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When an excited state couples to the vacuum, it has an infinite number of directions of the quantized electromagnetic field to couple to. Does it evolve into a superposition of all those directions at the same time and only collapses once the photon is measured, or does it couple to only one? (Or, of course, is there no experimental way to tell?)

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There isn't really an answer to this. If your initial conditions are spherically symmetric then the system remain spherically symmetric and the emitted light will be in a superposition of all directions. The superposition will collapse, and the symmetry be broken, only when something interacts with your system e.g. a CCD detector.

On the other hand, if the emission was triggered by an incoming photon then your system isn't sperically symmetric, and the outgoing photon will be emitted in the same direction of the incoming one.

So how your system evolves with time depends on how you set it up to begin with. Your question implies that you're thinking of a spherically symmetric initial state, and in this case yes the emission will be in a superposition of all directions.

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