You have a photomultiplier tube pointed at a distant star, exactly 100 light years away. It's perfectly set up so that nothing can get into the tube unless it came from that star. Every hour or so, you get a click in the detector.
Each time you hear a click, are you justified in saying that exactly 100 years ago, a photon was emitted from that star?
Or to put it more precisely: let's say your photomultiplier tube is pre-filtered so for all intents and purposes it only responds to a certain arbitrary atomic transition, say something in the potassium spectrum. The next time you hear a click, are you justified in saying that exactly 100 years ago, a particular potassium atom on that star made that particular transition from higher to lower energy?
Obviously, if I'm asking the question, I don't think you are allowed to make that connection. But I wonder what people think?
EDIT: We can sharpen up the question a little more if we look, for example, at the sun's corona. As Wikipedia explains,
The Fraunhofer lines are typical spectral absorption lines. These dark lines are produced whenever a cold gas is between a broad spectrum photon source and the detector. In this case, a decrease in the intensity of light in the frequency of the incident photon is seen as the photons are absorbed, then re-emitted in random directions, which are mostly in directions different from the original one. This results in an absorption line, since the narrow frequency band of light initially traveling toward the detector, has been turned into heat or re-emitted in other directions. By contrast, if the detector sees photons emitted directly from a glowing gas, then the detector often sees photons emitted in a narrow frequency range by quantum emission processes in atoms in the hot gas, resulting in an emission line. In the Sun, Fraunhofer lines are seen from gas in the outer regions of the Sun, which are too cold to directly produce emission lines of the elements they represent.
If we look at the sun directly, we see absorption lines: but I want to look for emission lines. So let's look at the sun's corona; and let's set up our photomultiplier with appropriate filters and whatever so that we can say, with 90% confidence, that a click in the detector came from a particular potassium-atom transition in the corona. Then the question is perfectly clear: when we hear a click, can we say (with 90% confidence) that exactly 8 minutes ago, a particular potassium atom made a transition from a higher to a lower energy level,thereby emitting a photon...the exact same photon that was just captured in our photomultiplier?
I think the question is pretty clear, and my answer is of course: No. And I think the people who say yes are the same people who would say that in the two-slit experiment, the photon must have passed through either one slit or the other one. Or the people who say that in the Stern-Gerlach experiment, the silver atom jumps into either the spin-up or the spin-down states at the moment when it passed through the magnetic field.
I wonder what people think about this.