Minkowski space












1












$begingroup$




  1. In Minkowski space, coordinates which satisfy



    $x^2 = t^2 - X^2 > 0$



    are in the region of spacetime that is time-like.




  2. If it's



    $x^2 = t^2 - X^2 < 0$



    the region is space-like.




  3. But if



    $x^2 = t^2 - X^2 > 0$



    then its "trajectory of light-like particles".




I have understood the first two points about time- and space-like regions but I could not get the third one about "light-like particles".



My confusion is - why just light-like particles? There are many other particles at quantum level.






special-relativity mass metric-tensor causality







share|cite|improve this question











$endgroup$












  • $begingroup$
    In the future, please use MathJax, not HTML markup, to display math. Thanks.
    $endgroup$
    – G. Smith
    Apr 6 at 22:38
















1












$begingroup$




  1. In Minkowski space, coordinates which satisfy



    $x^2 = t^2 - X^2 > 0$



    are in the region of spacetime that is time-like.




  2. If it's



    $x^2 = t^2 - X^2 < 0$



    the region is space-like.




  3. But if



    $x^2 = t^2 - X^2 > 0$



    then its "trajectory of light-like particles".




I have understood the first two points about time- and space-like regions but I could not get the third one about "light-like particles".



My confusion is - why just light-like particles? There are many other particles at quantum level.






special-relativity mass metric-tensor causality







share|cite|improve this question











$endgroup$












  • $begingroup$
    In the future, please use MathJax, not HTML markup, to display math. Thanks.
    $endgroup$
    – G. Smith
    Apr 6 at 22:38














1












1








1





$begingroup$




  1. In Minkowski space, coordinates which satisfy



    $x^2 = t^2 - X^2 > 0$



    are in the region of spacetime that is time-like.




  2. If it's



    $x^2 = t^2 - X^2 < 0$



    the region is space-like.




  3. But if



    $x^2 = t^2 - X^2 > 0$



    then its "trajectory of light-like particles".




I have understood the first two points about time- and space-like regions but I could not get the third one about "light-like particles".



My confusion is - why just light-like particles? There are many other particles at quantum level.






special-relativity mass metric-tensor causality







share|cite|improve this question











$endgroup$






  1. In Minkowski space, coordinates which satisfy



    $x^2 = t^2 - X^2 > 0$



    are in the region of spacetime that is time-like.




  2. If it's



    $x^2 = t^2 - X^2 < 0$



    the region is space-like.




  3. But if



    $x^2 = t^2 - X^2 > 0$



    then its "trajectory of light-like particles".




I have understood the first two points about time- and space-like regions but I could not get the third one about "light-like particles".



My confusion is - why just light-like particles? There are many other particles at quantum level.






special-relativity mass metric-tensor causality




special-relativity mass metric-tensor causality






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Apr 7 at 10:02









Gallifreyan

1056




1056










asked Apr 6 at 20:07









sk9298sk9298

846




846












  • $begingroup$
    In the future, please use MathJax, not HTML markup, to display math. Thanks.
    $endgroup$
    – G. Smith
    Apr 6 at 22:38


















  • $begingroup$
    In the future, please use MathJax, not HTML markup, to display math. Thanks.
    $endgroup$
    – G. Smith
    Apr 6 at 22:38
















$begingroup$
In the future, please use MathJax, not HTML markup, to display math. Thanks.
$endgroup$
– G. Smith
Apr 6 at 22:38




$begingroup$
In the future, please use MathJax, not HTML markup, to display math. Thanks.
$endgroup$
– G. Smith
Apr 6 at 22:38










2 Answers
2






active

oldest

votes


















3












$begingroup$

Only particles with zero mass can travel between two events which are separated by a light-like distance. The trajectory is called light-like because photons (light) are massless, and historically the first example of a massless particle, as well as the only example in the 1910's. There are other massless particles, like gluons which would also be able to travel between two events separated by a light-like distance.



The reason why only massless particles are able to travel between two events separated by a light-like distance is that it requires you to travel at exactly the speed of light. You can see this by considering the equation $t^2-x^2=0$, this means that $x=pm t$. These equations are with the units such that the speed of light $c=1$. Thus the particle taking this trajectory is travelling at the speed of light.






share|cite|improve this answer









$endgroup$





















    5












    $begingroup$


    My confusion is about why just light like particles? there are many other particles at quantum level.




    You are correct. The terminology is historical in nature. Light was the first massless particle to be discovered. The terminology “lightlike” was established before any other massless particles were discovered. Once other massless particles were discovered it was shown that they also travel along lightlike geodesics, but by then the term “lightlike” was well established.



    An alternative term with the same meaning as “lightlike” is “null”. If you prefer then you can always use “null” and just understand that people saying “lightlike” mean the same thing.






    share|cite|improve this answer









    $endgroup$














      Your Answer








      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%2f470979%2fminkowski-space%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









      3












      $begingroup$

      Only particles with zero mass can travel between two events which are separated by a light-like distance. The trajectory is called light-like because photons (light) are massless, and historically the first example of a massless particle, as well as the only example in the 1910's. There are other massless particles, like gluons which would also be able to travel between two events separated by a light-like distance.



