SR, LET, FTL & Causality Violation

[PeterDonis]

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.

Before ionization, yes. But the energy transfer you were talking about (from the KE of gas flow to the plates) happens *after* ionization, because it's only after ionization that the gas is moving towards the plates at all! (Before ionization the gas flow is entirely parallel to the plates.) Where does the KE that the ions pick up, and deposit in the plates, come from? From the E field of the capacitor. Where else?

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.

You're mixing frames. In the gas rest frame, there is no "gross flow velocity" v. There is only the velocity v', perpendicular to v, that is caused by the E field of the capacitor when ionization occurs. I assume what you are trying to say is that this velocity v' causes a Lorentz force that is directed parallel to the plates. But since this Lorentz force is parallel to the plates, it has no effect on the momentum transfer normal to the plates.

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.

No, these are different processes. The ionically bonded molecules are bound states; the E field has to supply the binding energy to convert them into free states (more precisely, to move an electron from each molecule from a bound state to a free state, leaving behind an ion, which still has other electrons in bound states but can be viewed overall as a free particle).

The virtual pairs in vacuum are not bound states; they are free particle states with an average energy of zero (one particle of each pair has positive energy, one has negative energy). The E field has to supply the rest energy of a pair to make it real; that doesn't involve breaking any bonds or dissociating anything or driving particles from one state to another. It's just pumping energy into a state that starts out with zero energy.

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?

No, because your analogy fails.

The main gist is it's ok to roughly model vacuum breakdown, energetics wise, in analogy to gas breakdown.

No, it isn't. The link you provided is behind a paywall, so I can't read it. The abstract doesn't tell me anything useful except that it's talking about quantum field theory.

one might as well say dielectric breakdown has nothing to do with the dielectric!

I didn't say anything of the kind. I did not say the breakdown has nothing to do with the vacuum; I said that since there is an obvious ponderable medium present, the field source, it makes no sense to analyze the phenomenon as though that object wasn't there.

Dielectric/vacuum *plus* acting E -> breakdown.

No, vacuum plus acting E plus *source* of E -> breakdown. You can't have the E without a source for it. Therefore the properties of the source are relevant for analyzing the phenomenon. Again, why is this so hard to understand?

Opaque dielectric screens intervene between an observer and some source of static E. 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.

But different B--zero in one case, nonzero in the other. Easy to detect. But of course...

the B field present in the second case can either be ignored or exactly canceled via stationary source of opposing B.

In other words, you're destroying the evidence that distinguishes one case from the other, then claiming that they're the same. I expect this of politicians, but not here on PF.

(Oh, and before you object that the B field is irrelevant to pair creation, see further comment below.)

"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.

So you think that, if the pairs are moving relative to the source, they will have *less* energy relative to the source? Have you actually read what I wrote? I did not say anything about whether the rest frame of the source has the largest E, smallest E, or whatever. What I said was, the created pairs have minimum energy in the rest frame of the source; therefore, for the source to supply minimum energy to the pairs, they must be created in the rest frame of the source.

The paper you linked to makes the same assumption; I've already made that clear by pointing out their equation #21, which says that the time rate of change of the electric field is proportional to the current. By Maxwell's equations, that can only be true if the B field is zero; and the only frame in which the EM field of any source can be a pure E field, with no B, is the rest frame of the source. So the paper you linked to agrees with me that the pairs are created in the rest frame of the source. Do you think the paper is wrong?

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'.

Ecrit must be defined relative to a frame; the E field alone is not Lorentz covariant (only the full EM tensor is). Which frame do you think Ecrit is defined relative to, if it isn't the source's rest frame? (This question, btw, illustrates why you can't just ignore the B field. Yes, it has no direct effect on pair production because the B field can't pump any energy into the pairs, but it is certainly relevant in forming a properly Lorentz covariant description of what is going on. Ignoring the B field is basically pretending that the E field is covariant when it isn't.)

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

I'll take a look.

 

[PeterDonis]

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

Interesting paper. It does force me to concede one thing: I was only considering single sources of the E field, which is a limited case that may not fully explore the phenomenon. (The paper you linked to earlier focused on this case, which is why it stuck in my mind.) This paper shows that strong fields can be created by overlapping the fields from multiple sources (in this case, lasers and high energy electrons). This does change the game in some respects, since what is meant by "the rest frame of the source", as I was using the term, is no longer clear.

As far as the "temporal influence" on the process, the paper does indeed make that clear: the temporal influence is not separate from Ecrit, it is what *determines* Ecrit. Equations #5 and #6 in the paper show this. Basically, what these equations and the discussion surrounding them are saying is that virtual particles have an average "lifetime" determined by the uncertainty principle; the strength of the E field determines how fast the field can pump energy into the virtual particles; so in order for the field to pump enough energy into them to make them real, it has to exceed a critical value that depends on the average lifetime of the particles. (The paper also makes clear why the B field doesn't contribute: it does no work on the virtual particles, so it can't add any energy to them.)

Now for that bit about frames. Right before equation #10 in the paper, it says:

"As written, $\Upsilon$ is not Lorentz invariant since the electric field depends on the frame of reference in which it is viewed. Thus Eq.(4) should be expressed in terms of E*, the electric field in the rest frame of the produced pair"

However, equation #10, which immediately follows, looks like it has a typo; it appears to give two contradictory equations for E*, one that doesn't contain the Lorentz gamma factor and one that does. Based on the text just quoted, I think the correct form of equation #10 is this:

$$\Upsilon = \frac{E*}{E_{c}} = \gamma_{cm} \frac{E}{E_{c}}$$

It would be nice if someone much more expert than me in this area could check this, though.

