SR, LET, FTL & Causality Violation

[Dale]

But when Dalespam introduced cosmological considerations I think things got a bit muddled.

I didn't introduce it, and I agree that it is muddled, which is why I don't want to argue this line.

 

[PeterDonis]

Yes, I understand that ultimate causal connection, I was merely saying that for the purposes of the discussion of this thread the exact specific mechanism of production of the isotropy of the CMB is not reallly relavant, the fact it is isotropic is the relevant one rather than the specific mechanism for discussing how the dipole observed reflects (is more directly connected) to the relative motion of the Earth wrt to a rest comoving frame, the frame at which the "cosmologic fluid" or the galactic Hubble flow or whatever one wants to call it is at rest in the FRW coordinates and the possibility that this rest frame reflects what the OP calls a Lorentz eather frame.

The specific mechanism is not really relevant, but the fact that there *is* a physical mechanism involved certainly is.

I know this coordinates are arbitrarily chosen, but I think this thread is ultimately about the "happy coincidence" that in this arbitrary choice (historically made by Robertson in the 30s) a microwave radiation pervading all space was found in 1964. I tend to think too that there is something physical behind this coincidence rather than considering it a "magical coincidence"

The coordinates aren't really "arbitrarily" chosen; they're chosen based on the physical assumption that the universe is homogeneous and isotropic. It's true that when that assumption was first made, there wasn't a lot of data either way, but the data has steadily accumulated to support the assumption; the discovery of the CMBR was one such piece of data (and now, of course, the CMBR is telling us how accurate the assumption is--about one part in 10^5). So I agree that there is definitely something physical behind the "coincidence".

the OP apparently believes in a single 'absolute' LET rest frame, which cannot be reconciled with an expanding cosmos. I like to use the familiar (2+1)D analogue of expanding balloon with dots all over it. No single dot could be taken as marker of any 'absolute' rest frame, but if stationary wrt the local balloon surface, anyone could be taken to mark the 'local rest frame'.

You make a good point and I agree with your description, but I'm not sure how much it would add to the arguments already made against the idea of an "LET aether" in this thread. (The possibility of the CMBR's rest frame being the "aether" frame only came up fairly late in the thread, which may be why no one had yet hit on the argument you pose.) Anyone who believes in LET has already accepted the fact that they have to pick out one particular frame and call it "absolute rest", even though there is nothing that physically picks out that frame from all the others. So an LET theorist would just say that yes, you're right, I can't take the "comoving" frame (the rest frame of the CMBR) as the "aether frame" as it stands because that frame is not a single inertial frame (objects "at rest" in this frame are moving away from each other); but that just means there is some *particular* comoving observer whose current rest frame happens to be the aether frame--we just don't know which one.

Of course, *which* comoving observer happens to be "at rest" in the aether will *change* with time, as you note; but given the number of highly implausible things the LET theorist already believes in, what's one more? (Sounds like the LET theorist must have read Lewis Carroll, and likes to believe six impossible things before breakfast.)

guess most here would agree that applied to the 4D real-world case, that is how an LET 'rest frame' is to be taken?

No, most here would say that the idea of an "LET rest frame" is not valid in the first place.

 

[TrickyDicky]

The coordinates aren't really "arbitrarily" chosen; they're chosen based on the physical assumption that the universe is homogeneous and isotropic.

Which is a reasonable assumption and explains why and how they were chosen by Robertson, but I was referring to the accepted fact that there is nothing "absolute" about taking these coordinates to fix a comoving rest frame where observers see the CMB without the dipole anisotropy, they are merely "preferred" for practical reasons and the above mentioned assumptions, so in that sense they are arbitrary coordinates, or do you have reasons to think they are the only possible coordinates or that they are special and unique in some other way? I don't think so, that would put you in an equally or more awkward position than the "LET theorists".

 

[PeterDonis]

Which is a reasonable assumption and explains why and how they were chosen by Robertson, but I was referring to the accepted fact that there is nothing "absolute" about taking these coordinates to fix a comoving rest frame where observers see the CMB without the dipole anisotropy, they are merely "preferred" for practical reasons and the above mentioned assumptions, so in that sense they are arbitrary coordinates

Ah, I see, yes, with this meaning of "arbitrary" they are arbitrary; nothing requires us to describe the universe using "comoving" coordinates, it just looks simpler provided that the universe actually is homogeneous and isotropic, which it is to a good approximation, and the appearance of the CMB reflects that.

 

[Q-reeus]

No, most here would say that the idea of an "LET rest frame" is not valid in the first place.

Sure but I meant 'how it could make sense assuming it is predictively equivalent to SR'. Maybe this should be in a new thread, but here goes. Have been tossing around an heretical idea for a while re detecting an LET rest frame - which amounts to saying it could falsify SR. Vacuum polarization. When electric field strength reaches a critical value E_crit ~ 1.3*10¹⁶v/cm, QED predicts the vacuum undergoes 'dielectric breakdown' with copious production of electron-positron pairs (see e.g. http://arxiv.org/abs/0706.4363, eqn's (1) & (2)). These move under the action of the applied E to create a current. Creating the requisite enormous field intensity in the lab frame is still way beyond current technology, but as gedanken experiment that's not an issue.

