Charge and the Equivalence Principle

[GRDixon]

A charged particle is held at rest inside a box in gravity-free space. The box is accelerated uniformly. The charge theoretically radiates electromagnetic power. Now picture the same box held at rest in a gravitational field. Does the charge radiate?

 

[PAllen]

A charged particle is held at rest inside a box in gravity-free space. The box is accelerated uniformly. The charge theoretically radiates electromagnetic power. Now picture the same box held at rest in a gravitational field. Does the charge radiate?

There is about a century of debate about this. Feynman has argued that neither case radiates, analyzed classically (in particular, that in an inertial frame, a uniformly accelerating charge does not radiate). Reputable physicists have argued that both cases radiate if analyzed strictly classically. Using QED there are published proofs (that I cannot vouch for - outside of my expertise) that an accerated charge observed by an inertial observer radiates, and the static gravitational case doesn't. I believe the majority view is as follows:

Both classically and with QED, a detector comoving with a uniformly accelerating charge will detect no radiation.
Both classically and with QED, a stationary detector and charge in gravity will detect no radiation.

Experimentally, there is no information. The predicted effect for feasible experiments is too small to measure or isolate from other effects.

[Edit: Some corrections]

 

[atyy]

Yes, a uniformly accelerated charge radiates.

And the EP does not apply.

See reference [2] within http://arxiv.org/abs/0806.0464

 

[PAllen]

Yes, a uniformly accelerated charge radiates.

And the EP does not apply.

See reference [2] within http://arxiv.org/abs/0806.0464

At least the thrust of this paper is a different issue altogether. And I would argue that EP type arguments would immediately suggest an orbiting charge should not radiate because it is moving inertially. [EDIT: I see this is addressed and my interpretation is that an observer stationary relative to Earth would perceive radiation from the orbiting charge, but a detector in orbit next to the charge would not. More preciesly, according the paper, a comoving detector would not detect radiation from the current motion of the charge, but would from earlier motion of the charge, which is no longer inertial relative to the detector due to curvature].

When saying a uniformly accelerated charge radiates, you have to distinguish as observed by whom? A comoving detector or an inertial detector. I can point to strong recent consensus that the comoving detector will not detect radiation.

 

[PAllen]

Yes, a uniformly accelerated charge radiates.

And the EP does not apply.

See reference [2] within http://arxiv.org/abs/0806.0464

To get a violation of EP, you would need it to be true that a comoving detector detect radiation for the uniformly accelerating case, but not for stationary gravity case. My read of recent papers on this is that the former will not happen.

 

[atyy]

Maybe the EP can be "saved" in particular instances, although it generally doesn't apply to charged particles (eg. it's difficult to have a freely falling charged particle, since it will generally be acted on by its backreaction).

Anyway, to go with this line of thought, can a comoving observer ever detect radiation? I generally think of radiation as a far field concept.

 

[PAllen]

Maybe the EP can be "saved" in particular instances, although it generally doesn't apply to charged particles (eg. it's difficult to have a freely falling charged particle, since it will generally be acted on by its backreaction).

Anyway, to go with this line of thought, can a comoving observer ever detect radiation? I generally think of radiation as a far field concept.

Here is a reference with bibliography on the inability of a comoving detector to detect radiation for a uniformly accelerating charge. It used to be on arxiv, but I can't find it there now:

http://www.ofb.net/~wnoise/misc/deAlmeida_Saa_AJP74_p_Y05_unif_rad.pdf

I think the biggest issue for EP isn't the stationary case, but the falling charge case. The case to compare is an accelerated detector in the field of an inertial charge, versus a free falling charge in a gravitational field. Your reference says something about the latter case (indirectly). However, the former case is complicated by the fact that an accelerating detector detects radiation even in empty space in QED (the Unruh effect). However, sticking to classical, do you know of definitive reference on accelerted detector in coulomb field?

Oh, here's a good reference for that case:

http://arxiv.org/PS_cache/gr-qc/pdf/9405/9405050v1.pdf

This refers to classical analysis that an accelerated detector would detect radiation. This would rescue EP for falling charges. However, they argue that quantum mechanically, this is not true. But they also believe:

"In the case
studied above, every approaches must agree with the fact that an inertial electric charge
must stay at rest with respect to, say, a companion uncharged particle."

which your reference disputes. This is why I retain the feeling that this area is not completely settled, and it doesn't help that the effects are too small to measure.

 

[atyy]

It is a distinguished line of thought to say the EP does apply to charged particles, and it is "saved" by careful thinking in each specific case - eg. Peierls himself (!) in one of his two "Surprises" books, and more recently by Almeida and Saa http://arxiv.org/abs/physics/0506049 .

However, my own thinking is that it is better to say that the EP does not apply to charged particles in phenomena involving second derivatives. Eg. J L Martin's and Rindler's textbooks state this caveat, as do Sotiriou et al in their statement of the various EPs in http://arxiv.org/abs/0707.2748 . The inapplicability of the EP for charged particles due to backreaction has a long history, with recent articles being Poisson et al's http://arxiv.org/abs/1102.0529 and Gron and Naess's http://arxiv.org/abs/0806.0464

However, the laws involving charged fields and their interaction with force fields need only first derivatives to state, and can enter Lagrangians with minimal coupling to the metric, and in that sense - obeying minimal coupling - charged particles do obey the EP.

