What is the self energy of electrons and how can it be calculated accurately?

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    Electrons Energy Self
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Discussion Overview

The discussion revolves around the self-energy of electrons, specifically how to calculate it accurately using different models. Participants explore theoretical approaches and calculations related to the self-energy, considering both simplified and more complex representations of the electron's charge distribution.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes a calculation where the electron is imagined as two halves, each with charge e/2, and questions how much energy is needed to bring them together at a single point.
  • Another participant suggests that using classical methods for a point particle leads to an infinite answer, indicating that Quantum Electrodynamics (QED) addresses this issue.
  • A different viewpoint involves calculating the energy from the zero momentum frame, considering the bare mass of the electron and the energy density of the electric field, leading to an infinite energy result as the radius approaches zero.
  • One participant references graduate-level texts that discuss the self-energy problem, affirming that the approaches mentioned are reasonable but acknowledges that the limit of a point particle results in infinite energy, a problem recognized in QED.

Areas of Agreement / Disagreement

Participants express a consensus that the self-energy of a point particle leads to infinite energy, but there is no agreement on how to resolve this issue or on the adequacy of the proposed calculations. The discussion remains unresolved regarding the best approach to accurately calculate self-energy.

Contextual Notes

Participants note limitations in classical methods when applied to point particles and the dependence on the assumptions made regarding charge distribution. The discussion highlights unresolved mathematical steps and the complexities involved in accurately calculating self-energy.

microtopian
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The following two questions regard the self energy of electrons.. Does anybody know how to start these? I used this site as reference but I wasn't sure if they help with these following questions: http://quantummechanics.ucsd.edu/ph...tes/node44.html

Calculation 1: Pretend the electron is made up of two halves, each with charge e/2. How much energy is required to bring the two halves together, i.e., so that they occupy the same point in space?

Calculation 2: That calculation was a bit over-simplified. Let’s do a better job. Pretend that the charge of an electron is spread uniformly over the surface of a spherical shell with radius r0. Next calculate the electric field everywhere in space, i.e., at an arbitrary distance r from the center of the shell. Obviously the answer will depend on r and r0. Next, calculate the total energy stored in the field, by integrating the energy density u over all space. Finally, let the “electron” become a point particle, by letting r0 go to zero.
 
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If you're you taking the electron to be a point particle, you won't get a finite answer using classical methods. QED resolves this paradox.
 
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Assume that you're calculating/observing the energy from the zero momentum frame. You then calculate the energy of the particle's bare mass (the mass that would be there if no charge was present) and then calculate the electrons mass-energy from the expression for energy density of the E-field. The divide the energy by c^2.

When you take the limit r-> 0 you'll get an infinite amount for the energy.

Pete
 
Any graduate level text (Jackson, Panofsky and Phillips) will discuss the self energy problem. Your approaches are not unreasonable, and the last is more-or-less standard in the literature. But the plain fact remains, that in the limit of a point particle, the answer for the energy is infinite. This is true in QED as well. We're talking an unsolved and vexing problem.

Regards,
Reilly Atkinson
 

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