Why is 4 ∏ in so many physics formulas?

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Discussion Overview

The discussion centers on the frequent appearance of the constant 4π in various physics formulas, including Heisenberg's uncertainty principle, Coulomb's law, and the formula for magnetic permeability. Participants explore the underlying reasons for this phenomenon, considering both geometric and physical implications.

Discussion Character

  • Exploratory, Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the prevalence of 4π in physics formulas and seeks a simple explanation.
  • Another participant suggests that the surface area of a sphere, which is 4πr², indicates that phenomena spreading uniformly from a point source will likely involve this constant.
  • A different viewpoint posits that π represents a fundamental spatial relationship in scenarios with spherical symmetry and isotropic space, while also drawing a parallel to the constant e in relation to natural variations over time.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants present different perspectives on the significance and implications of 4π in physics.

Contextual Notes

Some assumptions regarding the uniformity of space and time are not explicitly stated, and the relationship between geometric properties and physical laws remains open to interpretation.

tucanaz
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I don't understand why 4 ∏ is in so many physics formulas.

For instance, Heisenberg's uncertainty uses h / 4∏.

Or Coulomb's law for the electric force

Or the formula for the Magnetic permeability of free space:

Many formulas use 4 ∏ or 8 ∏. I just don't understand why the relationship between a circle's diameter and its circumference comes into play so much.

I am sure there is a simple explanation I am just not seeing.
 
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The surface area of a sphere is 4.pi.r^2 so anything that is spreading uniformly from a point source will tend to have that in there somewhere.
 
Π is one of those constants that show a basic spatial relationship where there is spherical symmetry and an isotropic space. e is similar in that it is a basic constant involving natural variations (decay and growth) in a linear time frame.

The two constants are not constants once space and time stop being uniform.
 
Thanks very much, that makes sense...
 

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