Consider this situation:

A) An aeroplane travels a distance from point A to point B which are located on the opposite sides of the Earth. The aeroplane has taken the shortest possible distance to travel and reach point B. From the perspective of a passenger the plane has travelled in a straight line. The passenger also records its velocity to be uniform.

B) According to a person in space he observes the Earth’s surface to be curved. So the shortest path taken by the plane isn’t a straight line but actually a curve.

Analysis: Therefore the plane is accelerating for the observer in space and is not for passenger.

Is this analysis correct?

According to general relativity acceleration is deviation from geodesic so

If you travel on curved paths (geodesics)(which are actually straight for person on earth) you won’t accelerate but if you travel on straight paths(which are actually curved (geodesics) then you are accelerating.

Is this reasoning accurate?

  • $\begingroup$ "From the perspective of a passenger the plane has travelled in a straight line." that is the "feeling", feelings cannot be modeled by mathematical functions used in physics..in addition this set up is for newtinian gravity $\endgroup$
    – anna v
    May 4 at 6:11
  • $\begingroup$ I think the problem here is that you are thinking about general relativity for no real reasons. The point you make is really pretty classical, is a problem of non-inertial reference of frames. In my opinion, it's always good practice to spend some time thinking about it. ;) $\endgroup$ May 4 at 9:21

A. No, the shortest possible distance would go through the Earth. Humans don't inhabit two-dimensional positively-curved space. We just happen to live on a ball of rock, so our map of the world looks like that.

And even "from the perspective of the passenger", the trip is not a straight line. The velocity is not uniform because they would be able to measure many different effects of this curved path. (the velocity changes direction)


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