But now the question arises, how is the Lorentz gamma factor on the RHS determined? If there were only two frames in the experiment (the frame in which the pair is created at rest, and the "lab" frame), it would be simple: the gamma factor is just that between the two frames. But looking at Figure 1 in the paper, which shows the experimental setup, I see *three* possible frames of reference in this experiment, not two:

(F1) The frame in which the pairs are created at rest;

(F2) The frame in which the experimental apparatus is at rest;

(F3) The frame in which the high energy electrons in the beam that interacts with the lasers are at rest.

Which two of these three frames are to be compared to get the gamma factor? Based on looking further on, at equation #16 and the discussion around it, it's possible that the answer is "none of the above". The discussion talks about the interaction of the high energy electrons with the laser field, which creates an E field that, viewed from the electrons' rest frame, is close enough to E_crit to have observable effects. But then they say that the breakdown is actually induced by scattering a high energy gamma ray photon through the laser field, and equation #16 gives a formula for the gamma factor that is basically the ratio of the energy of the gamma photon to the average energy of the laser photons--the electron properties don't appear at all (except that the paper notes later on that the high energy gamma photons are produced by back-scattering from the electrons in the laser field). Essentially this is saying that the frame F1 above, in which the pairs are created at rest, is the frame in which the gamma ray photon has the same energy as four laser photons do in the lab frame. (The factor of 4 is based on how many photons need to be absorbed to create a pair.) This is close to F3, the rest frame of the high energy electrons, but not quite the same.

Another thing that is not clear from the paper is the role of conservation of momentum in all this. In frame F1, the momentum of a pair when it is created is zero; so whatever photons are absorbed by the virtual particles to give them enough energy to become real particles must also have a net momentum of zero. The paper appears to indicate that those photons are absorbed from the laser field, but the laser photons are set up, as far as I can tell, to have zero net momentum in the *lab* frame, F2. This indicates that what actually has to happen to induce breakdown is that a gamma ray photon has to also be absorbed by the virtual particle pair being converted to a real pair; that photon's momentum, since it is backscattered by the electron in the laser field, should be opposite to that of the laser photons. However, the photon energies are very different, meaning the magnitudes of their momenta are also very different, so I'm not sure how this can work.

Bottom line, I don't think I can say right now what this experiment tells us about how the frame F1 is determined. As I said above, it would be nice if someone more expert than me in this area could weigh in.

 

[Q-reeus]

Q-reeus: "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."
Before ionization, yes. But the energy transfer you were talking about (from the KE of gas flow to the plates) happens *after* ionization, because it's only after ionization that the gas is moving towards the plates at all! (Before ionization the gas flow is entirely parallel to the plates.) Where does the KE that the ions pick up, and deposit in the plates, come from? From the E field of the capacitor. Where else?

Mixing up issues - transverse motion/energy inherent in gas flow, vs normal motion under applied E. Chalk and cheese. Dissociation allows the transfer of transverse energy/momentum, but adds nothing to it.

Q-reeus: "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."
You're mixing frames. In the gas rest frame, there is no "gross flow velocity" v.

I did make a sign error there that suggested mixing of frames; should have read B = -vxE, the -v referring to plate motion wrt gas frame.

There is only the velocity v', perpendicular to v, that is caused by the E field of the capacitor when ionization occurs. I assume what you are trying to say is that this velocity v' causes a Lorentz force that is directed parallel to the plates. But since this Lorentz force is parallel to the plates, it has no effect on the momentum transfer normal to the plates.

(I made an error of omission; should have read F = e(v'xB)). Yes of course it has (virtually) no effect on normal momentum. More importantly, it has precisely zero effect on energy exchange associated with motion along E - which is quite my point! Electrostatic energy gain of a pair, in the stationary capacitor frame, is simply the path independent integral of E.dl, for each of the pair, from point of creation to point of 'absorption' on the plates, and has nothing to do with the matter of tangent momentum/energy transfer going on.

The virtual pairs in vacuum are not bound states; they are free particle states with an average energy of zero (one particle of each pair has positive energy, one has negative energy). The E field has to supply the rest energy of a pair to make it real; that doesn't involve breaking any bonds or dissociating anything or driving particles from one state to another. It's just pumping energy into a state that starts out with zero energy.

In both cases a threshold energy and associated applied E is involved. In both cases that threshold E will according to the LT's be less in the E source frame if either molecule or vp pair has transverse relative motion. In that context I therefore see apt similarity not fundamental difference.

No, it isn't. The link you provided is behind a paywall, so I can't read it. The abstract doesn't tell me anything useful except that it's talking about quantum field theory.

My apologies. It was freely downloadable and when posting the link I didn't bother to check it's current status. AccessScience might be better titled "OccasionallyFreeAccessScience". Just one interesting passage from that, dealing specifically with supercritical nucleii:
"Clearly, the charged vacuum is a new ground state of space and matter. The normal, undercritical, electrically neutral vacuum is no longer stable in overcritical fields: it decays spontaneously into the new stable but charged vacuum. Thus the standard definition of the vacuum, as a region of space without real particles, is no longer valid in very strong external fields."

For me this is the clue: The normal vacuum exhibits symmetries that completely hide any evidence of a preferred frame, but breakdown destroys that symmetry - detection of a preferred frame is now feasable. Admittedly it is a somewhat nebulous assertion, but your alternative, standard position entails worse assumptions imo. But as mentioned many times before, minimum duration and thus source geometry ensures it's not as simple as just the vacuum responding to an E referenced to a nominal local preferred rest frame (one presumes CMBR).

I didn't say anything of the kind. I did not say the breakdown has nothing to do with the vacuum; I said that since there is an obvious ponderable medium present, the field source, it makes no sense to analyze the phenomenon as though that object wasn't there.

Accept that point, but let me quote you from #281:"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.". That sort of prepped me.

(Oh, and before you object that the B field is irrelevant to pair creation, see further comment below.)

