Am I right in thinking that you're thinking about classical physics on flat spacetime? If so, a static charge does not radiate (regardless of the observer's acceleration). Unruh radiation is a quantum phenomenon, and it is associated with the non-uniqueness of the quantum vacuum. It is unrelated to classical radiation.

Dear David.

Thank you for the answer. There is a similar topic in Electrodynamics Q&A section added by Paolo Miocchi which is entitled as: „Does a free-falling, electrically-charged body fall to the Earth's surface with the usual 9.8 m per square second acceleration?“ I’m really puzzled by conclusions of the paper which is referred there: http://arxiv.org/abs/gr-qc/0006037. The conclusive statement of Shariati & Khorrami is: „That is, in a static spacetime, a supported charge does not radiate according to another supported observer; neither does a freely falling charge according to a freely falling observer. Also, a freely falling charge does radiate according to a supported observer, and a supported charge does radiate according to a freely falling observer.“ I understand that radiation is a relative quantity undergoing Lorentz transformation between two inertial reference frames. But what I don’t understand is that if the radiation does NOT exist in one reference frame, how can it exist in another, even non-inertial, reference frame? Maybe I did not understand the conlusion correctly.

Hi Jaromir,

This is a very subtle topic. I can make sense of it from a classical perspective by noting that the observer has to measure the electromagnetic field in the appropriate part of spacetime in order to 'see' radiation. An accelerating observer may not be able to access the radiation field. What I find more intriguing is to think about the problem from a quantum perspective. Does a photon detector click if you drop it near a static charge?

I'm still thinking about it!

Hi Jaromir,

As far as relativistic considerations go, the charge must radiate in the accelerated frame, whether you are speaking classically or quantum mechanically. And, yes, the detector must click depending on the selected energy range, efficiency and orientation.

And regarding your puzzlement on the existence of radiation in the accelerated frame and the non-existence in the inertial frame, it is natural in relativity theory. Are we puzzled about existence of acceleration in the accelerated frame and its non-existence in the inertial frame? Therefore, it is the same with all such entities and quantities associated with acceleration which exists in one frame and does not exist in another.

Dear Mozafar,

What do you mean by acceleration of the field? The em field cannot be accelerated, If at all they move, they always move with constant speed i.e. speed of light in vacuum. We should not be thinking of the particle as detached from its field. It is commonly said that the particle "produces" a field. But this is certainly not as if the charged particle was, once upon a time, living without its field and one fine morning it produced a field! The charge and its static field coexist. We cannot even think of a charge without its field. The moment the particle is , the field is. In no frame the field will completely vanish leaving the particle "bare"! It will be present in some form or the other: as E or as E&B together.

Now, when the charge starts moving uniformly in some frame, in addition to electric field a static magnetic field appears in that frame only (and not in its proper frame in which the charge continues to be at rest). We are not surprised at the appearance of the B-field in the moving frame and its non-appearance in the proper frame.

Similarly, when it accelerates in some frame, there is radiation of em waves with respect to that frame only, and not with respect to a non-inertial frame in which the charge is at rest.

what's perplexing in relativity is the existence of photons in the accelerated frame and their non-existence in another inertial frame, since we take for granted that all things must exist with respect to all frames, and their properties may only differ from frame to frame. What relativity tells us is that even existence itself becomes a frame-dependent property. what is existence? Existence is relative and results from the interaction of one entity with another. Things mutually exist with respect to each other. (Can we ever say that something exists w.r.t. us and it has absolutely no interaction with us, in any manner whatsoever under any circumstance?)

Relativity brings in one further factor, the frame, as a determinant of existence.

Yes Mozafar,

I see your point. It makes perfect sense to talk about acceleration of the field considering that it carries energy density, and hence as demanded by the equivalence principle, it should be possible to get it have an acceleration in a gravitational field. But the question is the acceleration of the charge has to go with that of the field always, since the charge and the field are not separate entities. They together form one whole. So whether the charge is in an accelerating frame or you are falling freely in an elevator, it is the same thing. You are going to see radiation from the charge both ways. The question can best be settled by experiments. Is there any experimental evidence that the static charge does not radiate viewed from an accelerated frame?

Mozafar,

(1) You are partly correct in saying that the field and the charge are different entities. Well they look like being different, actually they are not. When the charge does radiate, it does not radiate away all of its field and become bare ! Part of Its field remains intact as well. Next, as an aside, even if a photon gets radiated from the accelerated charge, it remains entangled with it all along, and this entanglement is an experimentally observed fact.

(2) You cannot kick the electron without first kicking its surrounding EM field. In fact ,the same QFT as well as CFT tell us that the kicking (interaction with the electron) can occur only through the field. No direct kicking of a bare electron is possible, and there is no bare electron available either.

