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Does the equivalence principle hold for charged particles?

  1. Apr 18, 2005 #1
    I'm new here so this may be an old question. The equivalence principle states (roughly) that one can't distinguish between an accelerating frame and a uniform gravitational field. But an accelerated charged particle radiates. Thus the EP seems to imply that a stationary charged particle in a gravitational field will radiate, but this doesn't happen. The other possibility is that an observer in a frame accelerating along with a charged particle sees no radiation. This seems reasonable, but this question still seems to be the subject of active debate. The question appears to boil down to whether radiation is frame independent (i.e., seen by all observers) or frame dependent (not seen by an accelerated observer). The latter view is advanced in a paper by Shariati in Found. Phys. Lett. 2 (1999) 427–439, entitled "Equivalence principle and radiation by a uniformly accelerated charge" and the former view is held by Parrott in his paper "Radiation from a uniformly accelerated charge and the equivalence principle" in Found. Phys. 32 (2002) 407-440. This guy claims that the EP fails for charged particles. Any ideas on who is right?
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  3. Apr 18, 2005 #2

    Meir Achuz

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    I believe that the EP does fail for charged particles. It is just intended for gravitiation in the absence of any EM effects. Einstein tried for 30 years to include EM and GR in a unified theory and failed. Poor fellow did not believe in QM.
    He stopped his quest 50 years ago today.
  4. Apr 18, 2005 #3


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    Funny, exactly the same question puzzled me for a while.
    I still don´t know the answer, but I think that radiation is frame independent. There must be some other rules.
  5. Apr 18, 2005 #4


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    It seems that answering this question is actually quite tricky, and that our current theories of electromagnetism may not be up to the job. See the lengthy discussion here:


    Here are the first three paragraphs:
  6. Apr 18, 2005 #5


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    So we don´t know?
  7. Apr 18, 2005 #6


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    I think that radiation (in the sense of "photon number") is "frame independent" only for inertial frames. There's no good short name for an arbitrary coordinate system, but photon number is not conserved by general coordinate transformations. Look at unruh radiation for an example.

    So it doesn't suprise me that one observer claims the photon number is zero and the other observer claims the photon number is not zero if one of the observsers is in an inertial frame and the other is in an accelerating coordiante system - because "photon number" isn't conserved by that sort of coordinate transformation.

    I don't quite understand why people (Ich apparently isn't alone) think that "radiation" is coordiante-independent. I'm not sure if it's an actual difference in belief, or whether their defintions don't match mine.

    This is one of those questions I've been meaning to dig into more "someday". Meanwhile I will happily continue to believe that radiation is not coordinate independent unless someone can show me some reason why it should be.
    Last edited: Apr 18, 2005
  8. Apr 18, 2005 #7
    The detection of radiation is frame dependant. This is true for both uniform and non-uniform g-fields. This is a topic which comes up often here so I placed some references online. See http://www.geocities.com/physics_world/misc/falling_charge.htm

    The former is correct. Parrot is incorrect.

    Last edited: Apr 18, 2005
  9. Apr 18, 2005 #8


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    Pete is correct. It is frame dependent. A charge will appear to radiate any time it is accelerating with respect to the observer. It does not matter which one is accelerating, the charge or the observer. An observer coaccelerating with a charge will not observe it to radiate. If acceleration were a manifestation of absolute motion, all charges would appear to radiate and the intensity would fluctuate seasonally due to variations in earths orbital acceleration.
    Last edited: Apr 18, 2005
  10. Apr 18, 2005 #9


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    Seems like this would be an easy effect to confirm experimentally. Has it been? If not, why not?
  11. Apr 18, 2005 #10


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    It is tricky, but Maxwell's theory is fine as long as we don't try to force it to accomodate the fantasy of (classical) point particles.

    Anyway, the textbook derivations (which are incomplete) say that a charge with nonzero 3-acceleration with respect to an inertial frame in flat spacetime will appear to radiate in any such frame. This result does not apply to a charge sitting on the surface of the earth. As others have mentioned, even the definition of radiation becomes nontrivial in accelerated frames (or ones in curved spacetime).

