Deriving Multiplication Factor for Geometrized Units: Help Needed!

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Discussion Overview

The discussion focuses on deriving the multiplication factor used in geometrized units, specifically how to convert mass to length using the factor G/c². Participants explore the implications of setting c and G to 1 and seek clarification on related conversions, such as from Coulombs to length.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Shane introduces the topic by asking how to derive the multiplication factor G/c² for converting mass to length in geometrized units.
  • Ich provides a calculation showing how to derive the relationship between G and c, indicating that 1 kg can be expressed in terms of meters using G and c.
  • Shane expresses understanding of the G/c² factor and requests further assistance in deriving the factor for converting Coulombs to length, suggesting a connection to electric field or force equations involving 4πε₀.
  • Ich references a Wikipedia page on geometrized units, which Shane acknowledges but notes lacks derivations for the multiplication factors.

Areas of Agreement / Disagreement

Participants appear to agree on the basic relationships between G, c, and their implications for geometrized units, but the discussion remains open regarding the derivation of the Coulombs to length conversion factor.

Contextual Notes

Shane's understanding of the G/c² factor is based on the assumption that c and G can be set to 1, but the derivation process for the Coulombs to length conversion remains unresolved.

ofeyrpf
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Geometrized units use the multiplication factor to convert for example mass to length, in this case the factor would is G/C^2. I know this is to do with setting c=G=1. How does one derive the multiplication factor from this?

Any help greatly appreciated.

Shane
 
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You have
c = 1 = 3e8 m/s, therefore 1 s = 3e8 m
G = 1 = 6.67e-11 m³/(kg*s²) = 6.67e-11/(3e8)² m/kg, therefore 1 kg = 6.67e-11/(3e8)² m
 
Thank you Ich. I now see where G/c^2 comes from.

Similarily would you be able to show me where \sqrt(G/(4\pi\epsilon_0))^{1/2}/c^2 come from for converting Coulombs to length? I presume it has soemthing to do with the equation for either electric field or electric force as both these contain 4\pi\epsilon_0.

Thanks for your help so far.
 
Yes I have checked out wiki. Thank you. But there they only gave the multiplication factors but not where they came from. But I know where the factor for converting from Coulumbs to length comes from now. Thanks
 

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