By any usual reasoning that is the case. But it may be there is some weird QFT reason a B field could suppress pair production except in source rest frame. Hard to see how though! Can you offer a theory?

Q-reeus: "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."
So you think that, if the pairs are moving relative to the source, they will have *less* energy relative to the source?

No and you misunderstand. Of course I agree that if the perspective is purely one of 'pumping' vp's to real status in source rest frame, there is minimum net energy if the pair com is stationary. But that need not be the whole picture. More later.

Have you actually read what I wrote? I did not say anything about whether the rest frame of the source has the largest E, smallest E, or whatever. What I said was, the created pairs have minimum energy in the rest frame of the source; therefore, for the source to supply minimum energy to the pairs, they must be created in the rest frame of the source.

Have understood that as your position for quite some time and have explicitly said so previously. Naturally I disagree with it, but that's nothing new here.

Ecrit must be defined relative to a frame; the E field alone is not Lorentz covariant (only the full EM tensor is). Which frame do you think Ecrit is defined relative to, if it isn't the source's rest frame? (This question, btw, illustrates why you can't just ignore the B field. Yes, it has no direct effect on pair production because the B field can't pump any energy into the pairs, but it is certainly relevant in forming a properly Lorentz covariant description of what is going on. Ignoring the B field is basically pretending that the E field is covariant when it isn't.)

I don't want to seem impertinent but this position strikes me as the result of relativist 'brainwashing' of sorts. Everything has to be covariant/invariant or it's nothing of use. What's the matter with accepting the possibility that frame dependent 'variants' like good old E could play a critical role here? I mean E.B or (E² - B²) are invariants, but what actually induces breakdown? As stated clear back in #285:
"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."

So here's my necessarily somewhat wooly synthesis that deals with your key position: energy minimization for pair production demands E_crit is referenced to source rest frame. Just allow for now the possibility of an underlying preferred frame (or rather an infinity of such each defined locally by the CMBR). In a perfectly homogenous BB universe, everywhere matter is at rest wrt the local preferred frame. But we know that gravity + quantum fluctuations has led to the lumpy universe we see, and that includes local velocities like our apparent ~370 km/s motion wrt CMBR. Suppose in our frame we induce vacuum breakdown inside of a long coax capacitor oriented in that 370 km/s drift direction. Suppose as per above this represents vacuum symmetry breaking - Lorentz symmetry no longer necessarily holds and we have 'tapped into' the underlying preferred frame. We are shocked to find the breakdown current is not perfectly uniform and normal to the coax axis but has a certain drift speed component along the axis. Where would the extra energy come from to account for that? From the universe of course. Gravity acting over time catapulted our local galactic neighbourhood to a 370 km/s relative motion. The axial drift is merely tapping into that energy in a small way. So no big deal really. Transverse energy budget accounted for. And to boot, has made breakdown just slightly easier. This all assumes source geometry is such that duration is not an issue. More on that below.

Finally (I hate these mega posts!), another scenario to contemplate. Consider the case of a very long strip parallel plate capacitor, bent around on itself to form a pair of circular hoops. We set it in spinning motion to relativistic speed, and apply a large voltage between the plates. Mechanical stresses of rotation can be dealt with by making radius very large, and supporting the hoops via an outer guard ring etc. Anyway in this case duration is irrelevant and we find that there can be, in the local rest frame of a hoop element, an applied E well below E_crit, yet well above it in the non-spinning frame. The vacuum vp's should care not to respond to that situation? Get's back to that 'Turing test' thing. Supply a credible 'B field breakdown suppression' theory and I might take notice of your frame-linkage is all that matters position. Will respond to your interesting #317 when I can.

 

[PeterDonis]

I did make a sign error there that suggested mixing of frames; should have read B = -vxE, the -v referring to plate motion wrt gas frame.

I wondered about that; I was getting results that looked backwards with the positive sign.

I won't make any other comments about the gas flow scenario since it is irrelevant to the vacuum breakdown scenario, as I said before:

In both cases a threshold energy and associated applied E is involved. In both cases that threshold E will according to the LT's be less in the E source frame if either molecule or vp pair has transverse relative motion. In that context I therefore see apt similarity not fundamental difference.

In other words, they look superficially the same, so they must be the same. Not so.

"Clearly, the charged vacuum is a new ground state of space and matter. The normal, undercritical, electrically neutral vacuum is no longer stable in overcritical fields: it decays spontaneously into the new stable but charged vacuum. Thus the standard definition of the vacuum, as a region of space without real particles, is no longer valid in very strong external fields."

Which is just another way of saying that the field pumps energy into the virtual particles and turns them into real ones. All the stuff about "new ground state", "undercritical", "overcritical", etc. is just jargon to make it sound more impressive. And calling it a "new ground state" when it obviously has more energy than the original vacuum state is not, IMO, a very good choice of words; in cases of spontaneous symmetry breaking, such as superconductivity or the electroweak phase transition in the early universe, the new "ground state" always has *lower* energy than the original one did. Also, spontaneous symmetry breaking happens without any external field being applied; that's why it's called "spontaneous".

So from what I'm reading here it looks like the authors are trying to draw an analogy with a "hot" area of physics that isn't really justified. Without seeing the actual details in the paper I can't tell whether these authors are just making unfortunate word choices in their abstract, or whether it's something else.

But as mentioned many times before, minimum duration and thus source geometry ensures it's not as simple as just the vacuum responding to an E referenced to a nominal local preferred rest frame (one presumes CMBR).

Oh, so the source geometry is relevant? I thought you said the source could be ignored, since only the E field itself mattered.

By any usual reasoning that is the case. But it may be there is some weird QFT reason a B field could suppress pair production except in source rest frame. Hard to see how though! Can you offer a theory?

Why should I? I haven't said the B field suppresses pair production. I said it has no effect on it one way or the other.

