Why does an Accelerating Charge Radiate - Solved or Unsolved?

[controlfreak]

Are the questions

a) why does an accelerating charge radiate

and

b) why does an uniformly accelerating charge not radiate

satisfactorily answered and accepted by the physics community?

or are there still some unresolved inconsistencies in theory regarding this?

I read two articles related to this:

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

http://citebase.eprints.org/cgi-bin/fulltext?format=application/pdf&identifier=oai%3AarXiv.org%3Agr-qc%2F9303025

which got me thinking. Is this an unsolved thing?

Any takers? I am not sure whether this belongs to quantum physics or classical physics?

 

[ZapperZ]

Are the questions

a) why does an accelerating charge radiate

and

b) why does an uniformly accelerating charge not radiate

Eh? Isn't (b) a subset of (a)? You are contradicting yourself.

Simple answer on why accelerating charge radiate: conservation of energy.

Zz.

 

[controlfreak]

Simple answer on why accelerating charge radiate: conservation of energy.

Zz.

conservation of energy.- Elaborate please.

and also:

Please explain why an uniformly accelerating charge doesn't radiate in order to uphold "conservation of energy" (or whatever you mean by that)?

The two questions where to distinguish the cases : an non uniformly accelerating charge and uniformly accelating charge, but also to illustrate that the uniform accelaration as an exception case to the theory which proclaims accelerating charges radiate. The contradiction in my question was intentional. I am glad that it struck a note and produced the desired effect

 

[ZapperZ]

conservation of energy.- Elaborate please.

and also:

Please explain why an uniformly accelerating charge doesn't radiate in order to uphold "conservation of energy" (or whatever you mean by that)?

The two questions where to distinguish the cases : an non uniformly accelerating charge and uniformly accelating charge, but also to illustrate that the uniform accelaration as an exception case to the theory which proclaims accelerating charges radiate. The contradiction in my question was intentional. I am glad that it struck a note and produced the desired effect

Do you think "uniformly accelerating charge" is not included in "accelerating charge"? I said earlier that "uniformly accelerating charge" is a SUBSET of "accelerating charge". From basic mechanics, this should have been obvious.

And also from basic mechanics: an object moving with a constant velocity requires NO WORK to be done on it. An object moving with an acceleration (be it uniform, non-uniform, etc, etc..) requires that work be done on it. Since you said that you already have an "M.S", I would leave the rest for you to check up in either Griffith or Jackson to figure out where the work done on a charged particle would go to.

Zz.

 

[controlfreak]

Do you think "uniformly accelerating charge" is not included in "accelerating charge"? I said earlier that "uniformly accelerating charge" is a SUBSET of "accelerating charge". From basic mechanics, this should have been obvious.

And also from basic mechanics: an object moving with a constant velocity requires NO WORK to be done on it. An object moving with an acceleration (be it uniform, non-uniform, etc, etc..) requires that work be done on it. Since you said that you already have an "M.S", I would leave the rest for you to check up in either Griffith or Jackson to figure out where the work done on a charged particle would go to.

Zz.

I am not saying that "uniformly accelerating charge" is not included in the concept of an "accelerating charge". I agree the former is a subset of latter, I only said that, I intentionally made a contradiction (mistake) in my statement to highlight the discrepancy with respect to the fact that the theory for a set doesn't hold good for a subset.I see you have missed that subtelity in my questioning. Anyway that is besides the main question.So let is not argue on this. I give it to you.

I am well aware of radiation fields, Larmor Formula and derivation (supposed) of abraham-lorentz formula for the radiation reaction force (possibly self force of a point charge) from conservation of energy.But abraham-lorentz formula has some implications/classical inconsistencies which are listed by grifiths which you can very well read from that book.

Anyway leaving that, what I don't understand is the fact that why then should an "uniformly accelarting charge" not emit radiation (as shown in experiments)? The theory given in grifiths doesn't preclude it.

What theory explains this discrepancy or exception?

 

[ZapperZ]

Anyway leaving that, what I don't understand is the fact that why then should an "uniformly accelarting charge" not emit radiation (as shown in experiments)? The theory given in grifiths doesn't preclude it.

What theory explains this discrepancy or exception?

What experiment has shown that uniformly accelerating charge does NOT emit radiation? If this is true, why the hell is there so much shielding around all those synchrotrons and cyclotrons?

Zz.

