# Experimental proof that uniformly accelerated charges radiate

universal_101
Hello friends,

I recently, was reading all about the accelerating charges and radiation, but somehow the classical electrodynamics treatment is still inadequate, that is, the radiation reaction force(derived for oscillating charges) vanishes for uniformly accelerating charges. In this view, people tried to investigate self interaction during acceleration, but all in vain because of undefinable quantities at the position of the charge.

Now, in between all this do we even have any experiment that confirms the presence of radiation for uniformly accelerated charges. If yes, then does it stick to the Larmor's formula of power dissipation ?

Q-reeus
I recently, was reading all about the accelerating charges and radiation, but somehow the classical electrodynamics treatment is still inadequate, that is, the radiation reaction force(derived for oscillating charges) vanishes for uniformly accelerating charges. In this view, people tried to investigate self interaction during acceleration, but all in vain because of undefinable quantities at the position of the charge.

Now, in between all this do we even have any experiment that confirms the presence of radiation for uniformly accelerated charges. If yes, then does it stick to the Larmor's formula of power dissipation ?
Hi universal_101. I'm pretty certain there is zero experimental proof. Apart from the vexed matter of gravitational influence, one can never achieve indefinitely sustained uniform acceleration for obvious reasons. But it is possible to achieve it for sufficient time such that transient effects (starting and stopping) are not present or at least minimal. However just try a back-of-the-envelope calculation and it's clear any possible radiation field from uniform acceleration achievable in any laboratory situation will be far too small to detect. How would one measure the Coulombic, let alone any radiative field, of say a single electron accelerating between two charged capacitor plates!? As far as theory goes, there is still much debate - one example right here at PF:https://www.physicsforums.com/showthread.php?t=72035

universal_101
Hi universal_101. I'm pretty certain there is zero experimental proof. Apart from the vexed matter of gravitational influence, one can never achieve indefinitely sustained uniform acceleration for obvious reasons. But it is possible to achieve it for sufficient time such that transient effects (starting and stopping) are not present or at least minimal. However just try a back-of-the-envelope calculation and it's clear any possible radiation field from uniform acceleration achievable in any laboratory situation will be far too small to detect. How would one measure the Coulombic, let alone any radiative field, of say a single electron accelerating between two charged capacitor plates!? As far as theory goes, there is still much debate - one example right here at PF:https://www.physicsforums.com/showthread.php?t=72035
Thanks Q-reeus, The thing is, I'm not interested in the gravitational portion of the problem, that is, the violation of equivalence principle, or motion of charged particle under gravitation.

Of-course having put that aside, we have the accelerating charges in EM fields and radiation due to acceleration. Now, you are right in saying that if there is some radiation due to uniformly accelerating electrons it is extremely small and cannot be detected(radiation). But I think there could be ways around it, if instead of the radiation we track the energy of these charge particles in uniform acceleration and deceleration experiments.

Whereas, on the other hand, the term uniform acceleration itself is quite complicated, when we include relativity(increase in mass) in static fields, the acceleration should converge to zero when we approach the speed 'c' ,

Moreover, if there is any radiation during uniform acceleration and therefore radiation reaction force, it would most probably depend on the magnitude of acceleration which would again make the original acceleration non-uniform. And if we extend it further, this non-uniform acceleration again induce radiation and radiation reaction by the known formula.

In this light how good is the question about uniform acceleration and radiation ?