    It is also not true that all accelerated charges radiate. The statement that they do is a simplification. The actual conditions are extremely complicated (they're not even completely known except in implicit form), and highly dependent on non-standardized definitions.

    Although this is personal preference, I actually prefer not to use the word "radiation" very much. It is a concept which only makes sense far away from the source(s), so it often makes things very difficult to discuss.
  12. Apr 19, 2005 #11


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    It´s just ignorance. I don´t know much about the topic, so I stick to the notion that photons either exist or don´t exist, just like massive particles (I hope they do at least). Guess I should read more about it.
  13. Apr 19, 2005 #12
    If you've noticed, I've try to restrict myself to saying that its the "detection" of radiation that is coordinate dependant and stayed away from assertions such as a photon exists etc. The Am. J. Phys. articles covers this part in one of the sections. I'll quote it later. All in all its good to restrict yourself to what you can measure rather than what "exists" or not.

  14. Apr 19, 2005 #13
    A closely related question is whether a charged particle radiates when in freefall in a gravitational field. The consensus seems to be that it wouldn't. But would an observer not in freefall see it radiate? The EP would seem to imply that no observer would see radiation. Does this make sense?
  15. Apr 19, 2005 #14
    OK, here's something for pmb_phy. After a little Googling I came up with this recent title and abstract, which states that (classical) radiation is observer independent. The author also states that "A freely falling charge in curved spacetime does not move along a geodesic and therefore radiates." The paper can be found at
    http://arxiv.org/abs/gr-qc/9909035. This seems to contradict what a bunch of you guys are saying. Any reaction?

    Notes on covariant quantities in noninertial frames and invariance of radiation in classical and quantum field theory
    Hrvoje Nikoli´c
    Theoretical Physics Division, Rudjer Boˇskovi´c Institute, Croatia
    August 25, 2004

    A local observer can measure only the values of fields at the point of his own
    position. By exploring the coordinate transformation between two Fermi frames, it is shown that two observers, having the same instantaneous position and velocity, will observe the same values of covariant fields at their common instantaneous position, even if they have different instantaneous accelerations. In particular, this implies that in classical physics the notion of radiation is observer independent, contrary to the conclusion of some existing papers. A “freely” falling charge in curved spacetime does not move along a geodesic and therefore radiates. The essential feature of the Unruh effect is the fact that it is based on a noninstantaneous measurement, which may also be viewed as a source of effective noncovariance of measured quantities. The particle concept in Minkowski spacetime is clarified. It is argued that the particle concept in general spacetime does not depend on the observer and that there exists a preferred coordinate frame with respect to which the particle number should be defined.
  16. Apr 19, 2005 #15
    Thanks for the reference. However at this time I'm in a power down more where I've stopped reading everything to do with science/physics. I kinda need a break after doing this for 7 years straight.
    They do seem to contradict each other. At this point it comes to a few reasons such as each uses a different set of postulates or each uses a different interpretation of results etc.

    This comment makes no sense to me. An uncharged object with no external forces on it (i.e. a free object) need not follow a geodesic in a curved spacetime so I don't see why a charged particle would be expected to. However in a flat spacetime all objects must follow geodesics and therefore the path taken by a charged object must as well. Note that you can't think of a point charge as a pointlike object since the field itself is treated as part of the object itself and the field is not a local object.

  17. Apr 19, 2005 #16


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    The are differing opinions about accelerating observers:

    Classical roots of the Unruh and Hawking effects
    Authors: Massimo Pauri, Michele Vallisneri

    This paper has a pretty decent citation history.
    Last edited: Apr 19, 2005
  18. Apr 21, 2005 #17


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    Teasers about Equivalence Principle: Charged Particles and Radiation

    Often people asked if charged particles will radiate or not in the 2 diff
    reference frames of "thought experiment" suggested by Einstein and
    seemingly argued that Equivalence Principle did not apply due to a
    "dilemma" (I'm going to show you that this dilemma is fictitious) that
    the man in the accelerating lift will see nothing radiating from the charge
    while the outsider will see it radiate.