 

[GRDixon]

Thanks, guys. I personally think that the following resolves the conundrum: A charge, subjected to a constant FORCE, does not radiate (although it accelerates). Thus the accelerating charge does not radiate, and, as per the EP, it does not radiate when held at rest in the gravitational field. But note that if the force on the accelerating charge is not constant, then it will radiate. Or, equivalently, when the charge's position is changed in a non-constant gravitational field, it will radiate (even if the change occurs at a constant velocity).

 

[atyy]

Although I think it is generally not useful to talk about the EP and charged particles, I do think this is paper by Harpaz and Saoker is really very cute http://arxiv.org/abs/physics/9910019

 

[PAllen]

Although I think it is generally not useful to talk about the EP and charged particles, I do think this is paper by Harpaz and Saoker is really very cute http://arxiv.org/abs/physics/9910019

More to the point, it also shows how, in a century, there does not appear convergence on these issues. The Saa paper rescues the EP in precisely the opposite way, saying neither radiates.

 

[bcrowell]

The classic paper on this, which I don't think anyone has referenced yet, is C. Morette-DeWitt and B.S. DeWitt, "Falling Charges," Physics, 1,3-20 (1964).

Some other papers, which people may or may not have referenced already:
http://arxiv.org/abs/gr-qc/9303025
http://arxiv.org/abs/physics/9910019
http://arxiv.org/abs/0905.2391
http://arxiv.org/abs/0806.0464

PF user Sam Gralla has done research in this area -- he's a co-author of one of the papers above.

An excellent, readable presentation of Feynman's point of view is available online here: http://www.mathpages.com/home/kmath528/kmath528.htm

 

[atyy]

More to the point, it also shows how, in a century, there does not appear convergence on these issues. The Saa paper rescues the EP in precisely the opposite way, saying neither radiates.

Oh, I'm not sure Harpaz and Soker were serious. Their construction is so nonlocal that I think no one expects the EP to apply, except by accident, which is why their paper is cute. (And no, I don't think a non-vanishing Poynting vector indicates the presence of radiation.)

More generally, within GR, local for the EP means no second derivatives or higher, and how can one have radiation without second derivatives?

 

[PAllen]

The classic paper on this, which I don't think anyone has referenced yet, is C. Morette-DeWitt and B.S. DeWitt, "Falling Charges," Physics, 1,3-20 (1964).

Some other papers, which people may or may not have referenced already:
http://arxiv.org/abs/gr-qc/9303025
http://arxiv.org/abs/physics/9910019
http://arxiv.org/abs/0905.2391
http://arxiv.org/abs/0806.0464

PF user Sam Gralla has done research in this area -- he's a co-author of one of the papers above.

An excellent, readable presentation of Feynman's point of view is available online here: http://www.mathpages.com/home/kmath528/kmath528.htm

Some more interesting papers. The following was meant (in part) to refute an earlier version of the Parott paper that is first in the list above (it clearly supports the equivalence principle for charges):

http://arxiv.org/abs/gr-qc/0006037

And the following argues violation of EP for charges:

http://arxiv.org/abs/gr-qc/9909035

So, between all the papers on this thread (all modern), virtually every possible point of view as to which cases radiate and which don't is argued. Further, the EP is considered successful for opposite reasons in different papers; and considered violated for opposite reasons.

It does not appear to me there is any strong consensus.

 

[PAllen]

Here is a recent review of this whole controversy from April of this year (I've just started reading this, so don't know the conclusions or plausibility yet):

http://www.itp.uni-hannover.de/~giulini/Heraeus/Seminar475/Talks/Lyle.pdf

This author wrote a whole book on this a while ago.

 

[PAllen]

I highly recommend the reference in my last post. While I doubt it settles the matter to everyone's satisfaction, it reviews and critiques the whole history in a refreshingly accessible yet adequately technical level.

 

[GRDixon]

For those who wonder if Abraham and Lorentz (vs. Lamor) got it right re radiated power, a Google search on "a non-radiating accelerating charge" may be of interest.

 

[cosmik debris]

Tom Roberts explained it like this:


"This really hinges on what one means by "radiation", and classically there are
two reasonable but different meanings:

A) a nonzero radiation term in the Lienard-Wiechert fields, which is
proportional to beta-dot, the charge's acceleration

B) a self-propagating disturbance in the electromagnetic field with E,
B, and v mutually orthogonal (v is the direction of propagation)

In addition, we also require radiation fields to be time dependent -- constant
fields are never considered to be radiation. (B) always satisfies this, but in
certain highly-symmetric situations, (A) can have a non-zero beta-dot term and
yet have constant fields and thus nothing we consider to be radiation.


In classical electrodynamics, the claim "any accelerated charge emits radiation"
refers to radiation(A), but is rather simplistic as it ignores the requirement
of time-dependent fields. Radiation(B) is, of course, the type in a light beam
or radio wave. A uniformly accelerated charge emits radiation(A) but not
radiation(B).

In classical electrodynamics, an observer co-accelerated and co-moving with a
uniformly accelerated charge will see constant E and B fields (from the symmetry
of the physical situation), so this observer will see no radiation of either
type. This is the situation that applies via the equivalence principle to a
charged particle sitting on the surface of the earth, observed by an observer on
the same surface.

In the above-referenced forum thread, someone claimed a dc current in a bent
wire is prevented from radiating by quantum effects. This is wrong, and in
classical electrodynamics that current has a non-zero beta-dot term in the L-W
fields, but it is constant in time and thus is not considered to be radiation.
(Nobody in that thread pointed out the two different meanings of "radiation",
and they got confused by puns.)"