Q-reeus
Of-course having put that aside, we have the accelerating charges in EM fields and radiation due to acceleration. Now, you are right in saying that if there is some radiation due to uniformly accelerating electrons it is extremely small and cannot be detected(radiation). But I think there could be ways around it, if instead of the radiation we track the energy of these charge particles in uniform acceleration and deceleration experiments.
Still a no-go for absolutely uniform acceleration owing to the extreme feebleness of any energy loss. You may find appealing a fairly simple argument based on conservation of energy given here: http://arxiv.org/abs/gr-qc/9811030 Not saying I endorse it though.
Whereas, on the other hand, the term uniform acceleration itself is quite complicated, when we include relativity(increase in mass) in static fields, the acceleration should converge to zero when we approach the speed 'c' ,
Not sure on this, but think that in a frame where the accelerating q is relativistic, feebler acceleration is exactly countered by Lorentz contraction of charge's field lines, intensifying transverse field that matters re radiation. Assuming there is any radiation to start with.
Moreover, if there is any radiation during uniform acceleration and therefore radiation reaction force, it would most probably depend on the magnitude of acceleration which would again make the original acceleration non-uniform. And if we extend it further, this non-uniform acceleration again induce radiation and radiation reaction by the known formula.
In this light how good is the question about uniform acceleration and radiation ?
Right, and how possible is it to achieve any useful level of uniform acceleration in the first place, quite apart from those higher order feedback issues? Seems to be purely a theorist's playground, interesting though it is.

universal_101
Still a no-go for absolutely uniform acceleration owing to the extreme feebleness of any energy loss. You may find appealing a fairly simple argument based on conservation of energy given here: http://arxiv.org/abs/gr-qc/9811030 Not saying I endorse it though.
Alright, let me have another shot, suppose we have a electrostatic linear accelerator which can accelerate charges to speeds approaching 'c', Now if there is present a radiation reaction force then the speed of the particle approaching the end of the accelerator would be less than the expected speed without radiation. i.e.

$E - (e^2 a c^2/6{\pi}) = m_e c^2(γ-1)$ and for appropriately chosen E of the accelerator and its length, it seems the other two energy comes close for 1.05≤γ≤1.1 and normal accelerations(a). If I did everything correctly.

Therefore, now by injecting these accelerated particles in a magnetic fields and separating them by their energies can easily show if the particles radiated or not. If I assume my calculations are correct.
Not sure on this, but think that in a frame where the accelerating q is relativistic, feebler acceleration is exactly countered by Lorentz contraction of charge's field lines, intensifying transverse field that matters re radiation. Assuming there is any radiation to start with.
Before we go further, is there any straight forward proof of the intensification (synchrotron should not be included), that is, do we experience intensified electric field near a CRT or any other linear motion ?
Right, and how possible is it to achieve any useful level of uniform acceleration in the first place, quite apart from those higher order feedback issues? Seems to be purely a theorist's playground, interesting though it is.
I think classical electrodynamics has more potential than Maxwell's equations, but to have any arguments we should have observations, which we are lacking here.

Are we talking uniform in magnitude and direction? Or magnitude only? Because for later, an electron passing through a bend in an accelerator (E.g. J-Lab) is a fine example.

Q-reeus
Alright, let me have another shot, suppose we have a electrostatic linear accelerator which can accelerate charges to speeds approaching 'c', Now if there is present a radiation reaction force then the speed of the particle approaching the end of the accelerator would be less than the expected speed without radiation. i.e.

E−(e2ac2/6π)=mec2(γ−1) and for appropriately chosen E of the accelerator and its length, it seems the other two energy comes close for 1.05≤γ≤1.1 and normal accelerations(a). If I did everything correctly.

Therefore, now by injecting these accelerated particles in a magnetic fields and separating them by their energies can easily show if the particles radiated or not. If I assume my calculations are correct.
Without checking veracity of your calculations, just ask you to consider the practicalities here. A linear accelerator as used at say Stanford is not electrostatic in nature but uses a phased arrays of cavity Klystrons etc. that always induces some significant back-and-forth accelerations en-route. A pure electrostatic accelerator would be of the electron-gun cold-cathode type, and accelerations are far from uniform. Nearest one might suppose would be a parallel-plate capacitor with tiny holes in the middle of each plate. Firing a charge through both holes and one would have near-uniform acceleration in between plates. But then there is the matter of induced currents and back-reaction fields as the charge enters and exits the hole regions. Some tricky calculations needed but my guess is those back reaction effects will swamp any conceivable pure uniform radiation component.
Not sure on this, but think that in a frame where the accelerating q is relativistic, feebler acceleration is exactly countered by Lorentz contraction of charge's field lines, intensifying transverse field that matters re radiation. Assuming there is any radiation to start with.

