are any of Euclid's 5 postulates false in Minkowski spacetime ?

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
3
down vote

favorite












I often hear that Minkowski spacetime is non-euclidean. Euclidean geometry is characterized by Euclid's five postulates being true. Which of those postulates are untrue in Minkowski spacetime (if any), and what physical consequences do we observe from them?






special-relativity metric-tensor distance







share|cite|improve this question

























    up vote
    3
    down vote

    favorite












    I often hear that Minkowski spacetime is non-euclidean. Euclidean geometry is characterized by Euclid's five postulates being true. Which of those postulates are untrue in Minkowski spacetime (if any), and what physical consequences do we observe from them?






    special-relativity metric-tensor distance







    share|cite|improve this question























      up vote
      3
      down vote

      favorite









      up vote
      3
      down vote

      favorite











      I often hear that Minkowski spacetime is non-euclidean. Euclidean geometry is characterized by Euclid's five postulates being true. Which of those postulates are untrue in Minkowski spacetime (if any), and what physical consequences do we observe from them?






      special-relativity metric-tensor distance







      share|cite|improve this question













      I often hear that Minkowski spacetime is non-euclidean. Euclidean geometry is characterized by Euclid's five postulates being true. Which of those postulates are untrue in Minkowski spacetime (if any), and what physical consequences do we observe from them?






      special-relativity metric-tensor distance




      special-relativity metric-tensor distance






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 1 hour ago









      marjimbel

      562




      562




















          2 Answers
          2






          active

          oldest

          votes

















          up vote
          4
          down vote













          The Pythagorean distance formula doesn't hold for arbitrary shapes, thanks to the negative sign in the metric. It's also pretty easy to say that boosts obey hyperbolic angle addition rules rather than circular ones. Since the postulate about the congruency of right angles is needed to prove the Pythagorean distance relation, and angle addition rules for timelike intervals are different than those for spacelike intervals, one would conclude that the "all right angles are congruent" postulate doesn't hold-- the "right angle" between two null directions is different than that between two spacelike directions.






          share|cite|improve this answer



























            up vote
            0
            down vote













            Minkowski space with the Minkowski metric has non-Euclidean geometry (as Jerry stated in his answer, it has hyperbolic properties). This means that Euclid's parallel postulate is violated: basically, if the parallel postulate does hold for a given geometry, then the sum of the angles of a triangle is $pi$ radians since the separation between parallel lines is constant. The geometry is non-Euclidean when the sum of the angles of a triangle is greater than (spherical) or less than (hyperbolic) $pi$ radians, since the separation between parallel lines increases or decreases, respectively.






            share|cite|improve this answer




















              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',
              convertImagesToLinks: false,
              noModals: false,
              showLowRepImageUploadWarning: true,
              reputationToPostImages: null,
              bindNavPrevention: true,
              postfix: "",
              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%2f436826%2fare-any-of-euclids-5-postulates-false-in-minkowski-spacetime%23new-answer', 'question_page');

              );

              Post as a guest

















              2 Answers
              2






              active

              oldest

              votes








              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes








              up vote
              4
              down vote













              The Pythagorean distance formula doesn't hold for arbitrary shapes, thanks to the negative sign in the metric. It's also pretty easy to say that boosts obey hyperbolic angle addition rules rather than circular ones. Since the postulate about the congruency of right angles is needed to prove the Pythagorean distance relation, and angle addition rules for timelike intervals are different than those for spacelike intervals, one would conclude that the "all right angles are congruent" postulate doesn't hold-- the "right angle" between two null directions is different than that between two spacelike directions.






              share|cite|improve this answer
























                up vote
                4
                down vote













                The Pythagorean distance formula doesn't hold for arbitrary shapes, thanks to the negative sign in the metric. It's also pretty easy to say that boosts obey hyperbolic angle addition rules rather than circular ones. Since the postulate about the congruency of right angles is needed to prove the Pythagorean distance relation, and angle addition rules for timelike intervals are different than those for spacelike intervals, one would conclude that the "all right angles are congruent" postulate doesn't hold-- the "right angle" between two null directions is different than that between two spacelike directions.






                share|cite|improve this answer






















                  up vote
                  4
                  down vote










                  up vote
                  4
                  down vote









                  The Pythagorean distance formula doesn't hold for arbitrary shapes, thanks to the negative sign in the metric. It's also pretty easy to say that boosts obey hyperbolic angle addition rules rather than circular ones. Since the postulate about the congruency of right angles is needed to prove the Pythagorean distance relation, and angle addition rules for timelike intervals are different than those for spacelike intervals, one would conclude that the "all right angles are congruent" postulate doesn't hold-- the "right angle" between two null directions is different than that between two spacelike directions.






                  share|cite|improve this answer












                  The Pythagorean distance formula doesn't hold for arbitrary shapes, thanks to the negative sign in the metric. It's also pretty easy to say that boosts obey hyperbolic angle addition rules rather than circular ones. Since the postulate about the congruency of right angles is needed to prove the Pythagorean distance relation, and angle addition rules for timelike intervals are different than those for spacelike intervals, one would conclude that the "all right angles are congruent" postulate doesn't hold-- the "right angle" between two null directions is different than that between two spacelike directions.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 1 hour ago