Suppose then we have say a very long length of fully evacuated straight coax line. Inner line is held at a high potential wrt outer coax tube; and we fancifully assume it could yield some reasonable fraction say 0.5 E_crit at the inner line surface. In an SR setting it matters not if an observer, moving parallel to the coax axis at some large fraction of c sees a transverse E >> E_crit - if there no breakdown in the lab frame, none can be occurring in the observer's frame either. There is of course a large transverse B field present in that frame, but a B field has no influence on initiating breakdown - it could only modify the flow of an existing breakdown current.

But what is the viewpoint in LET setting. If our original setup corresponds to the 'true' LET rest frame, and we now propel the coax setup to the same relative speed as before - but now relative to 'the rest frame', can it now be said that an E >> E_crit in LET rest frame doesn't matter? That is surely inconsistent with the notion that the vacuum should not distinguish between an E field generated by a source at rest or moving (as before, the added B field is irrelevant re initiating breakdown). In other words, LET scenario predicts breakdown occurring because coax motion is wrt rest frame. Put in another way - the vacuum 'knows' what is the true rest frame when breakdown is imminent. OK, throwing it over to the pros - what is wrong with this argument?

 

[PeterDonis]

Put in another way - the vacuum 'knows' what is the true rest frame when breakdown is imminent. OK, throwing it over to the pros - what is wrong with this argument?

The rest frame is determined by the rest frame of the apparatus that is producing the E field, not the vacuum. If we launch the field generator on a rocket and accelerate it to near the speed of light, relative to the lab, it's still the E field in the rest frame of the field generator, not the lab, that determines when "breakdown" occurs (so we, in the lab, will see breakdown occur at a much *higher* value of E, because of the relative motion). So the vacuum doesn't pick out a particular rest frame.

 

[Q-reeus]

The rest frame is determined by the rest frame of the apparatus that is producing the E field, not the vacuum. If we launch the field generator on a rocket and accelerate it to near the speed of light, relative to the lab, it's still the E field in the rest frame of the field generator, not the lab, that determines when "breakdown" occurs (so we, in the lab, will see breakdown occur at a much *higher* value of E, because of the relative motion). So the vacuum doesn't pick out a particular rest frame.

That is partly a restatement of the SR situation in my middle paragraph in #255, but omits two things which imo are critical to the argument. There is one additional consideration I omitted there - duration. As eq'n (2) in the reference shows, the applied E must be sustained for a minimum time for breakdown to be appreciable. Take say an atom of Uranium with a large nucleus and near critical field E field there in it's rest frame. Whizzing by at near light speed, the transverse E field may be much higher than Ecrit, but it matters not either in SR setting (your argument), or in LET setting owing to the briefness of E field duration. This is why I specified a very long coax - make it as long as one likes so that even at v -> c the transverse E is sustained uniformly for sufficient time.
You will have to explain then why, in LET perspective, it should matter that E is owing to static or moving source. In reference to the second consideration recall here that unlike a ponderable dielectric medium where your argument re higher observer dependent breakdown strength makes sense [i.e. dielectric say is moving relative to the transverse B field in that frame such that there is an offset against the transverse E in that frame], the vacuum is supposed to exhibit the same properties at any speed. Certainly in SR! And, if my argument has merit, mostly in LET.

 

[PeterDonis]

As eq'n (2) in the reference shows, the applied E must be sustained for a minimum time for breakdown to be appreciable. Take say an atom of Uranium with a large nucleus and near critical field E field there in it's rest frame. Whizzing by at near light speed, the transverse E field may be much higher than Ecrit, but it matters not either in SR setting (your argument), or in LET setting owing to the briefness of E field duration.

Since we are talking about a breakdown of the vacuum, the Uranium nucleus is irrelevant. The "breakdown" the paper is talking about is a production of electron-positron pairs from *vacuum*--i.e., in a region where there is *no* matter present. (However, that does *not* mean there is "nothing" present--see further comments at the end of this post.)

This is why I specified a very long coax - make it as long as one likes so that even at v -> c the transverse E is sustained uniformly for sufficient time.

Do you mean you are trying to sustain a transverse E field in the lab frame even though the power source that the field generator uses is moving at v -> c relative to the lab frame? You do realize that electricity does not travel down the coax at infinite speed, right? It travels at the speed of light. So as the generator moves away, it will be impossible for the electricity from the coax to travel back down it fast enough to sustain the E field.

In any case, when I talked about a "field generator", I was not talking about the energy source; I was talking about the actual apparatus that *produces* the electric field: the Van De Graff generator or whatever it is. What I am saying is that the rest frame of that apparatus is what determines the "rest frame" with respect to which the E field has to reach E_crit for breakdown to occur. It doesn't matter how you feed power to the apparatus. And you can't take such an apparatus and somehow pipe its output via a coax cable to somewhere else; that doesn't make sense, because its output is the E field, directly; it's not something that somehow gets turned into the E field.

