Gravitational time dilation compensated by acceleration












4












$begingroup$


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









$endgroup$












  • $begingroup$
    I am curious why you come to your original assumption: There are two close-by objects which are not moving relative to each other. How could one be accelerated while the the other one is not? Is it that the one on the mountain is suspended by solid matter while the one in the helicopter is (at least indirectly) suspended by gaseous matter? That should not, well, matter. Is it that the helicopter must burn fuel in order to stay aloft? It is a bit unintuitive, but there is no energy transferred to or from the object; it is all wasted by heating the air.
    $endgroup$
    – Peter A. Schneider
    2 hours ago


















4












$begingroup$


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









$endgroup$












  • $begingroup$
    I am curious why you come to your original assumption: There are two close-by objects which are not moving relative to each other. How could one be accelerated while the the other one is not? Is it that the one on the mountain is suspended by solid matter while the one in the helicopter is (at least indirectly) suspended by gaseous matter? That should not, well, matter. Is it that the helicopter must burn fuel in order to stay aloft? It is a bit unintuitive, but there is no energy transferred to or from the object; it is all wasted by heating the air.
    $endgroup$
    – Peter A. Schneider
    2 hours ago
















4












4








4





$begingroup$


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 13 hours ago









François RitterFrançois Ritter

606




606












  • $begingroup$
    I am curious why you come to your original assumption: There are two close-by objects which are not moving relative to each other. How could one be accelerated while the the other one is not? Is it that the one on the mountain is suspended by solid matter while the one in the helicopter is (at least indirectly) suspended by gaseous matter? That should not, well, matter. Is it that the helicopter must burn fuel in order to stay aloft? It is a bit unintuitive, but there is no energy transferred to or from the object; it is all wasted by heating the air.
    $endgroup$
    – Peter A. Schneider
    2 hours ago




















  • $begingroup$
    I am curious why you come to your original assumption: There are two close-by objects which are not moving relative to each other. How could one be accelerated while the the other one is not? Is it that the one on the mountain is suspended by solid matter while the one in the helicopter is (at least indirectly) suspended by gaseous matter? That should not, well, matter. Is it that the helicopter must burn fuel in order to stay aloft? It is a bit unintuitive, but there is no energy transferred to or from the object; it is all wasted by heating the air.
    $endgroup$
    – Peter A. Schneider
    2 hours ago


















$begingroup$
I am curious why you come to your original assumption: There are two close-by objects which are not moving relative to each other. How could one be accelerated while the the other one is not? Is it that the one on the mountain is suspended by solid matter while the one in the helicopter is (at least indirectly) suspended by gaseous matter? That should not, well, matter. Is it that the helicopter must burn fuel in order to stay aloft? It is a bit unintuitive, but there is no energy transferred to or from the object; it is all wasted by heating the air.
$endgroup$
– Peter A. Schneider
2 hours ago






$begingroup$
I am curious why you come to your original assumption: There are two close-by objects which are not moving relative to each other. How could one be accelerated while the the other one is not? Is it that the one on the mountain is suspended by solid matter while the one in the helicopter is (at least indirectly) suspended by gaseous matter? That should not, well, matter. Is it that the helicopter must burn fuel in order to stay aloft? It is a bit unintuitive, but there is no energy transferred to or from the object; it is all wasted by heating the air.
$endgroup$
– Peter A. Schneider
2 hours ago












2 Answers
2






active

oldest

votes


















10












$begingroup$

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
    12 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
    12 hours ago










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



















3












$begingroup$

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









$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "151"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f460163%2fgravitational-time-dilation-compensated-by-acceleration%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    10












    $begingroup$

    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
      12 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
      12 hours ago










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
















    10












    $begingroup$

    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
      12 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
      12 hours ago










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














    10












    10








    10





    $begingroup$

    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 12 hours ago









    John RennieJohn Rennie

    275k43546791




    275k43546791












    • $begingroup$
      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
      12 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
      12 hours ago










    • $begingroup$
      Thank you so much !
      $endgroup$
      – François Ritter
      12 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
      12 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
      12 hours ago










    • $begingroup$
      Thank you so much !
      $endgroup$
      – François Ritter
      12 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
    12 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
    12 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
    12 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
    12 hours ago












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




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











    3












    $begingroup$

    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









    $endgroup$


















      3












      $begingroup$

      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









      $endgroup$
















        3












        3








        3





        $begingroup$

        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 12 hours ago









        Michele GrossoMichele Grosso

        1,830212




        1,830212






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Physics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f460163%2fgravitational-time-dilation-compensated-by-acceleration%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            "Incorrect syntax near the keyword 'ON'. (on update cascade, on delete cascade,)

            Image
            .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 2 total noob sorry any help greatly appreciated. I keep getting this "Incorrect syntax near the keyword 'ON'." heres my codes code one CREATE TABLE supplier ( supplierID INT PRIMARY KEY, ISBN INT FOREIGN KEY REFERENCES book(ISBN), price DECIMAL (5,2), ON UPDATE CASCADE, ON DELETE CASCADE, ); code two CREATE TABLE orders ( orderID INT PRIMARY KEY, customerID INT FOREIGN KEY REFERENCES customer(customerID), ISBN INT FOREIGN KEY REFERENCES book(ISBN), orderDate date, ON UPDATE CASCADE, ON DELETE CASCADE, ); Ive run out of stuff to try other than dumbing it down to uselessness. ...
            Read more

            Alcedinidae

            Image
            Alcedinidae Martin-pêcheur à dos bleu ( Alcedo azurea ) Classification (COI) Règne Animalia Embranchement Chordata Sous-embr. Vertebrata Classe Aves Ordre Coraciiformes Famille Alcedinidae Rafinesque, 1815 Les Alcédinidés ou Alcedinidae forment une famille d'oiseaux plus connus sous les noms de martins-pêcheurs et martins-chasseurs. Sommaire 1 Description 2 Répartition et habitat 3 Systématique 3.1 Liste alphabétique des genres 3.2 Liste des espèces 4 Chez les Anciens : l'alcyon 4.1 Étymologie (Littré) 4.2 Oiseau « fabuleux » ? 5 Notes 6 Articles connexes 7 Liens externes 7.1 Bibliographie Description | Ce sont des oiseaux compacts de taille petite à moyenne (10 à 46 cm), au bec droit et long, en forme de poignard. Leurs pattes sont courtes, et ils portent un plumage aux couleurs vives. Répartition et habitat | Cosmopolites, ils fréquentent surtout ...
            Read more

            Origin of the phrase “under your belt”?

            Image
            .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0; } 17 1 Today, I found myself discussing what students should have "under their belts" during a lecture, and I wondered to myself if there was some inappropriate undertone here that I might be unaware of. Question : What is the origin of the phrase "under your belt"? A google search revealed some webpages (e.g. [1]) that assert its origin is related to consumption of food -- once a meal has been eaten, it's under your belt (which is a relief). However, with such websites, I have no way to determine fact from "random guy on the internet making stuff up". etymology idioms ...
            Read more