Density of photons in an expanding image?

Question

This is a question from an interested amateur. Math welcome (as I or another may investigate it some day) but don't expect me to understand it in your answer.

Consider a star emitting light. In order to talk about it simply, think of a point light source, and ignore spatial perturbations (for the sake of phrasing the question). At at time t, the light emitted at a single instant at now-t forms a sphere at a distance from the source. What is the density of photons in the surface of that sphere?

Perhaps the reply is that the energy is traveling as a wave, but I understand light energy is quantized - that is, the energy has no representation described by infinitesimals, but will be in minimum quantities.

How much must the sphere expand so that there are gaps in the image when sampled at different locations on the 'instant-sphere' image?

Or, is there an explanation as to why the energy is quantized, yet can manifest at any separation (due to distance) despite the energy density falling below the quantization when the sphere is of sufficient size? What if the source is a candle? Is the original source always sufficient to 'map' adequate photons to any sphere that may be created in the dimensions of our universe?

Are there objects we cannot see because they are so far away (or dim) that we are 'in-between' the photons that form their expanding image?

Of course, I may simply not understand, but the explanation would be welcome.

Answer 1

How much must the sphere expand so that there are gaps in the image when sampled at different locations on the 'instant-sphere' image?

The photons (at least prior to detection), don't have a specific defined location. So there isn't a defined gap between them. But as the density decreases, it becomes less likely that a detector will interact with one and capture it.

We could calculate that (for example) at our distance a source is producing a photon density of 1 photon per square centimeter per second. So a sensor with a collection area of less than 1 square centimeter could expect to not detect anything over a period of less than a second.

Are there objects we cannot see because they are so far away (or dim) that we are 'in-between' the photons that form their expanding image?

Many objects don't "flash" instantaneously, but transmit continuously. Even if it's quite dim, we can keep waiting for more photons later. Or we can build a detector that has a greater capture area.

But yes, if you have a continuously transmitting object, you can get so far from it that a given detector looking at it picks up only individual photons from time to time.

Once the rate of those real detections at your sensor falls below the rate of noise detections, it is too dim to be discerned.

Answer 2

If you consider light as individual photons radiating spherically from a point source then technically at any radius beyond the origin there would be gaps. The energy is quantized because it's radiated in individual packets of energy called photons. Yes there objects we cannot see because they are so far away (or dim) that we are 'in-between' the photons that form their expanding image?

Answer 3

What if the source is a candle? Is the original source always sufficient to 'map' adequate photons to any sphere that may be created in the dimensions of our universe?

The chemical process of oxidation releases energy. The light of the candle is produced by the relaxation of excited electrons. With each reversion to lower energy states, the electron emits photons.

Indentation: Photons are part of the Standard model of elementary particle physics, their existence is real. However EM radiation is described mathematically, a description as a stream of photons must always be possible.

Every photon beam diverges, thus becomes wider with increasing distance. In the case of the candle, it shines anyway undirected, thus in almost every direction. However, the photon density, i.e. the number of photons per unit area - for example our eye iris) decreases drastically with the distance to the candle. And thus there is inevitably a distance at which the radiation of the candle is so low that only single photons hit our experimental surface at irregular intervals.