Before we go further, is there any straight forward proof of the intensification (synchrotron should not be included), that is, do we experience intensified electric field near a CRT or any other linear motion ?
Nothing much to speak of in CRT case (a few tens of KV only mildly relativistic). It is part and parcel of SR that such contraction exists though.
I think classical electrodynamics has more potential than Maxwell's equations, but to have any arguments we should have observations, which we are lacking here.
Got me there - can you explain how classical electrodynamics is different from Maxwell's eqn's?

universal_101
Are we talking uniform in magnitude and direction? Or magnitude only? Because for later, an electron passing through a bend in an accelerator (E.g. J-Lab) is a fine example.

Of-course both, uniform in direction as well as magnitude.

universal_101
Without checking veracity of your calculations, just ask you to consider the practicalities here. A linear accelerator as used at say Stanford is not electrostatic in nature but uses a phased arrays of cavity Klystrons etc. that always induces some significant back-and-forth accelerations en-route. A pure electrostatic accelerator would be of the electron-gun cold-cathode type, and accelerations are far from uniform. Nearest one might suppose would be a parallel-plate capacitor with tiny holes in the middle of each plate. Firing a charge through both holes and one would have near-uniform acceleration in between plates. But then there is the matter of induced currents and back-reaction fields as the charge enters and exits the hole regions. Some tricky calculations needed but my guess is those back reaction effects will swamp any conceivable pure uniform radiation component.
I just thought it would be very nice to have an experimental proof, but even though I think that charges accelerating in EM fields(uniform or not) would/should radiate.
Nothing much to speak of in CRT case (a few tens of KV only mildly relativistic). It is part and parcel of SR that such contraction exists though.
Ofcourse, it is this contraction which is sometimes used to explain the magnetic field as a relativistic effect of electric field. But the only problem is we don't have any scientific experimental proof of the contraction, but it is off topic, even though SR is supposed to be the consequence of Maxwell's equations, in other words, ME's are Lorentz invariant.
Got me there - can you explain how classical electrodynamics is different from Maxwell's eqn's?
We did not have point charges when Maxwell's equations were formulated ! and classical electrodynamics is all about point charges.

Q-reeus
Ofcourse, it is this contraction which is sometimes used to explain the magnetic field as a relativistic effect of electric field. But the only problem is we don't have any scientific experimental proof of the contraction, but it is off topic, even though SR is supposed to be the consequence of Maxwell's equations, in other words, ME's are Lorentz invariant.
There has by now been quite some decades of experience involving particle accelerators of the cyclotron/synchrotron type. Specially designed versions of the latter now supply high intensity x-rays as primary objective. To explain x-ray output frequencies given fundamental 'jiggle' frequencies in the MHz range requires SR, or something exactly equivalent to it. The Lienard-Wiechert potentials, fully consistent with Maxwell's eqn's and SR, provide extraordinary accurate predictions for the entire frequency spectrum and angular intensity distribution of emitted radiation. There is a viable alternative?
We did not have point charges when Maxwell's equations were formulated ! and classical electrodynamics is all about point charges.
It's true afaik the notion of electron wasn't used by Maxwell, but isn't that putting things the wrong way around? A point charge cannot be explained classically - certainly not given high energy particle-smashing experiments. Must go. :zzz:

Mentor
That's not uniform acceleration (constant magnitude and direction).

universal_101
That's not uniform acceleration (constant magnitude and direction).
I may not know the term for constant magnitude and direction, but I meant exactly that by uniform acceleration. On the other hand, why not!

Q-reeus
I may not know the term for constant magnitude and direction,...
That would be uniform rectilinear. And sad to say, not much achievable as per earlier earlier post.

universal_101
That would be uniform rectilinear. And sad to say, not much achievable as per earlier earlier post.