You will have to explain then why, in LET perspective, it should matter that E is owing to static or moving source.

I don't have to explain anything relative to LET, since I don't think it's a correct interpretation of the physics anyway.

In reference to the second consideration recall here that unlike a ponderable dielectric medium where your argument re higher observer dependent breakdown strength makes sense, the vacuum is supposed to exhibit the same properties at any speed. Certainly in SR!

The vacuum *does* exhibit the same properties at any speed. What exhibits properties that are "speed dependent" (if you insist on looking at everything from a single inertial frame) is the E field generator, as I explained above; what E field strength you observe it to be generating when electron-positron pairs start to appear will depend on its state of motion relative to you.

Also, saying that the electron-positron pairs come "from the vacuum" is really a misstatement; the pairs are being produced from the energy that is being pumped into the E field generator from some power source. The phrase "from vacuum" is used only because there is no other matter already present in the region where the pairs are produced; but there is not "nothing" present either, because the field is there, and the energy that produced it had to come from somewhere.

 

[Q-reeus]

Since we are talking about a breakdown of the vacuum, the Uranium nucleus is irrelevant. The "breakdown" the paper is talking about is a production of electron-positron pairs from *vacuum*--i.e., in a region where there is *no* matter present.

You seem not aware of the spontaneous beta-decay arguments re supercritical nucleii (nucleii not yet created, but the theory is long established)

Originally Posted by Q-reeus:
"This is why I specified a very long coax - make it as long as one likes so that even at v -> c the transverse E is sustained uniformly for sufficient time."

Do you mean you are trying to sustain a transverse E field in the lab frame even though the power source that the field generator uses is moving at v -> c relative to the lab frame? You do realize that electricity does not travel down the coax at infinite speed, right? It travels at the speed of light. So as the generator moves away, it will be impossible for the electricity from the coax to travel back down it fast enough to sustain the E field.

Where did this all come from?! A gedanken experiment for pete's sake! Did I once say the power source (and it need only be a voltage source really) was moving wrt the coax? Or ultrarelativistic speeds were needed? Coax is primarily a capacitor acting as source of transverse E. So we can simply charge it up in lab frame, and rather than sustained breakdown, we observe for the moving coax (can be moving at moderately relativistic speed) a precipitous decline in E concommitant with onset of breakdown. Or whatever - this is a standard type thought experiment and we don't have to worry about grease, nuts and bolts etc.

In any case, when I talked about a "field generator", I was not talking about the energy source; I was talking about the actual apparatus that *produces* the electric field: the Van De Graff generator or whatever it is. What I am saying is that the rest frame of that apparatus is what determines the "rest frame" with respect to which the E field has to reach E_crit for breakdown to occur. It doesn't matter how you feed power to the apparatus. And you can't take such an apparatus and somehow pipe its output via a coax cable to somewhere else; that doesn't make sense, because its output is the E field, directly; it's not something that somehow gets turned into the E field.

Peter - please go back and slowly re-read #255, then #257. You appear to have totally misunderstood my argument - your passage above has nothing to do with anything I wrote and you are arguing against a phantom. You do realize for instance as per previous comments that the coax is not taken as a power source per se, but simply a tubular capacitor? That was not made ultra clear enough in #255!? How did you figure it becomes a power-lead?

Originally Posted by Q-reeus: "You will have to explain then why, in LET perspective, it should matter that E is owing to static or moving source."

I don't have to explain anything relative to LET, since I don't think it's a correct interpretation of the physics anyway.

And I'm not claiming this LET-trumps-SR argument is necessarily true, but imo it does deserve a properly targeted response.

Originally Posted by Q-reeus:
"In reference to the second consideration recall here that unlike a ponderable dielectric medium where your argument re higher observer dependent breakdown strength makes sense, the vacuum is supposed to exhibit the same properties at any speed. Certainly in SR!"

The vacuum *does* exhibit the same properties at any speed. What exhibits properties that are "speed dependent" (if you insist on looking at everything from a single inertial frame)...

I obviously didn't in #255 - where again is the issue?

...is the E field generator, as I explained above; what E field strength you observe it to be generating when electron-positron pairs start to appear will depend on its state of motion relative to you.

Once you cotton-on the coax is a *capacitor* until breakdown occurs, (and so what if an on-board generator sustains or not the breakdown current thereafter) I think this extraneous issue will thankfully also evaporate.

Also, saying that the electron-positron pairs come "from the vacuum" is really a misstatement; the pairs are being produced from the energy that is being pumped into the E field generator from some power source. The phrase "from vacuum" is used only because there is no other matter already present in the region where the pairs are produced; but there is not "nothing" present either, because the field is there, and the energy that produced it had to come from somewhere.