(3) The above applies to the freely-falling elevator frame also.

Dear Jaromir, for single electron with respect to the vacuum energy you can define absolute value of acceleration (as the rotation of four-velocity), but you can not define absolute value of velocity. So electron emits electromagnetic energy with power P = 2e^2a^2/(3c^3), where a is acceleration with respect to vacuum but not to the observer. Note that the situation will be different if observer will interact with charge.

Thank you all for inspiring answers. I think it is quite apparent that the charge radiates, whenever it is accelerated with respect to the observer; the only frame in which no radiation is detected is the co-moving frame. From this point of view, it partly resolves my puzzlement why radiation can exist in one frame and does not exist in another. This part is quite intuitive. But what I still find counter-intuitive is the “radiation emanating from static charges” when viewed from accelerating frames.

In my opinion, this question could be answered experimentally with use of RF acceleration cavity or, even better, with laser wakefield accelerator, as the accelerating particles should Compton-scatter the “photons emanating from static charges”. However, this still leads me to the same contradiction: How can we Compton-scatter photons which do not exist in our (static) reference frame, but exist in the accelerated frame? Will the Compton scattering occur actually? This sounds like nonsense to me.

PS. Rajat, is there any reference dealing with the entanglement between the radiated photon and the accelerated charge? I would be thankful if you post the link.

"What relativity tells us is that even existence itself becomes a frame-dependent property". I find that statement very hard to accept and to reconcile not only with common sense, but perhaps even with thermodynamics. Please consider the following example:

The accelerated detector and the static charge. If the detector detects photons, it could trigger for example a bomb that makes it explode. Rajat, are you telling us that for an observer in one reference frame the detector explodes and for another observer in a different reference frame it doesn't?

Dear Pedro Almendral,

For bomb explosion in one frame and non-explosion in another and many more such examples, Please see Spacetime Physics by J. Wheeler and E. Taylor for your second part.

The remark referred to in the first part is a little more general and philosophical as a comment, but nevertheless, it is true in Relativity theory.

Please see my previous posts on this thread for clarification.

Regards

Rajat.

Dear jaromir,

That comment was an intuitive insight from me. But I found upon a search that people have already worked on that idea. Please see this article :

(!) arxiv.org/pdf/0910.4764 by S Varro - ‎2009

and also

(2) the following 2005 thesis by M. Weber;

Quantum optica experiments towards atom-photon entanglement.

Regards,

Rajat

Dear Rajat,

I am having a look at "Spacetime Physics" by Wheeler and Taylor but this book deals with special relativity and I do not find any example similar to what I mentioned (existence of an explosion in one frame but not in another due to the detection of photons in one reference and not in the other). Could you please tell me in which chapter should I look?

I have read your previous post but I still do not understand what is your opinion about what would happen with the photon-activated bomb. If we had a static charge in our laboratory and if an accelerated detector passing by there sees photons and explodes, that explosion (of the accelerated detector) should exist in our laboratory reference frame too: we had to conclude that the charge is constantly emitting energy although we are not able to detect it in the laboratory frame, but in that case where does the energy come from?.

This question keeps getting asked in one form or another on RG and other forums.  Has anyone compiled a list of answers?  I have a question ... what is unsatisfactory about the existing answers that it keeps getting asked?

Einstein begins, in the first paragraph of his paper on SR, not with an abstract, but with: "Maxwell’s electrodynamics ... when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. ... if the magnet is in motion and the conductor at rest, there arises in the neighbour- hood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electro- motive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case."

In other words, if the charge accelerates we say it is radiation, but if the conductor moves, we say it is induction.

Feynman, in the second link below, argues that radiation only occurs when a 3rd derivative of position is present, i.e. acceleration is not uniform.  In the usual sinusoidal case, of course any order of derivative is present since they are all just 90 degree phase shifts, and this question does not arise.  This has, I think, resulted in the "sloppy thinking" that it is acceleration that produces radiation.  The proper term for the 3rd derivative is, I think, "jerk."

Kevin Brown (3rd link below) gives an extensive discussion, but begins with the issue that is really behind this question most of the time, that of a charge which is stationary, but in a gravitational field and in some sense "accelerating."  He points out that if it really radiated, we'd have a perpetual source of free energy, therefore it does not.

