01 The submarine Paradox of Supplee




Hello!

  Today I would like to introduce ‘the submarine paradox of Supplee’ which appears in the theory of relativity. In 1989, Supplee raised questions about relativistic buoyancy. Picture a submarine floating in the sea. This submarine does not sink or float, so we can say that we have ‘neutral buoyancy’. 

    Suppose this submarine is now running fast. Suppose you are running at a relativistic speed, ignoring the resistance of water. This is a very important topic for black hole research. Understanding the situation of paradox is simple. Suppose a person on the bottom of the sea observes this submarine. The submarine shrinks in length because it runs at relative speed. However, as the mass increases the density also increases.




If so, a submarine cannot maintain neutral buoyancy and must inevitably sink. As shown in the picture below.




 Now let's take a look at the position of the crew on the submarine. The crew on board the submarine seems to be at a standstill and the waters are moving at relative speed.


  If so, the density of seawater is greatly increased because the seawater runs at relative speed and the seawater shrinks and the mass increases. So, the density of the submarine is relatively small, so the submarine must float above the surface. This picture is shown below.





    The shrinkage of the seawater and the increase in density are expressed in the above picture as the waveform is narrowed. In conclusion, does the submarine crash to the ocean floor? Or does it float over the surface of the water? Depending on who observes, it falls to the floor and floats on the surface of the water. We call it the subdivision paradox of Supplee.




  There are some people who have tried to solve this. Proponent Supplee's method is criticized for adjusting gravity. And Matsas has done many calculations using general relativity, but he has suspected that the process of calculation is unclear.

  If you read this article, can you observe the philosophy of relativity and solve this paradox without contradiction?

  If you can solve this problem by length contraction, please let me know too! If you interpret using length contraction, this problem is impossible forever. Strictly speaking, length contraction is not a theory of relativity. Length expansion is the length of legitimate theory of relativity.


  When interpreted as a length expansion, this does not constitute the paradox itself. Now let's interpret it as the expansion of the length.


  When interpreted as a length expansion, the volume increases as the mass increases. Therefore, the density does not change. The expression is as follows.



  No matter how fast you run, the density never increases because the volume also increases as the mass increases. Therefore, the submarine always maintains neutral buoyancy. You do not have to adjust gravity and you do not have to do a lot of buoyancy calculations. It is logical, and there is no contradiction.




  However, the expansion of the length will be uncertain. The expansion of the length has already been proven by experiment and formula. If you have any questions, please leave a comment.

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