Gravitational time dilation compensated by acceleration












5












$begingroup$


I would like to compare the time indicated by two clocks: clock A is located at the top of a mountain, the clock B is in an helicopter flying stationnary at the same altitude than the clock A.



Clock A and B are at rest with each other and located at the same altitude. Clock A has a 0 proper acceleration, and clock B has a non zero proper acceleration (is it correct ?).



If we neglect the Earth rotation/tidal effects, does the general relativity predicts that both clocks will be equivalent thanks to the clock hypothesis ?



Why this simple experiment has never been done, instead of sending 2 planes in opposite directions with complex trajectories ?



Thank you!






general-relativity time-dilation







share|cite|improve this question









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    5












    $begingroup$


    I would like to compare the time indicated by two clocks: clock A is located at the top of a mountain, the clock B is in an helicopter flying stationnary at the same altitude than the clock A.



    Clock A and B are at rest with each other and located at the same altitude. Clock A has a 0 proper acceleration, and clock B has a non zero proper acceleration (is it correct ?).



    If we neglect the Earth rotation/tidal effects, does the general relativity predicts that both clocks will be equivalent thanks to the clock hypothesis ?



    Why this simple experiment has never been done, instead of sending 2 planes in opposite directions with complex trajectories ?



    Thank you!






    general-relativity time-dilation







    share|cite|improve this question









    $endgroup$















      5












      5








      5





      $begingroup$


      I would like to compare the time indicated by two clocks: clock A is located at the top of a mountain, the clock B is in an helicopter flying stationnary at the same altitude than the clock A.



      Clock A and B are at rest with each other and located at the same altitude. Clock A has a 0 proper acceleration, and clock B has a non zero proper acceleration (is it correct ?).



      If we neglect the Earth rotation/tidal effects, does the general relativity predicts that both clocks will be equivalent thanks to the clock hypothesis ?



      Why this simple experiment has never been done, instead of sending 2 planes in opposite directions with complex trajectories ?



      Thank you!






      general-relativity time-dilation







      share|cite|improve this question









      $endgroup$




      I would like to compare the time indicated by two clocks: clock A is located at the top of a mountain, the clock B is in an helicopter flying stationnary at the same altitude than the clock A.



      Clock A and B are at rest with each other and located at the same altitude. Clock A has a 0 proper acceleration, and clock B has a non zero proper acceleration (is it correct ?).



      If we neglect the Earth rotation/tidal effects, does the general relativity predicts that both clocks will be equivalent thanks to the clock hypothesis ?



      Why this simple experiment has never been done, instead of sending 2 planes in opposite directions with complex trajectories ?



      Thank you!






      general-relativity time-dilation




      general-relativity time-dilation






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 10 hours ago









      François RitterFrançois Ritter

      626




      626






















          2 Answers
          2






          active

          oldest

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          9












          $begingroup$

          Both clocks have the same proper acceleration. The calculation of the proper acceleration is described in What is the weight equation through general relativity? The proper acceleration for an object stationary at a distance $r$ from the centre of the Earth turns out to be:



          $$ A = frac{GM}{r^2}frac{1}{sqrt{1-frac{2GM}{c^2r}}} $$



          It makes no difference that one clock is stationary on a mountain at the distance $r$ from the centre of the Earth while the other is stationary in a helicopter at the distance $r$ from the centre of the Earth.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Wikipedia " Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero."... so gravitation causes a proper acceleration and this wikipedia page is wrong ?
            $endgroup$
            – François Ritter
            9 hours ago






          • 2




            $begingroup$
            @FrançoisRitter that means an object falling freely under gravity has a zero proper acceleration. The objects in your question are being held stationary not falling freely.
            $endgroup$
            – John Rennie
            9 hours ago










          • $begingroup$
            Thank you so much !
            $endgroup$
            – François Ritter
            9 hours ago



















          2












          $begingroup$

          The reference frames of clock $A$ and clock $B$ are equivalent. They are stationary with respect to the spacetime given by the earth mass/energy at the same radial coordinate. They measure a proper acceleration as the frames are not along a geodesic.



          The time of clock $A$ and clock $B$ runs with the same rate.






          share|cite|improve this answer









          $endgroup$













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            2 Answers
            2






            active

            oldest

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            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            9












            $begingroup$

            Both clocks have the same proper acceleration. The calculation of the proper acceleration is described in What is the weight equation through general relativity? The proper acceleration for an object stationary at a distance $r$ from the centre of the Earth turns out to be:



            $$ A = frac{GM}{r^2}frac{1}{sqrt{1-frac{2GM}{c^2r}}} $$



            It makes no difference that one clock is stationary on a mountain at the distance $r$ from the centre of the Earth while the other is stationary in a helicopter at the distance $r$ from the centre of the Earth.






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Wikipedia " Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero."... so gravitation causes a proper acceleration and this wikipedia page is wrong ?
              $endgroup$
              – François Ritter
              9 hours ago






            • 2




              $begingroup$
              @FrançoisRitter that means an object falling freely under gravity has a zero proper acceleration. The objects in your question are being held stationary not falling freely.
              $endgroup$
              – John Rennie
              9 hours ago










            • $begingroup$
              Thank you so much !
              $endgroup$
              – François Ritter
              9 hours ago
















            9












            $begingroup$

            Both clocks have the same proper acceleration. The calculation of the proper acceleration is described in What is the weight equation through general relativity? The proper acceleration for an object stationary at a distance $r$ from the centre of the Earth turns out to be:



            $$ A = frac{GM}{r^2}frac{1}{sqrt{1-frac{2GM}{c^2r}}} $$



            It makes no difference that one clock is stationary on a mountain at the distance $r$ from the centre of the Earth while the other is stationary in a helicopter at the distance $r$ from the centre of the Earth.