Thanks Q-reeus for the effort, on the other hand it seems that non-radiating uniform acceleration can also be a valid scenario, as long as Larmor's formula is characterized as "only applicable for bound charges".

Q-reeus
Thanks Q-reeus for the effort, on the other hand it seems that non-radiating uniform acceleration can also be a valid scenario, as long as Larmor's formula is characterized as "only applicable for bound charges".
Yes that is a valid viewpoint given how the the derivation of radiative back-reaction force Frad is obtained from Larmor formula applied to periodic oscillations:http://en.wikipedia.org/wiki/Abraham–Lorentz_force#Derivation
Frad is proportional only to da/dt, hence formally vanishes for uniform a = du/dt. My feeling is the problem stems from the unrealistic assumption uniform acceleration has 'always been there'. Drop that, and radiation must be happening. But as to what extent, too much subtle arguing either way for me to place any bets.

universal_101
Yes that is a valid viewpoint given how the the derivation of radiative back-reaction force Frad is obtained from Larmor formula applied to periodic oscillations:http://en.wikipedia.org/wiki/Abraham–Lorentz_force#Derivation
Frad is proportional only to da/dt, hence formally vanishes for uniform a = du/dt. My feeling is the problem stems from the unrealistic assumption uniform acceleration has 'always been there'. Drop that, and radiation must be happening. But as to what extent, too much subtle arguing either way for me to place any bets.

Whereas, Power radiated is essentially dependent on (acceleration)2 only(that is independent of da/dt), which was(Larmor formula) essentially can be derived from the consideration of uniform rectilinear acceleration! That is, there is NO restriction whatsoever on the type of acceleration even on the derivation of Larmor formula itself. This is a big problem ! This somehow suggests we should reanalyze our fundamentals.

Q-reeus
Whereas, Power radiated is essentially dependent on (acceleration)2 only(that is independent of da/dt), which was(Larmor formula) essentially can be derived from the consideration of uniform rectilinear acceleration! That is, there is NO restriction whatsoever on the type of acceleration even on the derivation of Larmor formula itself. This is a big problem ! This somehow suggests we should reanalyze our fundamentals.
When harmonic motion occurs, it all sorts out nicely enough with power having a2 dependency ~ Erad2 and reaction force having da/dt phasing opposing velocity as required. More difficult to get consistency in uniform case for sure. There is a lot of talk about any radiation being observer-frame dependent when it comes to uniform acceleration in particular - as per that link in #2. Another that may or may not help: http://physics.fullerton.edu/~jimw/general/radreact/ Keep searching!

universal_101
When harmonic motion occurs, it all sorts out nicely enough with power having a2 dependency ~ Erad2 and reaction force having da/dt phasing opposing velocity as required. More difficult to get consistency in uniform case for sure. There is a lot of talk about any radiation being observer-frame dependent when it comes to uniform acceleration in particular - as per that link in #2. Another that may or may not help: http://physics.fullerton.edu/~jimw/general/radreact/ Keep searching!

I think this is another failure of Maxwell's Equations, explaining experimental classical electrodynamics.

A group is currently doing the experiment to detect Larmor radiation:

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Staff Emeritus
I think this is another failure of Maxwell's Equations, explaining experimental classical electrodynamics.

PF is not the place to be discussing the validity of classical electrodynamics. We provide provide a place for people to learn and discuss science as it is currently generally understood and practiced by the professional scientific community, not a place to develop alternatives.

If you want uniform acceleration, and enough acceleration to see the radiation, you need a lot of space. That's not practical.

The way that radiation from non-uniform accelerations is calculated is to divide things up into infinitesimal uniform accelerations. Those calculations match the data. The assumption that somehow this stops working when things are uniform is rather pathological.

harrylin
[..] The way that radiation from non-uniform accelerations is calculated is to divide things up into infinitesimal uniform accelerations. Those calculations match the data. The assumption that somehow this stops working when things are uniform is rather pathological.
Good one! You seem to imply that there is no fixed relationship between uniform acceleration and non-uniform acceleration in common applications to this date, not even approximately. That sounds extremely plausible and is probably easy to prove. Then antenna experiments have settled that point.
The German team seems indeed not concerned with that question, they look for other things.

