is going in order to create the pairs.

When you say that the source is not explicitly referred to be at rest (frame where "the pairs are created at rest") because it is not necessary since it is the only way a pure electric field can be produced, I think you are implicitly saying the vacuum is picking a very specific electric field's frame to produce the pairs, not *any* frame, even if all 4-velocity frames can be locally Lorentz transformed to get this particular frame.

No; once again, it has nothing to do with the vacuum.

First, the paper specified two things: that they were working in a frame in which pairs are created at rest, and in that frame, the EM field was purely electric. Those two facts are already enough to require that the EM field source is at rest in the same frame; if it were moving in that frame, the field in that frame could not be purely electric; that's ruled out by Maxwell's equations. There would have to be a magnetic component. (If you look later on in the paper, you will also see that their equation #21, IIRC, explicitly says that the time rate of change of the electric field in this frame is proportional to the current. That can only be the case if the magnetic field is zero, again by Maxwell's equations.)

Second, as I said before, the vacuum is not "picking" which frame the pairs are created at rest in. The field source is doing that. The field has to supply enough energy to create each pair: the smallest possible amount of energy that will suffice to do that is the rest energy of the pair. To create a pair at that minimum energy, the pair must be at rest in the frame of the field source.

 

[PeterDonis]

Naturally - their ugly anti-crackpot bias shows all to strongly.

lol

No insofar as the phenomenon of vacuum breakdown itself has imo an arbitrariness re source of applied Ecrit. Will elaborate later here, where you refer to the matter of pair creation at rest in a given preferred frame.

See my post just before this one, in response to TrickyDicky.

True as far as it goes to this point, but one should ask how the pairs 'know' which frame is the one to be created at rest in

They "know" because the field source tells them; more precisely, the field source at the threshold of breakdown can only supply the minimum possible energy to create a pair, and that energy is the rest energy of the pair, which requires that the pair be created at rest with respect to the source. If the pair is moving relative to the source at creation, more energy is required to create it.

Also, the pair initial KE argument only has use at all when relative motion is transverse to the applied E.

Not sure I follow this; see below.

At a certain applied E = E_crit molecules will dissociate into ions that strike the plates with a tangent speed and momentum which has absolutely no effect on the concommitant discharge of capacitor voltage/stored energy (a path independent, quasi-static energy balance).

The electric field between capacitor plates is normal to the plates. So motion tangential to the plates is perpendicular to the E field, and it makes sense that it would have no effect on capacitor discharge energy. The motion of the ions *towards* the plates is *parallel* to the E field.

However ionization followed by impact with the plates has effected the mechanical energy/momentum residing in the gas flow. Momentum, and energy (as heat) has been transferred from gas flow KE to capacitor plates.

After first being transferred from the capacitor's electric field to the KE of gas flow.

It is also here that magnetic interaction (as seen in the molecules frame) plays a part in that transverse mommentum/energy exchange.

Elaborate, please.

The analogy with vacuum pair production should be obvious - the 'extra energy' of pairs is supplied by the system KE of relative motion

No, it isn't, because the ions in your scenario are pre-existing objects that you can specify as being in motion however you like relative to the capacitor plates. But the pairs are *created* by the source; they don't exist until the source supplies their energy. So you can't just arbitrarily specify the pairs' state of motion when they are created. There is no way for anything other than the source electric field to exchange energy with the pairs before they are created, so their state of motion when created can only be a function of what energy is available from the source electric field. At the threshold of breakdown, that must be the minimum possible, which will be the rest energy of the pair, requiring it to be created at rest relative to the source.

And notice that E_crit for flowing gas molecules is *less* than if not flowing, as, by the LT's, they 'see' a larger E_crit in their rest frame. Ditto surely for vacuum pair production

No, they're different scenarios. You specified that the gas is flowing relative to the plates, meaning it's moving relative to the source of the electric field, hence it sees a higher field. The gas's rest frame is not the source's rest frame. In the breakdown case, you can't arbitrarily specify the pairs' state of motion when created; they must be created at rest relative to the source, so a frame that is moving relative to the source will see a higher E_crit, as the gas does, but that frame will *not* be the rest frame of the pairs. See above.

I can supply one part critique of the above, but it won't help your argument. By definition, a vacuum (not undergoing breakdown) can have no sense of underlying flow - so in that sense the flowing gas analogy is wrong, but is relevant for breakdown condition discussion.