It's not called vacuum breakdown for nothing. Let's not keep getting bogged down in irrelevancies. Of course energy is supplied etc - can you point to me suggesting otherwise?

 

[PeterDonis]

You seem not aware of the spontaneous beta-decay arguments re supercritical nucleii (nucleii not yet created, but the theory is long established)

I'm aware of them, but that's a different phenomenon from "vacuum breakdown". Which phenomenon do you want to talk about?

Where did this all come from?! A gedanken experiment for pete's sake! <much further comment snipped>

I am trying to understand the scenario you are describing, but it's difficult because you are not describing it clearly. Let me try to describe, clearly, the scenario I have been understanding you to describe, and then you can tell me if my description matches the scenario you were trying to describe.

There is some object which produces an electromagnetic field. Call it the "source". In the rest frame of that object, the EM field produced appears as a pure electric field, E. In *that* frame, the field strength that induces breakdown (i.e., the production of electron-positron pairs when no other matter is present) is given by the formula in the paper you quoted for the "critical" field, E_crit.

In a frame in which the source is moving, the EM field it produces will no longer be a pure electric field; it will have both electric and magnetic parts, E and B. The E part will not be the same as it is in the source's rest frame (in the particular case you were describing, motion parallel to the E field, E will be larger in the moving frame).

So if we are in the moving frame (i.e., we are moving relative to the source), the E field *we* observe when breakdown occurs will be different than E_crit. But that's because we are moving relative to the source; it has nothing to do with any preferred frame picked out by the vacuum.

And I'm not claiming this LET-trumps-SR argument is necessarily true, but imo it does deserve a properly targeted response.

First the term "LET" needs to be properly defined so we know what to respond to. The OP has been requested a number of times to do that but hasn't.

 

[Q-reeus]

Originally Posted by Q-reeus:
"You seem not aware of the spontaneous beta-decay arguments re supercritical nucleii (nucleii not yet created, but the theory is long established)"

I'm aware of them, but that's a different phenomenon from "vacuum breakdown". Which phenomenon do you want to talk about?

Actually 'spontaneous positron emission' was probably closer to the correct terminolgy, but anyway the issue here is whether vacuum breakdown can be explained in SR setting the same as in LET setting. So just forget atoms! Moral was sustained E is needed for significant vacuum breakdown.

I am trying to understand the scenario you are describing, but it's difficult because you are not describing it clearly. Let me try to describe, clearly, the scenario I have been understanding you to describe, and then you can tell me if my description matches the scenario you were trying to describe.

There is some object which produces an electromagnetic field. Call it the "source". In the rest frame of that object, the EM field produced appears as a pure electric field, E. In *that* frame, the field strength that induces breakdown (i.e., the production of electron-positron pairs when no other matter is present) is given by the formula in the paper you quoted for the "critical" field, E_crit.

Fair summary so far - although I specified E transverse to any subsequent relative motion is what matters.

In a frame in which the source is moving, the EM field it produces will no longer be a pure electric field; it will have both electric and magnetic parts, E and B. The E part will not be the same as it is in the source's rest frame (in the particular case you were describing, motion parallel to the E field, E will be larger in the moving frame).

WRONG! I specified, as per above, motion is parallel to axis of coaxial capacitor, and therefore normal to applied E. Hence SR transformation for transverse E component is relevant. Longitudinal E never exists, and anyway such would be unaffected by relative motion.

So if we are in the moving frame (i.e., we are moving relative to the source), the E field *we* observe when breakdown occurs will be different than E_crit. But that's because we are moving relative to the source; it has nothing to do with any preferred frame picked out by the vacuum.

If the E is transverse, yes, and this circular discussion brings me back to the points made in the second paragraph in #255, and last paragraph of #257. You have simply repeated the standard SR perspective of which we both agree on.

First the term "LET" needs to be properly defined so we know what to respond to. The OP has been requested a number of times to do that but hasn't.

The kernel issue re LET is that vacuum breakdown, determined in an assumed LET rest frame, will by the moving capacitor argument given, be different - specifically less in any other LET lab frame where capacitor is stationary. In other words, in principle one could determine the 'true' rest frame by tests of breakdown strength at various velocities. As I have repeated before and do so again, to avoid that conclusion and square with SR, it has to be shown how LET vacuum could somehow distinguish between an E source that is static or moving wrt lab frame. I don't think anything beyond that is required re defining LET. The fact that in SR, transverse E breakdown strength is *not* a function of velocity is a statement that vacuum polarization has some very strange linkage to the source of transverse E (E aint just E) it seems to me.

 

[Dale]

AFAIK the vacuum polarization in QED is a rank-2 tensor, so it is guaranteed to transform correctly.

 

[stglyde]

True. But the source of the CMB is the surface of last scattering, not the aether. So again, the fact that it is measured to be isotropic provides no evidence about the velocity wrt the aether.

I encourage you to work through the math. According to LET, what would a detector measure for the radiation in each direction along the x and y axes for the case where the surface of last scattering and the detector are both moving at v=0 and both moving at v=.6c wrt the aether?

