SR, LET, FTL & Causality Violation


by stglyde
Tags: causality, violation
TrickyDicky
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#361
Dec19-11, 11:20 AM
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Quote Quote by PeterDonis View Post
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which means that if there were a violation of Lorentz invariance for spin 1/2, then the pair would not be spin 0 in all frames, so there would be a violation of LI for spin 0 as well.
But where do you get that LI violation of virtual spin 1/2 particles from?, I'm not sure what you are referring to.
PeterDonis
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#362
Dec19-11, 01:59 PM
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Quote Quote by TrickyDicky View Post
But where do you get that LI violation of virtual spin 1/2 particles from?, I'm not sure what you are referring to.
You had originally posted that you didn't think LI violation for virtual particles required LI violation for spin 1/2, only for spin 0, because virtual spin 1/2 particles always come in pairs whose spins cancel. (See the string of posts starting with #347.) I have merely been pointing out that, since the virtual pair being spin 0 depends on the spins of the two spin 1/2 members of the pair cancelling, if LI violation were observed with regard to the virtual pairs (spin 0), it would imply LI violation for each individual member of the pair (spin 1/2) as well.
PeterDonis
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#363
Dec19-11, 02:48 PM
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Quote Quote by Q-reeus View Post
Whether source of E there is a micron or a million miles long is irrelevant in such a view.
Only as long as the source can produce an EM field that, in the source's rest frame, is a pure E field oriented in a single direction with a constant strength. That's the simplest possible kind of field, so that's what I chose to start with. But obviously such a field will be limited in spatial extent.

Quote Quote by Q-reeus View Post
But it fails to consider the pov from a vp pair that cares only that E >= E crit for a minimum HUP time span in it's own rest frame, and can't care less what the source rest frame sees.
What does "vp rest frame" even mean? The vacuum is Lorentz invariant (at least, it is in the absence of the field--nothing in this long post of yours addresses the fact that, in the *presence* of the field, the vacuum is *not* Lorentz invariant, because it's polarized by the field). That means there is no single "rest frame" for virtual pairs; *every* frame is a rest frame for *some* virtual pairs.

For the rest of your post, do you have any actual math? I see a lot of English words and some equations with symbols in them but I can't give them any precise meaning. It's still handwaving. Can you write down some precise covariant condition like the one I wrote down?
Q-reeus
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#364
Dec19-11, 03:06 PM
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Quote Quote by PeterDonis View Post
Q-reeus: "But it fails to consider the pov from a vp pair that cares only that E >= E crit for a minimum HUP time span in it's own rest frame, and can't care less what the source rest frame sees."
What does "vp rest frame" even mean?
What it seems to mean - the instantaneous rest frame of any chosen vp or vp pair.
The vacuum is Lorentz invariant (at least, it is in the absence of the field--nothing in this long post of yours addresses the fact that, in the *presence* of the field, the vacuum is *not* Lorentz invariant, because it's polarized by the field). That means there is no single "rest frame" for virtual pairs; *every* frame is a rest frame for *some* virtual pairs.
Naturally and I thought it clear the focus is on breakdown criteria for a given vp pair - in that pair's instantaneous rest frame. As opposed to setting the source rest frame as the sole arbiter of breakdown condition.
For the rest of your post, do you have any actual math? I see a lot of English words and some equations with symbols in them but I can't give them any precise meaning. It's still handwaving. Can you write down some precise covariant condition like the one I wrote down?
I'll leave the covariant expressions to you. There should be enough clarity in the plain english I think. If there's some conceptual point needing clarification - fire away. But as said last post, the game has changed for me. Something is not right. Either the vacuum vp model is basically flawed, which seems unlikely, or breakdown criteria is different than thought and far from just being Ecrit. Or - gamma rays exit from high-tension power lines etc.!!! (very unlikely).
PeterDonis
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#365
Dec19-11, 03:12 PM
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Quote Quote by Q-reeus View Post
What it seems to mean - the instantaneous rest frame of any chosen vp or vp pair.
There are an infinite number of them, with an infinite number of different instantaneous rest frames. How do you choose which one you are talking about?