                  Jerry Schirmer

                  30.4k255102




                  30.4k255102




















                      up vote
                      0
                      down vote













                      Minkowski space with the Minkowski metric has non-Euclidean geometry (as Jerry stated in his answer, it has hyperbolic properties). This means that Euclid's parallel postulate is violated: basically, if the parallel postulate does hold for a given geometry, then the sum of the angles of a triangle is $pi$ radians since the separation between parallel lines is constant. The geometry is non-Euclidean when the sum of the angles of a triangle is greater than (spherical) or less than (hyperbolic) $pi$ radians, since the separation between parallel lines increases or decreases, respectively.






                      share|cite|improve this answer
























                        up vote
                        0
                        down vote













                        Minkowski space with the Minkowski metric has non-Euclidean geometry (as Jerry stated in his answer, it has hyperbolic properties). This means that Euclid's parallel postulate is violated: basically, if the parallel postulate does hold for a given geometry, then the sum of the angles of a triangle is $pi$ radians since the separation between parallel lines is constant. The geometry is non-Euclidean when the sum of the angles of a triangle is greater than (spherical) or less than (hyperbolic) $pi$ radians, since the separation between parallel lines increases or decreases, respectively.






                        share|cite|improve this answer






















                          up vote
                          0
                          down vote










                          up vote
                          0
                          down vote









                          Minkowski space with the Minkowski metric has non-Euclidean geometry (as Jerry stated in his answer, it has hyperbolic properties). This means that Euclid's parallel postulate is violated: basically, if the parallel postulate does hold for a given geometry, then the sum of the angles of a triangle is $pi$ radians since the separation between parallel lines is constant. The geometry is non-Euclidean when the sum of the angles of a triangle is greater than (spherical) or less than (hyperbolic) $pi$ radians, since the separation between parallel lines increases or decreases, respectively.






                          share|cite|improve this answer












                          Minkowski space with the Minkowski metric has non-Euclidean geometry (as Jerry stated in his answer, it has hyperbolic properties). This means that Euclid's parallel postulate is violated: basically, if the parallel postulate does hold for a given geometry, then the sum of the angles of a triangle is $pi$ radians since the separation between parallel lines is constant. The geometry is non-Euclidean when the sum of the angles of a triangle is greater than (spherical) or less than (hyperbolic) $pi$ radians, since the separation between parallel lines increases or decreases, respectively.







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered 52 mins ago









                          N. Steinle

                          72719




                          72719



























                               

                              draft saved


                              draft discarded















































                               


                              draft saved


                              draft discarded














                              StackExchange.ready(
                              function ()
                              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f436826%2fare-any-of-euclids-5-postulates-false-in-minkowski-spacetime%23new-answer', 'question_page');

                              );

                              Post as a guest
































































                              Comments

                              Post a Comment

                              Popular posts from this blog

                              Long meetings (6-7 hours a day): Being “babysat” by supervisor

                              Image
                              Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote 31 down vote favorite 4 I hold a PhD in mechanical engineering with a 7 year background in self-guided, self-paced research including 2 years as a graduate level course instructor and a subject matter expert for various engineering projects in a university setting in the United States. For the last 10-11 months, I am working in a research industry in France where my task is to debug C++ spaghetti code written over a period of several years by my current supervisor. It is a team of 2: just I and my supervisor. Diurnally, I am posed with a "bug of the day" to get out of this C++ code. My supervisor generally gives me about 15-30 minutes to solve it and then accosts me about whether or not the task is completed and then rinses and repeats this until the end of the day. Off-late, my supervisor has been holding 6-7 hour long "meetin
                              Read more

                              Is the Concept of Multiple Fantasy Races Scientifically Flawed? [closed]

                              Image
                              Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite Many fantasy worlds have multiple humanoid species (elves, orcs, humans, etc) living in the same world, in addition to that, they often have the ability to interbreed. And I can't help but question their believability... fantasy-races reproduction interspecies-relations share | improve this question edited Aug 9 at 14:46 Michael Kjörling ♦ 21.1k 10 85 161 asked Aug 9 at 13:13 Chlodio 118 6 closed as unclear what you're asking by MichaelK, Gryphon, John, Vincent, Frostfyre Aug 9 at 15:25 Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question. 3 Stack Exchange exist to
                              Read more

                              Confectionery

                              Image
                              Prepared foods made with a lot of sugar or other cabohydrates "Sweetmeat" redirects here. For the racehorse, see Sweetmeat (horse). Not to be confused with Sweetbread. This Kransekake is a traditional Scandinavian baker's confection. Confectionery is the art of making confections , which are food items that are rich in sugar and carbohydrates. Exact definitions are difficult. [1] In general, though, confectionery is divided into two broad and somewhat overlapping categories, bakers' confections and sugar confections. [2] Bakers' confectionery, also called flour confections , includes principally sweet pastries, cakes, and similar baked goods. Sugar confectionery includes candies ( sweets in British English), candied nuts, chocolates, chewing gum, bubble gum, pastillage, and other confections that are made primarily of sugar. In some cases, chocolate confections (confections made of chocolate) are treated as a separate category, as are sugar-free versions of
                              Read more