I don't know how to say again what I have repeatedly told to you. The CMB IS light and Lorentz's position (as was Einstein's) is that light IS isotropic c. For Lorentz this is because,the properties of the aether, namely its coefficient of compressibility (u) and density z deterimes this speed:

c = Sqrt(1/uz)

For Einstein it just a given that it is such for 'empty space'

OK then, do the math I suggested above and prove me wrong.

There are no surfaces of last scattering there is only the universal CMB field. That we see and measure to be universal and uniform and smooth to at least five decimal places. IF you are moving wrt to this sea of photons you WILL! measure a Doppler, period, end of story. From the Lorentzian model this identifies the aether background.


PeterDonis and others. Please describe in your own words where I got wrong because I may be stuck with DaleSpam particular language or chain of reasoning. Thanks.

 

[stglyde]

But you still haven't said what LET is. Even without going beyond the standard model, there are many concepts including the http://www.tu-harburg.de/rzt/rzt/it/Ether.html, the http://www.nobelprize.org/nobel_prizes/physics/laureates/2006/smoot_lecture.pdf, or the quantum vacuum which have been called "aethers" because they have some relationship to Lorentz's. That is not contested (by me). However, to have a good discussion of the similarities and differences between these different things, we need a sharp definition of LET, and give each of these aethers different names. For example, if one includes that the aether of LET is undetectable, then we can straightaway say that the CMB as a preferred frame does not have that property, since it is detectable. So could we please have your precise definition of LET, along the lines suggested by D H?

Which came first, Lorentz's version or Eistein's? And again. Lorentz NEVER! claimed the aether itself is undetectable he simply say that trying to determine one's speed within it
cannot be done using TWL path processes. But, he never proposed that his aether was anything but 'the aether'.

GR's equations are expressly hydrodynamical in nature. Einstein and others realize this and the implication should be obvious to any thinking being. But again, since GR encompasses SR and SR encompasses 'luminiferous' behavior there is NO! separate aethers except perhaps, in the concepts of 'your' mind.

 

[Dale]

I don't know how to say again what I have repeatedly told to you.

It doesn't matter how you say it, what you are saying is wrong. This isn't a miscommunication, just an incorrect idea.

The CMB IS light and Lorentz's position (as was Einstein's) is that light IS isotropic c.

Do you agree or disagree with the following statements:
1) in LET the speed of light IS isotropic only in the aether frame
2) in LET the speed of light is MEASURED to be isotropic in all frames

That we see and measure to be universal and uniform and smooth to at least five decimal places. IF you are moving wrt to this sea of photons you WILL! measure a Doppler, period, end of story.

Yes, I agree.

From the Lorentzian model this identifies the aether background.

No, it doesn't. Prove your point with math. Use the Lorentz transform to show that LET requires that if a given configuration of photons is measured to be isotropic then it must be at rest wrt the aether. I.e. that it is impossible to measure isotropic photons while moving relative to the aether in LET.

 

[Aether]

...the OP apparently believes in a single 'absolute' LET rest frame, which cannot be reconciled with an expanding cosmos. I like to use the familiar (2+1)D analogue of expanding balloon with dots all over it. No single dot could be taken as marker of any 'absolute' rest frame, but if stationary wrt the local balloon surface, anyone could be taken to mark the 'local rest frame'. I guess most here would agree that applied to the 4D real-world case, that is how an LET 'rest frame' is to be taken?

LET is exactly the same physical theory as is the standard formulation of SR, but it uses a different coordinate system. Both LET and SR are similarly limited to application within small space-time regions.

If the OP really does, as you say, "believes in a single 'absolute' LET rest frame...", then the simple existence of gravity here on Earth would be enough to falsify that belief; just as it is entirely sufficient to falsify the standard formulation of SR itself if/when the theory is applied to any suitably large space-time region.

 

[Aether]

stglyde,
You can't properly apply LET to the CMB any more than someone else could properly apply the standard formulation of SR to a simple problem involving gravity here on earth.

GR is the proper tool for dealing with gravity and the CMB, and GR let's you choose any coordinate system that you want.

 

[PeterDonis]

WRONG! I specified, as per above, motion is parallel to axis of coaxial capacitor, and therefore normal to applied E. Hence SR transformation for transverse E component is relevant. Longitudinal E never exists, and anyway such would be unaffected by relative motion.

Ah, sorry, I should have said E perpendicular to the direction of motion, not parallel.

If the E is transverse, yes, and this circular discussion brings me back to the points made in the second paragraph in #255, and last paragraph of #257. You have simply repeated the standard SR perspective of which we both agree on.

Ok, good, that means we at least agree on what standard SR says.

The kernel issue re LET is that vacuum breakdown, determined in an assumed LET rest frame, will by the moving capacitor argument given, be different - specifically less in any other LET lab frame where capacitor is stationary.

