[graham.d]

It is not that I don't "believe" in GR, Ron. Generally I do. But I do not understand the action of an accelerating charge in a gravity field. And, it seems surprisingly, neither does anyone else, although they clearly understand it a lot more than me. Eriksen's paper is not definitive but is valuable because he quotes the conflicting results that have been presented by lots of people including Pauli(!), Unruh, Rohrlich, Teitelboim etc. plus commentary on their work by others. I have read the paper a few times but not enough to grasp all of it and I find the maths very hard with some Tensor notations that I am not familiar with; also I have never used tensors much for about 35 years so to say I'm rusty would be a severe understatement. Not to mention the fact that the paper quotes equations without defining the terms, which does not help a lot. I am trying though :-) The results are really quite counter-intuitive.

[Ron Hughes (OP)]

Maybe I don't fully understand the question. An electron falling toward a star will emit radiation to all observers except an observer falling with the electron. An electron orbiting a star will emit radiation to a far away observer stationary with respect to the star but to an observer at the center of the star.

[graham.d]

Maybe I don't fully understand the question. An electron falling toward a star will emit radiation to all observers except an observer falling with the electron. An electron orbiting a star will emit radiation to a far away observer stationary with respect to the star but to an observer at the center of the star.

I guess you intended "[...] with respect to the star but NOT to an observer at the center of the star." [...]

otherwise the words don't make sense.

An electron falling toward a star will emit radiation... True according to recent papers but not what Pauli thought in 1911.

An electron falling toward a star will emit radiation to all observers except an observer falling with the electron... True (I think) because of equivalence principle, but I am not wholly sure. There is potentially the detectable difference because of the tidal nature of the divergent field. What also seems to be true is that a non-charged body falls at the same rate. The challenge, debated in the Ericsen paper, is to explain how the charge can radiate energy, with no apparent limit, yet not feel the reaction force from the radiation i.e. why does it not fall more slowly?

An electron orbiting a star will emit radiation to a far away observer stationary with respect to the star but not to an observer at the center of the star... Not true. An electron orbiting a star will not emit any radiation (to any observer), despite being accelerated by the gravitational centripetal force. It cannot or its orbit would decay and this does not occur. This is explained by the Eriksen paper but is very complex. The reason for the difference is to do with the boundary conditions which, in this case, are periodic (the electron starts and finishes its orbit on the same point).

This is reasoned from the derived equations but does not seem obvious to me.

[Ron Hughes (OP)]

I think the problem is this, energy is only energy from an observers frame of reference. Suppose your out in space in your rocket ship. You see an electron parked outside your window. The electron starts accelerating and you see that it is emitting radiation. You turn on your engines and start to accelerate at the same rate. You notice that the radiation has magically disappeared.

[yor_on]

"But I do not understand the action of an accelerating charge in a gravity field. And, it seems surprisingly, neither does anyone else"

I soo agree Graham
And I really like this discussion.

Like, how to define a 'free electron'.
One definition I saw was this..

"A free electron mean an isolated electron. If the electron is accelerating, it cannot be free or isolated, and there must be external fields acting on it."

But that is wrong in this case, isn't it? Gravity may look like a 'field' in that it is everywhere and decide all motions, from light to matter, but it's more like the stress lines in a jelly (aka SpaceTimes Geodesics) than a 'force' to me. Now, considering if 'gravity waves' is 'energy'?

I liked Vernons definition there "General Relativity does not offer such a close relationship, though; the gravitational field is simply a fixed region of curved space, and a gravitational wave is a moving ripple of space." But there is something strange with the concept. If it 'moves' relative me and, nota bene, against SpaceTimes geodesics shouldn't that take 'energy'?

So, it seems to fall back to if gravity can be seen as energy again
Or is there some other way to see it?
==

And how about inertia? Existing everywhere, reacting instantaneously on course change. doesn't that state something different than those 'gravity waves'. To me inertia is a 'refusal' to change, aka the 'jello' being SpaceTime 'braking' a proceeding/interaction by it's predefined geometry?

[graham.d]

Ron, I think you should go through Eriksen's paper. If it were as simple as you state, I would not have any problem with the subject. I did not appreciate the complexity until digging into it. In your example, and to remove any magic, put the "parked" electron on another rocket ship so we can see what is providing the force to accelerate it. When the rocket ship accelerates with the electron, you will see the electron radiate and the result will be as the Larmor equation predicts. However, will the rocket ship's acceleration be very slightly reduced by the presence of the electron (compared with the presence of another particle of similar rest mass)? The (surprising) answer is "no". The energy for radiation seems to come from the mysterious (at least to me) Schott energy which seems to have no physical limit and can go infinitely negative in value!! This is what is being discussed in the Eriksen paper. The equations also have to be modified because it seems the rate of change of proper acceleration has a significant effect too.

If you accelerate your rocket to match the electron's acceleration, both you and the electron should be experiencing the same gravitational field as you are both existing in the same linearly accelerating frame. As electrons do not radiate in a constant gravitational field, then I agree, you will not observe radiation. I think you may see radiation at the start of the electron's and your acceleration because of the term associated with the derivative of the acceleration, even if you are in the same frame. The maths is too hard, but I think this would be the case.

[yor_on]

Here is one definition of Schott energy

And this Generalization of the Schott energy in electrodynamic radiation theory

--Quote--

It arises from the fact that the power supplied by an external force to a charged particle not only contributes to the energy radiated (acceleration fields) but also to the velocity fields. This feature is not connected with the well-known eficiencies of the Abraham-Lorentz theory (runaway solutions, etc.). Previous discussions of the Schott energy arose in the context of the Abraham-Lorentz equation of motion for a radiating electron. In this paper we define a (generalized) Schott energy that is applicable not only to the Abraham-Lorentz theory but to all theories of a radiating electron.

