SR, LET, FTL & Causality Violation

[PeterDonis]

They only come in virtual pairs. I don't think you can consider virtual particles as spin 1/2 but a reference would help. All virtual bosons obviously don't have spin 1/2 and they are interchangeable with any virtual pair.
Real pairs of course do have spin 1/2.

Virtual electrons and positrons are spin 1/2, just like real ones. The fact that they are virtual particles doesn't affect their spin. Also, virtual bosons aren't "interchangeable" with virtual fermions; they are separate kinds of virtual particles, just as they're separate kinds of real particles. I'll try to find a reference, but AFAIK this is basic QFT; virtual particle states are described by the same kinds of fields as real ones, just off the mass shell (which means their energy and momentum don't satisfy the equations of motion); being on or off the mass shell doesn't affect spin, since spin has to do with a different set of symmetries (pure spatial rotations vs. pure boosts).

 

[PeterDonis]

Average lifetime of vp's is *not* frame dependent from vacuum pov - things look the same in every frame - same spectrum of vp's regardless.

<rest of post mainly along similar lines>

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. It's true that the virtual particle spectrum "looks the same" in every frame, but which particular modes of that spectrum get energy transferred into them from the source is *not* the same in every frame; it depends on the state of motion of the source.

What does "the vp spectrum looks the same in every frame" actually mean? A Lorentz transformation acts on the virtual pairs just like it does on everything else: if I pick out a particular virtual pair that is at rest in frame F, and I apply a LT, that particular pair will *not* be at rest in frame F'; it will have a much higher energy, and hence a much shorter lifetime. There will be some *other* pair that gets shifted by the LT into being at rest in frame F', so the totality of all the virtual pair field modes (since there are an infinite number) will look the same, including the *average* lifetime integrated over the infinite spectrum of vp modes.

So the lifetime of any *particular* virtual pair depends on which frame it is seen from; the higher the pair's energy in a given frame, the shorter its lifetime in that frame. So the pair with the *longest* lifetime in any given frame will be the pair which has minimum energy in that frame, which is the pair at rest in that frame. That will be the pair that is easiest for the field to turn into a real pair. But since we are dealing with a quantum phenomenon, there is some (smaller) probability of the field being able to turn a vp with higher energy in that frame into a real pair; when you average over all the modes, you get that the average lifetime of vp's is what determines E_crit, as the second paper you linked to says.

But again, that reasoning depends on the fact that we are applying E >= E_crit in the source's rest frame. Put another way, it depends on the fact that the field produced by the source does not affect the minimum energy required to create a vp. That is true in the source's rest frame (assuming that the field is a pure E field in that frame). But how do things look from a frame in which the source is moving? As I said in a previous post, in that frame the field is no longer a pure E field, so there will be a nonzero current in that frame due to the nonzero B field. That means the minimum energy of a pair in that frame, *given the field produced by the source*, is no longer just the pair rest energy; it is the pair rest energy plus the kinetic energy added by the current. Which in turn means that the average lifetime of pairs in a frame in which the source is moving is *smaller* than it is in the source's rest frame. So to calculate what the critical E field would be in *that* frame, we have to *increase* the required field strength in that frame to compensate for the reduced average lifetime.

Can you make sense of that position for the example of rotating hoops capacitor I gave in #318 (last paragraph)?

I haven't even considered it yet. One scenario at a time.

 

[Dale]

IMO discerning whether nonlinear QED qualifies as relativistic or not is maybe a theoretically debatable point but outside the scope of this thread's discussion or even this relativity subforum.

Linear QED certainly is, but I can't contribute to the theoretical debate beyond that. In any case, I think that the "handwaving" nature of the vacuum breakdown argument is rather absurd. This is something that simply needs to be calculated out rigorously.

 

[TrickyDicky]

Virtual electrons and positrons are spin 1/2, just like real ones. The fact that they are virtual particles doesn't affect their spin. Also, virtual bosons aren't "interchangeable" with virtual fermions; they are separate kinds of virtual particles, just as they're separate kinds of real particles. I'll try to find a reference, but AFAIK this is basic QFT; virtual particle states are described by the same kinds of fields as real ones, just off the mass shell (which means their energy and momentum don't satisfy the equations of motion); being on or off the mass shell doesn't affect spin, since spin has to do with a different set of symmetries (pure spatial rotations vs. pure boosts).