Quote Quote by Q-reeus View Post
I'll leave the covariant expressions to you. There should be enough clarity in the plain english I think. If there's some conceptual point needing clarification - fire away. But as said last post, the game has changed for me. Something is not right. Either the vacuum vp model is basically flawed, which seems unlikely, or breakdown criteria is different than thought and far from just being Ecrit. Or - gamma rays exit from high-tension power lines etc.!!! (very unlikely).
Agree the last possibility is highly unlikely. But there is not nearly enough clarity in your not so plain English. I have already asked several times about the key conceptual point, but I'll state it once more. I have written a covariant expression of the breakdown criterion, one which is taken from the first paper you linked to (the second, as I've said before, involves multiple interacting field sources and so is more complicated, let's stick with the simpler case first). So if you're disagreeing with my criterion, you're disagreeing with the paper that you yourself linked to, but we'll let that pass for now. The point is: if there really is a clear way of picking out what you call the "vp rest frame", then you should be able to write down a covariant expression for it, the same way I wrote one down for my criterion. If you can't, then as far as I'm concerned you don't really have a clear criterion; you're just waving your hands again. I'm not going to try to parse your English description into a covariant expression; that's your job.
Q-reeus
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#366
Dec19-11, 03:46 PM
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Quote Quote by PeterDonis View Post
There are an infinite number of them, with an infinite number of different instantaneous rest frames. How do you choose which one you are talking about?
The context, how to apply the notion, is set out clearly in #360.
...But there is not nearly enough clarity in your not so plain English.
An opinion freely expressed in a democratic society.
I have already asked several times about the key conceptual point, but I'll state it once more. I have written a covariant expression of the breakdown criterion, one which is taken from the first paper you linked to (the second, as I've said before, involves multiple interacting field sources and so is more complicated, let's stick with the simpler case first). So if you're disagreeing with my criterion, you're disagreeing with the paper that you yourself linked to, but we'll let that pass for now.
Not me. I have clearly stated my objection to your covariant formulation - last occasion in #360. Also, I haven't approached the authors re my idea, so that they use a convenient criteria to model their arrangement speaks nothing about whether they would disagree with my argument necessarily. And hell, I'm simply aplying LT's, so where is the point of controversy in that anyway?
The point is: if there really is a clear way of picking out what you call the "vp rest frame", then you should be able to write down a covariant expression for it, the same way I wrote one down for my criterion. If you can't, then as far as I'm concerned you don't really have a clear criterion; you're just waving your hands again. I'm not going to try to parse your English description into a covariant expression; that's your job.
Then my stipulation of a minimal |E|*|l| ~ 104v/cm.cm combined with a minimum vp pair gamma seen in source rest frame yielding source E -> Ecrit in vp rest frame, as per #318, #338, #356, is incomprehensible? Sorry - if that's the roadblock to further discussion then so be it. If this is a campaign of attrition, I concede defeat. Been burning the candle too much as is. Too bad though, I'd still love to know how you would explain your position re that rotating setup of #318 - I think this is the 4th time I've asked. But whatever - cherio it's snooze time for me.
TrickyDicky
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#367
Dec19-11, 04:36 PM
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Quote Quote by PeterDonis View Post
You had originally posted that you didn't think LI violation for virtual particles required LI violation for spin 1/2...
To avoid further (intended or unintended) confusion my #355 made clear what I meant, vacuum LI of virtual particles is not affected, violation only appears for real particles in a putative preferred frame scenario. Do you agree?
DaleSpam
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#368
Dec19-11, 04:39 PM
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Quote Quote by PeterDonis View Post
This is the breakdown condition, in covariant terms, for a single source such as a capacitor:

[tex]F_{ab} u^{a} e^{b} >= E_{crit}[/tex]
Do you have a reference or derivation for this? If so, it seems pretty clearly covariant.
PeterDonis
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#369
Dec19-11, 04:39 PM
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Quote Quote by Q-reeus View Post
Then my stipulation of a minimal |E|*|l| ~ 104v/cm.cm combined with a minimum vp pair gamma seen in source rest frame yielding source E -> Ecrit in vp rest frame, as per #318, #338, #356, is incomprehensible?
Until you can give an actual unambiguous definition of what the "vp rest frame" is, yes. There are an infinite number of "vp rest frames". Which one are you talking about?