 

[controlfreak]

Quoting from an article:
http://www.mathpages.com/home/kmath528/kmath528.htm

In Feynman's "Lectures on Gravitation" he says "we have inherited a prejudice that an accelerating charge should radiate", and then he goes on to argue that the usual formula giving the power radiated by an accelerating charge as proportional to the square of the acceleration "has led us astray" because it applies only to cyclic or bounded motions.The radiation reaction force (and therefore the radiated power) is proportional to the third derivative of position, so if the particle is undergoing constant acceleration it does not radiate.

This claim of feynman has been rubbished by other people.

Richard Becker says:

"Absurd results are obtained if [feynman's eqn] is applied to other forms of motion, such as the retardation of a free electron in a constant opposing field. In this case only the second derivative would be different from zero, and [feynman's eqn] would therefore predict no radiation damping at all.

The above derivation of the radiation damping is unsatisfactory, because it is not at all clear how the emitted spherical wave influences the electron's motion. In order to gain a closer understanding of the nature of this "self-reaction" it is necessary to compute the resultant force on all electron volume elements... Types of motion [such as that of the free electron] can only be treated in the light of a more precise knowledge of the structure of the electron...
"

My question is that has the physics community reached a conculsion on this debate??

 

[ZapperZ]

Quoting from an article:

In Feynman's "Lectures on Gravitation" he says "we have inherited a prejudice that an accelerating charge should radiate", and then he goes on to argue that the usual formula giving the power radiated by an accelerating charge as proportional to the square of the acceleration "has led us astray" because it applies only to cyclic or bounded motions.The radiation reaction force (and therefore the radiated power) is proportional to the third derivative of position, so if the particle is undergoing constant acceleration it does not radiate.

This claim of feynman has been rubbished by other people.

Richard Becker says:

"Absurd results are obtained if [feynman's eqn] is applied to other forms of motion, such as the retardation of a free electron in a constant opposing field. In this case only the second derivative would be different from zero, and [feynman's eqn] would therefore predict no radiation damping at all.

The above derivation of the radiation damping is unsatisfactory, because it is not at all clear how the emitted spherical wave influences the electron's motion. In order to gain a closer understanding of the nature of this "self-reaction" it is necessary to compute the resultant force on all electron volume elements... Types of motion [such as that of the free electron] can only be treated in the light of a more precise knowledge of the structure of the electron...
"

My question is that has the physics community reached a conculsion on this debate??

Correct me if I'm wrong, but you DID SAY "... as shown in experiments...", didn't you? None of what you talk about above has anything remotely connected to any experimental observation, no?

Zz.

 

[controlfreak]

I supposed that there were experiments which proved that the uniform accelarted charges doent radiate considering the fact that a lot of work in theory has been done exactly to prove that. I assumed that nobody tries to prove opposite of experimental result.

Anyway that (experimental results or not) is besides my actual question as I have to search more of the internet for that.

BUT There is still exists a confusion in the physics world that whether a uniformly accelerated charge radiates or not.

Please read this article for more clarity on what I am trying to say:
http://www.hep.princeton.edu/~mcdonald/accel/unruhrad.pdf

"all accelerating charges radiate" is a debatable issue when considering the uniformly accelerated charge. The evidence of this debates is all over. I have already provided 3 articles which contain further references on this specific debate.

My question is that whether this debate is over and have we reached a consistent non debatable theory?

 

[ZapperZ]

I supposed that there were experiments which proved that the uniform accelarted charges doent radiate considering the fact that a lot of work in theory has been done exactly to prove that. I assumed that nobody tries to prove opposite of experimental result.

Anyway that (experimental results or not) is besides my actual question as I have to search more of the internet for that.

Then you will pardon me if I, as an experimentalist, will WAIT till you can produce some.

Zz.

 

[Andrew Mason]

I supposed that there were experiments which proved that the uniform accelarted charges doent radiate considering the fact that a lot of work in theory has been done exactly to prove that. I assumed that nobody tries to prove opposite of experimental result.

Anyway that (experimental results or not) is besides my actual question as I have to search more of the internet for that.

BUT There is still exists a confusion in the physics world that whether a uniformly accelerated charge radiates or not.
...

My question is that whether this debate is over and have we reached a consistent non debatable theory?

The question can be posed on several different levels:

1. Does a charge radiate when it is accelerated by means of an electromagnetic force?

The answer is most certainly YES. This is what Zapperz is referring to when he talks about synchrotron radiation. Very high speed electrons radiate enormous quantities of EM radiation when subjected to magnetic forces. These magnetic forces can be uniform (as in bending magnets) or non-uniform (as in 'wiggler' or undulator magnets).