Now we get into the question of what, exactly, the term "LET" means. The standard usage of that term (or what most of us thought the standard usage was until it started getting thrown around in this thread) is a theory that makes exactly the same experimental predictions as SR, but interprets them differently. So "LET" by this definition would *not* predict any behavior different than SR; it would predict that the breakdown threshold is determined by the E field in the rest frame of the source. This "LET" would just attribute that to the fact that, even though the source is moving relative to the aether, the field it generates is moving with it, so they both get transformed the same way and the experimental results are the same as SR predicts.

If there is some other "LET" that makes different predictions, the onus is on whoever is propounding such a theory to explain how it makes those predictions.

The fact that in SR, transverse E breakdown strength is *not* a function of velocity is a statement that vacuum polarization has some very strange linkage to the source of transverse E (E aint just E) it seems to me.

No, it's a statement that the "breakdown" phenomenon is produced by pumping energy into the EM field until there is enough of it to produce electron-positron pairs, and the critical field threshold is determined in the rest frame of the source. I really don't see what is so mysterious about this.

 

[kmarinas86]

In the spirit of the title of this thread "SR, LET, FTL & Causality Violation" I would just like to say that it would far easier to adapt FTL with LET than with SR. A Lorentzian ether can easily be amended with one or more other types of transformation that are not Lorentzian (i.e. not based on \sqrt{1-v^2/c^2}) which coexist in the same "absolute space" (different than the "deformable electron" model). Relativity, on the other hand, presents a paradox as it would require some kind of wormhole or other way to "skip" space, if you will, or require that neutrinos didn't really originate with the STL muons but that somehow STL muons entrained itself with a pre-existing FTL substance not a part of the muons themselves and that the FTL substance rolled into FTL neutrinos as a result (as the light speed barrier according to SR cannot be breached from either side), all while at the same time still having the observed change in mass giving rise to the necessity of the neutrino hypothesis in the first place (so you would have to have another (but STL) particle or a strange alternate type of light-like energy traveling at c being emitted from the muon in addition to the FTL neutrino, yet somehow having the same energy!). In LET modified with additional transformations, you neither have to skip space through some other dimension nor require that something is already residing in the experiment moving faster than the speed of light, as things would be able to traverse the light speed barrier rather than be stuck on one side of it.

 

[stglyde]

It doesn't matter how you say it, what you are saying is wrong. This isn't a miscommunication, just an incorrect idea.

Do you agree or disagree with the following statements:
1) in LET the speed of light IS isotropic only in the aether frame
2) in LET the speed of light is MEASURED to be isotropic in all frames

Agree.

No, it doesn't. Prove your point with math. Use the Lorentz transform to show that LET requires that if a given configuration of photons is measured to be isotropic then it must be at rest wrt the aether. I.e. that it is impossible to measure isotropic photons while moving relative to the aether in LET.

If #1 & #2 are true the LT is irrelevant to the issue. If #1 is true and the CMB is universal, uniform, and isotropic it can only meet that condition, according TO Lorentz's model, due to the local aether properties. This is what makes #1 true according to the medium model.
Therefore the only state that can, in the aether model, result in a universal uniform (a.k.a. observable isotropic) radiation field IS the rest frame. All others because of the motion relative to the field produces a distinctive measurable Doppler. The LT have no place in this logic.

 

[ghwellsjr]

1) in LET the speed of light IS isotropic only in the aether frame
2) in LET the speed of light is MEASURED to be isotropic in all frames

If #1 & #2 are true the LT is irrelevant to the issue. If #1 is true and the CMB is universal, uniform, and isotropic it can only meet that condition, according TO Lorentz's model, due to the local aether properties. This is what makes #1 true according to the medium model.
Therefore the only state that can, in the aether model, result in a universal uniform (a.k.a. observable isotropic) radiation field IS the rest frame. All others because of the motion relative to the field produces a distinctive measurable Doppler. The LT have no place in this logic.

#2 is an example or a situation described by both LET's and SR's first postulate.

#1 is LET's second postulate that distinguishes LET from SR.

SR's second postulate is: "the speed of light IS isotropic in any frame"

SR's second postulate "is only apparently irreconcilable" with the first postulate shared by both LET and SR.

However, contrary to what you state, neither second postulate is observable. Choose any inertial frame you want, call it the one and only aether state, and it will take on all the characteristics that you believe apply only to the aether state. That's Einstein's point.

 

[harrylin]

In the spirit of the title of this thread "SR, LET, FTL & Causality Violation" I would just like to say that it would far easier to adapt FTL with LET than with SR. A Lorentzian ether can easily be amended with one or more other types of transformation that are not Lorentzian (i.e. not based on \sqrt{1-v^2/c^2}) which coexist in the same "absolute space" (different than the "deformable electron" model). [..] In LET modified with additional transformations, you neither have to skip space through some other dimension nor require that something is already residing in the experiment moving faster than the speed of light, as things would be able to traverse the light speed barrier rather than be stuck on one side of it.

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".

 

[harrylin]

[..] SR's second postulate is: "the speed of light IS isotropic in any frame" [..]

