Is the Gravitational Constant G Dependent on Unit Definitions?

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Discussion Overview

The discussion revolves around the nature of the gravitational constant G and whether its value is dependent on the definitions of the units used to measure it. Participants explore the implications of changing unit definitions on G, considering both theoretical and conceptual perspectives.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions if changing the definition of a meter would necessitate a change in the value of G, suggesting that G's value might be arbitrary based on unit definitions.
  • Another participant supports this view by noting that in relativity, using units where G and c equal 1 highlights that the values of these constants reflect our choice of units rather than fundamental physical properties.
  • A different perspective is introduced, stating that G measures the strength of gravity, implying that variations in G would correspond to changes in gravitational strength.
  • One participant references Planck units as a system that extends the discussion of unit dependency to other physical quantities.
  • A later reply reassures the original poster that their understanding is valid but emphasizes that the dependence of physical constants on units is not inherently problematic, drawing a parallel to measuring personal height in different units.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the implications of unit dependency for G, with some agreeing on the conceptual nature of constants in relation to units, while others focus on the physical interpretation of G itself. The discussion remains unresolved regarding the broader implications of these ideas.

Contextual Notes

Participants do not fully explore the implications of their claims, and there are unresolved assumptions regarding the nature of physical constants and their relationship to unit definitions.

polaris12
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I learned about G (the gravitational constant) a while ago, but ever since then it was bugging me. I did not like how a seemingly random, irrational number whose existence could not be explained existed. Then I started thinking about this: if we arbitrarily changed the definition of a meter to, for example, slightly more than what a meter currently is, then wouldn't G have to change as well? So now I started thinking that if we changed the definitions of kilograms and meters, then eventually G would be 1N meter squared per kilogram squared, and its existence would be explained by the need to change the units into Newtons. Is there a flaw in my logic?
 
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hopefully my post wasn't too vague.
 
That is a good way to look at it. In relativity we often use units where G and c both equal 1. It then becomes clear that the value of these constants only tells us about our choice of units and not about physics.
 
Here's another way of looking at it. Originally posted in this thread https://www.physicsforums.com/showthread.php?t=398900
George Jones said:
In some sense, G is a measure of the strength of gravity. If G were larger, gravity would be stronger; if G were smaller, gravity would be weaker.
 
polaris12 said:
I learned about G (the gravitational constant) a while ago, but ever since then it was bugging me. I did not like how a seemingly random, irrational number whose existence could not be explained existed. Then I started thinking about this: if we arbitrarily changed the definition of a meter to, for example, slightly more than what a meter currently is, then wouldn't G have to change as well? So now I started thinking that if we changed the definitions of kilograms and meters, then eventually G would be 1N meter squared per kilogram squared, and its existence would be explained by the need to change the units into Newtons. Is there a flaw in my logic?
No, you seem to understand fine...

...but it seems to trouble you that a physical constant would be such a slave to its units. It shouldn't. Consider your own height: whether you measure it in meters or feet, it doesn't change how tall you are.
 

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