2. Does a charge radiate because it is experiencing acceleration?

The answer to this is not so clear. If it radiated em energy because of the acceleration, one would predict that a charge accelerating due to a gravitational field would radiate. But it doesn't. Nor does a charge at 'rest' in a gravitational field whose weight is opposed by an equal and opposite electrical force (as in the Millikan experiment) radiate (according to Einstein's General Theory of Relativity, this is equivalent to an electron uniformly accelerating in the absence of gravity).

3. Is the radiation caused by acceleration but only non-uniform acceleration?

The answer to this is also not clear. It appears that all non-uniformly acclerating charges do radiate. But if the answer is 'yes', then one would expect that all uniform acceleration - whether produced by gravity or electromagnetic force - would not cause the charge to radiate. But this is not the case - as Zapperz will tell you from working with electrons in a synchrotron uniformly accelerated as they pass a bending magnet.

The contention that an electron radiates when accelerated is based on a theory that the electron interacts with its own field when accelerated. It is, as far as I can tell, unproven and still controversial. Feynman appears to have taken different positions on that. He may have ended up believing that it all depends on how you want to look at it, suggesting that there may be more than one 'correct' equivalent explanations.

I would highly recommend that you read Feynman's Nobel Lecutre to get a sense of his thinking on this most interesting subject (at least in 1965):
http://nobelprize.org/physics/laureates/1965/feynman-lecture.html

If we could find a particle that possessed charge but no mass, we might be able to answer this question. But it appears that charge and mass cannot be separated.

In any event, to answer your question: this appears to be still an open question in physics (but one for which there may not be a 'correct' answer).

AM

 

[controlfreak]

Thanks a lot AM for that comprehensive and lucid answer, especially the way you have linked the presence of radiation to the means of acceleration (gravity/EM).

Question:
Are we very sure that the electron doesn't radiate due to graviational field or could it be just that the raditation is very less that one is not able to detect it?

 

[Andrew Mason]

Thanks a lot AM for that comprehensive and lucid answer, especially the way you have linked the presence of radiation to the means of acceleration (gravity/EM).

Question:
Are we very sure that the electron doesn't radiate due to graviational field or could it be just that the raditation is very less that one is not able to detect it?

Good point. Experimental evidence shows that a charge does not radiate when accelerating in a gravitational field but it is very difficult to measure because the amount radiation (ie. for the equivalent electrical force) is very small.

If it did radiate, General Relativity would go out the window. GR says that a mass in free fall in a locally uniform gravitational field (ie. gravitational force on all parts of the mass is same - no tidal forces) is equivalent to an electron in uniform motion in the absence of gravity.

The evidence, to me, indicates that it is the interaction of the electrical/magnetic force with the field of the charge that causes radiation. Since the charge also has mass, the charge accelerates as well. But the acceleration is not the cause of the radiation.

AM

 

[Antiphon]

A charge at rest in a gravitational field is accelerated (assume uniformly)
yet does not radiate. Therefore (by equivalence) a charge at rest in a
uniformly accelerating reference frame does not radiate *in that frame*.

Thus if you suppose you are next to a charge in an elevator that is
undergoing uniform 1 G acceleration, it will not appear to emit radiation
to *you*.

But an observer in a nearby non-accelerated frame will measure the
presence of both electric and magnetic fields changing as a function
of time. Time-changing fields (in free space) will result in radiation.
There IS radiation coming from the accelerating charge which can be observed in other frames. The energy for this radiation comes from the mechanical source which is accelerating the charge, it's prime mover.


The observer in the elevator sees no radiation, but *does* measure
an anisotropic field in the elevator *and through all of space*.
That is, the static electric Coulomb field at the top of the elevator
is different than at the bottom. There is a time-static spatial potential
energy variation in this Coulomb field that has an equivalent mass which
takes work by the elevator's prime mover to accelerate.

If you transform this time-static spatial variation of the Coulomb field
back into the uniformly moving reference frame, you will recover the
radition fields.

 

[Andrew Mason]

..But an observer in a nearby non-accelerated frame will measure the presence of both electric and magnetic fields changing as a function of time. Time-changing fields (in free space) will result in radiation.
There IS radiation coming from the accelerating charge which can be observed in other frames. The energy for this radiation comes from the mechanical source which is accelerating the charge, it's prime mover.

There is, of course, no such thing as a mechanical force. There is only eletromagnetic force and gravity (nuclear interactions do not apply). So are you saying that it must be the electromagnetic interaction that provides the energy for this radiation?