Read carefully what I wrote, I talked about exchange with virtual pairs, not individual virtual particles, hopefully you have previously seen a diagram of a virtual photon with a loop representing the virtual pair. I have never heard of a virtual electron or positron on their own in the context of QED and vacuum polarization. In this physical context virtual particles are considered to have 0 spin. You may choose to think of the virtual electrons and positrons in a virtual pair as having each spin 1/2 with different sign but the result is the same, the virtual pair has spin 0. Real, measurable electrons and positrons have spin 1/2 but fotunately for us they are not all paired, there are many more electrons than positrons otherwise the universe would be in real trouble.

 

[TrickyDicky]

I'll correct my initial statement so the subsequent argument is not necessary.

Also note that the hypothetical existence of an absolute frame would be compatible with a Lorentz invariant vacuum, the violation of LI would only pertain to REAL 1/2 spin particles.

 

[Q-reeus]

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.

Peter - you seem to have memory problems. Above is practically verbatim what you claimed in #321 - what did I demonstrate in #338 re that false reasoning? A specific setup chosen at whim, but it showed your position is simply not true. It should have been evident there that merely boosting to any higher gamma factor will not change the result. Seems you were not convinced. If you really need it, I can easily prove 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. No rocket science is required. Unless you want a fairly lengthy and messy but otherwise straighforward derivation presented, please concede and do not repeat the false reductio ad absurdum arguments of #321 and #352.

It's true that the virtual particle spectrum "looks the same" in every frame, but which particular modes of that spectrum get energy transferred into them from the source is *not* the same in every frame; it depends on the state of motion of the source.

Which means no more than: singling out any particular vp (particular mode in that frame), it transforms according to LT's. Sure - but askew of the real issue.

What does "the vp spectrum looks the same in every frame" actually mean? A Lorentz transformation acts on the virtual pairs just like it does on everything else: if I pick out a particular virtual pair that is at rest in frame F, and I apply a LT, that particular pair will *not* be at rest in frame F'; it will have a much higher energy, and hence a much shorter lifetime. There will be some *other* pair that gets shifted by the LT into being at rest in frame F', so the totality of all the virtual pair field modes (since there are an infinite number) will look the same, including the *average* lifetime integrated over the infinite spectrum of vp modes.

And that's my point; vacuum looks the same, acts the same, in any inertial frame (again - true only till breakdown condition). It follows that vacuum cannot care whether source of E is in motion or not in any frame - E is acting on the same vp spectrum regardless. The rest of your #352 gets back to minimum energy argument I dealt with many times earlier and showed were false (e.g. in #304,313,318).

There's a possible way out for both of us here, but only partially I suspect. While a frame dependent B field makes no contribution to the energy requirements of pair creation, it might just effectively act in another way as a frustration mechanism. In plasma physics it is well known that motion of plasma particles under crossed E and B static fields can lead to cycloidal drift in a direction normal to both. Without working out the details, maybe in a certain regime vacuum vp's are thus prevented from separating in sufficient time. It would at most be partial cycloidal motion, but maybe enough to make a substantial difference. That needs balancing though against the reduction in E_crit associated with relative motion that provides the B in the first place. This idea likely fails badly though when a system is just short of E_crit in source rest frame and needs just a mild velocity boost to exceed E_crit. Needs a closer look.
[On further thought, it would seem to afford effective suppression of breakdown current magnitude for large l, and large gamma where E/B ~ c, but not prevent breakdown as such]

 

[PeterDonis]

Peter - you seem to have memory problems.

I remember perfectly well what I wrote, but it's obvious that we are having communication problems. I suspect we are partly talking past each other; we use similar words but mean different things by them, and we describe things that are actually similar using very different words. Also, we are using English instead of math to express our ideas, which is much less precise. I'll make an attempt at fixing that below.

As an example of the communication problem, take this:

It should have been evident there that merely boosting to any higher gamma factor will not change the result.

Which is exactly what I've been saying all along: "boosting to a higher gamma factor", in the sense of making the source of the EM field move faster and faster, will not change the result: you will still need E > E_crit *in the source's rest frame*, regardless of the source's state of motion. And yet you are evidently disagreeing with me.