I don't want to seem impertinent but this position strikes me as the result of relativist 'brainwashing' of sorts. Everything has to be covariant/invariant or it's nothing of use. What's the matter with accepting the possibility that frame dependent 'variants' like good old E could play a critical role here?

The E field does play a role; I never said it didn't. All I said was that whatever role it plays, must be capable of being expressed in covariant terms. I never said that was the *only* way to express it, or even the most useful way. It just has to be *possible* to express things that way. Otherwise the results of an experiment that I run would be dependent on your state of motion, when you are not interacting with my experiment in any way, which is absurd.

"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."

Because it's not *just* the E field. Both papers you have cited make that perfectly clear: they explicitly state (I've given you the quotes) that it is the E field in the frame in which the pairs are created at rest that is crucial. The first paper also makes it clear that, in their scenario, the frame in which the pairs are created at rest is also the rest frame of the E field source (since the field is pure E field in that frame). The second paper uses multiple sources, and as I said in my last post, it's not clear to me how the frame in which the pairs are created at rest is determined in their experiment. But whatever frame it is, it has a 4-velocity as its timelike basis vector, and contracting the EM field tensor with that 4-velocity gives the electric field vector that must be compared with E_crit to determine when breakdown occurs. In other words, the breakdown criterion *can* be stated in covariant terms; I just did it. That's all I am saying must be the case.

So here's my necessarily somewhat wooly synthesis that deals with your key position: energy minimization for pair production demands E_crit is referenced to source rest frame.

*If* that is the frame in which the pairs are created at rest. In your first paper, as I said just now, that is certainly the case. It's not entirely clear in the second, since there are multiple possible "sources" in relative motion. But I remark that *if* you are correct, then there is, as I said before, an obvious "ponderable object" that is picking out the "preferred frame"; i.e., the source has a 4-velocity, so it's now obvious that that is the 4-velocity we use to contract with the EM field tensor to determine the E field that gets compared to E_crit. And again, that is *all* I am saying is required to be consistent with SR.

So here's my necessarily somewhat wooly synthesis that deals with your key position...Finally (I hate these mega posts!), another scenario to contemplate...

I can't really comment on these since it all seems like handwaving to me. You're not making predictions from any kind of actual theoretical model that I can see. In particular, I don't see what criterion you're applying to predict what the observed breakdown threshold E field will be in which frame. But I need to think about this some more.

One note on "duration", though: as I noted in a previous post, the second paper you linked to makes it clear that duration is what *determines* E_crit; the virtual particles have an average lifetime, and the E field strength determines how fast energy is pumped into the particles. So E_crit is the value at which, on average, the field pumps energy into the particles just fast enough to supply their rest mass energy in their average lifetime.

Get's back to that 'Turing test' thing. Supply a credible 'B field breakdown suppression' theory...

Irrelevant; I was merely pointing out that *you* were forbidding me to use the B field as evidence, and then claiming that both of your scenarios were the same when the difference could obviously be detected by using the B field. Doing that in no way requires that the B field have any direct effect on breakdown; it just requires that it be detectable, so I can know the entire EM field tensor instead of just the E field component.

...and I might take notice of your frame-linkage is all that matters position.

Where have I taken such a position? You seem to be persistently misunderstanding what I am saying. Please read my comments in this post carefully, particularly those about what is and is not required by SR with regard to covariant descriptions of things.

 

[Q-reeus]

Which is just another way of saying that the field pumps energy into the virtual particles and turns them into real ones. All the stuff about "new ground state", "undercritical", "overcritical", etc. is just jargon to make it sound more impressive. And calling it a "new ground state" when it obviously has more energy than the original vacuum state is not, IMO, a very good choice of words; in cases of spontaneous symmetry breaking, such as superconductivity or the electroweak phase transition in the early universe, the new "ground state" always has *lower* energy than the original one did. Also, spontaneous symmetry breaking happens without any external field being applied; that's why it's called "spontaneous".

They argue on the basis of an overall balance that includes spontaneous positron emission (from the electron/positron pair creation). Could be hype s'pose, but maybe chase up their cv's etc. Sorry but I had better not post more here and risk an infringement notice!

"But as mentioned many times before, minimum duration and thus source geometry ensures it's not as simple as just the vacuum responding to an E referenced to a nominal local preferred rest frame (one presumes CMBR)."
Oh, so the source geometry is relevant? I thought you said the source could be ignored, since only the E field itself mattered.

No from the start always maintained it's not just E, but on an entirely different basis to your one.

...I haven't said the B field suppresses pair production. I said it has no effect on it one way or the other.

Could have fooled me; from #316: "(Oh, and before you object that the B field is irrelevant to pair creation, see further comment below.)"
Could not find any continuation there relating to B, though.

"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."
Because it's not *just* the E field. Both papers you have cited make that perfectly clear: they explicitly state (I've given you the quotes) that it is the E field in the frame in which the pairs are created at rest that is crucial. The first paper also makes it clear that, in their scenario, the frame in which the pairs are created at rest is also the rest frame of the E field source (since the field is pure E field in that frame). The second paper uses multiple sources, and as I said in my last post, it's not clear to me how the frame in which the pairs are created at rest is determined in their experiment. But whatever frame it is, it has a 4-velocity as its timelike basis vector, and contracting the EM field tensor with that 4-velocity gives the electric field vector that must be compared with E_crit to determine when breakdown occurs. In other words, the breakdown criterion *can* be stated in covariant terms; I just did it. That's all I am saying must be the case.

But it carries baggage; once one decides source rest frame is 'the' determinant for E_crit, of course covariant expression follows. But it follows from your energy creation argument, which as said umpteen times before, implies vacuum 'knows' not to respond to higher E fields seen in other frames.