AM

 

[Antiphon]

There is, of course, no such thing as a mechanical force. There is only eletromagnetic force and gravity (nuclear interactions do not apply). So are you saying that it must be the electromagnetic interaction that provides the energy for this radiation?

AM

There are two (equivalence-based) situations. The uniformly accelerated
reference frame (man next to charge in elevator going up at 1 G) and the
uniform gravitational field (charge sitting still in lab on "earth").

In the uniform gravitational field the charge does not radiate, period.

In the uniformly accelerated case, the charge *does* radiate but not
to the observer in the accelerated frame. It only radiates to other observers.

My comment about the energy was this: The source of the energy which
is radiaitaing away in the second case is *work* done by whatever is
accelerating the charge. It doesn't matter what the source of this energy
is. You may assume it is a chemical rocket engine.


Lest anyone conclude that this violates the equivalence principle, rest
assured it does not, any more than the fact that a mass in a uniformly
accelerated frame gains kinetic energy while a mass in a gravitational field
does not. The equivalence princile says that it is impossible to distinquish
a difference between the two by doing expeiments *in those two frames.*

 

[Andrew Mason]

There are two (equivalence-based) situations. The uniformly accelerated reference frame (man next to charge in elevator going up at 1 G) and the uniform gravitational field (charge sitting still in lab on "earth").

In the uniform gravitational field the charge does not radiate, period.

In the uniformly accelerated case, the charge *does* radiate but not
to the observer in the accelerated frame. It only radiates to other observers.

This is still somewhat controversial. I have never been able to understand how the radiation could be inaccessible to the co-accelerating observer. It is not as if the em wave from the charge does not pass through the 'co-accelerating' observer. How does the radiation escape detection? This paper seems to conclude that the co-accelerating observer exception theory is not correct, if I understand the abstract correctly.

My comment about the energy was this: The source of the energy which is radiaitaing away in the second case is *work* done by whatever is
accelerating the charge. It doesn't matter what the source of this energy
is. You may assume it is a chemical rocket engine.

You seem to be saying that the force supporting the charge at rest in a gravitational field is doing work. But I don't see any distance that the supporting force acts over.

AM

 

[Antiphon]

[I cannot acess the link below for some reason.]

This is still somewhat controversial. I have never been able to understand how the radiation could be inaccessible to the co-accelerating observer. It is not as if the em wave from the charge does not pass through the 'co-accelerating' observer. How does the radiation escape detection? This paper seems to conclude that the co-accelerating observer exception theory is not correct, if I understand the abstract correctly.

You seem to be saying that the force supporting the charge at rest in a gravitational field is doing work. But I don't see any distance that the supporting force acts over.

AM

In the accelerating frame, there is no radiation but there is a distortion of
the usual Coulomb field through all space as seen by the accelerating
observer. So it is seen by the accelerating observer- just not *as*
radiation.


Regarding the force, the work is supplied by the motor to the charge, not
by the charge's support. The observer in the elevator sees no work being
done on the charge (as you say, no distance).

 

[Andrew Mason]

[I cannot acess the link below for some reason.

It appears that the link to the actual paper is a transient one. You can find the paper by clicking the link and searching for "ashok k. singal".

In the accelerating frame, there is no radiation but there is a distortion of the usual Coulomb field through all space as seen by the accelerating
observer. So it is seen by the accelerating observer- just not *as*
radiation.

Thanks for this explanation. I am not sure I understand it though. I am having trouble understanding how there could be a time dependent field in the inertial rest frame and a static field in the co-accelerating frame (ie. stationary observer in gravitational field at the same location as the charge) but it may just be my general ineptness in this area, particularly in tensor analysis.

AM

 

[FourthD]

Relativity and Radiation

I would ask about the internal nature of the charge (electron) that emits a photon.

Do you think that all the internal energy of an electron has mass and is "sublight".

If so, how can it emit a photon at c? Given that relativity implies that no mass can be accelerated to c.

Or do you think its internal energy is already at c and is simply released?

The acceleration (change of direction) of charges (electrons) in the ring at the end of the Stanford Linear Accelerator appears to cause many of them to radiate Xrays and thus lose velocity and drop out of the experiment.

 

[ZapperZ]

I would ask about the internal nature of the charge (electron) that emits a photon.

Do you think that all the internal energy of an electron has mass and is "sublight".

If so, how can it emit a photon at c? Given that relativity implies that no mass can be accelerated to c.

Or do you think its internal energy is already at c and is simply released?

