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Does a free falling charge radiate ? 
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#1
Feb1613, 03:35 PM

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It appears paradoxical because to an observer falling with the charge it is as though the charge is at rest and therefore should not radiate.
Also, if we place a charge on a table, shouldn't it radiate as there is a normal reaction force from the table? 


#2
Feb1613, 03:57 PM

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Frequently asked question. See the links to previous discussions at the bottom of the page. Yes it radiates, because a charge is not a point object. The field surrounding it is extended, and even though the center may be following a geodesic, the other parts of the field are not.



#3
Feb1613, 04:14 PM

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#4
Feb1613, 05:03 PM

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Does a free falling charge radiate ?
The electron itself is a pointlike object. But any charged object is surrounded by a Coulomb field which contains stressenergy and extends to infinity. For a charge falling in the Earth's gravitational field, for example  part of the EM field is on the other side of the planet!
In addition to radiating electromagnetic waves, a falling charge gets distorted by the varying gravitational field as it goes along, and radiates gravitational waves too. 


#5
Feb1613, 06:20 PM

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#6
Feb1613, 09:06 PM

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Indeed, I remember watching Edward Purcell standing in front of a blackboard, describing the physics in exactly those terms, just so that we couldthen consider what would happen when the point particle was instantaneously displaced by a small amount.... 


#7
Feb1613, 09:12 PM

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#8
Feb1613, 09:49 PM

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By the way, Rindler's text has a small discussion on this caveat but it pretty much just reiterates the point made by Bill already.



#9
Feb1713, 04:27 AM

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I should disagree. The Coulomb field external to electron does not carry electrical charge.
If you calculate the Gauss integral for the electric field of the electron, such that the electron is not enclosed by integrating surface, the integral is zero Coulombs. On the other hand, if the accelerating electric field generates EM radiation, then it could be the the explanation. BR, Topi 


#10
Feb1713, 05:14 AM

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The Earth itself is a "freely falling particle", following a geodesic in its orbit around the sun. If the Earth had a net charge (and it may well have!), the problem lies entirely within the classical physics of Newton and Maxwell, and the circular motion of this charge would necessarily produce an outgoing EM wave.



#11
Feb1713, 05:28 AM

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#12
Feb1713, 01:37 PM

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The Coulomb gauge is not Lorentz covariant, why would you use it in a QED context?



#13
Feb1713, 11:02 PM

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This is notorious question. Part of the reason for disagreements is that the situation is often not specified well enough, leaving the contributors to let their imagination fill in the details.
I propose to focus to the original question which is stated almost well enough: This is the answer just for the situation proposed in the question above. It does not say anything about any other scenario, like what free falling observer sees. That is a different question. 


#14
Feb1813, 02:32 AM

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How should we define 'radiation' in curved and nonstationary spacetimes?
 nongeodesics trajectories  nonconservation of energy along a trajectory  1/r behaviour in the Coulomb potential for large r  ... 


#15
Feb1813, 05:40 AM

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What I'd like to get right is if from Bill's reply we must infer that point charges don't exist.



#16
Feb1813, 05:46 AM

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#17
Feb1813, 07:47 AM

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Bill, we had this discussion a couple of times and my answer was always that this definition does not work in notasymptotically flat spacetimes, therefore one should look for a local definition; this is a general idea in GR: replace global definitions by local ones, look at all horizon discussions where one tries to get rid of nullinfinity
(of course "field" Is correct and "potential" was nonsense, I am sorry for the confusion) So why not using a comparison of trajectories of a noncharged and a charged particle? Of course this does not answer the radiation question directly, but it turns it round: we do no longer ask whether free falling particles radiate, but whether charged particles are in free fall according to the equivalence principle. In parallel we should address the question whether (why) charged particles which are not in free fall do or don't radiate, i.e. particles which are stationary in a gravitational field, e.g. at fixed radius in a lab on the earth. 


#18
Feb1813, 09:29 AM

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