Electron charge^2 as a product of radius, mass, and c^2?

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Discussion Overview

The discussion revolves around the expression of the electron's charge squared as a product of its radius, mass, and the speed of light squared. Participants explore the validity and motivation behind this relationship, particularly in the context of synchrotron radiation and its implications in electrodynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the motivation for expressing the electron's charge squared in the form e^2 = m_er_ec^2, noting that the units do not match up and seeking clarification on its validity.
  • Another participant suggests that the expression might relate to a definition of some electron "radius," linking e^2/r to electrostatic energy and mc^2 to rest energy.
  • Some participants highlight that the electron is considered a quantum "point particle," implying it does not possess a classical radius, which complicates the interpretation of such expressions.
  • A participant mentions the Compton radius in relation to equating rest mass with electrostatic energy, cautioning against misinterpretations and suggesting that electrons may not conform to expected behaviors associated with point-like particles.
  • There is a repeated emphasis on the need for caution in interpreting the concept of the Compton radius and its usefulness, with some participants expressing skepticism about the validity of thinking of an electron in this manner.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the motivation and validity of the expression relating charge, mass, and radius. Multiple competing views exist about the interpretation of the electron's properties, particularly concerning its classification as a point particle and the implications of the Compton radius.

Contextual Notes

There are limitations regarding the assumptions made about the electron's properties, the definitions of terms used, and the unresolved nature of the mathematical relationships discussed. The discussion does not reach a consensus on the validity of the expression or its implications.

Shawnyboy
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Hello Physics Peeps,

It just came up in the notes for my electrodynamics class that an electrons charge squared can be expressed as the radius times the mass times the speed of light squared.

e^2 = m_er_ec^2

I don't understand the motivation for doing this. I've tried to search for other people doing this online to no avail. Is this just some kind of weird approximation or is it actually valid? If so why?

As far as I can see the units don't even match up although I may be missing something we have energy times distance on the right, charge on the left.

For a little more context this came up in a problem about synchroton radiation where we were using the formula for power emitted by an electron in a synchrotron which is:

P = \frac{2e^2}{3c}\omega^2\beta^2\gamma^4

And by using the relation in question we simplified the question by saying:

\frac{2e^2}{3c} = \frac{2(.5MeV)(2.8*10^{-13}cm)}{3c} \approx 3 * 10^{-24 }MeV s

Thanks for any help you can give me :oldbiggrin::oldbiggrin::oldbiggrin:
 
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What unit system are you using? cgs perhaps? and mind the equivalence of e-v and Joules.
 
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Ah-hah! cgs! That at least explains the units, because according to wikipedia a Statcoulomb = erg^1/2 * cm^1/2. However it is still not entirely clear the motivation. I mean you can't just do something because the units work.
 
It's maybe a definition of some electron "radius".
e^2/r is an electrostatic energy. mc^2 is the rest energy.
 
I think that nasu is right. The electron is a quantum "point particle" meaning that it has no internal structure. The electron doesn't have a radius, per se, not in quantum mechanics and not classically either.
 
Easy Googling, folks! Compton radius is the name for what you get when equating rest mass with electrostatic energy.

But beware, you end up with superstition and fantasy in no time...
For all we know, electrons are pointlike. And yet they aren't obeying all the expected accompanying behaviour rules.
Can't find a reasonable quotation for the upper limit; thought it was around 10-30 m. Anyone know where to look ?
 
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BvU said:
Easy Googling, folks! Compton radius is the name for what you get when equating rest mass with electrostatic energy.

But beware, you end up with superstition and fantasy in no time...
For all we know, electrons are pointlike. And yet they aren't obeying all the expected accompanying behaviour rules.
Can't find a reasonable quotation for the upper limit; thought it was around 10-30 m. Anyone know where to look ?
Thank You! That's exactly what it is. That explains it perfectly, although a strange concept this "Compton Radius". I wonder how useful it actually could be. It seems very incorrect to think of an electron in this way.
 

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