The acceleration (change of direction) of charges (electrons) in the ring at the end of the Stanford Linear Accelerator appears to cause many of them to radiate Xrays and thus lose velocity and drop out of the experiment.

You should be VERY careful with your phrasing here. An electron DOES NOT emit a photon. That's just impossible and violates a bunch of conservation laws.

In an atomic transition, it is the ATOM that emits a photon. An electron droping to a lower energy level simply reflects the "relaxation" of the atom. Secondly, the radiation emitted along the beamline at Stanford isn't due to an emission by the electron. Rather, it is due to ANY charged particle being accelerated (per Maxwell equations). Such radiations are achieved using insertion devices like an undulator or wiggler. It causes the electrons (in this case) to make a side-to-side oscillation of its path. THIS is what causes the radiation.

Zz.

 

[Antiphon]

Thanks for this explanation. I am not sure I understand it though. I am having trouble understanding how there could be a time dependent field in the inertial rest frame and a static field in the co-accelerating frame (ie. stationary observer in gravitational field at the same location as the charge) but it may just be my general ineptness in this area, particularly in tensor analysis.

AM

Think of it this way. The static field is in an accelerating frame, so viewed from
any other inertial frame, it's a time-changing field. It's precisely because
it's not a time changing field in the accelerating frame that it is not seen
as radiation in that frame.

Since we're having fun with this, let me confound the issue even more.
An interesting consequence of this is that the radiation of a uniformly
accelerating charge does not appear as radiation in ANY uniformly
accelerating frame so long as the rate of acceleration is the same in
both frames.

Elevator 1 with a charge starts falling at time T=0. We all see the radiation
except for the observer on the elevator. At time T=15, a second not-colinear
elevator starts dropping. The radiation field in the second elevator must
disappear and appear to be the field of charge moving uniformly with
velocity V. This is because with the same rate of acceleration, two
falling frames will have a constant velocity of separation.

I reach my own limit of knowledge on the subject when the two elevators
reach relativistic speeds. I don't know if the velocity of separation would
still be a constant as observed from the second elevator. It probably is.

Edit: Thanks for the link. It looks quite impressive and I'll check it out.

 

[Andrew Mason]

Think of it this way. The static field is in an accelerating frame, so viewed from
any other inertial frame, it's a time-changing field. It's precisely because
it's not a time changing field in the accelerating frame that it is not seen
as radiation in that frame.

For uniform acceleration, I should think that the field would be distorted but I don't see why the distortion would be time dependent.

AM

 

[Andrew Mason]

You should be VERY careful with your phrasing here. An electron DOES NOT emit a photon. That's just impossible and violates a bunch of conservation laws.

In an atomic transition, it is the ATOM that emits a photon. An electron droping to a lower energy level simply reflects the "relaxation" of the atom.

This is a very important point. Could one not say that energy is stored in the field between the electron and nucleus and the field energy is reduced by the energy of the emitted photon?

AM

 

[FourthD]

You should be VERY careful with your phrasing here. An electron DOES NOT emit a photon. That's just impossible and violates a bunch of conservation laws.

No it doesn't

In an atomic transition, it is the ATOM that emits a photon. An electron droping to a lower energy level simply reflects the "relaxation" of the atom. Secondly, the radiation emitted along the beamline at Stanford isn't due to an emission by the electron. Rather, it is due to ANY charged particle being accelerated (per Maxwell equations). Such radiations are achieved using insertion devices like an undulator or wiggler. It causes the electrons (in this case) to make a side-to-side oscillation of its path. THIS is what causes the radiation.

In the ring, not the tube!

Also, you are sidestepping the point? Why, did I say something to arouse hostilty?

There should be no room for egos in serious science!

Zz.

You are reasonably correct for an atom but not for my point!

It was the Stanford research people who told me that the electrons themselves emit! that it was a problem with their Accelerator. But I also had learned it in textbooks before they told me.

Some years ago a Stanford professor and research scientist that I encountered in the College bookstore got it right away! He admitted that they liked to "sweep it under the rug", I will always remember those words, because it is a serious unexplained anomaly in the theory.

He got it right away because the Stanford Linear Accelerator, rather than bound electrons gives the best examples of this anomaly.


Perhaps what I need to say, is that a free electron can decide to emit a photon. When it does, the electron's mass drops by the energy of the emitted photon divided by c squared.

Said another way: The ELECTRON LOSES MASS WHEN IT EMITS A PHOTON! Its velocity also slows reflecting the loss of energy of the emitted photon

According to the standard assumption: Initially, the electron had NO photon to emit. All of its energy was tied up in its mass. So it had to "manufacture" that photon to emit it. IT HAD TO TAKE MASS AND CONVERT IT TO A "MASSLESS" PHOTON!