Quote Quote by Q-reeus View Post
Too bad though, I'd still love to know how you would explain your position re that rotating setup of #318 - I think this is the 4th time I've asked.
And it isn't the 4th time I've answered, but I have answered: one scenario at a time. Trying to tackle your rotating setup when we don't even have common ground on the scenario with a simple capacitor would be like trying to tackle calculus when we don't have agreement on simple arithmetic.
Q-reeus
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#370
Dec20-11, 04:23 AM
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Quote Quote by PeterDonis View Post
Q-reeus: "Then my stipulation of a minimal |E|*|l| ~ 104v/cm.cm combined with a minimum vp pair gamma seen in source rest frame yielding source E -> Ecrit in vp rest frame, as per #318, #338, #356, is incomprehensible?"

Until you can give an actual unambiguous definition of what the "vp rest frame" is, yes. There are an infinite number of "vp rest frames". Which one are you talking about?
Hard to believe you are not perfectly cognizant by now of my argument. Willing though to run through it all again, explicitly dealing with above. But first there are two issues.

1: I have shown your reductio ad absurdum claims of #321 and #352 were wrong, but there has been no concession from you. That makes it difficult to continue any discussion. Either explicitly prove my rebuttal in #338 (elaborated slightly in #356) wrong, or concede. Not a throwaway issue for me.
2: Focus has now moved afar of OP's topic, and rightly to continue a new thread should be opened - properly citing this one as background reference.

Your choice on these two matters.
PeterDonis
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#371
Dec20-11, 08:53 AM
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Quote Quote by Q-reeus View Post
1: I have shown your reductio ad absurdum claims of #321 and #352 were wrong, but there has been no concession from you. That makes it difficult to continue any discussion. Either explicitly prove my rebuttal in #338 (elaborated slightly in #356) wrong, or concede. Not a throwaway issue for me.
Your "rebuttals" basically amount to claiming you know what the "vp rest frame" is, or equivalently that you know in what frame the criterion E > E_crit is to be applied (since you don't agree that the source rest frame is that frame). Yet you haven't been able to say what frame that is, despite repeated requests from me. Let me put it this way: if you know in what frame the criterion E > E_crit is to be applied, then you ought to be able to write down a formula for the 4-velocity of that frame relative to the rest frame of the source, in terms of quantities already known or measurable. Can you?

