A Problem from "Incandescence" - Comments

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Discussion Overview

The discussion revolves around a problem related to the concept of "incandescence" as presented in a PF Insights post. Participants are examining the representation of forces and accelerations in a diagram, particularly focusing on the conventions used for depicting weight and proper acceleration in the context of geodesics and tidal gravity.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant argues that the arrows indicating proper acceleration in the diagram are incorrectly directed, stating they actually represent geodesic deviation due to tidal gravity.
  • Another participant defends their convention of depicting weights, suggesting that the arrows point in the direction an object would move if it were force-free, which they consider a natural representation.
  • A further contribution questions whether the direction of weight should be treated as a matter of convention, emphasizing that weight is a force and should be described by an invariant observable.
  • A participant mentions revising the insights article to clarify the distinction between "weight" and "four-acceleration," suggesting an attempt to address the concerns raised in the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the conventions used for depicting forces and accelerations, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

The discussion highlights potential ambiguities in the definitions and conventions used for weight and acceleration, as well as the implications of these choices on the interpretation of the diagram.

pervect
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pervect submitted a new PF Insights post

A Problem From “Incandescence”

Incan.title_-1.png


Continue reading the Original PF Insights Post.
 

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pervect said:
Figure 2 shows a sketch of the map seen "head on" that was sketched in perspective in figure 1.

If the arrows are supposed to show the direction of proper acceleration required for a body to keep the same spatial position on the plane, their directions are backwards. The arrow directions shown are the directions of geodesic deviation due to tidal gravity, i.e., the directions in which neighboring geodesics will move relative to each other. The direction of proper acceleration required to keep neighboring worldlines from deviating will be opposite to the direction of geodesic deviation.
 
The convention I used has the weights point in the direction the object would move if it were force-free. To give an example, if I were drawing arrows for weights on the Earth, using the convention I used in my diagram, the arrows representing weight would point "downwards", towards the center of the Earth. I didn't really think much about the convention to be honest, I just used what seemed natural to me.
 
pervect said:
The convention I used has the weights point in the direction the object would move if it were force-free.

I'm not sure this is a matter of convention, unless you are also treating the term "weight" as a matter of convention. In the usual usage, "weight" is a force and its direction should be a direct observable, which must be describable by an invariant. "The direction the object would move if it were force-free" seems more like geodesic deviation to me.
 
I revised the insights article considerably from the original pair of posts, in order to distinguish "weight" from "four-acceleration", I hope that addresses the point that was raised.
 

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