From: fortunati.luigi@gmail.com   
      
   Jonathan Thornburg [remove -color to reply] il 09/01/2024 09:37:45 ha   
   scritto:   
   > Recalling the ships-moving-on-the-Earth's-surface analogy for general   
   > relativity which I posted on 2023-12-21, Luigi's question is analogous to   
   > the following situation:  We have ships P and Q (each with perfectly   
   > symmetrical hull forms) moving on the (idealised, spherical and entirely   
   > oceanic) Earth's surface.  P moves westward at fixed speed (relative to   
   > the Earth's rotating surface -- the fact that the Earth rotates is irrelevant   
   > here) along the equator.  Q moves westward at half of P's speed at a *fixed   
   > latitude* of 60 degrees north latitude.  Initially Q is directly north of P.   
   >   
   > By symmetry we can see that P's rudder must be centered in order to stay   
   > on the equator.  By what about Q?  If Q (initially moving westward at   
   > latidude 60 degrees north) were to center its rudder, it would follow a   
   > great circle, so it wouldn't stay at latitude 60 degrees north: its latitude   
   > would start decreasing.  We thus see that in order to *stay* at latitude   
   > 60 degrees north, Q must have its rudder set for a steady turn to the right.   
      
   Ok, it's true: your ship Q, which moves while remaining at 60 degrees   
   north latitude, is an accelerated reference frame because there is the   
   force of the rudder that makes it deviate from its geodesic and your   
   ship P is an inertial reference frame because there is no force that   
   makes it deviate from its equatorial geodesic.   
      
   And although the two ships are one accelerated and the other is not,   
   their distance does not change over time.   
      
   And, so far, we agree.   
      
   But I don't agree with your implication that it corresponds   
   (1)  your ship Q to my elevator A (stopped on the floor)   
   (2)  your ship P to my elevator B (stationary at the center of the   
   Earth)   
   (3) the force of the rudder, which curves the trajectory of the ship Q,   
   to the force of the cables that keep my elevator A at the floor   
   because these correspondences are incorrect.   
      
   And in fact, if the rudder of your ship Q breaks, it moves forward   
   inertially and no one forces it to necessarily go towards ship P until   
   it hits it (so much so that it doesn't hit it!).   
      
   Instead, if the cables of my elevator A break, its free fall is not as   
   free to go wherever it happens but *must* necessarily head towards   
   elevator B until it hits it and this is not inertial behavior!   
      
   Luigi Fortunati   
      
   [[Mod. note -- The analogy isn't precise.   
      
   Notably, the ships are moving in 2 spatial dimensions (the Earth's   
   surface), whereas the elevators are (as I understand it) constrained   
   to move in a tunnel drilled radially through the Earth, and so are   
   constrained to move ONLY along that radial direction.   
      
   But this problem is (gedanken) easy to solve: we can arrange for the   
   ships P and Q to always have equal longitudes.  (For example, we could   
   have P continuously broadcast radio messages giving its current longitude,   
   and hvae Q receive these messages and continually adjust its speed so   
   as to match P's longitude.)  The result is that if Q were to center its   
   rudder, then yes, after a time P and Q would collide.   
   -- jt]]   
      
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