Quote Quote by Q-reeus View Post
2: Focus has now moved afar of OP's topic, and rightly to continue a new thread should be opened - properly citing this one as background reference.
Well, you originally brought up the "vacuum breakdown" issue as a possible way of distinguishing some version of "LET" from standard SR. But I agree it's not very closely related to the causality issue in the OP. I would have no problem moving the discussion to a new thread entitled something like "Does the vacuum breakdown phenomenon violate Lorentz invariance?" or something similar, if you want to start one.
Q-reeus
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#372
Dec20-11, 10:32 AM
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Quote Quote by PeterDonis View Post
Your "rebuttals" basically amount to claiming you know what the "vp rest frame" is, or equivalently that you know in what frame the criterion E > E_crit is to be applied (since you don't agree that the source rest frame is that frame).
No my rebuttal amounted to showing that, *additionally* to E >= Ecrit in any given vp rest frame, a minimal El product (or impulse Edt) must exist or pair creation is impossible, no matter how great the vp gamma factor may be in source rest frame. Recall you claim in #321:
"But you, standing next to me, can, it seems to me, argue as follows: as soon as I turn on the E field source, as soon as it is producing *any* nonzero E field at all, there will be *some* frame in which E > E_crit. (The field won't be a static, pure E field in that frame, since there will be a large B component, but we've agreed that B doesn't directly affect breakdown, and the E *component* will be greater than E_crit. More on this below.) And since the vacuum can "detect" E > E_crit in *any* frame, breakdown should occur immediately when I turn on the field source.
Since this latter conclusion is obviously grossly contrary to observation, there must be something wrong with the argument."
And that specific claim is wrong. Yes there can be an E > Ecrit in some other frame 'immediately upon switch-on', but that alone is *not* sufficient. It must be sustained for a minimum period of time, seen in that frame. That in turn imposes minimal restraints on the combination of size and applied E of the E source, which I gave before as |E|*|l| >= ~ 104v/cm.cm, true for any frame whatsoever. Further, as E >= Ecrit must hold in the rest frame of any chosen vp pair, the additional constraint follows that, in E source rest frame, gamma factor of vp pair passing through is gamma >= Ecrit/E. Provided these simple criteria hold, virtual-to-real creation is possible. It is vp frame centric, not source frame centric. And that's it! Now I have asked you to either accept that argument or prove me wrong. Which is it?
Yet you haven't been able to say what frame that is, despite repeated requests from me.
Any frame consistent with above. Recall I have said that invariant vacuum vp spectrum demands a finite ultra-relativistic flux of vp's in a source rest frame. Provided source parameters meets minimal impulse criteria |E|*|l| >= ~ 104v/cm.cm, one simply singles out for attention *any* vp pair having sufficient gamma factor wrt source rest frame such that transformed into that vp pair's rest frame, E >= Ecrit applies. Source parameters then gaurantee that Ecrit will be sustained in that frame for the minimal HUP time for real pair creation. Do you insist on some invariant expression? Is this scenario not simple enough to follow? Apply that to any other vp pairs meeting those requirements, and voila, real pair creation courtesy of vacuum spectrum - or so it seems from what I presented in #360.
Let me put it this way: if you know in what frame the criterion E > E_crit is to be applied, then you ought to be able to write down a formula for the 4-velocity of that frame relative to the rest frame of the source, in terms of quantities already known or measurable. Can you?
See above. Assuming there are no comprehension difficulties with my basic argument, have a shot yourself at casting it into some fancier mathematical form with raised and lowered indices or whatever, if that really seems essential for acceptance. Won't change the argument though.
I would have no problem moving the discussion to a new thread entitled something like "Does the vacuum breakdown phenomenon violate Lorentz invariance?" or something similar, if you want to start one.
And if above can be satisfactorally sorted out, that is now the way to go, but I would choose a different title - the issue has for me become about how vacuum vp's interact with an electrostatically charged structure.
PeterDonis
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#373
Dec20-11, 04:38 PM
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Quote Quote by Q-reeus View Post
Yes there can be an E > Ecrit in some other frame 'immediately upon switch-on', but that alone is *not* sufficient.
Of course not. I was not arguing that it was.

Quote Quote by Q-reeus View Post
It must be sustained for a minimum period of time, seen in that frame.
As far as I can tell, by "that frame" you mean *any* frame at all. Correct?

Quote Quote by Q-reeus View Post
That in turn imposes minimal restraints on the combination of size and applied E of the E source, which I gave before as |E|*|l| >= ~ 104v/cm.cm, true for any frame whatsoever.
So, cancelling the units, we have E * L >= V_crit, since the units of the product are now volts. (Btw, I would really prefer using the capital L as it's easier to read; the small l looks like just another vertical line and it took me a while to realize what you were trying to write.) And L is some characteristic length associated with the source, such as the distance between the capacitor plates, correct? And is L supposed to be measured in the source rest frame? That seems the most natural interpretation, but please confirm.

Quote Quote by Q-reeus View Post
Further, as E >= Ecrit must hold in the rest frame of any chosen vp pair, the additional constraint follows that, in E source rest frame, gamma factor of vp pair passing through is gamma >= Ecrit/E.
How do I measure gamma? After all, as you agree above, I can always find *some* frame in which E_crit / E is greater than any gamma value I choose. So if I measure E in a given frame, and take the ratio (since E_crit is known in terms of physical constants, I don't have to measure it), how do I tell if your criterion is met? What gamma do I compare it to? I see a possible answer below, but it would be nice, once again, to have confirmation.

