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Somerschool
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Thanks, Todd. The folks at "Ask the Physicist" have been very kind to respond to my questions, as has this board.
Falling down an infinitely deep well
- Context: Graduate
- Thread starter Somerschool
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Discussion Overview
The discussion revolves around the theoretical exploration of motion in a scenario involving an infinitely deep well with a constant gravitational pull. Participants are examining the mathematical implications of such a scenario, including comparisons to Kaluza's fifth dimension and the effects of relativistic physics on displacement under constant force.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants discuss Kaluza's concept of a curled-up fifth dimension and its implications for light and particle behavior in a cylindrical space.
- One participant seeks a formula for the motion of a rock thrown down an infinitely deep well with constant gravitational pull, distinguishing it from scenarios involving rockets with varying acceleration.
- Another participant suggests an alternate scenario involving a gravity generator to illustrate the same principles, raising questions about the feasibility of such constructs.
- Concerns are raised about the implications of an unvarying force producing varying acceleration as mass approaches the speed of light.
- Participants provide differing equations for displacement, with some emphasizing the need for a reference frame to define displacement accurately.
- There is a discussion about the differences between constant coordinate force and constant proper force, particularly in the context of relativistic motion.
- One participant expresses frustration over the perceived difficulty of the question and the lack of straightforward answers, suggesting that the physics should remain consistent regardless of the feasibility of the scenarios presented.
- There is mention of the Schwarzschild metric and its implications for motion near a black hole, indicating that the equations for such scenarios differ from those discussed for the infinitely deep well.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the specific formula for displacement under the conditions described. Multiple competing views and interpretations of the physics involved remain, particularly regarding the nature of forces and reference frames in relativistic contexts.
Contextual Notes
Limitations include the unresolved nature of the mathematical steps involved in deriving the desired formula, the dependence on definitions of displacement, and the implications of relativistic effects on motion under constant force.
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