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'relativity' of radiation of uniformly accelerating charge

  1. Sep 27, 2010 #1

    PAllen

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    I notice this question has been touched in a general physics thread, but the discussions there on relativistic aspects of the question seemed clearly misleading to me. My questions focus specifically on the view from different frames and the application of the principle of equivalence, so this seems the best forum to me. This question was triggered by scanning two papers:

    http://arxiv.org/PS_cache/physics/pdf/0506/0506049v5.pdf

    http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.3968v1.pdf

    These papers come to opposite conclusions about (both argued from special relativity point of view, but the first has, perhaps, more of a GR flavor) what an observer comoving with an accelerating charge would observe (on all other questions, they seem to agree, though using completelhy different techniques; as I understand it, there is one other subtle disagreement: the first paper above suggests that the question of what an accelerating observer would see for an inertial charge is unclear treated using Maxwell/SR, while QFT indicates they would see no radiation; this is at the end of the paper. Meanwhile, the second paper suggests this result can be derived strictly clasically, no quantum theory needed).

    One more bit of background before I pose my main question: mine. I studied physics in college as my major for 3 semesters before dropping out and pursuing a career in software. In some ways, I know more than this implies, as tought myself enough tensor calculus and GR in highschool to solve simple problems in GR rigorously. However all of this was 35 years ago. Since, I have avidly followed physics qualitatively but not quantitavely.

    My question concerns the following line of reasoning (my own) which leads me to a seemingly impossible conclusion if I accept the first paper's point of view:

    The conclusion of the first paper is that a uniformly accelerating charge radiates as observed by an inertial observer, but not as observed by a comoving observer. It must follow that for a charge on the surface of a planet (by equivalence principle), that free falling observer detects radiation but not an observer on the surface. If this were not true (the conclusion from equivalence principle), it would become possible to distinguish acceleration in a rocket from gravity without recourse to tidal effects (put a charge on a table, drop a photon counter; if the result were different in these cases, a closed small lab could distinguish rocket acceleration from gravity non-tidally). Given this conclusion, imagine a charged, nonrotating planet (hey, it's a thought experiment, not plausible reality; non-rotating as otherwise rotating charge effects would swamp other effects). Imagine a network of detectors mounted on pedestals above the surface, and another set of free falling detectors. As they pass each other, the falling set detect outflow of radiation, while the adjacent fixed detectors do not. More generally, distant inertial observers would seem to perceive the planet as radiating (and thus, perforce, losing mass), while the surface observers detect no radiation or mass loss. This seems impossible - one observer sees the planet evaporate, and the other sees no such thing.

    The claims of the second paper avoids this contradiction at the expense of saying both obersvers see the planet evaporate (if one uses my equivalence reasoning on the conclusions of the second paper).
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    Any thoughts on which paper is right or on the merits of my equivalence reasoning would be appreciated, especially from professional physicists. (As a long time physics dabbler who knows real physicists, I perceive a huge gulf between others like me and the professional).
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    From reading the one thread I found vaguely related to this topic on these forums, let me disagree with three opinions expressed there, and make a fourth general observation:

    1) Equivalence arguments for uniform acceleration of charges are misleading because of tidal effects. I say nonsense. There is no limit in GR to how closely a planetary field can be free of tidal effects. GR in no way prevents construction of a gravitational field that for a 1 lightyear cube and a year of time differs from uniform acceleration by no more than one part in 10**50 (for example).

    2) Principle of equivalence is not really important, e.g. quotes from Synge. Synge is one of the books I read in highschool and loved, but with all due respect, I find his view on this is nonsense. Mathematically, equivalence is precise in the limit, and for any finite region to any chosen experimental sensitivity, in practice (thought not necessarily on earth). Clifford Will has made a career out of precise definitions of flavors of principle of equivalence and which experiments validate which flavor. I think this fully displaces Synge's view.

    3) While it is somewhat bizare to imagine a charge on a table radiating, the claim the it can't happen because no work is done is inadequate. To an inertial observer, the work done by atoms of a planet pushing on a 'stationary' charge is just as real as the work done by a rocket pushing on a charge from the point of view an inertial observer in/near the rocket.

    4) I am aware that a big issue in all of this is that 'what is radiation' is non-local and non-trivial in Maxwell/SR. Classical fields make the field local, with finite propagation speed, but radiation has no local definition. Instead, you must define some feature propagating in a certain way, or integrate around a region to compute power balance. Meanwhile, in QFT, a field is more complex (virtual particles, one, two, three... loop effects), while radation is local and trivial: did a photon counter detect a photon. I perceive this conundrum is related to why there is disagreement between two papers in the 21st century about something that 'ought' to have been resolved before mid 20th century.
     
    Last edited: Sep 27, 2010
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  3. Sep 27, 2010 #2

    bcrowell

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    There are basically two things that make this debate inconclusive. (1) There is no mathematically rigorous statement of the equivalence principle (see Sotiriou, http://arxiv.org/abs/0707.2748 for a review). (2) There is no mathematically rigorous way to classify fields as radiative or nonradiative. Both #1 and #2 are basically issues having to do with the meaning of locality.

    That's not my reading of the paper. As I read p. 5, they're saying that they've already answered the question in a purely classical theory, but they want to come back and see what else they've learned from a quantum-mechanical point of view. Since the problem never gets anywhere close to the Planck scale, I think a satisfactory resolution would have to be purely classical.

    You've presented two possibilities: (1) the e.p. is unimportant; (2) the e.p. is important and precisely defined. My opinion is that (3) the e.p. is important and not precisely defined. The key here is the word "precisely." Will works at the interface between theory and experiment. The e.p. is sufficiently precise so that in real-world experiments its ambiguity is unimportant. The possible violations of the e.p. that we discuss in the "falling charges" debate are many orders of magnitude smaller than that, and completely impossible to test empirically.
     