    I'm here to tell you how this Equivalence Principle should be carefully
    applied as afterwards you can see not just it applies for charged
    particles and radiation but also any other physical phenomena so far
    discovered by human kind.

    To detect radiation from a charged particle, the man in the lift MUST
    rely on a sensor of certain kind (maybe in his brain) that can interact
    with the EM wave emitted from the charge, before he can tell that
    the charge radiates. Now this sensor must also carry charges so as to
    detect the radiation. During the "thought" experiment, you the outsider
    "see" that the charged particle in the lift, even though it's fixed in certain
    solid state in the lift, it will still radiate because it's accelerating away
    from you the outsider ...

    However, do you, being now the outsider, also see that the charges in
    the sensor MUST also radiate? Now, you get the answer. The man
    in the lift, by using that sensor alone, can never detect any radiation
    from the charged particle; because for the outsider, even though he
    observes radiations from the charge and the sensor, these two will
    counter each other and the sensor will still read nothing. To the man
    in the lift, he still cannot detect any radiation from the charge no
    matter what experiment he carries out, given that the experiment
    must be carried out within the world of the lift!

    The second "thought" experiment will be like this: the charge in the lift
    is not fixed to certain solid, but freely in the air. When the lift accelerates,
    to the outsider, no radiation is observed from the charge. But the sensor
    which is fixed w.r.t. the lift is now radiating. Hence the sensor will still
    read and the man can detect the charge radiation and "think" that the
    charge really radiates by dropping towards the floor due to "gravity."

    Can you tell a charge radiates or not by NOT using a device with EM
    interaction? To interact and know the existence of a target, you need
    to play the same game of interaction.

    Similarly, once trained up a bit for the thought experiment, you can
    now easily distinguish among all the FALLACIES posted in the Internet
    while they can hardly get into any Physical Review Letters. Examples
    like the energy in any mass built-up after a long period of time in the
    lift will smash things like crazy bombs while forgetting that the whole
    lift and the person and any detector in the lift will also gain such crazy
    energy in such crazy thought experiment and hence overlooking the
    experiment in the lift in fact still cannot detect such crazy energy.
    There can be any no. of examples of fallacy that you can draw from
    if you apply the Principle wrongly.

    We must be VERY CAREFUL when applying the Equivalence Principle.
    All things happened in the lift must also be considered since they are
    all accelerating away from the outsider. If the man in the lift really
    carries out an experiment to read things, you have to "think" about
    how the experiment will undergo and all the appliances will suffer the
    same "accelerating" effect. You "cheat" if you suddenly let the man
    in the lift obtains information or points of views from the outsider
    (being a God-like being w.r.t. him alone).

    As a last reminder, Einstein raised the thought experiment to demonstrate
    the equivalency of respective observers and experimental results. Newton
    knew that it applies to inertial frames because it's instinctive, but Einstein
    boldly pushed it further into non-inertial frames. This move is a belief (as
    Einstein didn't know any positive experimental result supporting his theory
    during that time). And the result is that space-time is curved. Our feeling
    of gravity alone is NOT sufficed to prove this reality. Readings from our advanced GPS system can prove this (ok, I won't tell you where I work).

    Equivalence Principle is a very important principle in this universe for if it's
    broken, what you see is not what I see and we can go into a monastery
    and practise Zen and give up materialism. Well, this is another topic.

  19. Apr 21, 2005 #18
    Does this make sense?
  20. Apr 21, 2005 #19
    Chronos: I thought this was a well-defined problem in classical physics. It's really surprising to me that there's such disagreement among experts.

    Qoo: Where DO you work?

    yogi: good question.
  21. Apr 21, 2005 #20


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    This paragraph is confusing to me. You change POV from inside to outside and apparently judge what the inside observer sees from what the outside observer sees him doing. But it seems to me that being very careful as you justly caution, we should not mix up the experience of these two observers but keep them separate. Compare the analogous case of an astronaut falling into a black hole and a distant observer watching the fall. They have two completely different reports of what happens.
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