From: noelturntive@live.co.uk   
      
   On Sunday, 15 May 2022 at 11:10:45 UTC+1, Tom Roberts wrote:   
   > 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.   
   >   
   An interesting point you make. It follows that there is no such   
   thing as an inertial frame because no matter how small you make two   
   points in space and how close together they are they will always be   
   seperate “inertial” frames. Being pulled towards the Center of gravity   
   from slightly different angles. So an inertial frame cannot actually   
   exist in 3D space.   
   > 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   
      
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