Seems you were not convinced. If you really need it, I can easily prove 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...Unless you want a fairly lengthy and messy but otherwise straighforward derivation presented...

I'll present my own below; it will not be "lengthy and messy", but will only take a few lines.

And that's my point; vacuum looks the same, acts the same, in any inertial frame (again - true only till breakdown condition).

And this is the key thing you missed from my post #352: once you turn on a source of an EM field, *the vacuum no longer looks the same in any inertial frame*. What the papers you linked to call "vacuum polarization" happens *as soon as you turn the field on*. What you are calling "breakdown" is not the *start* of the polarization: it's the point at which the polarization gets strong enough to make virtual pairs into real ones.

But that's all English again; here's the math. This is the breakdown condition, in covariant terms, for a single source such as a capacitor:

$$F_{ab} u^{a} e^{b} >= E_{crit}$$

where $F_{ab}$ is the EM field tensor, $u^{a}$ is the source's 4-velocity, $e^{b}$ is the spacelike 4-vector that defines the orientation of the source (for example, if the source is a capacitor it points in the direction normal to the plates, from one plate to the other), and $E_{crit}$ is defined purely in terms of physical constants, as in the first paper you linked to. (Btw, in so far as any "properties of the vacuum" affect the result, they do so purely through their contribution to $E_{crit}$. This includes any effect of "minimum duration", as I said before.)

The LHS of the above equation is a scalar invariant; i.e., you can compute it using the components of $F_{ab}$, $u^{a}$, and $e^{b}$ in any frame you like, and it will give the same result, a number. Call that number $E_{0}$. Then we can re-write the above, for additional clarity, as

$$F_{ab} u^{a} e^{b} = E_{0} >= E_{crit}$$

Since we can calculate the invariant in any frame, I'll pick the easiest one: the source's rest frame. In that frame, the components of all three geometric objects are simple. $F_{01} = - F_{10} = E_{0}$, with all other components of the EM field tensor zero. $u^{0} = 1$, with all other components of the source 4-velocity zero. And, if we define the "x" axis of the source rest frame as the one along which the source is oriented (which we can do without loss of generality), then $e^{1} = 1$, with all other components of the orientation vector zero. Compute the contraction of these three objects and you will obtain $E_{0}$.

Now in a frame where the source is moving, the computation won't be as simple. But it will still give the same final answer. Apply the same Lorentz transform to $F_{ab}$, $u^{a}$, and $e^{b}$, and then contract the transformed objects; the result will still be $E_{0}$. So the covariant expression above is the precise way of saying what I've been saying all along, that E > E_crit *in the source's rest frame* is the correct breakdown criterion.

 

[harrylin]

Oh, no. I just perceived you might be saying quantum relativistic mechanics is exactly the same thing as QFT.
IMO discerning whether nonlinear QED qualifies as relativistic or not is maybe a theoretically debatable point but outside the scope of this thread's discussion or even this relativity subforum.

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).

 

[PeterDonis]

Read carefully what I wrote, I talked about exchange with virtual pairs, not individual virtual particles, hopefully you have previously seen a diagram of a virtual photon with a loop representing the virtual pair. I have never heard of a virtual electron or positron on their own in the context of QED and vacuum polarization. In this physical context virtual particles are considered to have 0 spin.

Yes, the *pair*, considered as a single quantum system, has zero spin; it has to, by conservation of angular momentum. Although I suppose, since we're dealing with virtual particles that can violate conservation laws within the limits of the uncertainty principle, that there could also be virtual particle states where the spins of the electron and positron were parallel instead of antiparallel, so the pair as a whole would have spin 1 instead of spin 0. I haven't really seen a good discussion of this in a reference.

You may choose to think of the virtual electrons and positrons in a virtual pair as having each spin 1/2 with different sign but the result is the same, the virtual pair has spin 0.

The *pair* does. But the individual electron and positron each have spin 1/2; the pair as a whole has spin 0 because the two spins are antiparallel (at least, in what I think would be the usual case--see above). So the pair as a whole being spin 0 *depends* on each of the individual particles being spin 1/2 and on the spins cancelling--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.

