Falling down an infinitely deep well

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SUMMARY

The forum discussion centers on the mathematical exploration of Kaluza's concept of a fifth dimension, referred to as the "w" dimension, and its implications for understanding motion under constant gravitational forces. The original poster seeks a formula for displacement as a function of time for an object subjected to a constant gravitational pull, akin to falling down an infinitely deep well. The conversation reveals complexities in deriving such a formula, particularly in the context of relativity, with participants suggesting various equations and emphasizing the need for a clear frame of reference. Key formulas discussed include d = (c²/a)(sqrt[1 + (at/c)²] - 1) and d = 0.5at², highlighting the nuances of relativistic motion.

PREREQUISITES
  • Understanding of Kaluza-Klein theory and the concept of extra dimensions.
  • Familiarity with relativistic physics and Lorentz transformations.
  • Knowledge of kinematic equations in classical mechanics.
  • Basic grasp of gravitational physics and the effects of constant forces.
NEXT STEPS
  • Study Kaluza-Klein theory and its implications for modern physics.
  • Learn about relativistic kinematics and the derivation of motion equations under constant forces.
  • Research the Schwarzschild metric and its relevance to black hole physics.
  • Explore advanced mathematical techniques for solving differential equations in physics.
USEFUL FOR

Physicists, graduate students in theoretical physics, and anyone interested in the intersection of gravity, relativity, and higher-dimensional theories.

  • #31
Thanks, Todd. The folks at "Ask the Physicist" have been very kind to respond to my questions, as has this board.
 
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  • #32
since the original post asked for x as a function of t, not v, I have added a calculation of x to the above link
 

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