I can't really comment on these since it all seems like handwaving to me. You're not making predictions from any kind of actual theoretical model that I can see. In particular, I don't see what criterion you're applying to predict what the observed breakdown threshold E field will be in which frame. But I need to think about this some more.

Here's both hands waving: If frame is preferred frame, regardless of E source geometry, breakdown is at a maximum value E_crit, and the current shows no directional bias. In another frame moving at a gamma factor wrt the preferred frame, breakdown field is E_crit/gamma, provided source configuration and orientation is such minimum duration (referenced to preferred frame) is well exceeded. Otherwise detailed calcs are in order.

"Get's back to that 'Turing test' thing. Supply a credible 'B field breakdown suppression' theory..."
Irrelevant; I was merely pointing out that *you* were forbidding me to use the B field as evidence, and then claiming that both of your scenarios were the same when the difference could obviously be detected by using the B field. Doing that in no way requires that the B field have any direct effect on breakdown; it just requires that it be detectable, so I can know the entire EM field tensor instead of just the E field component.

I said at the start of TT bit that only E was to be relevant to test, but later threw in the bit about B anticipating your objections. And now it is turned around on me! You agree (here) that B has no influence on breakdown - then please agree TT is relevant to what matters - one E is as good as another E regardless of source motion. And I say the vacuum feels that way - it breaks down in that frame where E is maximum and minimally sustained. Rotating hoops capacitor 'hand-waves' that matter clearly enough imo. You can explain clearly why breakdown would *not* occur in non-rotating frame, rather than refuse coz in rotating frames E is less than E_crit? Oh, I forgot, the vacuum has no say.

"...and I might take notice of your frame-linkage is all that matters position."
Where have I taken such a position? You seem to be persistently misunderstanding what I am saying. Please read my comments in this post carefully, particularly those about what is and is not required by SR with regard to covariant descriptions of things.

But imo you have many times now; over and over maintaining covariant description is inevitably referenced to source rest frame - the 'pure E frame' as where E_crit is defined. Need I cite a dozen or two passages? :zzz:

 

[PeterDonis]

"(Oh, and before you object that the B field is irrelevant to pair creation, see further comment below.)"
Could not find any continuation there relating to B, though.

I guess you missed this, then:

Ecrit must be defined relative to a frame; the E field alone is not Lorentz covariant (only the full EM tensor is). Which frame do you think Ecrit is defined relative to, if it isn't the source's rest frame? (This question, btw, illustrates why you can't just ignore the B field. Yes, it has no direct effect on pair production because the B field can't pump any energy into the pairs, but it is certainly relevant in forming a properly Lorentz covariant description of what is going on. Ignoring the B field is basically pretending that the E field is covariant when it isn't.)

The question I asked in that quote is relevant, as you will see.

But it carries baggage; once one decides source rest frame is 'the' determinant for E_crit, of course covariant expression follows. But it follows from your energy creation argument, which as said umpteen times before, implies vacuum 'knows' not to respond to higher E fields seen in other frames.

<rest of post basically along these same lines>

Let's take this argument of yours to its logical conclusion. I set up an E field source and turn it on. In the source's rest frame, the field is a pure E field in a single direction (say along the x-axis). Since I am saying that E must equal E_crit in the source's rest frame (well, actually it's the frame in which the pairs are created at rest, but I think we've established that for a single source this is the source rest frame--we'll leave aside the lasers and electron beams for a bit, but I'll come back to them below), I do not expect to see breakdown until I measure E = E_crit (we're assuming that I'm not moving relative to the source.)

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. But the only new assumption made is that the vacuum can "detect" E > E_crit in any frame. So that assumption must be false. This has been behind the arguments I've been making all along, but maybe it will seem more compelling now that I've stated it and the conclusion it leads to explicitly.

But if the assumption is false, then there must be *something* that constrains which frame the pairs can be created at rest in (or, equivalent, which frame the E > E_crit criterion can apply in). What is it? We've been grappling with this question for a number of posts, but I think I have a possible answer. Remember I commented above that the E field is only a static, pure E field in one frame, the rest frame of the source. (This is really the same as saying that the contraction of the EM field tensor with the source's 4-velocity takes a certain particular form, which is how I've stated it in previous posts.) What if *that* is the constraint? In other words, what if the pairs must be created at rest (i.e., E > E_crit) in whatever frame the EM field looks like a pure static E field?

Obviously this can't be completely right, because no real field source can produce an exactly static pure E field. Also, it doesn't cover the case from your second paper, with the lasers and high energy electron beams. But the condition can be generalized easily: the pairs will be created at rest in whatever frame *minimizes* the *B* field. More precisely, if the B field is zero in some frame, the pairs will be created at rest in that frame; if not, the pairs will be created with some minimum kinetic energy in whatever frame gives the B field its minimum value.

Which obviously raises the question, why is the B field relevant? One of the papers said the B field "does no work" on the pairs, but though that's true, it's not the whole picture. Consider what happens if a pair is created in motion instead of at rest. In that case, there will be a nonzero electric current due to the pair. But by Maxwell's equations, the current can only be nonzero if there is a nonzero B field; if B = 0, the current must be 0 as well. And if B is not 0, the current goes up as B goes up. That tells us two things: first, that a pair can *only* be created at rest in a frame with B = 0; second, that if B is not 0, the current will be minimized in the frame where B is minimized. And since the current equates to additional energy that must be supplied to the pair, the pair will be created with minimum energy in the frame where B is minimized.

 

[TrickyDicky]

What if *that* is the constraint? In other words, what if the pairs must be created at rest (i.e., E > E_crit) in whatever frame the EM field looks like a pure static E field?

Obviously this can't be completely right, because no real field source can produce an exactly static pure E field.

Unless there was a preferred rest frame, no?

the pair will be created with minimum energy in the frame where B is minimized.

Again, how is this not a preferred frame where physics is different, i.e. breakdown occurs only when is determined by this particular frame?

