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Constant c and not its invariance.

  1. Mar 21, 2012 #1

    dpa

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    hi,
    value of c is experimental
    however c itself is theoretically lorentz invariant.
    So value of c depends upon fabric of cosmos right?

    Thanks.
     
  2. jcsd
  3. Mar 23, 2012 #2

    Bill_K

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    The existence of c is of cosmic importance, but the value is entirely manmade. With dimensions LT-1, c is just a way of relating our distance units to our time units. The only fundamental values are the ones that are dimensionless, such as the fine structure constant.
     
  4. Mar 23, 2012 #3
    The value is historical, the unit of length was originally based on a king's arm, later a fraction of the circumference of the Earth, and the unit of time is roughly a heartbeat but also a fraction of the period of rotation of the Earth. The Babylonians liked counting based on 60 because you could divide it by 2, 3, 4, 5, 6, 10 and 12 easily.

    Scientists just use c=1 (in units of light seconds per second).

    Just think of "299792458 m = 1 second" in the same way as "25.4mm = 1 inch".
     
  5. Mar 23, 2012 #4
    I'd say take it a step further & call c a concept of geometry. Specifically from measure & geometry (Euclid). Is that manmade or the nature of physical stuff?

    Opps I just read you said value,
     
    Last edited: Mar 23, 2012
  6. Mar 23, 2012 #5
    Free space (vacuum) has two universal Lorentz invariant constants; the permeability of free space μo, and the permittivity of free space εo.

    the speed of light is then defined as
    [tex] c = \frac{1}{\sqrt{\epsilon_o \mu_o}} [/tex]
    So c depends on the fabric of the vacuum.
     
  7. Mar 23, 2012 #6

    Bill_K

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    This is an unfortunate consequence of the SI system, the belief that ε0 and μ0 are somehow fundamental. Even more than c, these quantities are nothing more than conversion factors between manmade units. They do not in any way characterize nature.
     
  8. Mar 23, 2012 #7
    I don't know what the squiggly lines mean, did you say that length & time do not in any way characterize nature?
     
  9. Mar 23, 2012 #8
    There are actually four quantities in the SI system that characterize the (fabric of the) vacuum; permeability (Henrys per meter), permittivity (Farads per meter), characteristic impedance (ratio of E/H of radio wave in ohms), and speed of light. All are Lorentz invariant. Only two are independent. Only two can be measured in dc circuits.
     
    Last edited: Mar 23, 2012
  10. Mar 24, 2012 #9
    Right. Of course the value of c is different in different units, but as long as* you express it as an independent length standard divided by an independent time standard, the value that you obtain depends on those standards and on the fabric of space.
    For how this works, see for example the Shapiro effect:
    http://en.wikipedia.org/wiki/Tests_of_General_Relativity#Light_travel_time_delay_testing

    *for increased precision nowadays our length standard depends on c
     
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