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universal_101
A group is currently doing the experiment to detect Larmor radiation:

A very good link indeed !

But do you realize that it does not matter if the result of the experiment is positive or negative, we must alter some concepts in our theoretical understanding of classical electrodynamics, so to speak.

Since, if the result is positive, we are liable to explain the missing back reaction force in our theoretical treatment.

and if it is negative, then we should tag the Larmor formula as only for harmonics(non-uniform acceleration).

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universal_101
PF is not the place to be discussing the validity of classical electrodynamics. We provide a place for people to learn and discuss science as it is currently generally understood and practiced by the professional scientific community, not a place to develop alternatives.
If there is something wrong logically, I think we should discuss it. And I never presented/discussed any alternative, because there is none yet!
The way that radiation from non-uniform accelerations is calculated is to divide things up into infinitesimal uniform accelerations. Those calculations match the data. The assumption that somehow this stops working when things are uniform is rather pathological.

Then why is this same calculation, says there is NO radiation reaction on the uniformly accelerating charges ! Until and unless we assume that somehow uniformly accelerated charge can radiate EM energy is such a way that there is NO back reaction force, there is a logical disagreement.

And why do you think it is an assumption, it should be named as valid argument, since there is NO logical assessment of radiation from a uniformly accelerating charge yet.

Gold Member
2022 Award
PF is not the place to be discussing the validity of classical electrodynamics. We provide provide a place for people to learn and discuss science as it is currently generally understood and practiced by the professional scientific community, not a place to develop alternatives.

Of course you are right in stating that a forum like this should discuss the usual well-established science (here particularly physics) as established by experimental facts and their theoretical description and interpretation.

On the other hand I do not understand how you can say that this forum "is not the place to be discussing the validity of classical electrodynamics". This is a contradiction to the above statement! Classical electrodynamics (CED) is an effective theory with a wide but limited applicability range. It is well known by established science that CED is an approximation of the more comprehensive quantum electrodynamics (QED).

Particularly the here discussed experiment(s) about acceleration of charges is clearly not within the validity range of CED. Of course, you can calculate the radiation of charge with a given acceleration through the well-established Lienard-Wiechert potentials (retarded propagator applied to a four-current $j^{\mu}(x)=q v^{\mu} \delta^{(4)}[x-y(\tau)]$, where $y(\tau)$ is the world line of the particle and $\vec{v}=\vec{u}/u^0$ with the four-velocity $u=\frac{\mathrm{d} u}{\mathrm{d}\tau}$. However, it comes to the radiation back reaction to the particles motion, this is still an open problem within CED after more then 100 years of research! Only to first order in perturbation theory one can establish an approximate solution of this problem (Abrham-Dirac equation). For the current status of this issue see the brilliant textbook by Fritz Rohrlich, Classical Charged Particles (new edition 2007).

The status of QED in this questions is quite better since one can establish the charged-particles' self energy at any order of perturbation theory within this renormalizable relativistic QFT.

Here also some very interesting questions are open. Particularly the here discussed issues concerning the motion of particles in strong laser fields are of high interest. See, e.g., the already cited experiment described here

Another very interesting prediction is also the pure quantum-field theoretical prediction of Schwinger pair creation, i.e., the creation of electron positron pairs out of the vacuum in a strong electrostatic (homogeneous) field. This could not be established experimentally yet, because it is very hard to get the necessary field strength in the lab (if this is possible technically at all!). It's a challenging question both theoretically and even more experimentally, what happens in strong (standing-) wave fields of lasers. Here one also expects spontaneous pair creation. Theoretically it's a challenging problem in non-equilibrium quantum field theory.

For a related question (pair creation and em. radiation of quarks with time-dependent mass) see the recent preprint

http://de.arxiv.org/abs/1208.6565

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