Expansion of Plane of Projection: Terrel & Penrose

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SUMMARY

The discussion centers on the Terrel effect as presented in the papers by Terrel and Penrose, specifically regarding the expansion of the plane of projection. Both papers assert that the plane of projection expands by a factor equivalent to the Doppler factor in certain scenarios. However, a critical analysis reveals that while Terrel's paper indicates that each side of an infinitesimal rectangle increases by this factor due to relativistic aberration, it raises the question of whether the area should expand by the square of that factor. Links to both papers are provided for further examination.

PREREQUISITES
  • Understanding of the Terrel effect in relativistic physics
  • Familiarity with the Doppler effect in the context of light
  • Knowledge of relativistic aberration concepts
  • Basic comprehension of geometric projections in physics
NEXT STEPS
  • Read Terrel's paper on the Terrel effect for foundational knowledge
  • Examine Penrose's paper for additional insights on projection theory
  • Research the mathematical implications of relativistic aberration
  • Explore the relationship between the Doppler factor and geometric projections
USEFUL FOR

Physicists, students of relativity, and anyone interested in the mathematical implications of the Terrel effect and its applications in understanding projection in relativistic contexts.

Tahmeed
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In two papers of Terrel and Penrose, the concept of Terrel effect were presented. Both of the papers say that "the plane of projection is expanded by a certain factor, which is equal to Doppler factor for certain cases." Now does it mean the area of the projected plane is expanded by that factor? But according to Terrel's paper, which used relativistic aberration to derive, each side of an infinitesimal rectangle is increased by that factor(the subtended angle of the sides increases therefore the sides). If that's the case, shouldn't the area of the projection plane be expanded by the square of that factor??
 
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Can you provide any links to the source that we are able to discuss on a common base? This would help a lot to answer "does it mean" questions.
 
Here are the links: https://dx.doi.org/10.1103/PhysRev.116.1041 (Terrel's paper)
https://dx.doi.org/10.1017%2FS0305004100033776(Penrose's)
Both are pretty simple and you just have to read first two-three pages to see what i meant. If you want i can upload screenshots.
 

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