 

[PeterDonis]

Unless there was a preferred rest frame, no?

How does that make a difference?

Again, how is this not a preferred frame where physics is different, i.e. breakdown occurs only when is determined by this particular frame?

Because it isn't "determined by this particular frame". It's determined by the field configuration produced by the source. I really fail to see why this is so difficult for people to grasp. The source is a physical object. It has a particular 4-velocity. That 4-velocity defines a frame. In this frame, the field produced by the source will have properties that are correlated with the physical properties of the source, because the field is produced by the source. Calling this a "preferred frame" is like saying being at rest on the Earth is a "preferred frame" because the direction of "down" is determined by the Earth's gravity.

In the case of multiple sources, like the lasers and high energy electron beams, figuring out the field configuration is more difficult, but the principle is the same: you have actual physical objects that interact to produce a field, and the field's properties are determined by the interactions, which include the states of motion of the objects. One of those field properties is that there will be some state of motion, some "frame", in which the B component of the field is minimized; which state of motion that is is determined by the states of motion of the things that interact to produce the field.

 

[TrickyDicky]

How does that make a difference?

Because in the putative case an absolute frame existed, a source at rest in that frame would have a "pure" electric field.

 

[PeterDonis]

Because in the putative case an absolute frame existed, a source at rest in that frame would have a "pure" electric field.

Why? A pure electric field is certainly not the only possible kind of field. Why would it be the one that a "preferred" frame would pick out?

 

[TrickyDicky]

Why? A pure electric field is certainly not the only possible kind of field. Why would it be the one that a "preferred" frame would pick out?

By definition in an absolute static frame you get an absolute (pure) static E field.

 

[PeterDonis]

By definition in an absolute static frame you get an absolute (pure) static E field.

In a frame that is static *with respect to the source*, yes. But you appear to be saying it will be a pure E field with respect to an "absolute static frame" even if the source is not at rest in that frame. By what logic do you conclude that?

 

[TrickyDicky]

In a frame that is static *with respect to the source*, yes. But you appear to be saying it will be a pure E field with respect to an "absolute static frame" even if the source is not at rest in that frame. By what logic do you conclude that?

Nope, I was under the impression that I was clear that the source should be at rest in that frame (maybe you are mixing my position with Q-reeus' ). Actually IMO what you say suggests a way to check experimentally the putative existence of an absolute frame, which would be the only one where "vacuum breakdown" in earnest could be achieved. Of course first you got to get a lab setting in the CMB motion frame.:tongue2:

 

[Dale]

Out of curiosity, which theory predicts vacuum polarization/breakdown?

 

[TrickyDicky]

out of curiosity, which theory predicts vacuum polarization/breakdown?

qft.

 

[Dale]

qft.

AFAIK all modern QFT are fully relativistic. So it seems impossible from first principles that a prediction from a relativistic theory would be non relativistic.

 

[TrickyDicky]

AFAIK all modern QFT are fully relativistic. So it seems impossible from first principles that a prediction from a relativistic theory would be non relativistic.

Do you consider GR a relativistic theory?
Do you know that certain predictions of QFT are incompatible with GR and viceversa and therefore some folks are desperate to find a theory to unify GR and quantum theory because both theories can't be completely right at the same time?

"Those are my principles, and if you don't like them... well, I have others. "
Groucho Marx

 

[Dale]

Do you know that certain predictions of QFT are incompatible with GR and viceversa and therefore some folks are desperate to find a theory to unify GR and quantum theory because both theories can't be completely right at the same time?

I am aware of that, but I don't see how GR is relevant to a prediction of QFT. If you are discussing a prediction of theory X then only theory X is important. If theory X is relativistic then the predictions of theory X must necessarily be relativistic.

 

[TrickyDicky]

I am aware of that, but I don't see how GR is relevant to a prediction of QFT. If you are discussing a prediction of theory X then only theory X is important. If theory X is relativistic then the predictions of theory X must necessarily be relativistic.

Non-linear QED (where I think the prediction about vacuum breakground comes from) is not "fully" relativistic in the restricted sense I think you are using then. (Neither is GR BTW)

 

[Dale]

Non-linear QED (where I think the prediction about vacuum breakground comes from) is not "fully" relativistic

That is why I asked the above question. Normal QED is relativistic, but I don't know about non-linear QED.

Can anyone confirm exactly which theory is being discussed?

 

[TrickyDicky]

That is why I asked the above question. Normal QED is relativistic, but I don't know about non-linear QED.

Can anyone confirm exactly which theory is being discussed?

I thought I confirmed it in the last post. How else do you think the high energies necessary to produce the breakground are dealt with?
I'm afraid you have a somewhat naive conception about theories in general and QFT in particular, non-linear QED is as "normal" as "normal" (linear) QED. It would be good if you defined what you mean by "relativistic" in this context, but the whole QFT includes procedures like Renormalization to adapt the "relativistic linearity" that produces nonsensical infinite results to the "non-linearity" of the real physical situations.

 

[Dale]

It would be good if you defined what you mean by "relativistic" in this context

If the basic equations that govern the experimental predictions of a theory are unchanged under a Lorentz transform then the theory is Lorentz covariant. If the basic equations that govern the experimental predictions of a theory are unchanged under arbitrary coordinate transforms then the theory is generally covariant. That is what I mean by "relativistic".

My knowledge of QM in general is not strong, but I am certainly not alone in the belief that QFT (including QED) is relativistic: https://qed.princeton.edu/main/Principedia/PHY_509:_Relativistic_Quantum_Theory

 

[Q-reeus]

Let's take this argument of yours to its logical conclusion. I set up an E field source and turn it on. In the source's rest frame, the field is a pure E field in a single direction (say along the x-axis). Since I am saying that E must equal E_crit in the source's rest frame (well, actually it's the frame in which the pairs are created at rest, but I think we've established that for a single source this is the source rest frame--we'll leave aside the lasers and electron beams for a bit, but I'll come back to them below), I do not expect to see breakdown until I measure E = E_crit (we're assuming that I'm not moving relative to the source.)
But you, standing next to me,...

