# Effect of a charge's own field on itself (Feynman Lec. Vol. [I]-28 )

• Swamp Thing
In summary, Feynman discusses the unsolved problem of calculating the field from all charges, including the charge itself, which leads to difficulties when trying to find the distance between a charge and itself. This problem has not yet been fully solved and it affects our ability to accurately predict and solve certain physical problems. However, there are approximations and alternative approaches that can be used, such as the Landau and Lifshitz modification of the Abraham-Lorentz-Dirac equation, or using continuum mechanics instead of point-particle mechanics in relativity. A further discussion on this topic can be found in J. Rafelski's book, "Relativity Matters".
Swamp Thing
From Feynman's Lectures, Part I , Ch. 28
There was a problem that was not quite solved at the end of the 19th century. When we try to calculate the field from all the charges including the charge itself that we want the field to act on, we get into trouble trying to find the distance, for example, of a charge from itself, and dividing something by that distance, which is zero. The problem of how to handle the part of this field which is generated by the very charge on which we want the field to act is not yet solved today. So we leave it there; we do not have a complete solution to that puzzle yet, and so we shall avoid the puzzle for as long as we can.
Purely in terms of predictive success and useful applications, what kind of physical / practical problems are we not able to calculate because of this gap in our understanding? Have things become clearer in any way, as of 2019?

FAPP there's nothing we can't handle with appropriate approximations. The point is that classical point particles don't exist, i.e., they are at best an approximation. The resolution FAPP is to use not the Abraham-Lorentz-Dirac equation but the modification by Landau and Lifshitz of it, which is accurate to the same order of approximation but doesn't suffer from all the trouble.

Another way out, known for more than 100 years, is not to use point-particle mechanics in relativity at all but only continuum mechanics, where no problems of this kind exist.

For a nice discussion, see

J. Rafelski, Relativity Matters, Springer International
Publishing AG, Cham (2017).
https://dx.doi.org/1007/978-3-319-51231-0

kith, Swamp Thing, Delta2 and 1 other person

## 1. What is the concept of a charge's own field?

The concept of a charge's own field refers to the electric field that is produced by a charged particle in its own vicinity. This field interacts with the original charge and affects its behavior.

## 2. How does a charge's own field affect itself?

A charge's own field affects itself by exerting a force on the original charged particle, causing it to move or accelerate. This is known as self-interaction or self-force.

## 3. What is the significance of the Feynman Lecture on the effect of a charge's own field on itself?

The Feynman Lecture on the effect of a charge's own field on itself is significant because it provides a theoretical framework for understanding the behavior of charged particles in their own electric fields. It also helps to explain phenomena such as self-energy and radiation damping.

## 4. How does the effect of a charge's own field on itself differ from the effect of an external field?

The effect of a charge's own field on itself differs from the effect of an external field in that the former is a result of the charge's own presence, while the latter is caused by an external source. Additionally, the self-force is a continuous and infinite interaction, while the external force can be turned on and off.

## 5. What are some practical applications of understanding the effect of a charge's own field on itself?

Understanding the effect of a charge's own field on itself has practical applications in various fields such as electromagnetism, quantum mechanics, and particle physics. It can help in the design of electronic devices, the study of atomic and molecular interactions, and the development of theories in quantum electrodynamics.

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