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If I am not mistaken, an incoherent light wave is a light wave made out of waves with random phases: it consist of photons with random phases.

Now I am wondering what we would see if we would somehow measure the electric field of such a light wave. Would the electric field oscillate with ever changing amplitudes and directions, or would there still be some sort of regularity in its behavior?

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  • $\begingroup$ you can use the superposition principle if you know the amplitudes,frequency and phase differences between these waves. $\endgroup$ – Paul Feb 3 '15 at 1:34
  • $\begingroup$ Another consideration is that there is no such thing as perfectly incoherent source, all lights sources have some degree of coherency. $\endgroup$ – PhysicsDave May 1 '20 at 2:35
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I think that the thermal light is a good example. It is emitted by any object of temperature above absolute zero. Thermal light is a chaotic state, not described by a quantum state but by a diagonal density matrix whose elements describe the probability of different wavelengths, different polarizations, and in general no polarization is preferred, i.e. any polarization is equally probable.

However, I have a comment about your question, "Would the electric field oscillate with ever changing amplitudes and directions?". No, it's not true that there is a general electric field, of a certain type of polarization, but it changes direction very rapidly. You won't find such a common organization, you will find chaos.

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