That could be risky! :tongue2:

...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.

No no no, and honestly how can you not be well aware by now how many times I have emphasized *duration* as a necessary ingredient. Time to put just a bit of meat on that - been getting hand-wave fatigue. Consider then an evacuated parallel plate cap, 1cm x 1cm area, x 0.1cm plate separation. Charged to 10² v -> E = 10³ v/cm, that's a nice figure to start with. We know to get significant pair creation E = E_crit = 1.3*10¹⁶ v/cm. So wrt our lab frame, the cap has to be propelled to a relative velocity gamma factor of 1.3*10¹⁶/10³ ~ 1.3* 10¹³. By the LT's the plates have thus contracted in direction of motion in lab frame to l = 1cm/gamma. So any patch of vacuum in lab frame experiences Ecrit from cap for a duration of dt = l/c = 1cm/(gamma*c) = 1/(1.3*10¹³*3*10¹⁰cm/s) = 2.6*10^-24 seconds. Not long. A virtual electron can gain in that blip of time at most a normalized velocity of v/c = a*dt/c = (e*Ecrit/me)*dt/c = (1.6*10^-19C*1.3*10¹⁸v/m/9.1*10^-31Kg)*2.6*10^-24s/(3*10⁸m/s) = 0.02. That calc assumed relativistic mass would not become significant - justified in the circumstances. Square that and one has roughly the fractional shortfall before pair creation is likely.

So do I accept your devastating critique? Not likely. Recall that from the outset in #255 I emphasized this is a gedanken experiment and practical realization of any test along such lines is utterly unfeasable. What matters is the logic involved. If Ecrit as intensive factor makes any sense then it inevitably leads to the notion of an underlying reference frame(s) in order to avoid absurdities. If I follow your reasoning continued in the #321 post we have a situation where Ecrit *cannot* simply be an intensive that vacuum responds to in an unmysterious way. Maybe nature is that weird, but I prefer otherwise. You really, really don't want to contemplate the rotating hoops scenario in #318, I can tell that. But give it more thought maybe.

 

[TrickyDicky]

If the basic equations that govern the experimental predictions of a theory are unchanged under a Lorentz transform then the theory is Lorentz covariant. If the basic equations that govern the experimental predictions of a theory are unchanged under arbitrary coordinate transforms then the theory is generally covariant. That is what I mean by "relativistic".

My knowledge of QM in general is not strong, but I am certainly not alone in the belief that QFT (including QED) is relativistic: https://qed.princeton.edu/main/Principedia/PHY_509:_Relativistic_Quantum_Theory

Ok, I see where you are coming from wrt QM. There's an interesting paper by fellow PFer Demystifier that might help you clarify some things: http://arxiv.org/abs/quant-ph/0609163 points 7 and 8

 

[Haelfix]

Quantum field theory is fully relativistic. It has to be, as it is trivially built out objects that transform properly under lorentz transformations.

For instance, in the path integral formulation of the theory, the lagrangian is required to be a lorentz scalar. You can also show that all the other objects (creation/annihilation operators, commutation relationships, scattering amplitudes etc) are necessarily LI.

You can of course drop some of these assumptions, and the resulting field theories can break lorentz invariance, but they will always suffer from pathologies (for instance CPT is broken and a great deal of finetuning is required to prevent certain non LI operators from producing effects which are clearly not observable)

 

[TrickyDicky]

Of course, but frankly this is not what this thread is about.
You might want to take a look at Nikolic's paper too.

 

[Dale]

Ok, I see where you are coming from wrt QM. There's an interesting paper by fellow PFer Demystifier that might help you clarify some things: http://arxiv.org/abs/quant-ph/0609163 points 7 and 8

OK, I read those points but I don't get your implication. Are you saying that the math for deriving the experimental predictions of QED is indeed covariant, but that there are "interpretational" problems?

 

[PeterDonis]

No no no, and honestly how can you not be well aware by now how many times I have emphasized *duration* as a necessary ingredient.

But without ever explaining why. However...

Time to put just a bit of meat on that

Now you have, and what your explanation amounts to is: the vacuum has to "detect" E_crit for a minimum amount of time. What is this minimum amount of time? It's the average lifetime of the virtual particles. But time is frame-dependent; so in order to apply this criterion, we *have* to know *in what frame* to apply it!

Now go back and read what I've said several times about the second paper you linked to, and how it shows that the duration is what *determines* E_crit. What did I say? I said: the strength of E determines how fast the field can pump energy into the virtual particles; the average lifetime of the virtual particles determines how fast the field *has* to pump energy into the virtual particles; put these two things together and you get a critical value for the field, E_crit.

Now, once again: *in what frame* is the "average lifetime" defined? In the frame in which the virtual particles are created at rest, which for a single source is the same as the frame in which the source is at rest, which is what I've been saying all along. And this is basically what you are now saying! You have a single source: a parallel plate capacitor. You argue that in a frame in which the source is moving, the E field of the capacitor is higher, but the vacuum experiences it for a shorter time. So if the field is E_crit in a frame in which the source is moving, the vacuum won't detect it for long enough to induce breakdown. The field has to be E_crit in a frame in which the source is at rest for the duration requirement to be satisfied.

In other words, you have basically been in agreement with me all along.

If Ecrit as intensive factor makes any sense then it inevitably leads to the notion of an underlying reference frame(s) in order to avoid absurdities.

Yes, exactly: the "underlying reference frame" is the rest frame of the source.

If I follow your reasoning continued in the #321 post we have a situation where Ecrit *cannot* simply be an intensive that vacuum responds to in an unmysterious way.