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf

http://www.applet-magic.com/feynmanEM.htm

http://www.mathpages.com/home/kmath528/kmath528.htm

Let me point out that there is a related thread, in which some of these questions have been discussed in more detail:

https://www.researchgate.net/post/Does_electromagnetic_dipole_radiation_satisfy_general_covariance_in_GR#55cdab3b6225ffc4c18b4660

Robert,

I do not know what Feynman really said in detail about accelerating charges, but I am almost sure that the explanation given in http://www.applet-magic.com/feynmanEM.htm is wrong or at least incomplete. Here's the problem: the pretendedly correct formula for radiation losses is stated  to be: (dW/dt) = −(2/3)(e²/c³)v·(da/dt). This means that a moving charge whose acceleration increases (da/dt>0, v and a parallel) would pick up energy!

It does not help assuming that the formula should have the opposite sign, because then a charge whose acceleration decreases in time should pick up energy, which is equally absurd to believe. For if you accelerate a charge uniformly in its own frame, its acceleration will always decrease in an inertial frame (where this formula from classical electrodynamics is supposed to hold), simply because it cannot become faster than the speed of light. The "exact" radiation formula would then predict that a charge in hyperbolic motion will absorb energy from empty space!

Klaus, I did not read the applet-magic reference in detail, thanks for the info.  That author probably just made some mistake.  Somewhere long ago I did find and read what Feynman said but could not locate it when I made that post.  What do you think of Kevin Brown's discussion in Math Pages (the last link)?

He is somewhat more critical about the applicability of the basic equations on which the idea is based that a uniformly accelerating charge does not radiate. But he cites the same equations as the applet-magic reference. So I am wondering a bit. People emphasize that these equations give zero back reaction (from which they conclude zero radiation), but why don't they comment on the sign change, which seems to suggest even the "sucking in" of energy by the charge? (This happens according to the formula, when the acceleration increases with time, which it certainly cannot do forever, but which is definitely possible for some finite time.)

It is a bit hard for me to be sure I understand Brown's (quoting Feynman) equation (1). But when it comes to equation (2), the ordinary part (proportional to acceleration) is positive, and for the right hand portion, in the sinusoidal case, it oscillates in such a way as to contribute nothing and can be discarded.  It would appear there isn't a sign issue with (2), wouldn't you say?  Is there any question about getting from (1) to (2)?  

The formulas are identical. (Just use the product rule to evaluate the derivative of the second term of (2).)

The case I discussed was that of linear monotonously changing acceleration, aligned with velocity. In the case of sinusoidal motion, dx/dt and d3x/dt3 always have opposite sign, so there is no sign issue. In the case of linear monotonously changing acceleration, dx/dt is parallel or antiparallel to d3x/dt3 between two zeros of dx/dt, and in such an interval any sign change of d3x/dt3  will switch between a case of energy loss by radiation and energy gain by radiation (probably incoming radiation from advanced sources, i.e. "radiation from the future"...)

I understand the sign switch (and the ambiguous interpretation, though in a real problem I think that can be re-absorption from the same field as it bends and unbends).

But the sign question is one of what is the work term in equation (1).  Brown writes as if it is work done on the particle by a force opposing radiation reaction.  But whether those "words" actually match the meaning of the sign ... I'd have to work through a derivation of (1) to tell.  Sometimes people write loosely with respect to their sign conventions.  I don't know that's what Brown did, it's just what I'd investigate first.

Going back to a visual approach, in case anyone else is reading this exchange, one can think of it this way.  You have seen pictures, probably, of field lines bent because a particle is accelerating?  In the (non-inertial) frame of the particle, if there is no change in those bent field lines, there is no radiation.  (This doesn't prevent induction with respect to relatively moving observers.)  In intro EE field books, radiation is usually drawn as a "kink" in the field lines which moves outward from the particle ... no matter what frame one is in.

An example of the uniform acceleration case is hard to find, but see first link below.

Examples of the propagating kinks are all over the place, see second link below.

In the first (uniform) case, even though the field lines are bent, one cannot identify a feature that could be moved.

http://file.scirp.org/Html/6-4500200/791a9173-39a1-4f6a-8cef-d9e2adb62951.jpg

https://www.google.com/search?q=image+electric+field+of+accelerating+charge&tbm=isch&tbo=u&source=univ&sa=X

The best way to answer is to calculate. You will find the results in this paper:

http://adsabs.harvard.edu/abs/2017CQGra..34s5008C

I copy the conclusions (the electromagnetic and gravitational flux of a charged black hole are calculated in the frame of an accelerated observer):

"We obtain the energy–momentum tensor of the gravitational field in a stationary frame, and we calculate its contribution to the total energy of the system. We study the same gravitational field measured by an accelerated frame and we analyze how the energy–momentum tensor is transformed. We found that in the accelerated frame, a Poynting-like flux appears for the gravitational field but not for the electromagnetic field."