Quantum theory can give probabilities that the electron will emit a photon, but Quantum theory offers NO explanation as to the mechanism.

Meanwhile, RELATIVITY THEORY SAYS THAT THE ELECTRON CAN'T! IT CAN'T TAKE MASS AND MAKE IT GO AT THE SPEED OF LIGHT. But we all know that it does!

So the electron cheats, it converts to massless, that which previously had mass. HOW?

ANOMALY, BUST IN THE THEORIES, "HIDE IT UNDER THE RUG!"

That Accelerator takes normal negative electrons and positive electrons (anti-matter) and accelerates them with rows of huge high power klystrons down a mile long tube which terminates in an electromagnetic ring which sends the matter electrons in one direction around the ring and the anti-matter the opposite direction for several turns around the ring and the they are brought into collision. Matter and anti-matter. There is usually total annihilation leaving high energy gamma photons.

The total energy of the gamma photons is equivalent to the total combined energies of the masses of two antimatter particles. Again, mass to photons.

All conservation laws are fulfilled.

As the electrons and positrons circle the ring they are continuosly being accelerated to change direction. Many emit Xrays and are lost from the experiment. Large mounds of Earth had to be erected to pacify nearby residents who fear the radiation.

So the Stanford Scientists are well aware of the "anomaly".

I am not incorrect on this matter. It has long been Known to many prominent physicists.

I have been trying to resolve this anomaly for many years. And I have made some surprising progress.

http://www.slac.stanford.edu/

 

[FourthD]

X-rays from Free Electrons

X-rays from Free Electrons:

This should answer the main topics of this post with pretty diagrams and all! Complimenta of NASA!


http://imagine.gsfc.nasa.gov/docs/science/how_l2/xray_generation_el.html

 

[yoron]

A charge at rest in a gravitational field is accelerated (assume uniformly)
yet does not radiate. Therefore (by equivalence) a charge at rest in a
uniformly accelerating reference frame does not radiate *in that frame*.

Thus if you suppose you are next to a charge in an elevator that is
undergoing uniform 1 G acceleration, it will not appear to emit radiation
to *you*.

But an observer in a nearby non-accelerated frame will measure the
presence of both electric and magnetic fields changing as a function
of time. Time-changing fields (in free space) will result in radiation.
There IS radiation coming from the accelerating charge which can be observed in other frames. The energy for this radiation comes from the mechanical source which is accelerating the charge, it's prime mover.


The observer in the elevator sees no radiation, but *does* measure
an anisotropic field in the elevator *and through all of space*.
That is, the static electric Coulomb field at the top of the elevator
is different than at the bottom. There is a time-static spatial potential
energy variation in this Coulomb field that has an equivalent mass which
takes work by the elevator's prime mover to accelerate.

If you transform this time-static spatial variation of the Coulomb field
back into the uniformly moving reference frame, you will recover the
radition fields.

I saw you stating that it didn't disturb the equivalence principle Antiphon?
I'm sorry but I have severe problems understanding that sentence :)
To me it should be the same for both cases?

Can you show any experimental proof for your view?
I would really like to understand if this is correct?

 

[jtbell]

Antiphon posted his remarks almost five years ago. He may no longer be around here to respond.

 

[yoron]

Antiphon posted his remarks almost five years ago. He may no longer be around here to respond.

Okay, but his answer was sort of bugging me :)
The equivalence principle seems rather important to special relativity?

And I've seen all kinds of definitions on the net. So, I just thought that now when the participants had had five years to mull it over, perhaps their ideas had matured into a definite answer:)

Nah, I just missed the 'time stamp' here.
So if someone has a view, or that definite link to answer it?

 

[Antiphon]

I saw you stating that it didn't disturb the equivalence principle Antiphon?
I'm sorry but I have severe problems understanding that sentence :)
To me it should be the same for both cases?

Can you show any experimental proof for your view?
I would really like to understand if this is correct?

Sorry for the (gulp) 5-year delay between posts. To answer your question Yoron I have no experimental proof. These are conclusions I have drawn from thinking about accelerated charges and radiation for quite a while via thought experiments.

