Should Equation (30) be Revised to '2πfn=2nc'π/L'?

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Discussion Overview

The discussion revolves around the correctness of a specific equation related to photon modes in a transmission line, particularly focusing on whether equation (30) should be revised to include a modified term for propagation velocity. The scope includes theoretical considerations and clarifications of terms used in the equation.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question whether the equation should be revised from "2πfn=2nπ/L" to "2πfn=2nc'π/L".
  • There is uncertainty regarding the definitions of variables such as fn, n, and L, with some participants suggesting that context from the original source material is necessary for clarity.
  • Some participants emphasize the need to define the quantities in the equation to facilitate understanding.
  • One participant notes that the derivation is part of a larger discussion on Johnson noise, which spans several pages in the referenced book.
  • Another participant asserts that the frequency must have the dimension of 1/time, implying that the inclusion of c' in the equation is necessary for dimensional consistency.
  • Some participants express that the first equation cannot be correct while the second one could be, but this remains a point of contention.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the original equation is correct or if the proposed revision is necessary. Multiple competing views remain regarding the definitions and implications of the terms involved.

Contextual Notes

There are limitations in the discussion due to missing definitions and assumptions regarding the variables in the equation, as well as the dependence on the context provided in the original source material.

vaatmoly
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Just above equation (30), it says "2πfn=2nπ/L". Should it be "2πfn=2nc'π/L" instead?
 
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vaatmoly said:
Just above equation (30), it says "2πfn=2nπ/L". Should it be "2πfn=2nc'π/L" instead?
Is fn a spatial or a temporal frequency?
What is n and L?
Maybe you could make pdf of the section, so one can see the context.
 
You have to get the book and read it. It's part of the derivation of Johnson noise. The derivation is several pages long.
 
vaatmoly said:
You have to get the book and read it. It's part of the derivation of Johnson noise. The derivation is several pages long.
Maybe you could just define the quantities in the equation?
 
Yes, sure.
We are considering photon modes in a transmission line(an electromagnetic system in one dimension). The transmission line has 2 photon modes(one propagating in each direction) of frequency "2πfn=2nπ/L" where L is the transmission line length, c' is the propagation velocity on the line, n is the mode number
 
vaatmoly said:
Yes, sure.
We are considering photon modes in a transmission line(an electromagnetic system in one dimension). The transmission line has 2 photon modes(one propagating in each direction) of frequency "2πfn=2nπ/L" where L is the transmission line length, c' is the propagation velocity on the line, n is the mode number
Then it's pretty clear. The frequency has dimension 1/time so you need the c in the equation to get the dimensions right.
The 2nd equation could be right, the 1st can't be.
 

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