Classical Aberration Formula: Understanding & Application

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Discussion Overview

The discussion revolves around the classical aberration formula for light and its physical relevance, particularly comparing the relativistic and non-relativistic forms. Participants explore the application of these formulas in real-world scenarios, such as the observation of rain while driving, and the implications of emission points on the validity of the formulas.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses understanding of the relativistic aberration formula and questions the physical relevance of the non-relativistic version, wondering if it applies to real situations like sound or is merely an approximation for small velocities.
  • Another participant uses a driving analogy to illustrate the perception of rain direction, suggesting it relates to the aberration effect.
  • A participant raises concerns about defining angles ##\sin \theta## and ##\sin \theta'## due to the ambiguity of the rain's emission point.
  • Another participant counters that the emission point is irrelevant, emphasizing that the angles are related to the velocity of the particle and coordinate axes.
  • There is a question about the validity of the formula for different types of emission sources, such as a plane versus a point source.
  • A later reply mentions that stellar aberration is small enough that the non-relativistic expression is adequate, referencing historical observations by James Bradley.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the applicability of the non-relativistic formula in various contexts, and there are differing views on the significance of the emission point in defining the angles involved.

Contextual Notes

Participants express uncertainty regarding the definitions of angles and the implications of different emission sources, indicating a need for clarity on these aspects without resolving them.

Kairos
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I believe I have understood the formula of aberration of light ##\tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} \sqrt{1-\beta^{2}} ##

but I wonder if the non-relativistic formula ## \tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} ## has a physical relevance. Does this formula apply to a real physical situation (for sound ?) or is it just an approximation for small ## \beta ##?
 
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Did you ever drive a car in rain? Did the rain seem to be coming from ahead?
 
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Yes I did. But as the point of emission of the rain is not well defined, I have difficulty in defining ## \sin \theta ## and ## \sin \theta' ##
 
Kairos said:
Yes I did. But as the point of emission of the rain is not well defined, I have difficulty in defining ## \sin \theta ## and ## \sin \theta' ##
The emission point is irrelevant. The only relevant thing is the angle of the rain relative to the velocity of the car.
 
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Does this mean that this formula is valid for an emission by a plane but not for a point source?
 
Kairos said:
But as the point of emission of the rain is not well defined, I have difficulty in defining ## \sin \theta ## and ## \sin \theta' ##
##\theta## and ##\theta'## have nothing a priori to do with the emission point, they're related to the angle between the velocity of the particle and the coordinate axes i.e. ##\mathbf{v} = (v\cos{\theta}, v\sin{\theta})## and ##\mathbf{v}' = (v'\cos{\theta'}, v'\sin{\theta'})##.
 
thank you
 
Stellar aberration is so small that the the NR expression, derived and observed in 1729 by James Bradley,
is sufficient. A simpler measurable result is ##\theta -\theta'=\beta \sin\theta.##
 

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