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If we look at light as a collection of little particles, we can say that dimmer light has its photons more spread out.

But if we look at light as a wave, then there no gaps unless specifically placed there on purpose.

So how can one interpret the formation of gaps between the photons?

Qmechanic
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  • This kind of thing can be fairly subtle to get right, and I'm not convinced that there's a simple answer. There is a history of people getting this kind of thing wrong, starting with G.I. Taylor in 1909, and continuing until as late as late as the 1970's, when experts like Pipkin still showed a lack of understanding of the fact that the single-photon interpretation of the G.I. Taylor experiment was invalid due to Bose-Einstein correlations. Even if the light was emitted by isolated atoms, we would at least need to compare the half-life for electric dipole radiation to the mean time... –  May 18 '18 at 04:10
  • ...between emission of photons by a star (which does turn out to be shorter by many orders of magnitude). So if a star was a pointlike source, this would establish that the wave-packets, which are like thin spherical shells, overlapped. But a star is not a pointlike source, so the spherical shells would not be concentric. And in any case a star is not a bunch of independent atoms that radiate. The radiation is thermal, and there are B-E correlations. And do we want an answer that refers to measurable quantities? The observables are probably transverse and longitudinal coherence lengths. –  May 18 '18 at 04:18

3 Answers3

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The resolution, such as it is, lies in the ideas of a particle's wave function and the probabilistic nature of measurement.

Each photon can be thought of as having a wave function that is propagating outwards from the light source. As this wave function expands, its amplitude decreases, just as a classical wave would.

However, the laws of quantum mechanics say that this wave function determines the probability of detecting the photon at any particular location. Specifically, the probability of measuring the particle near any point is proportional to the square of the magnitude of the wave function at that point. This means that we are much less likely to detect a photon within (say) 1 mm of a point 100 light-years away from the source than we are to detect it within 1 mm of a point 1 light-year from the source. Statistically, though, if we detect a large number of photons, all emitted from the source in the same manner, they will be evenly distributed over the sphere. Thus, the amount of light energy is evenly distributed over the sphere, just as we would expect classically.

Michael Seifert
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A photon typically has a definable (though not easily measurable) spatial extent. See, for example, Single Photon Hologram, which describes a way that the spatial (and temporal) extent can be measured -- as long as we have access to plenty of identical photons. Because the speed of light is the same for all frequencies/wavelengths, a photon propagating in the vacuum cannot spread out in its direction of propagation. However, it definitely spreads out in the directions perpendicular to its direction of propagation. In order to know if photons from a source can start out overlapping but at some distance no longer overlap, it would be necessary to know the details of the source and its size.

Note: "overlap" is a fuzzy concept in this context. If a contour surface could be drawn around the photon so that the surface enclosed a volume containing, say 99.99% of the photon's probability of being present, then we might for example agree to pretend the portion of the wavefunction outside the volume does not exist, and agree that in some cases the photons will not overlap. However, the wavefunction of a free photon has an at least extremely small but finite value everywhere, so in an absolute sense all the photons from the source will overlap (though no experiment is likely to be able to prove it).

S. McGrew
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When the light intensity gets weaker the statistical character of light becomes evident. The classical fields describe the average intensity but at low intensity you will increasingly see intensity fluctuations about this average. This phenomenon is called photon shot noise. If for example your detector detects an intensity corresponding to 10.000 photons during its integration time, then the intensity will follow a gaussian distribution with standard deviation of 100 or 1%. At even lower photon numbers poisson statistics applies. This is true for an incoherent source such as the star you mentioned, or a classical light bulb. You could say that between the individual photon detections there are gaps that display random length variation.

my2cts
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  • Most of this material doesn't really have much to do with the question. By analogy, I could ask whether or not legal parcels of real estate overlap, and in answering the question it would not be helpful to say that the statistical distribution of lot sizes in Italy follows a Pareto distribution. –  May 18 '18 at 03:35