From: tjroberts137@sbcglobal.net   
      
   On 5/8/22 9:21 AM, Julio Di Egidio wrote:   
   > On Sunday, 8 May 2022 at 09:41:41 UTC+2, Luigi Fortunati wrote:   
   >> How small must this be "locally"? As small as a brick? A half   
   >> brick? A tenth of a brick?   
   > [... verbiage that does not answer the question]   
      
   You both miss the key concept about locally inertial frames: they are   
   only APPROXIMATELY inertial, and the maximum size they can be is   
   determined by your measurement resolution; better resolution puts a   
   smaller limit on the size of the region in which they can be considered   
   inertial.   
      
   Here's a simple example.   
      
   Suppose you start with a 4-meter-wide elevator in freefall near the   
   surface of the earth, and you release two small ball bearings 3 meters   
   apart horizontally, at rest relative to the inside of the elevator. They   
   will APPROXIMATELY remain at rest relative to the elevator, but we know   
   that they are each falling toward the center of the earth, so they will   
   slowly approach each other as the elevator continues to fall.   
      
   Imagine you can measure the distance between them with a resolution of 1   
   millimeter. Since the earth radius is 6.371E6 meters, the elevator can   
   fall 1,460 meters until they are 2.999 meters apart, which will take   
   17.2 seconds.   
      
   Suppose, instead, that you can measure the distance between them with a   
   resolution of 1 micron. The elevator can fall 1.46 meters until they are   
   2.999999 meters apart, which will take 0.54 seconds.   
      
   Clearly the limited region of spacetime over which this locally inertial   
   frame is approximately inertial depends on how well you can measure.   
      
   Other types of measurements will put different constraints on the size   
   of the region. For instance, recent measurements of optical clocks at   
   NIST will put a limit of a few centimeters tall before such clocks at   
   rest in the elevator at its ceiling and floor will cease to remain in   
   sync.   
      
   Julio Di Egidio continued with an unrelated quest:   
   > [I] invite you to [...] reconsider [...] what it even means for a   
   > property to be a *true physical property* vs e.g. an artefact of the   
   > coordinate system.   
      
   Modern physics has a simple and very general requirement: "true physical   
   properties" must be invariant under changes of coordinates. This is why   
   modern physical theories are all expressed in terms of tensors, which   
   are completely independent of coordinates, and therefore invariant under   
   changes of coordinates.   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)