No, it isn't, because, as I said above, pairs don't exist until they are produced. After pairs are produced, they participate in current flow, but that doesn't change anything about pairs that haven't been produced yet, which is what's relevant for the breakdown threshold.

Vacuum, unlike ponderable media, is taken as possessing no property dependent on relative velocity - period. Vacuum breakdown should thus be quite unlike say electrostatic corona discharge which is necessarily anchored to ponderable media

And as I keep on saying, the breakdown phenomenon is *not* due to the vacuum. It's due to the source of the electric field that produces the pairs. (D'oh!) See my comments to TrickyDicky on why the term "vacuum polarization" is unfortunate applied to this experiment. So there is definitely a "ponderable medium" that the phenomenon is "anchored" to. To keep on pretending that the source is somehow not there makes no sense to me.

the tacit belief that vacuum breakdown is somehow anchored to the source charges rest frame

It's not a "tacit" belief at all; I've made it explicit a number of times. I certainly haven't been silent about it.

assumes some almost mystical linkage that 'trumps' the very idea of electric field as sole reason for such breakdown.

So you think that the linkage between an electric field and the source that produces it (which must always exist for the field to exist at all) is "mystical"?

 

[TrickyDicky]

Glad we share at least the most basic understanding, we disagree about a couple of things but that can't be helped I guess. A few remarks:

This part is what depends on the EM tensor being antisymmetric;

This is the only part I meant to be dependent on the antysymmetry, as I specified, maybe my introducing this fact previous to the Tex part made it look as otherwise.

The vacuum part has nothing to do with the frame; it just signals that we are considering the idealized case where there is absolutely zero density inside the experimental apparatus. In a real experiment, as I noted in an earlier post, you can't create a perfect vacuum, there will be some very low density plasma inside the apparatus. But if there is a vacuum inside the experiment, it is a vacuum regardless of which inertial frame we view it from; it is a vacuum in a frame in which the experimental apparatus is moving, just as much as it is in a frame in which the experimental apparatus is at rest.

I'm not sure we are talking about the same things here. Do you admit the possibility of the vacuum having its own frame:i.e in the case of the CMBR frame, do you consider it a vacuum frame? (maybe you don't consider the CMB frame a valid frame either?)
What's this got to do with the density inside the experimental apparatus?

Don't be misled by the term "vacuum polarization". A vacuum left to itself doesn't create any real electron-positron pairs, only virtual ones, which can exist only for a very short time, within the constraints of the uncertainty principle. The pairs created in this experiment are real ones, whose existence is not limited by the uncertainty principle. Such pairs require an applied field, and they are created from the energy in the applied field. That's why the rest frame of the field source is picked out as being "special".

Correct. I didn't mean anything contradicting this, sure an applied field is needed but I'm not sure why you make the distinction:virtual pairs are related to vacuum but real ones aren't because they require a field. On the other hand I'm not sure you are differentiating here the source of a field with the field itself which by the Maxwell equations you mention is referred to the vacuum.

Second, as I said before, the vacuum is not "picking" which frame the pairs are created at rest in. The field source is doing that.

See above comment

The field has to supply enough energy to create each pair: the smallest possible amount of energy that will suffice to do that is the rest energy of the pair.

Well, this would lead us to debate about the concept of rest-invariant energy (mass) and how exactly a relative rest can be invariant but maybe it should go to a new thread.

To create a pair at that minimum energy, the pair must be at rest in the frame of the field source.

Which in this case I would think is the vacuum frame. I guess we can't agree about everything.

 

[PeterDonis]

Do you admit the possibility of the vacuum having its own frame:

In SR (and in quantum field theory), the vacuum is Lorentz invariant: it looks the same from any inertial frame. That's what I was referring to. So in that sense, no, the vacuum does not have "its own frame".

in the case of the CMBR frame, do you consider it a vacuum frame?

No, of course not. The CMBR does not look the same from any inertial frame (actually, what you are calling the "CMBR frame" is not even an SR inertial frame--see below).

(maybe you don't consider the CMB frame a valid frame either?)

It's not an inertial frame, no. The CMBR looks isotropic to any "comoving" observer, but "comoving" observers are moving relative to each other.

Correct. I didn't mean anything contradicting this, sure an applied field is needed but I'm not sure why you make the distinction:virtual pairs are related to vacuum but real ones aren't because they require a field.

