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A Point source of light has radial symmetry.

If the source gets attenuated so that only a single photon is leaving each hour, can I still argue, that the field of the single photon is radial but the photon is detected on an arbitrary (random) point on the sphere, like it is the case for the wave function of a material particle?

In this case there could be interference caused by spatially very distant interfering objects (e.g. gravitation of stars, ...)

Or does the emitted photon have a narrow radiation coil from beginning?

MichaelW
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    Spherical, yes, but why do you make a conclusion that "there could be interference caused by spatially very distant interfering objects"? A photon interferes only with itself, newer with another photon. Can you clarify the logic that has led you to this conclusion? – safesphere Jan 13 '19 at 16:35
  • I mean objects that act like a slit in a double slit screen. – MichaelW Jan 13 '19 at 16:58
  • @safesphere: Show me the place in my question where I stated that! I meant objects that act similar like a slit in a double slit screen, but with slits very far apart. I wrote "caused by ", I didn't say "with". Downgrading my whole question just because of a possible misunderstanding is - in my feeling - very arrogant. Sorry to say that... – MichaelW Jan 13 '19 at 17:05
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    Not my downvote. Yes, you can use a mirror to observe the interference of a photon with itself, as if it is emitted in two (or all) directions at once: +1 – safesphere Jan 13 '19 at 17:11
  • @safesphere: sorry, ... can the downvoter tell me the reason for his downvoting? – MichaelW Jan 13 '19 at 17:15

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A single photon can be emitted with an outgoing "spherical" wavefront. I put "spherical" in quotes because most emission processes will produce a photon with a wavefunction that may have less symmetry but that is still significant in practically all directions, in close analogy with classical EM radiation. (This close analogy is not a coincidence, as illustrated quantitatively in another post.)

A photon is something that can be counted, not necssarily something that is localized or traveling in a narrow direction. However, if a source located in the middle of a large spherical cavity emits single a "spherically"-symmetric photon, and if the spherical wall of the cavity is lined with localized photon-detectors, then only one of those detectors will register the photon. This is a property of the measurement, and it does not imply that the photon had any narrow direction prior to the measurement.

Chiral Anomaly
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  • Nice answer. The first two paragraphs express something that I've spent many more paragraphs than two trying to say. The remainder also makes good points very well. – garyp Jan 13 '19 at 22:03
  • The OP didn't ask about two sources. I also thought so at first, but he clarified in the comments that he meant interference of light from a single source on two objects like two slits. Also, two photons don't interfere. In your example of two coordinated sources, the key word is coordinated. The relevant physical meaning of coordination here is that a single photon is emitted by both sources at the same time as a superposition like you described. If you know which source emitted the photon, there is no interference, just like in a double slit experiment. A photon interferes only with itself. – safesphere Jan 14 '19 at 16:19
  • @safesphere Good point that the OP wasn't asking about two sources; now I see that clarification in the comments. And your second point is also good: a star won't emit a photon without itself being modified in some way (e.g., reduced energy), so the state will never be like the superposition I described. Even if no human "knows" which star emitted the photon, the photon will still be entangled with the state of the stars (i.e., the stars will "know"), which is enough to eliminate the interference. I deleted that part of the answer. Thanks! – Chiral Anomaly Jan 15 '19 at 03:25