 

[Q-reeus]

Which is exactly what I've been saying all along: "boosting to a higher gamma factor", in the sense of making the source of the EM field move faster and faster, will not change the result: you will still need E > E_crit *in the source's rest frame*, regardless of the source's state of motion. And yet you are evidently disagreeing with me.

That's because you are not saying the same thing as me at all. I accept you think we are just talking past each other, but not so. Your criteria is simply E >= E_crit in source rest frame - period. The scalar invariant you express later in #357 follows from that imposed condition. Whether source of E there is a micron or a million miles long is irrelevant in such a view. Your statement further down "This includes any effect of "minimum duration", as I said before." is true only in the limited sense that, with the source rest frame E >= E_crit imposed, LT's naturally determine a frame dependent vp 'duration' that will be [STRIKE]less[/STRIKE] greater seen in another frame, as will E there - offset by a higher vp energy (thus inertia) seen there. That invariance recipe seems right because there is no 'moving observer causes physics' paradox. 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. [And btw, it's still ok to accept my request to apply your position to the rotating hoops (or annulus pair) capacitor scenario I gave in #318 (oh yeah, that Xmas present can still be yours).]

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), something quite different. That perspective that matters is that of vp's in their rest frame. Which in turn means that a source must have a minimal product of apllied E *and* length normal to E, measured in any given frame, before, seen in any other inertial frame, a 'rest' vp pair will receive a minimal impulse capable of boosting to real status. And then only if E >= E_crit in that vp 'rest' frame, or alternately where gamma factor of any vp pair passing through in source rest frame yields the equivalent. This criteria is very different from demanding E >=E_crit in source rest frame. On that basis it remains the case your reductio ad absurdum argument that immediately upon switching on any source of E breakdown should occur is wrong. 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.

Our criteria are thus fundamentally different - if nothing else on an elementary dimensional analysis level. For you, the source E 'does all the energy pumping'. For me, it is often the inherent KE of relative lateral motion (vacuum vp spectrum alone can provide that) that mostly 'does the pumping' - applied E has more the role of catalyst. Yes the E source discharges when breakdown current flows, but the source power drain per vp-pair->rp-pair creation is vastly different depending on relative motion of source. From my outlook there is a transverse energy budget that cannot be ignored. In past entries I have argued that transverse energy is a result of KE energy pumped into gross motion of the source making it move relative to the underlying local LET rest frame. But some more thought and it becomes obvious there are relevant transverse motions omnipresent and inherent in vacuum as vp 'sea'.

But this leads up to my new outlook. A logical conclusion from M = |E|*|l|>= ~ 10⁴ (v/cm)cm is that there must be some breakdown occurring just having a high voltage structure sitting around with such a perfectly achievable parameter mix. Why? Courtesy of the vacuum. We all agree vp spectrum is frame invariant. This immediately requires that in any frame there must be a finite ultra-relativistic random flux component of vp's, and some fraction will be exceeding breakdown criteria merely by passing between the plates of a suitably dimensioned and charged capacitor in the right directions. Some will strike the plates, some will simply pass through as newly created ultra-relativistic real pairs - subsequently smashing into say air molecules, or recombining to produce a presumably faint but finite ultra-high energy gamma-ray flux. The latter in particular seems disturbing because there is no evident energy drain from the E source involved at all. The vacuum itself seems to provide all the 'oomph' needed there. My own 'magnetic suppression' counter-argument in #356 cammot be germaine I think because seen in source rest frame, a high gamma factor vp passing through and elevated to real status simply executes an ever so slightly parabolic path; that's all.

Bizarre as that seems, imo above is the logical conclusion if the vacuum vp picture we have been working from is true. Somehow I doubt gamma rays emanating from certain electrostatically charged structures would have gone undetected till now, so not rushing to patent a 'free-energy-from-vacuum' device. After all the vacuum is generally believed to have either precisely or next to zero real energy density - despite the notorious ~ 10¹²⁰ order of magnitude problem.

Upshot is my new perspective renders prior arguing for LET over SR on vacuum breakdown criteria sort of moot. If there is a top notch QFT expert here that can knock the above on it's head - please step up now. Otherwise, maybe someone can pick the above matter up, wrap it a bit differently, and run it under their own banner on another thread. So be it. I'd rather end this windy-twisty saga on that note.

