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Because the moment of emission the polarization and the propagation direction , the direction of the wave vector is random. Spontaneous emission causes incoherent radiation.

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Q: Why the spontaneous radiation incoherent?
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Is there any completely incoherent light?

It's not clear exactly what you mean by "completely incoherent." Blackbody radiation is given off at any angle and any phase, but the shape of the intensity/frequency curve is determined by the temperature; is that close enough to "completely incoherent"?


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