What I meant was this: When a pencil sits on your desk for 5 years without being touched it has been accelerating at 1G for 5 years. Yet it has gained no kinetic energy in that time. If it had, it would potentially kill whoever came near it. By contrast, a pencil on a desk in an elevator being accelerated by a rocket motor for 5 years at 1G would be going at very nearly the speed of light, have immense kinetic energy, be able to cross the universe in a very short time in its own frame of reference, etc. In other words such an accelerating penicil is not even remotely "equivalent" to the one that's been on my desk for the last 5 years. Specifically, the pencil on my desk has roughly the same energy in relation to the Earth and universe as it had 5 years ago. The pencil in the elevator has vastly increased energy viewed from the Earth and other parts of the universe. It is different because vast amounts of energy have changed its state.

The equivalence principle says that there is no experiment one can do in my office on the one hand or in the elevator on the other hand that can distinguish between the gravity or spacetime curvature in those two places. They look the same when you are there at both places.

The equivalence principle certainly does *not* say that one cannot distinguish uniform acceleration from gravity by the effects as seen from other frames. You certainly can and the name of the experiment is "Duck: here comes a relativistic pencil!"

I hope this helps.

 

[yoron]

I can see your thinking Antiphon. Potential energy right :)

To me it comes how to see kinetic energy. Naively expressed every object in the universe will have a different kinetic energy relative you, depending on your choice of 'system' to observe. And they have it with you simultaneously. So kinetic energy, to me that is :), reminds me more of defining a relation than a actual 'energy'. That relation will fall out naturally with an collision f.ex with any of those objects and will be unique for each case but as long as we don't have an actual interaction it's only a possible outcome.

And potential energy in this relation is the description of what kinetic energy we can expect from our defining a system, like pencil Earth and pencil rocket in the other case. From your own frame of reference your heartbeat will have the same beat, according to your wristwatch, in the rocket as well as on Earth. So in that frame everything will be 'as usual' according to you in a black box scenario counting on a uniformly accelerating motion by your rocket at f.ex one G. And until death by tidal forces or other, to the one inside that black box, 'unexplainable circumstances' that frame will be equivalent to Earth. And whatever potential energy that have been built up will only be a relation, observed by you being at rest relative Earth, as a real 'energy' but as defined from inside that black box as non-existant as there is no way for you to realize it in that frame except in a interaction, like f.ex a collision.

I'm not discussing CBR and what that can do relative your acceleration in a vacuum here :) btw. In reality you have all kinds of 'interactions' possible in a vacuum as describer by the Rindler observer (Rindler effect) But I'm just using a isolated example, like the original 'black box' used for the equivalence principle. Would you agree to how I see it or do you think I missed out on things here?

Yoron.

 

[Antiphon]

I agree with you for those parts of your post that I know about and will take your word for the rest.

There are some interesting papers about acceleration and quantum fields which you may like. Look for publications by Ulrich Gerlach at the Ohio State University.

 

[yoron]

Thanks Antiphon.

I don't know that much, all to little in fact. It's just that I'm trying to learn :)
As we all are I guess. I will definitely look up your suggestions.

Be cool.

 

[ynot]

I think Antiphon hit upon it. If you drop an electron in a gravitational field, and it speeds by you, you should feel radiation from the accelerating charge. Conversely, if you are accelerating past an electron, you should also experience radiation, being that in classical physics electromagnetism is based on relativistic motion. I understand that if you stand next to the LHC while charges are circling through it, that there is enough radiation to kill you in a relatively short time because of the accelerating charges (the centripetal force of the magnets forcing the charges to curve in a circle). If you were riding along with the protons, or mercury nuclei in some cases, you would not experience any radiation, right? So it's relative, an electon sitting on a chair next to you is experiencing the same acceleration as you, and there is no relative spatial motion to you, so it doesn't radiate to you.

The earliest model of the atom (electrons orbiting a nucleus), was ridiculed because classical physics predicted that the electron would radiate and spiral into the nucleus. Quantum physics allowed atoms to be by preventing infinitesimal energy changes in a potential field. So that is one place where uniform acceleration (including relative motion) does not cause a charge to radiate.

 

[yoron]

I liked the explanation(s) too, it's just that I'm unsure. If you accept the idea of equivalence then the question seems to become how far you can 'draw it'? As Antiphon saw it, as I understood it, the difference between the frames was that one frame was expending energy (rocket) and the other wasn't.

And expending energy for velocity have very strange effects for that frame relative others. It's only without any comparative evidence those frames are equivalent, looking out a window would destroy the equivalence f.ex. Is there any way to expend energy without begetting a radiation btw? I was thinking of using the sun instead but it falls on that it will radiate there, and the reason for that one was the question if it was the 'energy spent' or 'velocity' that would create the effect if so.