Quote Quote by Q-reeus View Post
Any frame consistent with above. Recall I have said that invariant vacuum vp spectrum demands a finite ultra-relativistic flux of vp's in a source rest frame. Provided source parameters meets minimal impulse criteria |E|*|l| >= ~ 104v/cm.cm, one simply singles out for attention *any* vp pair having sufficient gamma factor wrt source rest frame such that transformed into that vp pair's rest frame, E >= Ecrit applies.
Hmm...so it looks like you are suggesting *two* criteria:

(1) In the source rest frame, E * L >= V_crit.

(2) In the rest frame of a pair being created, gamma > gamma_crit.

where gamma_crit is the gamma necessary to make E >= E_crit in the pair's frame. given that the first criterion is satisfied in the source rest frame (i.e., gamma_crit is calculated relative to the source rest frame).

My first comment is that I don't understand why the second criterion is even necessary; again, given that the first criterion is satisfied, there will always be *some* frame in which E >= E_crit, so I just figure out what the gamma is for that frame relative to the source rest frame, and say that that's the frame in which pairs will be created at rest. So if the first criterion is satisfied, the second must always be satisfied in some frame. Why then is the second criterion necessary? I can see why you might want to use the second formula to predict, for example, what the initial current due to the virtual pairs would be in the source rest frame (since that will depend on the velocity of the created pairs), but why is it a criterion for determining whether breakdown can occur at all, given that the first criterion is satisfied?

My second comment is that I can always meet the first criterion by making my capacitor plate separation large enough, given some limit on the E field I can produce at the plates. Basically your criterion is saying that there must be a certain amount of energy per unit charge available between the plates (since that's what voltage is, energy per unit charge). Your first criterion does *not*, so far as I can see, place any limit on how short a time that voltage needs to be applied; it only sets a lower limit on the voltage itself. So I don't quite see how your first criterion is related to your "minimum duration" requirement.