You have obviously not been following my reasoning. As I showed above, my reasoning is the same as yours: the vacuum has to sense E >= E_crit for a certain minimum duration. The formula for E_crit is *defined* in such a way that it equates to the E field that needs to be sensed for the minimum duration *as seen in the frame in which the source is at rest*. If you LT into a frame in which the source is moving, both E and the duration change in concert to keep the covariant expression of the breakdown criterion the same.

 

[PeterDonis]

Nope, I was under the impression that I was clear that the source should be at rest in that frame (maybe you are mixing my position with Q-reeus' ). Actually IMO what you say suggests a way to check experimentally the putative existence of an absolute frame, which would be the only one where "vacuum breakdown" in earnest could be achieved.

I'm certainly not trying to say that would be the case; I'm saying that any source which can achieve E >= E_crit in the frame in which it (the source) is at rest should be able to induce breakdown. If we did in fact discover that only sources in a particular state of motion, for example a state of motion in which the CMBR was isotropic, could induce breakdown by achieving E >= E_crit, while sources in other states of motion (such as at rest on the Earth) either couldn't induce breakdown at all, or had to achieve E >> E_crit in the source rest frame to induce breakdown, that would indeed be an experimental refutation of SR *and* current quantum field theory, both of which say that the vacuum is Lorentz invariant, implying E > E_crit in the rest frame of the source is all that is required.

 

[TrickyDicky]

OK, I read those points but I don't get your implication. Are you saying that the math for deriving the experimental predictions of QED is indeed covariant, but that there are "interpretational" problems?

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.

 

[TrickyDicky]

I'm certainly not trying to say that would be the case; I'm saying that any source which can achieve E >= E_crit in the frame in which it (the source) is at rest should be able to induce breakdown. If we did in fact discover that only sources in a particular state of motion, for example a state of motion in which the CMBR was isotropic, could induce breakdown by achieving E >= E_crit, while sources in other states of motion (such as at rest on the Earth) either couldn't induce breakdown at all, or had to achieve E >> E_crit in the source rest frame to induce breakdown, that would indeed be an experimental refutation of SR *and* current quantum field theory, both of which say that the vacuum is Lorentz invariant, implying E > E_crit in the rest frame of the source is all that is required.

Ok, I see, we agree about the empirical dependence of this whole issue. Absent that evidence, I understand that surely you are not saying that would be the case, I myself am merely exploring logical alternatives. Just in case...:tongue2:

 

[TrickyDicky]

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 1/2 spin particles.

 

[PeterDonis]

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 1/2 spin particles.

But the vacuum contains virtual spin 1/2 particles, so any violation of LI with respect to them would imply a violation of LI for the vacuum as well.

 

[TrickyDicky]

But the vacuum contains virtual spin 1/2 particles, so any violation of LI with respect to them would imply a violation of LI for the vacuum as well.

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.

 

[Q-reeus]

Now you have...

And thankfully for me no-one did close checks. My calcs were out by a factor of 10⁴ the wrong way (exponentiation errors - damm calculator), so have edited initial voltage to give the final correct result. By bumping up the voltage or lengthening the capacitor the required gamma factor goes down, but one is still widely outside anything experimentally attainable.

, and what your explanation amounts to is: the vacuum has to "detect" E_crit for a minimum amount of time. What is this minimum amount of time? It's the average lifetime of the virtual particles. But time is frame-dependent; so in order to apply this criterion, we *have* to know *in what frame* to apply it!

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. Otherwise, why are we even arguing about detecting the 'ether frame' - there would be an easily detectable 'flow' not needing breakdown to discover.

Now go back and read what I've said several times about the second paper you linked to, and how it shows that the duration is what *determines* E_crit. What did I say? I said: the strength of E determines how fast the field can pump energy into the virtual particles; the average lifetime of the virtual particles determines how fast the field *has* to pump energy into the virtual particles; put these two things together and you get a critical value for the field, E_crit.

That passage is ok - on it's own.

Now, once again: *in what frame* is the "average lifetime" defined? In the frame in which the virtual particles are created at rest, which for a single source is the same as the frame in which the source is at rest, which is what I've been saying all along.

And imo it doesn't hold water for the reason noted earlier that the vacuum, thanks to it's frequency spectrum, looks the same in any frame (until breakdown that is!).

And this is basically what you are now saying! You have a single source: a parallel plate capacitor. You argue that in a frame in which the source is moving, the E field of the capacitor is higher, but the vacuum experiences it for a shorter time. So if the field is E_crit in a frame in which the source is moving, the vacuum won't detect it for long enough to induce breakdown. The field has to be E_crit in a frame in which the source is at rest for the duration requirement to be satisfied.
In other words, you have basically been in agreement with me all along.

No. The (corrected) example I gave showed a shortfall, but adjusting as earlier described and we would be in breakdown regime. From SR perspective this leads to a bizarre picture. Positing an local LET preferred frame in which breakdown is maximal allows a sensible restraint on what is possible.

You have obviously not been following my reasoning. As I showed above, my reasoning is the same as yours: the vacuum has to sense E >= E_crit for a certain minimum duration. The formula for E_crit is *defined* in such a way that it equates to the E field that needs to be sensed for the minimum duration *as seen in the frame in which the source is at rest*.

That last bit is simply wrong. Again - the normal vacuum has a vp spectrum that means it appears the same in every frame. And for that reason I maintain it cares not about whether an applied E is from a source at rest or moving in any given frame.

If you LT into a frame in which the source is moving, both E and the duration change in concert to keep the covariant expression of the breakdown criterion the same.

Can you make sense of that position for the example of rotating hoops capacitor I gave in #318 (last paragraph)? Do that and maybe we see eye to eye. Yes, a Xmas present wil be yours!