--End of quote--

But I agree, it seems weird, and it can't relate to gravity wells?
If we haven't suddenly defined gravity as some sort of electromagnetic energy while I was sleeping?

[graham.d]

It is good you found some more papers on the subject, Yor_on, as all the ones I found were ones you have to pay for. Looking through these ones briefly it looks like the maths is much more manageable. I'm away tomorrow but will see if I can get some time between chores on Sunday. It's a hard life :-)

[yor_on]

Well Graham candles and nighttime is still free (okay, not the candles perhaps), just inform your spouse that you have more important things to do. And remember to duck when she delivers her 'answer'

[yor_on]

Ah Farsight?
"There's some interesting comments re Einstein and gravity, about point particles, and even the near field aka evanescent wave:"

Evanescent waves again?

Anyway, I have a question. At another place, not far away in cyberspace, I wrote this.

"As for dropping an electron into a gravitational field?

That one gives me a headache Consider it empty on other particles, just you and that electron 'free falling' down some No 'static' EM fields around, just that electron. Would it then radiate? And then have a far observer at rest versus the gravitational field 'accelerating' you. Would they see the same?

Why?"

As I'm still not sure how to see it. I got the answer that this question already was solved, pointing me to the Liénard–Wiechert potential by Alfred-Marie Liénard in 1898 and independently by Emil Wiechert in 1900 To my eyes it is not solved, but I'm curious to what degree any one else will agree or disagree with me? So take a look at the link and see if it defines the answer to my question here, as well as to the other ones discussed in this thread?

[graham.d]

I don't think this solves the issue with an accelerating charge as it is only consistent with Maxwell's equations (and special relativity) not necessarily GR. This whole issue is tied in with Action at a Distance problems and work started, but not finished, by Feynman with contributions by Wheeler (and some earlier work by Fokker) I think. Surprisingly perhaps, I don't think there is any general consensus view on the behaviour of accelerating charges in all conditions - at least I have not found one in my limited research. The concept (with Action at a distance theories) requires retarded and advanced waves and interaction of a charge with the rest of the universe so it is somewhat complex and depends crucially on the model of the universe too. Even Feynman found it a daunting task!

The issue with who sees what with a gravitationally accelerating charge should be simple; it is certainly an easy problem to state, but a wholly GR consistent answer is not easy to find.

[Pmb]

An accelerated charged particle emits radiation with respect to a stationary observer but if the observer is accelerated along with the particle does the observer still detect the particle emitting radiation?.

That depends on who is doing the observing. Radiation emitted by a charged particle can only be detected by an instruement when the instrument itself is not co-moving with respect to the rest frame of the charged article.

This point was addressed in The American Journal of physics in the

“Radiation from an Accelerated Charge and the Principle of equivalence,” A. Kovetz and G.E. Tauber, 37(4), April 1969

The abstract reads

The connection between an accelerated charge and one at rest in a (weak) gravitational field is discussed in accordance with the principle of equivalence . For that purpose, the fields produced by a freely falling charge and a supported one (i.e., at rest in a gravitational field) are transformed to the rest-frame of the observer, who may be similarly supported or freely falling. A nonvanishing energy flux is found only if the charge is freely and the observer supported. or vice versa. This agrees with previously established results.

[graham.d]

This may be right, Pmb, but it is still unclear to me in every circumstance. A distant observer would also be a free falling observer (though not falling very fast) and he would not see the charged particle radiate any more than someone falling next to the particle. Fair enough. Orbiting is also free falling so would the orbit decay? An observer on the ground should see that the particle is in free fall, and he is not, so he should see it emit shouldn't he? If it is emitting, the orbit should decay. But wait a minute. Someone in orbit with the particle (or a long way off) will not see it emit, so will the particle decay despite there being no apparent reason for it to do so?

[yor_on]

Pmb how is a electron thought to radiate?
Is it orthogonally (perpendicular) to its motion?
It seems to me that this should be the way?
But I may easily be wrong there.

(It's a EM radiation, right?)

If so, when are the instrument co-moving with respect to that rest frame of the charged article. Is it when having the same motion, being 'at rest' with the electrons motion, or is it when moving orthogonally, at rest with the radiation?
===

Or is this just plain silly
===

Those damn* eleclons, now they are taking my interest away from beloved photons too.
But that's all there is right?

Photons and those, whatever they were called?
I mean, how many do we need?
==

The electron is described as having at all times, moving or unmoving, a 'field', as follows by Maxwell's equations, called the 'coulomb field'. That field seems to 'stretch' in all directions around our electron. When the electron moves relative an observer, there will come two new fields, one is the electric current that is the 'electron' in itself while moving? And surrounding that a magnetic field. Together those two new fields are named the dynamic electric field. " It's useful to regard the dynamic electric field as the sum of two separate fields, one of which is in phase with the magnetic field and the other 90 degrees out of phase. We will call the in-phase component the radiation field and the out-of-phase component the induction field. It is the radiation field that carries energy from an antenna into the surrounding universe" 

So what exactly is it that radiates in our thought example before? And how does it radiate? Doesn't it need a magnetic field to be pre-existent before it can do so? If I assume a perfect vacuum and leave this electron free falling into a gravitational 'well' will this description still be correct? meaning that it will create a current, as well as a magnetic field??

Awh, I should have stayed with photons