
#361
Dec1911, 11:20 AM

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#362
Dec1911, 01:59 PM

Physics
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PF Gold
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#363
Dec1911, 02:48 PM

Physics
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PF Gold
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For the rest of your post, do you have any actual math? I see a lot of English words and some equations with symbols in them but I can't give them any precise meaning. It's still handwaving. Can you write down some precise covariant condition like the one I wrote down? 



#364
Dec1911, 03:06 PM

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#365
Dec1911, 03:12 PM

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PF Gold
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#366
Dec1911, 03:46 PM

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#367
Dec1911, 04:36 PM

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#368
Dec1911, 04:39 PM

Mentor
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#369
Dec1911, 04:39 PM

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PF Gold
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#370
Dec2011, 04:23 AM

P: 1,115

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



#371
Dec2011, 08:53 AM

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PF Gold
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#372
Dec2011, 10:32 AM

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#373
Dec2011, 04:38 PM

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PF Gold
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(1) In the source rest frame, E * L >= V_crit. (2) In the rest frame of a pair being created, gamma > gamma_crit. where gamma_crit is the gamma necessary to make E >= E_crit in the pair's frame. given that the first criterion is satisfied in the source rest frame (i.e., gamma_crit is calculated relative to the source rest frame). My first comment is that I don't understand why the second criterion is even necessary; again, given that the first criterion is satisfied, there will always be *some* frame in which E >= E_crit, so I just figure out what the gamma is for that frame relative to the source rest frame, and say that that's the frame in which pairs will be created at rest. So if the first criterion is satisfied, the second must always be satisfied in some frame. Why then is the second criterion necessary? I can see why you might want to use the second formula to predict, for example, what the initial current due to the virtual pairs would be in the source rest frame (since that will depend on the velocity of the created pairs), but why is it a criterion for determining whether breakdown can occur at all, given that the first criterion is satisfied? My second comment is that I can always meet the first criterion by making my capacitor plate separation large enough, given some limit on the E field I can produce at the plates. Basically your criterion is saying that there must be a certain amount of energy per unit charge available between the plates (since that's what voltage is, energy per unit charge). Your first criterion does *not*, so far as I can see, place any limit on how short a time that voltage needs to be applied; it only sets a lower limit on the voltage itself. So I don't quite see how your first criterion is related to your "minimum duration" requirement. I certainly agree that your criterion makes a very different experimental prediction from mine. My criterion requires E = E_crit in the source rest frame; your criterion requires only V > V_crit in the source rest frame, which is much easier to achieve. In fact, as far as I can see, if your criterion were correct, it should be trivially easy for any lab with a high voltage source to induce breakdown; after all, your criterion amounts to V_crit = 10,000 V, which is easy to achieve. So your route to a Nobel Prize is easy: just hire some test lab to fire up a high voltage source and connect it to a capacitor, and watch the electrons and positrons pour out. 



#374
Dec2111, 04:26 AM

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#375
Dec2111, 06:16 AM

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#376
Dec2111, 10:12 AM

P: 1,115

[In what follows, I will agree to your request and use L rather than l for length symbol, and further use V rather than v for volts]
"And taken to its logical conclusion, this would again imply that breakdown should occur *immediately* upon turning on any field source, regardless of its state of motion, since there will always be *some* vp that will sense E > E_crit. That's obviously false, so again something must be wrong with your argument." Up to you whether to admit that claim, made twice, is mistaken. Rereading #338, where this scenario began, it's more than clear E and L are to be taken as orthogonal in order to make any sense at all. And as quoted above, that criteria was expressly stated in #356. Forget it all somehow? Assuming no pair creation near hightension power lines etc., one conjecture might be to suppose that applied E somehow suppresses high gamma factor flux of vp's in source rest frame. Immediate problem with that is for a capacitor configuration, many high gammma vp's would be originating outside of appreciable applied E region, so subsequent reduction to gamma < gamma_{crit} within E region implies weird electrodynamics indeed. 



#377
Dec2111, 11:56 AM

Physics
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PF Gold
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#378
Dec2111, 01:19 PM

P: 1,115




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