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?

But the explanation Antiphon presented was quite good.
And understandable, which is even better :)

 

[0xDEADBEEF]

The problem is solved http://en.wikipedia.org/wiki/Liénard–Wiechert_potential
Look for \vec{ \dot{\beta}} that is the acceleration leading to the 1/r term typical for radiation. There is even a covariant formulation of electrodynamics that works in GRT. Maybe ask in the relativity forum, but this problem is solved and there is no question about the radiation except for intuitive insights into the formulas. Feynman simply tried to say that it is not as simple as people tend to tell you.

 

[Antiphon]

The problem is solved http://en.wikipedia.org/wiki/Liénard–Wiechert_potential
Look for \vec{ \dot{\beta}} that is the acceleration leading to the 1/r term typical for radiation. There is even a covariant formulation of electrodynamics that works in GRT. Maybe ask in the relativity forum, but this problem is solved and there is no question about the radiation except for intuitive insights into the formulas. Feynman simply tried to say that it is not as simple as people tend to tell you.

Thanks for the reference 0xDEADBEEF. The acceleration term of course is what gave life to part of this thread in terms of the equivalence principle. Why doesn't a charge sitting still in a gravity field radiate when (by the referenced equation) a charge in a "speeding up" elevator would? That seems to *violate* the equivalence principle.

To sum it all up, it is possible for the radiation from accelerated charges to show up as something other than radiation if the frames are chosen correctly. Common sense says that radition in one frame looks like radiation in any frame but it seems this is not the case. This has probably been the (historical) origin of the controversy.

Edit: Apparently someone has done the analysis on this in 2006 (a year after the thread started.) It's good to know the
thinking was correct. If they get a Nobel prize I want my cut.

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000074000002000154000001&idtype=cvips&gifs=yes&ref=no

 

[yoron]

Citing your link DB.

"Liénard-Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential. Built directly from Maxwell's equations, these potentials describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in arbitrary motion"

In my definition above, how do you get to a "time-varying electromagnetic field for a point charge in arbitrary motion" ? I'm not sure how to see a gravitational 'acceleration' at all. To you falling there just is a weightlessness, isn't there? Similar to a uniform motion in that you can have all kinds of speed as measured by an 'far observer' at rest with the gravitational field you're 'falling into' but still from your frame being unable to differ between those?

Just like different 'uniform motions' won't be measurable inside a black box scenario either. Also you won't have any external 'EM field' as observed by that 'free falling' electron, well, as I defined it above?

Anyone heard about "Schott energy, which seems to have no physical limit and can go infinitely negative in value." http://www.hep.princeton.edu/~mcdonald/examples/EM/eriksen_ap_297_243_02.pdf

Just to bring this to a new, even more refined, level of confusion, well, to me that is :)

 

[0xDEADBEEF]

In my definition above, how do you get to a "time-varying electromagnetic field for a point charge in arbitrary motion" ? I'm not sure how to see a gravitational 'acceleration' at all. To you falling there just is a weightlessness, isn't there? Similar to a uniform motion in that you can have all kinds of speed as measured by an 'far observer' at rest with the gravitational field you're 'falling into' but still from your frame being unable to differ between those?

It is all in the math. If you want to find the answer, you have to use the covariant formulation of the theory and derive the Lienard-Wiechert type potential in a curved space time metric. Then you know, but as I said that's a question more appropriate for the relativism subforum.

 

[GRDixon]

Are the questions

a) why does an accelerating charge radiate

and

b) why does an uniformly accelerating charge not radiate

satisfactorily answered and accepted by the physics community?

or are there still some unresolved inconsistencies in theory regarding this?

I read two articles related to this:

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

http://citebase.eprints.org/cgi-bin/fulltext?format=application/pdf&identifier=oai%3AarXiv.org%3Agr-qc%2F9303025

which got me thinking. Is this an unsolved thing?

Any takers? I am not sure whether this belongs to quantum physics or classical physics?

The accelerating charge (e.g. an oscillating charge) radiates because the surface integral of its Poynting vector, integrated over a cycle time, is nonzero. (The Poynting vector is constructed from the charge's E and B fields, as calculated/computed using Maxwell's equations.) Griffiths, "Introduction to Electrodynamics," provides the E and B field solutions for a point charge moving in any prescribed way.

BTW, to my knowledge it is a charge subject to a constant driving force that does not radiate, and not a charge moving with a uniform acceleration. Given a constant driving force, the charge's acceleration asymptotically approaches zero as its speed approaches c.