Not exactly, if I understand correctly what you mean with "IS". I cite:

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated.
[..this] "principle of the constancy of the velocity of light," is at
least for a coordinate system in a certain state of motion [..] made
plausible by the confirmation through experiment of the Lorentz theory
[1895], which is based on the assumption of an ether that is
absolutely at rest". - Einstein 1907 (German; translation mine).
http://www.soso.ch/wissen/hist/SRT/E-1907.pdf

The point of SR is that it only refers to measurements, without reference to hidden reality. It is purely an operational theory.

 

[harrylin]

[..] the only state that can, in the aether model, result in a universal uniform (a.k.a. observable isotropic) radiation field IS the rest frame. All others because of the motion relative to the field produces a distinctive measurable Doppler. The LT have no place in this logic.

Suppose that there was some kind of stuff at "the start of time" that was not "at rest" but moving in the ether (don't ask me why!), and that this stuff then somehow exploded (the "Big Bang"); and that some of the corresponding radiation is still present. Do you think that someone who measures that radiation can detect absolute velocity? Or do you hold that Big Bang theory is incompatible with ether concepts?

 

[ghwellsjr]

SR's second postulate is: "the speed of light IS isotropic in any frame"

Not exactly, if I understand correctly what you mean with "IS".

What do you think Einstein meant by "is" when he stated his second postulate as:

light is always propagated in empty space with a definite velocity c

I cite:

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated.
[..this] "principle of the constancy of the velocity of light," is at
least for a coordinate system in a certain state of motion [..] made
plausible by the confirmation through experiment of the Lorentz theory
[1895], which is based on the assumption of an ether that is
absolutely at rest". - Einstein 1907 (German; translation mine).
http://www.soso.ch/wissen/hist/SRT/E-1907.pdf

The point of SR is that it only refers to measurements, without reference to hidden reality. It is purely an operational theory.

Why do you link to the German and provide your own English translation when the full text of the paper is already available in English:
http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1907_Jahrbuch.pdf

Your quote is from the top of the third page, labeled 514, and if you read the paragraphs preceding and succeeding, you will see that he is not saying anything different in this 1907 paper than what he said in his original 1905 paper introducing Special Relativity.

In both papers, and in every other paper, book and talk that Einstein delivered, he always makes the point that remotely separated clocks are insufficient to establish a coordinate time unless we assume or define the one-way speed of light to be a constant in that particular coordinate system or Frame of Reference. There is no measurement possible to determine the light travel time between any two points which is a requirement in order to make a claim about the propagation of light or the one-way speed of light. The propagation of light is unobservable, unmeasurable, and unknowable and all we can do is make an arbitrary and unprovable assumption or definition or postulate or stipulation regarding it.

Your statement that SR "only refers to measurements, without reference to hidden reality" is very curious to me, not just because you say it "only refers to measurements" but because you think that the alternative is a "hidden reality". Rather, Einstein is creating a reality that did not previously exist, not revealing a hidden reality. He says that unless we have a rule by which to set all the remotely located clocks, we don't have a sufficient time to do physics. I fail to see how you can claim that SR only refers to measurements when Einstein clearly pointed out that we cannot make any measurements with regard to time until we create our definition of time.

 

[TrickyDicky]

If #1 & #2 are true the LT is irrelevant to the issue. If #1 is true and the CMB is universal, uniform, and isotropic it can only meet that condition, according TO Lorentz's model, due to the local aether properties. This is what makes #1 true according to the medium model.
Therefore the only state that can, in the aether model, result in a universal uniform (a.k.a. observable isotropic) radiation field IS the rest frame. All others because of the motion relative to the field produces a distinctive measurable Doppler. The LT have no place in this logic.

But then it wouldn't be LET, if by LET we understand a theory that makes the same predictions as SR and that holds that even if the ether absolute rest frame exists there is no way to detect it, for if the CMB is this frame we are obviously detecting it, don't you agree?

 

[TrickyDicky]

In the spirit of the title of this thread "SR, LET, FTL & Causality Violation" I would just like to say that it would far easier to adapt FTL with LET than with SR. A Lorentzian ether can easily be amended with one or more other types of transformation that are not Lorentzian (i.e. not based on \sqrt{1-v^2/c^2}) which coexist in the same "absolute space" ... In LET modified with additional transformations, you neither have to skip space through some other dimension nor require that something is already residing in the experiment moving faster than the speed of light, as things would be able to traverse the light speed barrier rather than be stuck on one side of it.

See my post above, if that definition of LET holds observable FTL motion wouldn't fit in LET, it would have to be a whole new theory.

 

[Dale]

Agree.

... If #1 is true and the CMB is universal, uniform, and isotropic it can only meet that condition, according TO Lorentz's model, due to the local aether properties.

I agree. The problem is that you keep on forgetting #2. We do not and cannot know that the cmb IS isotropic. All we can know is that it is MEASURED to be isotropic. Because of #2, that measurement provides no information about the speed of the cmb relative to the aether.

