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keji8341
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It is widely recognized in physics textbooks that Planck constant is a "universal constant". But I nerver see a proof. As we know, in the special theory of relativity, c is a universal constant, namely a Lorentz invariant, which is Einstein's hypothesis. But How do we know the Plack constant h is also a Lorentz invariant?
Suppose E=hv in the lab frame, while E'=h'v' in the moving frame.
Usually, one assume that photon's momentum and energy forms a momentum-energy 4-vector, generalized from a real particle, like an electron which has non-zero rest mass and of which the velocity is less than c. However the derivation of electron's 4-vector is not valid for a photon. (k, w/c) is Lorentz covariant from the invariance of phase, but we don't know if h is Lorentz invariant. [Of course, if h is Lorentz invariant, (h_bar*k, h_bar*w/c) is a Lorentz covariant momentum-energy 4-vector.]
Therefore, the Lorentz invariance of Planck constant is only an artificial assumption. Am I right?
Suppose E=hv in the lab frame, while E'=h'v' in the moving frame.
Usually, one assume that photon's momentum and energy forms a momentum-energy 4-vector, generalized from a real particle, like an electron which has non-zero rest mass and of which the velocity is less than c. However the derivation of electron's 4-vector is not valid for a photon. (k, w/c) is Lorentz covariant from the invariance of phase, but we don't know if h is Lorentz invariant. [Of course, if h is Lorentz invariant, (h_bar*k, h_bar*w/c) is a Lorentz covariant momentum-energy 4-vector.]
Therefore, the Lorentz invariance of Planck constant is only an artificial assumption. Am I right?