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Wikipedia " Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero."... so gravitation causes a proper acceleration and this wikipedia page is wrong ?
              $endgroup$
              – François Ritter
              9 hours ago






            • 2




              $begingroup$
              @FrançoisRitter that means an object falling freely under gravity has a zero proper acceleration. The objects in your question are being held stationary not falling freely.
              $endgroup$
              – John Rennie
              9 hours ago










            • $begingroup$
              Thank you so much !
              $endgroup$
              – François Ritter
              9 hours ago














            9












            9








            9





            $begingroup$

            Both clocks have the same proper acceleration. The calculation of the proper acceleration is described in What is the weight equation through general relativity? The proper acceleration for an object stationary at a distance $r$ from the centre of the Earth turns out to be:



            $$ A = frac{GM}{r^2}frac{1}{sqrt{1-frac{2GM}{c^2r}}} $$



            It makes no difference that one clock is stationary on a mountain at the distance $r$ from the centre of the Earth while the other is stationary in a helicopter at the distance $r$ from the centre of the Earth.






            share|cite|improve this answer









            $endgroup$



            Both clocks have the same proper acceleration. The calculation of the proper acceleration is described in What is the weight equation through general relativity? The proper acceleration for an object stationary at a distance $r$ from the centre of the Earth turns out to be:



            $$ A = frac{GM}{r^2}frac{1}{sqrt{1-frac{2GM}{c^2r}}} $$



            It makes no difference that one clock is stationary on a mountain at the distance $r$ from the centre of the Earth while the other is stationary in a helicopter at the distance $r$ from the centre of the Earth.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered 9 hours ago









            John RennieJohn Rennie

            275k43545790




            275k43545790












            • $begingroup$
              Wikipedia " Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero."... so gravitation causes a proper acceleration and this wikipedia page is wrong ?
              $endgroup$
              – François Ritter
              9 hours ago






            • 2




              $begingroup$
              @FrançoisRitter that means an object falling freely under gravity has a zero proper acceleration. The objects in your question are being held stationary not falling freely.
              $endgroup$
              – John Rennie
              9 hours ago










            • $begingroup$
              Thank you so much !
              $endgroup$
              – François Ritter
              9 hours ago


















            • $begingroup$
              Wikipedia " Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero."... so gravitation causes a proper acceleration and this wikipedia page is wrong ?
              $endgroup$
              – François Ritter
              9 hours ago






            • 2




              $begingroup$
              @FrançoisRitter that means an object falling freely under gravity has a zero proper acceleration. The objects in your question are being held stationary not falling freely.
              $endgroup$
              – John Rennie
              9 hours ago










            • $begingroup$
              Thank you so much !
              $endgroup$
              – François Ritter
              9 hours ago
















            $begingroup$
            Wikipedia " Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero."... so gravitation causes a proper acceleration and this wikipedia page is wrong ?
            $endgroup$
            – François Ritter
            9 hours ago




            $begingroup$
            Wikipedia " Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero."... so gravitation causes a proper acceleration and this wikipedia page is wrong ?
            $endgroup$
            – François Ritter
            9 hours ago




            2




            2




            $begingroup$
            @FrançoisRitter that means an object falling freely under gravity has a zero proper acceleration. The objects in your question are being held stationary not falling freely.
            $endgroup$
            – John Rennie
            9 hours ago




            $begingroup$
            @FrançoisRitter that means an object falling freely under gravity has a zero proper acceleration. The objects in your question are being held stationary not falling freely.
            $endgroup$
            – John Rennie
            9 hours ago












            $begingroup$
            Thank you so much !
            $endgroup$
            – François Ritter
            9 hours ago




            $begingroup$
            Thank you so much !
            $endgroup$
            – François Ritter
            9 hours ago











            2












            $begingroup$

            The reference frames of clock $A$ and clock $B$ are equivalent. They are stationary with respect to the spacetime given by the earth mass/energy at the same radial coordinate. They measure a proper acceleration as the frames are not along a geodesic.



            The time of clock $A$ and clock $B$ runs with the same rate.






            share|cite|improve this answer









            $endgroup$


















              2












              $begingroup$

              The reference frames of clock $A$ and clock $B$ are equivalent. They are stationary with respect to the spacetime given by the earth mass/energy at the same radial coordinate. They measure a proper acceleration as the frames are not along a geodesic.



              The time of clock $A$ and clock $B$ runs with the same rate.






              share|cite|improve this answer









              $endgroup$
















                2












                2








                2





                $begingroup$

                The reference frames of clock $A$ and clock $B$ are equivalent. They are stationary with respect to the spacetime given by the earth mass/energy at the same radial coordinate. They measure a proper acceleration as the frames are not along a geodesic.



                The time of clock $A$ and clock $B$ runs with the same rate.






                share|cite|improve this answer









                $endgroup$



                The reference frames of clock $A$ and clock $B$ are equivalent. They are stationary with respect to the spacetime given by the earth mass/energy at the same radial coordinate. They measure a proper acceleration as the frames are not along a geodesic.



                The time of clock $A$ and clock $B$ runs with the same rate.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 9 hours ago









                Michele GrossoMichele Grosso

                1,820212




                1,820212






























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