Does the Dimensionless Quantity from These Constants Have Physical Meaning?

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Discussion Overview

The discussion centers around the physical meaning of a dimensionless quantity derived from specific constants, including the Thomson cross section and the neutron Compton wavelength. Participants explore theoretical implications and mathematical relationships without reaching a consensus.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Krakers questions the physical meaning of a dimensionless quantity calculated from the Thomson cross section and the neutron Compton wavelength.
  • One participant challenges the idea by asking for an argument supporting the existence of meaning.
  • Another participant expresses skepticism with a simple "No." without further elaboration.
  • A different participant proposes a mathematical expression that equals the dimensionless quantity, suggesting a potential connection.
  • There is a mention of using software or online tools, such as Wolfram Alpha, to derive or verify mathematical relationships.
  • A participant provides context about the Thomson cross section, relating it to photon scattering on free electrons and the classical electron radius.
  • Another participant states that the dimensionless quantity can be expressed in terms of fundamental constants, specifically involving the fine-structure constant and mass ratios.
  • Krakers expresses gratitude for the contributions and knowledge shared in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the dimensionless quantity has physical meaning, with some expressing skepticism and others proposing mathematical connections.

Contextual Notes

Some mathematical steps and assumptions underlying the relationships discussed remain unresolved, and the implications of the dimensionless quantity are not fully explored.

Krakers
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Question: Does the dimensionless quantity derived from the constants below have any physical meaning?

6.6524585580E-29 = Thomson cross section in SI units
2.1001941382E-16 = neutron Compton wavelength / 2pi inSI units
1508.215132 = (Thomson cross section) * (neutron Compton wavelength / 2pi)^-2

Regards,
Krakers
 
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Can you argue why it should have a meaning?
 
No......
 
Maybe because:
\frac{55+150 \pi+1867 \pi^2}{4 \pi} = 1508.215132...

;)
 
Now I get it. Do you have software that does that for you?
 
The Thomson cross section (= 8 pi r02/3 = 0.66 barns) is the low energy limit of the total Compton cross section (photon scattering on free electrons). r0 is the classical electron radius (2.828 fermi).
 
The dimensionless quantity above is equal to \frac{8\pi}{3} (\alpha \frac{m_n}{m_e} )^2.
 
Thank you all for your time and the gift of your knowledge.

Regards,
Krakers
 

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