  4. Sep 27, 2010 #3
    From the perspective of the co-accelerated observer (in flat space), the field is constant in time, and so it is not "radiating" in any conventional sense (it would not induce oscillation in an antenna).

    Yes, this seems to contradict the implication made in one of those papers (so if you bother to defend their approach we could discuss further their calculation and interpretation of the Poynting vector). As a matter of etiquette when citing the arXiv, please always link to the abstract and not to the pdf. Next, did you check where those papers have been published (and whether they have been peer reviewed)?

    Your thought experiment of distant observers from a planet is ignoring the curvature of spacetime: far distant observers, exactly like those on the surface of the planet, do not measure the fields to be changing (that is, in any conventional sense, neither observe radiation). The fact they experience different amounts of inertial acceleration is irrelevent; in fact, the whole reason for this paradox is the mistake of trying to produce a general law linking radiation to "acceleration" instead of solving whatever problem in full.

    Regards your comments on particles and QFT, it may do well to look up Unruh radiation. Whether or not a real particle is present at an event in spacetime is not trivial and is even subjective.
     
  5. Sep 27, 2010 #4

    bcrowell

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    But how can this make any difference when we're nowhere near the Planck scale? The debate is a debate about a classical field theory.
     
  6. Sep 27, 2010 #5
    Are you saying the original post was was off-topic for mentioning particles and quantum fields? :wink:
     
    Last edited: Sep 27, 2010
  7. Sep 27, 2010 #6

    PAllen

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    This is a reply to cesiumfrog.

    "From the perspective of the co-accelerated observer (in flat space), the field is constant in time, and so it is not "radiating" in any conventional sense (it would not induce oscillation in an antenna). "

    That is exactly what these two papers disagree on. I certainly lack the expertise to distinguish their claims. However, we do have a professor of physics disputing this.

    "(so if you bother to defend their approach we could discuss further their calculation and interpretation of the Poynting vector)"
    I don't have the expertise to do so. I will read and attempt to understand what I can of any explanation of what is wrong with their analysis. I would appreciate anything you have to say on this.

    "As a matter of etiquette when citing the arXiv, please always link to the abstract and not to the pdf"
    Thanks for this tip. I did read all rules, faqs, and suggestions before making my first post here, but it is obviously unsurprising that all matters of etiquette are not covered.

    "Regards your comments on particles and QFT, it may do well to look up Unruh radiation. Whether or not a real particle is present at an event in spacetime is not trivial and is even subjective."
    I have read a little about Unruh radiation (enough to see that while the Unruh effect is not really disputed, Unruh radiation is, a bit). I guessed there might be a connection. However, as I never took a course in QFT, nor read any textbook on it, I felt I could not intelligibly relate it to these issues. Actually, I have have developed (stimulated by trying to undersand these papers) a perhaps uncoventional thought on this: It is accepted that a black hole emits Hawking radiation; it is accepted that an exterior observer never sees matter cross the event horizon (well, at least for 'normal' black holes; I am well aware that the the 'cosmic censorship' hypothesis is not only not proven, but disputed by numerical [but not rigorous] calculations). So at what point in the history of a body collapsing into a typical black hole does Hawking radiation start to be emitted? My equivalence argument applied to Unruh radiation suggests there could be a continuum between any mass radiating (once the amount exceeded a quantum threshold) , and hawking radiation. In this case, the second paper's point of view would fit in nicely, simply saying a charged mass might start radiating a tiny bit sooner. However this is all just a speculative handwave that I lack expertise to pursue.
     
  8. Sep 27, 2010 #7

    PAllen

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    This is a reply to bcrowell:

    Thanks very much for taking the time to respond. Having enjoyed a number of hours perusing Clifford Will's website, I never would have guessed your point about absence of complete precision in the equivalence principle, especially related to the scale of an unobservably small effect. I sort of had realized there there seems to be a real issue with an attempt to 'locally' define radiation in a classical field theory. Your confirmation of same is very useful to me. I am glad I chose to post here for the first time.
     
  9. Sep 27, 2010 #8

    PAllen

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    Further replay to cesiumfrog:

    "Next, did you check where those papers have been published (and whether they have been peer reviewed)?"

    Can you tell me how to do this? In the second paper there is acknowledgment that could be due to a peer reviewer (or not, I can't tell):

    "Acknowledgement
    We are grateful to C. A.P. GalvĖœao for bringing to our attention [1] and [2]."
     
  10. Sep 28, 2010 #9

    George Jones

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    Usually, but maybe not always, if an arXiv article is published, there will be reference near the bottom of its arXiv abstract page. Both articles were published in The American Journal of Physics (AJP), while the second paper was published in Annalen der Physik (Ann. Phys.).

    http://arxiv.org/abs/physics/0506049
    http://arxiv.org/abs/1009.3968
     
  11. Sep 28, 2010 #10
    The Poynting vector has the property that it doesn't always indicate radiation, often it just indicates circulation of virtual energy or some such, so it takes care to base claims of radiation on such argument. Also, worth noting that several longstanding paradoxes in relativity turned out to be just failures to convert between coordinate systems correctly.

    But it is straightforward for us to use global arguments: is the system becoming diminished? No. (Got any experience with perpetual motion designs?) Similarly, it is easy to see that no signal will be induced in the antenna of a radiation detector, because the external fields acting there are static.

    I suggest checking where those articles have been cited. That way, without expertise of your own, you can track how the experts have responded to either claim. With any luck you'll find a chain of papers leading to a consensus.
     
    Last edited: Sep 28, 2010
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