From: relativity@paulba.no   
      
   Den 29.01.2026 21:55, skrev Maciej Woźniak:   
   > On 1/29/2026 9:31 PM, Paul B. Andersen wrote:   
   >> Den 28.01.2026 21:02, skrev Maciej Woźniak:   
   >>> On 1/28/2026 8:04 PM, Paul B. Andersen wrote:   
   >>>>   
   >>>> Now I know that you still think that if a spacecraft   
   >>>> with mass 1000 kg is pushed by a rocket engine with   
   >>>> the force F = 10000 N, then the proper acceleration of   
   >>>> the spacecraft is a = 0  because the speed of the spacecraft   
   >>>> relative to itself is 0 m/s.   
      
   >>> Sure, and a proper shark eats grass.   
   >>>   
   >>> Still, 1+2=3. According to the definition   
   >>> you've invented  the proper acceleration of   
   >>> any object is always 0. Sorry, poor trash.   
      
   >> :-D   
   >>   
   >> Given v(t) = kt where k is a constant   
      
   >   
   > WHAT v(t)?   
      
     v(t) is a function of t defined by:   
     v(t) = kt where k is a constant, -∞ < t < ∞   
      
   > Quoting:   
   > "The "proper acceleration" of an object is by definition   
   > the acceleration measured in the object's rest frame. "   
   >   
   > Is your v(t) the velocity of the object in its rest   
   > frame, poor trash?   
   >   
   > Is your v(t) ANY velocity? You understand that with   
   > constant non-0 derivative v must raise to infinity,   
   > right? Or maybe you're too stupid even for that?   
      
   >>   
   >> What is v at t = 0?   
   >> What is dv/dt at t = 0?   
   >>   
   >> Still not got it?   
      
   Obviously not.   
      
   The point is that dv/dt = k for all t.   
      
   That includes at t = 0 when v = 0.   
      
   If v is a speed and t a time,   
   then k is a constant acceleration.   
      
   So dv/dt may be different from zero even if  v = 0.   
      
   --------------   
      
   If a spaceship with mass m = 1000 kg is pushed by a rocket engine   
   with the force F = 10000 N, then its proper acceleration is   
   a = F/m = 10 m/s².   
   You are in the spaceship, maybe on your way to Mars. But you are   
   far from Earth and Mars, and Mars is not in front of you yet.   
   Your acceleration is obviously the same as the spaceship's,   
   but you don't know what it is.   
   How will you measure your acceleration?   
   By dv/dt? Which v? Your speed relative to a planet? Which planet?   
   The only reference you have is your spaceship which is accelerating.   
      
   A physicist may define your proper acceleration something like this:   
   Your proper acceleration is the acceleration measured in the   
   momentarily co-moving inertial frame of reference.   
   That would probably not help you, so there is only one way to do it.   
   You would use an accelerometer. It will show the acceleration 10 m/s².   
      
   An accelerometer measures the acceleration in its own rest frame,   
   where its speed is zero. But dv/dt = 10 m/s² even if v = 0.   
      
   --   
   Paul   
      
   https://paulba.no/   
      
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