From: fortunati.luigi@gmail.com   
      
   Jonathan Thornburg [remove color- to reply] marted=EC 13/09/2022 alle ore   
   08:20:03 ha scritto:   
   > Luigi Fortunati  wrote:   
   > [[about a particle]]   
   >> I am asking how does it know how to "start" to move (along   
   >> 4-geodesic) and not how to "continue" to move.   
   >   
   > The simple answer is that it's always been moving.  When the particle   
   > first came into existence, it was already moving in spacetime, so it   
   > already had a nonzero 4-velocity.   
      
   Ok, in spacetime the elevator has always been in motion, even when it   
   is stopped at the floor.   
      
   Okay, it's true that his 4-velocity has always been non-zero.   
      
   But, when the cables break and the elevator goes into free fall, its   
   4-velocity changes (i.e. it's a new different 4-velocity that wasn't   
   there before) or is still the same as it was when it was bound to the   
   floor?   
      
   [[Mod. note -- I think I answered your question in a recent message   
   which may not have reached you yet:   
      
   Let's take the time the cable breaks to be t=0, and let's take our (x,y,z)   
   coordinates to be such that the elevator is at rest at x=y=z=0 before   
   the cable breaks.  Finally, let's orient our (x,y,z) coordinates such   
   that the external gravitational accelration g points in the -z direction.   
      
   To simplify the computation, let's assume that the elevator's 3-velocity   
   is much less than the speed of light.  This is fine for investigating what   
   happens around the time when the cable breaks.  This assumption means that   
   tau = t, so that the time component of 4-velocity is just 1.   
      
   Then Newtonian mechancis tells us that the elevator's 3-velocity (the usual   
   velocity of Newtonian mechanics) is   
            { (0  ,0,0)      if t <= 0   
     v(t) = {   
            { (-gt,0,0)      if t > 0   
   while the elevator's 4-velocity is   
            { (1,0  ,0,0)      if t <= 0   
     u(t) = {   
            { (1,-gt,0,0)      if t > 0   
   and hence the elevator's 4-momentum is   
                     { (m,0   ,0,0)      if t <= 0   
     p(t) = m u(t) = {   
                     { (m,-mgt,0,0)      if t > 0   
      
   You can see that v, u, and p are all continuous functions of time.   
   -- jt]]   
      
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