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I Does Noether theorem explain the constant speed of light?

  1. Dec 12, 2016 #1
    I learned in Analytical Mechanics: "Emmy Noether's theorem shows that every conserved quantity is due to a symmetry".
    The examples I learned where conservation of energy as symmetry in time and conservation of momentum as symmetries in space.

    Now I wonder, do universal constants are also due to symmetries like the speed of light?.
    Maybe if we lived in a word that couldn't help but be symmetric in space, then there would be a universal value for momentum for all things, or I don't know.

    The idea is that the speed of light is constant because of a symmetry inherent to the universe, but knowable nonetheless.

    The speed of light is the first one I thought about, but now I wonder if this could apply to other universal constants, like G for gravity and k for electromagnetism.

    Now, I have no idea what this symmetries would be, and maybe I am generalizing wrong, if so please illuminate me.

    Thanks
     
  2. jcsd
  3. Dec 13, 2016 #2

    mfb

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    Staff: Mentor

    The speed of light as constant is similar to the conversion between miles and kilometers: 1 mile = 1.609 km. This conversion is true everywhere in the universe, in every reference frame, but it is just a conversion between arbitrary man-made units.

    We could express all lengths in light-seconds, or all times in meters. It would not change physics, and in fact this is frequently done in particle physics, where energy, momentum and mass are all expressed in the same units (eV). In those unit systems, ##c=1##. There is no symmetry related to a constant that is 1.
    You can also set ##\hbar = 1 ##, then particle lifetimes can be expressed in 1/eV. Add ##G=1## (sometimes defined with a prefactor) and you get the Planck units.

    The really fundamental constants are dimensionless constants: their value does not depend on the unit system we choose. The most prominent example is the fine-structure constant, about 1/137. But those don't correspond to any symmetry either.
     
  4. Dec 13, 2016 #3
    Thanks. I wanted there to be a reason for some values to be constant, but I guess we still don't know the reason for the constants to exist nor they proportion to one another
     
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