I certainly agree that your criterion makes a very different experimental prediction from mine. My criterion requires E = E_crit in the source rest frame; your criterion requires only V > V_crit in the source rest frame, which is much easier to achieve. In fact, as far as I can see, if your criterion were correct, it should be trivially easy for any lab with a high voltage source to induce breakdown; after all, your criterion amounts to V_crit = 10,000 V, which is easy to achieve. So your route to a Nobel Prize is easy: just hire some test lab to fire up a high voltage source and connect it to a capacitor, and watch the electrons and positrons pour out.
TrickyDicky
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#374
Dec21-11, 04:26 AM
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Quote Quote by harrylin View Post
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.
Quote Quote by harrylin View Post
I also think that there's no need to go into non-linear theories, linear theories suffice: the "LET" of this thread closely corresponds to a major (or "mainstream") interpretation of relativistic QM (see my post #272).
Quote Quote by harrylin View Post
This is also at play with interpretations of QM. In particular Bell's theorem, if not refuted, points to a "LET"-like interpretation of SR as it suggests instant action at a distance, without however the possibility to detect our speed relative to the corresponding "absolute" frame. See: Tim Maudlin, "Quantum Non-Locality and Relativity".
Yes, see also the thread http://www.physicsforums.com/showthread.php?t=561128 where that author is quoted.
harrylin
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#375
Dec21-11, 06:16 AM
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Quote Quote by TrickyDicky View Post
Yes, see also the thread http://www.physicsforums.com/showthread.php?t=561128 where that author is quoted.
OK
Q-reeus
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#376
Dec21-11, 10:12 AM
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[In what follows, I will agree to your request and use L rather than l for length symbol, and further use V rather than v for volts]
Quote Quote by PeterDonis View Post
Q-reeus: "Yes there can be an E > Ecrit in some other frame 'immediately upon switch-on', but that alone is *not* sufficient."
Of course not. I was not arguing that it was.
Really? Go read my quote from your #321 again. Yes it is what you were arguing. And even more clearly so in your #352:
"And taken to its logical conclusion, this would again imply that breakdown should occur *immediately* upon turning on any field source, regardless of its state of motion, since there will always be *some* vp that will sense E > E_crit. That's obviously false, so again something must be wrong with your argument."
Up to you whether to admit that claim, made twice, is mistaken.
Q-reeus: "It must be sustained for a minimum period of time, seen in that frame."
As far as I can tell, by "that frame" you mean *any* frame at all. Correct?
Provided that frame, in which E >= Ecrit, relates to motion wrt to an E source meeting invariant |E|*|L| >= ~ 104V/cm.cm (E and L being orthogonal). As I have consistently maintained, two criteria must be met.
Q-reeus: "That in turn imposes minimal restraints on the combination of size and applied E of the E source, which I gave before as |E|*|L| >= ~ 104V/cm.cm, true for any frame whatsoever."
So, cancelling the units, we have E * L >= V_crit, since the units of the product are now volts.
Only nominally 'volts', as clearly explained in #356: "there is an invariant |E|*|L| product (E and source characteristic length L being orthogonal) that must be exceeded before breakdown is possible in *any* other inertial frame." Further, in #360: "I am claiming, based on example in #338 and codified in #356 as |E|*|L| >= 'volts'min (even though it is not really volts per se)" and later; "Putting it more concretely, from #338 example, a capacitor must roughly have M = |E|*|L|>= 104 (V/cm)cm before a vp pair passing through at any relative gamma factor whatsoever can be elevated to real pair status." Notice I expressed it variously as either (V/cm)cm, or V/cm.cm, in order to avoid any confusion that the quantity is really 'volts'.
Re-reading #338, where this scenario began, it's more than clear E and L are to be taken as orthogonal in order to make any sense at all. And as quoted above, that criteria was expressly stated in #356. Forget it all somehow?
And L is some characteristic length associated with the source, such as the distance between the capacitor plates, correct?
Clear by now surely that L is normal to applied E. And btw, just as clearly, relative velocity (re gamma factor) is also taken as normal to E, hence along the same axis as L. That was also explicit and implicit in #338 and later. Otherwise, frame dependent E coupled to frame dependent duration would make no sense.
And is L supposed to be measured in the source rest frame? That seems the most natural interpretation, but please confirm.
It's the most natural frame, but the invariant product (let's express it now as |ExL|, even though it's not a cross product) is all that matters here. Choose any frame you like, so long as E and orthogonal L, measured in that same frame, give a scalar product >= ~ 104V/cm.cm, which is *not* to be taken as volts.
Q-reeus: "Further, as E >= Ecrit must hold in the rest frame of any chosen vp pair, the additional constraint follows that, in E source rest frame, gamma factor of vp pair passing through is gamma >= Ecrit/E."
How do I measure gamma? After all, as you agree above, I can always find *some* frame in which E_crit / E is greater than any gamma value I choose. So if I measure E in a given frame, and take the ratio (since E_crit is known in terms of physical constants, I don't have to measure it), how do I tell if your criterion is met? What gamma do I compare it to? I see a possible answer below, but it would be nice, once again, to have confirmation.
