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How are One-Dimensional Numbers Useful (Coupling Constants)

  1. Jan 2, 2014 #1


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    How would it make any sense to use dimensionless numbers to represent physical things?

    From wikipedia:
    If you are comparing the strength of forces, and you are using these numbers to do so, I would have thought that these numbers would represent units of - well, force.

    Clearly I must be missing something.

  2. jcsd
  3. Jan 2, 2014 #2

    Meir Achuz

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    The size of any constant with units is ambiguous. Is g=980 cm/sec^2 large or 0.0098 km/sec^2 small?
    Expressed as a dimensionless number in 'natural' units, the electric charge of the electron is e^2=1/137 regardless of what units were used before it was made dimensionless, so the EM interaction is seen to be small.
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