A question on constants and dimensionless equations

  • Thread starter Thread starter help1please
  • Start date Start date
  • Tags Tags
    Constants
Click For Summary
SUMMARY

The discussion centers on the equation 2αħ = π²μ₀c, which involves the fine structure constant (α), Planck's constant (ħ), the speed of light (c), and permeability (μ₀). Participants question the dimensional integrity of this equation and explore the nature of dimensionless quantities. It is established that not all dimensionless objects are constants, as demonstrated by the example of angles, which are dimensionless but not constants.

PREREQUISITES
  • Understanding of fundamental physical constants such as the fine structure constant (α) and Planck's constant (ħ).
  • Knowledge of dimensional analysis and the significance of dimensionless quantities in physics.
  • Familiarity with electromagnetic constants, specifically permeability (μ₀).
  • Basic grasp of mathematical equations involving physical constants and their implications.
NEXT STEPS
  • Research the implications of dimensionless quantities in physics, focusing on their roles in various equations.
  • Study the derivation and applications of the fine structure constant (α) in quantum mechanics.
  • Explore the relationship between physical constants and their dimensional analysis in electromagnetic theory.
  • Investigate the significance of dimensionless parameters in different branches of physics, such as fluid dynamics and thermodynamics.
USEFUL FOR

Students and professionals in physics, particularly those studying quantum mechanics and electromagnetism, as well as anyone interested in the properties and implications of dimensionless quantities in scientific equations.

help1please
Messages
167
Reaction score
0

Homework Statement



There is not really a problem, just a question which i am about to ask. The known data is

[tex]\alpha[/tex] the fine structure constant
[tex]\hbar[/tex] Plancks constant
[tex]c[/tex] the speed of light
[tex]\mu[/tex] permeability

Homework Equations



[tex]2\alpha \hbar = \pi^2 \mu_0 c[/tex]

The Attempt at a Solution



A paper I downloaded a while back, but can't actually link to states this equation

[tex]2\alpha \hbar = \pi^2 \mu_0 c[/tex]

in a derivation. It seemed a little odd, are the dimensions right? I noticed all the data in this equation are actually made up of constants. Is it wise to say that when you deal with dimensionless objects, they are always constants (for a separate question).
Thank you!
 
Physics news on Phys.org
help1please said:

Homework Statement



Is it wise to say that when you deal with dimensionless objects, they are always constants (for a separate question).
Thank you!

No. For example, angles are dimensionless.
 

Similar threads

Attenuation and Phase constant values in wave equation
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Chunks of action smaller than Planck's constant
  • · Replies 2 ·
Replies
2
Views
2K
Calculating Dipole Moment In 3s To 2p Hydrogen Transition
  • · Replies 5 ·
Replies
5
Views
2K
Recombination Lines - Astrophysics
  • · Replies 3 ·
Replies
3
Views
2K
Adiabatic Approximation in Hydrogen Atom
  • · Replies 6 ·
Replies
6
Views
2K
Spin-3/2 particle and degeneracy in excited state
  • · Replies 2 ·
Replies
2
Views
2K
Using dimensional analysis to create dimensionless equation
  • · Replies 4 ·
Replies
4
Views
2K
Proving ##C## is constant in 4-dim ##R_{\mu\nu}=Cg_{\mu\nu}##
  • · Replies 3 ·
Replies
3
Views
2K
Equation of accelerated motion in GR
  • · Replies 2 ·
Replies
2
Views
2K
Harmonic Oscillator and Volume of Unit Cell in Phase Space
  • · Replies 4 ·
Replies
4
Views
4K