Huh? The 'possible answer' is directly given in what you quoted above! It's the second criteria, as stated, given first criteria is already met.
Q-reeus: "Any frame consistent with above. Recall I have said that invariant vacuum vp spectrum demands a finite ultra-relativistic flux of vp's in a source rest frame. Provided source parameters meets minimal impulse criteria |E|*|L| >= ~ 104V/cm.cm, one simply singles out for attention *any* vp pair having sufficient gamma factor wrt source rest frame such that transformed into that vp pair's rest frame, E >= Ecrit applies."
How much more explicit can I get!?
Hmm...so it looks like you are suggesting *two* criteria:
(1) In the source rest frame, E * L >= V_crit.
Actually, that's |ExL| >= ~ 104V/cm.cm, in any frame whatsoever, and understood that V/cm.cm does not mean volts.
(2) In the rest frame of a pair being created, gamma > gamma_crit. where gamma_crit is the gamma necessary to make E >= E_crit in the pair's frame. given that the first criterion is satisfied in the source rest frame (i.e., gamma_crit is calculated relative to the source rest frame).
Congrats - got that bit right.
My first comment is that I don't understand why the second criterion is even necessary; again, given that the first criterion is satisfied, there will always be *some* frame in which E >= E_crit, so I just figure out what the gamma is for that frame relative to the source rest frame, and say that that's the frame in which pairs will be created at rest. So if the first criterion is satisfied, the second must always be satisfied in some frame. Why then is the second criterion necessary?
Because, as discussed at length above, you got the first criteria wrong. The two criteria must be simultaneously met. Which amounts to nothing more than saying an E source must transform by the LT's into an applied E >= Ecrit in any vp's rest frame, for a minimum period of time in that frame given by HUP. For any given E value in say source rest frame, L minimum is thus set there. And vice versa. Minimum gamma factor for any vp's whizzing through in source rest frame is then set solely by E there according to gamma >= Ecrit/E. A no brainer combo.
I can see why you might want to use the second formula to predict, for example, what the initial current due to the virtual pairs would be in the source rest frame (since that will depend on the velocity of the created pairs), but why is it a criterion for determining whether breakdown can occur at all, given that the first criterion is satisfied?
The answer should by now be self-evident. And btw, I take it we agree transverse velocity of a created pair is an overall neutral mass flow, effecting the current along E only insofar as 'relativistic mass' of pair will be very high, making motion along E extremely sluggish as seen in source rest frame. In fact, as per discussion in #360, it implies many created pairs simply whiz right through without ever being collected by E source.
My second comment is that I can always meet the first criterion by making my capacitor plate separation large enough, given some limit on the E field I can produce at the plates.
And that error of understanding what L must be referring to invalidates the rest of your critique. Still, there is an issue regardless as per #360. While it's not simply a voltage V, but an an variant product |ExL| >= ~ 104V/cm.cm, it can be easily enough met. So the real task, once all the basic misunderstandings above are finally cleared away, is to figure out what is really going on and why. So far, no order of magnitude estimate of expected pair flux has been made. Could be typically so small as to go unnoticed. If QFT already has a pat answer making that moot, no-one here has so far offered it.
Assuming no pair creation near high-tension power lines etc., one conjecture might be to suppose that applied E somehow suppresses high gamma factor flux of vp's in source rest frame. Immediate problem with that is for a capacitor configuration, many high gammma vp's would be originating outside of appreciable applied E region, so subsequent reduction to gamma < gammacrit within E region implies weird electrodynamics indeed.
PeterDonis
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#377
Dec21-11, 11:56 AM
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Quote Quote by Q-reeus View Post
Clear by now surely that L is normal to applied E. And btw, just as clearly, relative velocity (re gamma factor) is also taken as normal to E, hence along the same axis as L.
Well, it's clear now that you've said so. So now my question is, how is L measured? Since it's normal to E, it isn't linked directly to something obviously physical like the distance between the capacitor plates. So how is L measured?
Q-reeus
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#378
Dec21-11, 01:19 PM
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Quote Quote by PeterDonis View Post
Well, it's clear now that you've said so. So now my question is, how is L measured? Since it's normal to E, it isn't linked directly to something obviously physical like the distance between the capacitor plates. So how is L measured?
In #338 the specific example was a cap measuring 1cm x 1cm area. The characteristic length L is 1cm. Naturally for some different geometry a different L would apply, and in certain situations that might be somewhat arbitrary (e.g. a spherical capacitor). In general L is to be referenced wrt direction of relative motion, and of course normal to applied E. A rectangular capacitor, out of the basic simplicity of the situation there, was an obvious model to work from re gedanken experiment. I should accept some blame for the ongoing confusion in that a diagram no doubt would likely have ended any doubts about what references to what. This has taken a very windy path, yes?


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