      The reason why only massless particles are able to travel between two events separated by a light-like distance is that it requires you to travel at exactly the speed of light. You can see this by considering the equation $t^2-x^2=0$, this means that $x=pm t$. These equations are with the units such that the speed of light $c=1$. Thus the particle taking this trajectory is travelling at the speed of light.






      share|cite|improve this answer









      $endgroup$


















        3












        $begingroup$

        Only particles with zero mass can travel between two events which are separated by a light-like distance. The trajectory is called light-like because photons (light) are massless, and historically the first example of a massless particle, as well as the only example in the 1910's. There are other massless particles, like gluons which would also be able to travel between two events separated by a light-like distance.



        The reason why only massless particles are able to travel between two events separated by a light-like distance is that it requires you to travel at exactly the speed of light. You can see this by considering the equation $t^2-x^2=0$, this means that $x=pm t$. These equations are with the units such that the speed of light $c=1$. Thus the particle taking this trajectory is travelling at the speed of light.






        share|cite|improve this answer









        $endgroup$
















          3












          3








          3





          $begingroup$

          Only particles with zero mass can travel between two events which are separated by a light-like distance. The trajectory is called light-like because photons (light) are massless, and historically the first example of a massless particle, as well as the only example in the 1910's. There are other massless particles, like gluons which would also be able to travel between two events separated by a light-like distance.



          The reason why only massless particles are able to travel between two events separated by a light-like distance is that it requires you to travel at exactly the speed of light. You can see this by considering the equation $t^2-x^2=0$, this means that $x=pm t$. These equations are with the units such that the speed of light $c=1$. Thus the particle taking this trajectory is travelling at the speed of light.






          share|cite|improve this answer









          $endgroup$



          Only particles with zero mass can travel between two events which are separated by a light-like distance. The trajectory is called light-like because photons (light) are massless, and historically the first example of a massless particle, as well as the only example in the 1910's. There are other massless particles, like gluons which would also be able to travel between two events separated by a light-like distance.



          The reason why only massless particles are able to travel between two events separated by a light-like distance is that it requires you to travel at exactly the speed of light. You can see this by considering the equation $t^2-x^2=0$, this means that $x=pm t$. These equations are with the units such that the speed of light $c=1$. Thus the particle taking this trajectory is travelling at the speed of light.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Apr 6 at 20:13









          LucashWindowWasherLucashWindowWasher

          38812




          38812























              5












              $begingroup$


              My confusion is about why just light like particles? there are many other particles at quantum level.




              You are correct. The terminology is historical in nature. Light was the first massless particle to be discovered. The terminology “lightlike” was established before any other massless particles were discovered. Once other massless particles were discovered it was shown that they also travel along lightlike geodesics, but by then the term “lightlike” was well established.



              An alternative term with the same meaning as “lightlike” is “null”. If you prefer then you can always use “null” and just understand that people saying “lightlike” mean the same thing.






              share|cite|improve this answer









              $endgroup$


















                5












                $begingroup$


                My confusion is about why just light like particles? there are many other particles at quantum level.




                You are correct. The terminology is historical in nature. Light was the first massless particle to be discovered. The terminology “lightlike” was established before any other massless particles were discovered. Once other massless particles were discovered it was shown that they also travel along lightlike geodesics, but by then the term “lightlike” was well established.



                An alternative term with the same meaning as “lightlike” is “null”. If you prefer then you can always use “null” and just understand that people saying “lightlike” mean the same thing.






                share|cite|improve this answer









                $endgroup$
















                  5












                  5








                  5





                  $begingroup$


                  My confusion is about why just light like particles? there are many other particles at quantum level.




                  You are correct. The terminology is historical in nature. Light was the first massless particle to be discovered. The terminology “lightlike” was established before any other massless particles were discovered. Once other massless particles were discovered it was shown that they also travel along lightlike geodesics, but by then the term “lightlike” was well established.



                  An alternative term with the same meaning as “lightlike” is “null”. If you prefer then you can always use “null” and just understand that people saying “lightlike” mean the same thing.






                  share|cite|improve this answer









                  $endgroup$




                  My confusion is about why just light like particles? there are many other particles at quantum level.




                  You are correct. The terminology is historical in nature. Light was the first massless particle to be discovered. The terminology “lightlike” was established before any other massless particles were discovered. Once other massless particles were discovered it was shown that they also travel along lightlike geodesics, but by then the term “lightlike” was well established.



                  An alternative term with the same meaning as “lightlike” is “null”. If you prefer then you can always use “null” and just understand that people saying “lightlike” mean the same thing.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Apr 6 at 20:17









                  DaleDale

                  6,6971829




                  6,6971829






























                      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%2f470979%2fminkowski-space%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

                      If I really need a card on my start hand, how many mulligans make sense? [duplicate]

                      Image
                      5 This question already has an answer here: How do you calculate the likelihood of drawing certain cards in your opening hand? 3 answers There is a funny modern deck where you play Treasure Hunt, but you really need to have it on the starting hand. How many mulligans should I take, if my deck contains 60 cards and contains 4 copies of Treasure Hunt? magic-the-gathering probability share | improve this question asked Nov 23 '18 at 12:12 dan dan 152 4
                      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

                      Can an atomic nucleus contain both particles and antiparticles? [duplicate]

                      Image
                      9 $begingroup$ This question already has an answer here: What happens if we put together a proton and an antineutron? 2 answers Is it theoretically possible to make a "deuterium" atom containing a proton and an antineutron in its nucleus? Would the strong nuclear force cause attraction between a proton and an antineutron? Would such a nucleus be stable, or would the proton somehow annihilate the antineutron when close enough? nuclear-physics antimatter share | cite | improve this question asked yesterday
                      Read more