Transcendental unit of measurement

Discussion in 'Physics & Math' started by currere, Oct 17, 2007.

  1. currere Registered Senior Member

    Messages:
    29
    What would be the mathematical consequences of having the "size" of a unit of measure result in the numeric value that defines a physical constant being closely related to a transcendental number?

    I had suggested to an individual that a slightly shorter meter could have been selected such that the velocity of electromagnetic waves would have a value of 314159265 m'/sec. This would make that numeric value match the value of pi to nine significant figures. That individual had a strong opinion that it wasn't a good idea, but no examples were given as to why.

    Transcendental numbers show up in equations dealing with physical law, so why would one more look-alike transcendental value make any difference?
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. mathman Valued Senior Member

    Messages:
    2,002
    Since rational numbers, algebraic numbers, and transcendentsl numbers are all dense within the real numbers, every measured number (such as the speed of light) will be as close as you want to a rational, algebraic, or transcendental number. Your suggestion doesn't have much meaning.
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. currere Registered Senior Member

    Messages:
    29
    I had a communications with a physicist on the subject and he stated, "If Pi were artificially incorporated into definitions so the speed of light had Pi in it, it would be a physically meaningless appearance of pi, and when it canceled or combined with other quantities that had physically meaningful factors of pi, it would be a mess."

    I didn't think it would make a difference but I don't know the correct argument(s) to refute his view, which is why I made this post.
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.

Share This Page