Because if there is no field present, no real pairs will be produced, but virtual pairs will be; we can confirm their presence by, for example, the Casimir effect, which occurs even in the absence of a field. Also, to clarify, I was not saying that the real pairs are not "related to vacuum"; there is a sense in which they are, because, as I mentioned earlier, the mechanism by which the field creates real pairs is to pump energy into the quantum field modes that, in the absence of the field, are associated with virtual pairs. But in the absence of the field, those field modes are Lorentz invariant; they look the same in all inertial frames. The applied field does not.

On the other hand I'm not sure you are differentiating here the source of a field with the field itself which by the Maxwell equations you mention is referred to the vacuum.

The field obeys Maxwell's equations, but I don't see how that means it is "referred to the vacuum". Maxwell's equations describe the relationship between fields and sources; they don't say anything about the vacuum.

Well, this would lead us to debate about the concept of rest-invariant energy (mass) and how exactly a relative rest can be invariant but maybe it should go to a new thread.

Probably, since I can't even understand the issue you're raising here.

Which in this case I would think is the vacuum frame.

No, it's the rest frame of the source of the field. The source of the field is a physical object, and it has a rest frame, defined by its 4-velocity vector. This is true of any object in SR. Why is this so hard to understand?

 

[harrylin]

[..] Which in this case I would think is the vacuum frame. [..]

It would be of course the "true" vacuum frame if the source was in "absolute rest". You could postulate that for the source of the CMBR; and perhaps there is an astrophysical motivation to why this may be plausible.

 

[TrickyDicky]

In SR (and in quantum field theory), the vacuum is Lorentz invariant: it looks the same from any inertial frame. That's what I was referring to. So in that sense, no, the vacuum does not have "its own frame".



No, of course not. The CMBR does not look the same from any inertial frame (actually, what you are calling the "CMBR frame" is not even an SR inertial frame--see below).



It's not an inertial frame, no. The CMBR looks isotropic to any "comoving" observer, but "comoving" observers are moving relative to each other.
No, it's the rest frame of the source of the field. The source of the field is a physical object, and it has a rest frame, defined by its 4-velocity vector. This is true of any object in SR. Why is this so hard to understand?

For one thing I didn't even know we were restricting our discussion to SR and inertial frames, certainly when I talk about frames I don't mean necessarily inertial unless I specify it.

Because if there is no field present, no real pairs will be produced, but virtual pairs will be; we can confirm their presence by, for example, the Casimir effect, which occurs even in the absence of a field. Also, to clarify, I was not saying that the real pairs are not "related to vacuum"; there is a sense in which they are, because, as I mentioned earlier, the mechanism by which the field creates real pairs is to pump energy into the quantum field modes that, in the absence of the field, are associated with virtual pairs. But in the absence of the field, those field modes are Lorentz invariant; they look the same in all inertial frames. The applied field does not.


The field obeys Maxwell's equations, but I don't see how that means it is "referred to the vacuum". Maxwell's equations describe the relationship between fields and sources; they don't say anything about the vacuum

These two paragraphs are a bit disappointing, but add nothing to the discussion so I won't nitpick.

 

[Q-reeus]

Q-reeus: "No insofar as the phenomenon of vacuum breakdown itself has imo an arbitrariness re source of applied Ecrit. Will elaborate later here, where you refer to the matter of pair creation at rest in a given preferred frame."

See my post just before this one, in response to TrickyDicky.

The following 2 excerpts from that #307 post seem to cover it:

1: "...Such pairs require an applied field, and they are created from the energy in the applied field. That's why the rest frame of the field source is picked out as being "special"..."
2: "...the vacuum is not "picking" which frame the pairs are created at rest in. The field source is doing that. The field has to supply enough energy to create each pair: the smallest possible amount of energy that will suffice to do that is the rest energy of the pair. To create a pair at that minimum energy, the pair must be at rest in the frame of the field source."

By now I'm quite aware that is your viewpoint, which is repeated several times in #308. More on that below.

Q-reeus: "At a certain applied E = Ecrit molecules will dissociate into ions that strike the plates with a tangent speed and momentum which has absolutely no effect on the concommitant discharge of capacitor voltage/stored energy (a path independent, quasi-static energy balance)."

The electric field between capacitor plates is normal to the plates. So motion tangential to the plates is perpendicular to the E field, and it makes sense that it would have no effect on capacitor discharge energy.