All of your arguments are circular: you assume that the cmb is at rest wrt the aether, use that fact to claim that the cmb is not just MEASURED to be isotropic but actually IS isotropic, and therefore conclude that the cmb is at rest wrt the aether.

 

[Q-reeus]

AFAIK the vacuum polarization in QED is a rank-2 tensor, so it is guaranteed to transform correctly.

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

 

[Q-reeus]

Originally Posted by Q-reeus:
"The kernel issue re LET is that vacuum breakdown, determined in an assumed LET rest frame, will by the moving capacitor argument given, be different - specifically less in any other LET lab frame where capacitor is stationary."

Now we get into the question of what, exactly, the term "LET" means. The standard usage of that term (or what most of us thought the standard usage was until it started getting thrown around in this thread) is a theory that makes exactly the same experimental predictions as SR, but interprets them differently. So "LET" by this definition would *not* predict any behavior different than SR; it would predict that the breakdown threshold is determined by the E field in the rest frame of the source. This "LET" would just attribute that to the fact that, even though the source is moving relative to the aether, the field it generates is moving with it, so they both get transformed the same way and the experimental results are the same as SR predicts.
If there is some other "LET" that makes different predictions, the onus is on whoever is propounding such a theory to explain how it makes those predictions.

OK perhaps it's best to recast the issue somewhat. Agreed that if we define LET such as to always make identical predictions to SR, it is nonsensical to argue one over the other. As both make strict use of the Lorentz transformation that seems settled. But the crux of my argument is the very existence of the phenomenon of vacuum breakdown implies a situation specific breakdown of LT's which is a dilemma for both. The main sticking point really is over your assertion below:

Originally Posted by Q-reeus: "The fact that in SR, transverse E breakdown strength is *not* a function of velocity is a statement that vacuum polarization has some very strange linkage to the source of transverse E (E aint just E) it seems to me."

No, it's a statement that the "breakdown" phenomenon is produced by pumping energy into the EM field until there is enough of it to produce electron-positron pairs, and the critical field threshold is determined in the rest frame of the source. I really don't see what is so mysterious about this.

'Pumping energy in' = application of an E_crit for some minimum duration - by whatever means. Current efforts are creeping towards achieving that in a controlled manner using ultrahigh power lasers. Particle smashers do it routinely but in a messy and extremely brief manner. The gedanken experiment here in principle would do so via electrostatic fields boosted via LT's - and that uncovers the issue we profoundly disagree on. You keep saying breakdown is defined in the apparatus/source rest frame. But on what basis other than sheer assertion? How many times do I have to repeat this: In what way can the vacuum 'know' that a field of given strength E is owing to a source that is moving or static wrt any given lab frame (apart from B field which is not germane to vacuum breakdown issue)?

I deliberately specified long, straight, evacuated coax to highlight this - LT's for motion parallel to axis simply alter the strength of E field uniformly. But pick a standard parallel-plate capacitor or whatever one is comfortable with. The LT's applied to transverse E is plain enough: E -> gamma E. From the start I covered the matter of associated B field in a transformed frame. All that matters here is - how possibly can the vacuum decide there is some 'quality' or 'essence' or whatever about a 'source rest frame' E_rf that sets it apart from another frame where transverse E could be, well, anything from close to E_rf to infinite? To repeat; "E aint just E" is somehow implied in all of this, but on what basis?
SR has by postulating the complete absense of any 'physical' vacuum, in principle no means of laying the groundwork for a resolution. LET however can at least suggest a resolution in that a 'true rest frame' would be the natural reference frame to define as having a maximal value for breakdown E_crit.
If you can't see any issue by now then I guess it's quits from me. No point bashing ones head against a brick wall.

 

[PeterDonis]

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

Ok, good, we have agreement that far.

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

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

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

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

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

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

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

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

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

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

 

[Dale]

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

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

 

[ghwellsjr]

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

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

 

[harrylin]

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

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

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

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

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

 

[Q-reeus]

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

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

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

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

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

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

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

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

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

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

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

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

 

[Q-reeus]

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

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

 

[Q-reeus]

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

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

 

[ghwellsjr]

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


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

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

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

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

 

[PeterDonis]

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

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

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

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

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

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

 

[TrickyDicky]

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

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

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

 

[Dale]

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

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

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

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

 

[Q-reeus]

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

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

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

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

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

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

 

[Q-reeus]

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

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

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

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

 

[Dale]

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

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

 

[PeterDonis]

The article focuses on relativistic plasma oscillations

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

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

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

They also don't discuss LET, of course.

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

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

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

 

[PeterDonis]

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

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

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

 

[stglyde]

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

No, I am not.

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

?

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

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

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

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

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

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

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

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

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

 

[Dale]

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

Such as the aether.

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

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

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

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

 

[Aether]

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

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

 

[stglyde]

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

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

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


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


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


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


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


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


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

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

I have no clue as to what you are thinking?