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A trivial question about the space of Euclidean

  1. Aug 27, 2010 #1
    Classical Mechanics define our space is [itex]E^3[/itex]
    that's also assumed to be [itex]R^3[/itex]x [itex]R_t[/itex]
    I just wondering what if [itex]Q^3[/itex]x [itex]Q_t[/itex]?
    will it make any significant difference? will it cause any logical paradox?

    thanks for reading!
    Last edited: Aug 27, 2010
  2. jcsd
  3. Aug 27, 2010 #2


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    The first thing I wonder about is how a particle in one dimension will get from coordinate a to coordinate b. In my mind, it should always do so in a continuous fashion. But you suppose it would "hop" from one rational to the "next"? You would solve Newton's laws (like F = m x'') in an interval with "holes" (e.g. [itex][a, b] \cap \mathbb{Q}[/itex])?
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