 

[TrickyDicky]

.
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]

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]

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.

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]

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 E_crit. Or - gamma rays exit from high-tension power lines etc.! (very unlikely).

 

[PeterDonis]

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?

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 E_crit. 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]

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 -> E_crit 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]

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?

 

[Dale]

This is the breakdown condition, in covariant terms, for a single source such as a capacitor:

$$F_{ab} u^{a} e^{b} >= E_{crit}$$

Do you have a reference or derivation for this? If so, it seems pretty clearly covariant.

 

[PeterDonis]

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 -> E_crit 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?

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]

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]

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?

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]

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 >= E_crit 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 > E_crit 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 >= E_crit 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 >= E_crit/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 >= E_crit applies. Source parameters then gaurantee that E_crit 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]

Yes there can be an E > E_crit in some other frame 'immediately upon switch-on', but that alone is *not* sufficient.

Of course not. I was not arguing that it was.

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?

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.

Further, as E >= E_crit 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 >= E_crit/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.

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 >= E_crit 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]

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.

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).

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 https://www.physicsforums.com/showthread.php?t=561128 where that author is quoted.

 

[harrylin]

Yes, see also the thread https://www.physicsforums.com/showthread.php?t=561128 where that author is quoted.

OK

 

[Q-reeus]

[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]

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 >= E_crit, 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 >= E_crit 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 >= E_crit/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 < gamma_crit within E region implies weird electrodynamics indeed.

 

[PeterDonis]

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]

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?

 

[PeterDonis]

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.

Ok, this is reasonably concrete. Probably a good way to state the criterion with reasonable generality would be that "L" is some constant (of order unity, presumably) times the square root of the area of the source normal to E. That generalizes the square capacitor to rectangular (just take the area of the rectangle), and even the spherical (just take the square root of the area of a characteristic sphere, say one halfway between the inner and outer spherical plates).

But you do realize, of course, that this criterion is open to a fairly similar objection to those I've made before? I do agree that this criterion will not automatically be satisfied in some frame as soon as the field is turned on; in that respect, my past objections were incorrect. But take the case of a parallel plate square capacitor with area A and hence L = k sqrt(A), where k is some dimensionless constant of order unity. The E field inside the capacitor is simply V / D, where V is the applied voltage and D is the distance between the plates. So your breakdown criterion E * L >= 10^4 becomes

$$V = 10^4 k \frac{L}{D}$$

which is easy to satisfy. Capacitors with voltages of 10,000 V exist, and a typical square or rectangular capacitor will have L / D ratios greater than one (i.e., typically the average length of a plate is larger than the plate separation). So again, it should be easy to make electrons and positrons in the laboratory. Since it isn't, I don't see how your criterion can be made to work as you state it.

The only possible way out would be to make the constant k very large [edit: wrote "small" originally but I meant "large", as it needs to make the required V larger in the above] instead of order unity. Since k needs to be dimensionless, and presumably should be a function only of physical constants (i.e., it should not depend on characteristics of the source), the possibilities are limited; there aren't many ways to make dimensionless ratios out of the small menu of physical constants that would seem to be relevant, basically the charge on the electron, Planck's constant, and the speed of light. The simplest such constant is the fine structure constant, but that's of order 10^-2; k would have to be some high inverse power [edit: left out "inverse" originally] of the fine structure constant, which would open up the question of why it has to be such a high power.

This has taken a very windy path, yes?

Yes, it has, but I wouldn't say it's a matter of "blame". Communication is difficult; we try our best but sometimes it takes time.

 

[Q-reeus]

...Communication is difficult; we try our best but sometimes it takes time.

Absolutely, and I have hopefully learned a bit from all this re tightening of specifications. Peter - thanks for at the least pursuing this matter at length. Trust we both agree the focus is now far removed from the original intent which related to showing a means for distinguishing LET from SR. So I propose ending discussion here, and will formulate this anew and probably post in QM section when ready. You are welcome to join in there if you wish.

 

[PeterDonis]

So I propose ending discussion here, and will formulate this anew and probably post in QM section when ready. You are welcome to join in there if you wish.

I'll look for it.