Oh good (I think). So there is acceptance that we have an energetics partitioning situation - collective transverse motion (wrt E field) of dissociated pairs has no connection with the conservative process of ionic movement along E axis.

The motion of the ions *towards* the plates is *parallel* to the E field.

Strictly true only at the moment of dissociation in the gross rest frame of the gas. Otherwise, the point is?

Q-reeus: "However ionization followed by impact with the plates has effected the mechanical energy/momentum residing in the gas flow. Momentum, and energy (as heat) has been transferred from gas flow KE to capacitor plates."

After first being transferred from the capacitor's electric field to the KE of gas flow.

How do you get that? If gross gas flow is v wrt stationary capacitor plates, we have E.v = 0, and there is zero energy transfer from capacitor E field to gas momentum/energy. There is a weak magnetic-type coupling of sorts but is subsequent to dissociation, not 'first', and has zero influence on energy source of E. More on that below.

Q-reeus: "It is also here that magnetic interaction (as seen in the molecules frame) plays a part in that transverse mommentum/energy exchange."

Elaborate, please.

Sure. In flowing gas rest frame, there is a B = vxE. Upon dissociation, ions accelerate initially just along applied E axis. As soon as finite velocity v' perpendicular to v is obtained, a magnetic Lorentz force F = v'xB acts against the gross flow velocity v. This is a 'soft' additional coupling mechanism, apart from pure mechanical impact, that effects the gas momentum/KE transfer to plates *normal* to E. In the frame of stationary capacitor, a different interpretation applies - we might use the discarded but useful concept of transverse relativistic momentum. Anyway it has absolutely *no* coupling to pair dissociation energetics - despite your insistence it does in the vacuum pair production case (as below).

Q-reeus: "The analogy with vacuum pair production should be obvious - the 'extra energy' of pairs is supplied by the system KE of relative motion"

No, it isn't, because the ions in your scenario are pre-existing objects that you can specify as being in motion however you like relative to the capacitor plates. But the pairs are *created* by the source; they don't exist until the source supplies their energy.

Recall the ions begin as ionically bonded molecules - they need to be dissociated under the action of E, just as vacuum 'virtual particle pairs' do in order to become real electron/positron pairs. So the analogy, though crude, contains all the essentials ingredients needed. From the foregoing, transverse motion, apart from making it easier for initial dissociation (higher observed E), calls for zero extra energy drain from E source.

So you can't just arbitrarily specify the pairs' state of motion when they are created. There is no way for anything other than the source electric field to exchange energy with the pairs before they are created, so their state of motion when created can only be a function of what energy is available from the source electric field. At the threshold of breakdown, that must be the minimum possible, which will be the rest energy of the pair, requiring it to be created at rest relative to the source.

And this line of reasoning has us going around in circles. I have shown above and previously the complete decoupling between any transverse motion and energetics of pair creation (by appropriate analogy with ionic molecular dissociation). Can we accept that and move the argument along?

Q-reeus: "And notice that E_crit for flowing gas molecules is *less* than if not flowing, as, by the LT's, they 'see' a larger E_crit in their rest frame. Ditto surely for vacuum pair production"

No, they're different scenarios. You specified that the gas is flowing relative to the plates, meaning it's moving relative to the source of the electric field, hence it sees a higher field. The gas's rest frame is not the source's rest frame. In the breakdown case, you can't arbitrarily specify the pairs' state of motion when created; they must be created at rest relative to the source, so a frame that is moving relative to the source will see a higher E_crit, as the gas does, but that frame will *not* be the rest frame of the pairs.

All covered above. Transverse motion relative to E source must in fact make dissociation easier, otherwise a denial of LT's is implied. The one caveat here is again the matter I covered in #257 and implicitly in #255 - minimum duration and thus some minimum spatial extension of E source when relative motion is considered. More on that later. Concept of vacuum under breakdown, and how it radically differs from normal vacuum, is presented in accessible to non-specialist form here:
http://accessscience.com/content/Supercritical%20fields/668750 The bias there is virtual particle centric - others think that naive and talk about Bogoliubov transformations or whatever. Let's leave that to QFT specialist nitpicking. The main gist is it's ok to roughly model vacuum breakdown, energetics wise, in analogy to gas breakdown. Consequently I maintain flowing gas analogy in #304 is apt in context.

