The equilibrium thermal radiation in a flat space-time or a curved space-time behaves like Planck black spectrum represented with coordinate quantities.We regard the fact that the radiation from a thermal equilibrium system shows Planck black spectrum as a basic physics law,from which it is demonstrated that the transitivity of clock rate synchronization is equivalent to the zeroth law of thermodynamics.The condition of clock rate synchronization is weaker than that constructing simultaneity surfaces.In the space-time satisfying the condition of clock rate synchronization,the zeroth law of thermodynamics is valid.On the other hand,in the space-time where the zeroth law is valid,one can define an identical clock rate.
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