The physical constants: relationship to mathematics?

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Discussion Overview

The discussion explores the relationship between physical constants and abstract mathematics, questioning whether physical constants can appear in mathematical contexts that do not directly apply to physics. Participants consider the implications of modifying these constants and their potential connections to mathematical concepts.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about examples of physical constants appearing in abstract mathematics, particularly in papers not focused on physics.
  • Another participant questions whether constants like ##1, \frac{h}{ħ}, i,## or ##e## could be considered relevant, suggesting that fixed numbers defined by units may not appear in mathematics.
  • A different participant notes that while constants like 2 and π are significant in both mathematics and physics, they may not be classified as "physical constants" due to their broader applicability.
  • It is proposed that the absence of a known method to calculate dimensionless physical constants suggests a lack of connection between those constants and certain areas of mathematics.
  • One participant emphasizes that physical constants are defined in terms of physical units and that their relationships often involve geometric characteristics, which may not align with all mathematical frameworks.

Areas of Agreement / Disagreement

Participants express differing views on the relevance and applicability of physical constants in abstract mathematics, indicating that no consensus exists on the matter.

Contextual Notes

The discussion highlights limitations in understanding the connections between physical constants and abstract mathematical concepts, particularly regarding the definitions and units involved.

CuriousLearner
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Do we have any examples of physical constants appearing in topics that are focused more on abstract mathematics? For example, do the values of the physical constants ever appear in the results of papers on mathematics that are not focused on direct applications to physics? Could they do so if we modified their values by some sort of scalar multiple? I mean for classes of constants that may be related to a particular phenomenon such as mass ratios with respect to the electron of the fermions.
 
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Do ##1, \frac{h}{ħ} \, , \, i ## or ##e## count? Or eigenvalues of matrices? If not, what makes you think randomly fixed numbers (due to the definition of units) could appear in math?
 
CuriousLearner said:
For example, do the values of the physical constants ever appear in the results of papers on mathematics that are not focused on direct applications to physics?
No, unless you count values like 2, pi or similar things.
Such a connection would be amazing, because currently there is no known way to calculate dimensionless physical constants - if the same numbers appear in mathematics somewhere it would indicate some connection between that part of mathematics and the physical constant.
 
Certainly there are many constants ( e, π, Fibinachi numbers, the Golden Ratio, etc. ) that are important in purely mathematical issues and also important in physics. However, I don't think they would be called "physics constants" because their use is more general.
 
Hey CuriousLearner.

The physical constants are (naturally) in terms of physical units and the relation is between constants that have physical significance - which often involve changes in quantities that have a visual characteristic (i.e. involve geometry in some capacity meaning it involves distance and angle).

Mathematics can be organized in a geometric way but it doesn't need to be.

Also - quantities in mathematics that are able to use arbitrary mappings are dimension-less (example - you can't say find e^x of a unit x since it will change the units).
 

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