Q-reeus: "Vacuum, unlike ponderable media, is taken as possessing no property dependent on relative velocity - period. Vacuum breakdown should thus be quite unlike say electrostatic corona discharge which is necessarily anchored to ponderable media

And as I keep on saying, the breakdown phenomenon is *not* due to the vacuum. It's due to the source of the electric field that produces the pairs. (D'oh!) See my comments to TrickyDicky on why the term "vacuum polarization" is unfortunate applied to this experiment. So there is definitely a "ponderable medium" that the phenomenon is "anchored" to. To keep on pretending that the source is somehow not there makes no sense to me.

TrickyDicky was imo right - takes two to tango and one might as well say dielectric breakdown has nothing to do with the dielectric! Dielectric/vacuum *plus* acting E -> breakdown. We all know that but your point presumably is pairs don't come from the vacuum, but from energy in E field. But you speak of virtual particles - where do they come from again? Oh, you agree these represent vacuum modes upon which the E field acts, so it's a little hard for me to see that breakdown has nothing to do with the vacuum.

Q-reeus: "assumes some almost mystical linkage that 'trumps' the very idea of electric field as sole reason for such breakdown."

So you think that the linkage between an electric field and the source that produces it (which must always exist for the field to exist at all) is "mystical"?

For the energetics separation, LT enhanced motional breakdown etc. reasons given above and in a previous thread, yes in the sense of your line of arguing used here.

You are no doubt familiar with the Turing test. A human is on one side of an opaque partition, and on the other is either another human or a computer. Communication is only via keyboard, and first human must determine whether human or computer is on the other side via a Q&A session. Well here's an adapted 'Turing test' for your consideration. Opaque dielectric screens intervene between an observer and some source of static E. Observer must decice the nature of E source based solely on effect of E field. One source is a pair of charged capacitor plates at rest wrt observer. The other is a 'conveyor belt' capacitor in rapid relative transverse motion, but where the LT's yield identical field strength E as for the stationary source case. The B field present in the second case can either be ignored or exactly canceled via stationary source of opposing B. Can the observer distinguish? Note 'observer' could be a slab of dielectric close to breakdown, or vacuum. There is perhaps a moral here.

If I were being smarty-pants facetious, would summarise the problem imo with your line of argument thus:
"Virtual particle filled Vac the vacuum knows it has the same properties in any inertial frame, and that by the LT's will have an easier time of it breaking down by choosing that frame with the largest applied E, consistent with a minimum duration for effecting breakdown. But Vac is not the cold-hearted chap people think. No. Vac is compassionate. Knows that, against Vac's own easy breakdown interests, it will apparently be harder on the poor old E source - a bigger energy drain it seems. So Vac unselfishly sacrifices it's own interests and dutifully breaks down in a frame at rest wrt E source. What a nice chap Vac is. No-one seems to have explained to Vac that by the LT's, relative motion tends to make breakdown occur at a lower E in source rest frame, but otherwise has no bearing on the source's energy budget (transverse energy budget is separate matter to static E source one, as per #304). But then who cares about Vac's problems."

But true gent that I am, will studiously avoid doing so!:tongue2: My point though is, the concept of a breakdown field Ecrit implies a purely intensive property, whereas linkage to the source frame implies something quite different - there is Ecrit + 'something else'. The sole something else I will admit belongs in this picture is minimum duration. I gave a link in #257 that mentioned temporal influence on breakdown, but a better article can be found here: http://www4.rcf.bnl.gov/~swhite/erice_proc/adrian2.ps

Combine LT's of E with duration/spatial-extent of source E, and I suspect one has a recipe for removing otherwise ambiguities. But yes it does seem to imply a rest frame exists where E_crit is maximal for a static E source. The alternative, covered at the end of #304, is to ascribe the linkage to source of E you insist on, as perhaps true but needing a purely QFT explanation quite outside the bounds of SR's jurisdiction. Sigh - hit the submit button and let's see.

 

[PeterDonis]

For one thing I didn't even know we were restricting our discussion to SR and inertial frames

Well, the title of the thread has "SR" in it. Sorry if that wasn't clear, but yes, this whole discussion has been in the context of SR and inertial frames.

 

[TrickyDicky]

Well, the title of the thread has "SR" in it. Sorry if that wasn't clear, but yes, this whole discussion has been in the context of SR and inertial frames.

Fine, but I'm sure you do realize that real physical situations demand to get out of the context of SR inertial frames, This was noticed by Einstein a long time ago. ;)