"Explain the statement that one's eyes could not detect the faint star-light if light were not particle like"


What comes to my mind is that when light from outside enters the atmosphere,it gets refracted...referred to as atmospheric refraction.For this,light bends before it reaches the earth surface.But,from a more realistic point of view,this bending is a scattering rather than a refraction.

If we look upon the atmosphere as a continuous medium with constant refractive index,the idea of refraction is correct.We might see the refraction using light as an EM wave.
But, basically, the air is not so.Its density, pressure etc. changes with time.Thus, we know it is composed of air molecules and what we know as refraction,is more precisely, a case of scattering.

And when a scattering is involved, we know that the corresponding light can be treated as particles...[Compton Scattering]

---This arguement has the virtue that, the wavelength is almost constant [remember that for visible light,Compton shift is negligible], yet it explains that the intensity is so small. By the action of scattering,many photons go away....they do not ultimately reach our eyes....and the observed intensity is much lower...

Please let me know what do you think about this problem.

Well I'm assuming the question comes from an authoritative source, so for argument's sake I'll treat it as true. While the atmosphere does indeed shift about at random, with changing temperatures, pressures, molecular arrangements, etc., these features average out so that the result doesn't change much if you just assume fixed atmospheric conditions.

So if I remember correctly, classical atmospheric scattering is calculated by assuming that light is absorbed by electrons bound to air molecules, which then oscillate and re-emit this light at the same frequency but a lower intensity. Some of the starlight is absorbed by the atmosphere as heat and perhaps scattered in small amounts at different frequencies, the rest gets re-emitted by the oscillating electrons, with the intensity of the resulting light varying by direction. If you take into account the fact that treating light as individual particles changes the results of these calculations, it just might make the difference between being able to and not being able to see faint starlight with the naked eye. I believe it was Einstein who first explained why the sky is blue, as classical calculations weren't getting the correct results, even though they did at least give predictions which worked in certain cases.

Isn't the explanation for faint intensity simply the inverse square law ?

The energy from the source is distributed over a larger and larger spherical surface and thus the density at any point falls off with radial distance. Wave particle duality is not an issue it would seem to me.

Isn't the explanation for faint intensity simply the inverse square law ?

The energy from the source is distributed over a larger and larger spherical surface and thus the density at any point falls off with radial distance. Wave particle duality is not an issue it would seem to me.

That's not the question though- the question is why faint starlight is scattered by the atmosphere in small enough amounts that we can still see it. I guess, if the question is correct, classical electromagnetism predicts too much scattering for us to see it, whereas in quantum physics, the particle nature of light reduces this scattering enough that we can still detect the light with our eyes. The inverse square law only explains why the starlight arriving at Earth is so faint in the first place, not why it's scattered.

That's not the question though- the question is why faint starlight is scattered by the atmosphere in small enough amounts that we can still see it.

Is it? From my reading the question is simply why couldn't we see faint star light if light wasn't particulate in nature. The part about atmospheric scattering is the OP's attempt to answer the question, and really isn't implied by the question itself.

That being said, I think he might have taken a wrong track. I would tend to lean towards an explanation that dealt more with the photo receptors of the eye.

Consider that it takes a minimum threshold of energy to trigger a receptor.

If light were wavelike, then below a given wave amplitude, it will not trigger the receptor, no matter how long the receptor is exposed to it. Even though the total energy the receptor receives would be more than enough to trigger it, it is too spread out over time to reach the threshold.

If light is a particle, the same total energy of light is delivered as a single "packets" each of which contain enough energy to trigger the receptor. Same amount of energy delivered over the same amount of time as the wave above, but as a series of particles each containing enough energy to individually trigger the receptor.

Ah I see, good points. I must have misunderstood the question. Your answer makes perfect sense to me :)