If you are going to use a "photon" interpretation, you are using quantum mechanics, and in QM "brightness" involves the probability of detecting a photon and does not require there to be an exact integral "number" of photons. So brightness is still continuous in QM; the probability of detecting a photon can keep getting smaller and smaller indefinitely, without ever having to discontinously jump to zero.
However, think of it another way ... if the stars had infinite time to pump out these "photon" particles you speak of (harmph! highly dubious), then there ought to be an infinite number of them in any given space, as they have had an infinity of time to reach you.
seconded, but i think youre misunderstanding the paradox's axioms. part of the assumptions are infinite homogenous distribution, which i think addresses your point (the "the paradox" section).
i think the salient point is why youd assume stars are both infinite (both in existence and lifespan?) but homogenous on an arbitrary scale.
edit: additionally, as long as orbital motion is included in this contrived model, blockage would certainly produce a less than perfectly bright sky.
I'm not a physicist so presumably I'm wrong. But why is this wrong? As far as I understand it, this paradox is the reason we have the theory that space is expanding at a rate which makes objects in effect move away from each other faster than the light they emit.
If it did, the same thing would happen not just for stars, but for all sorts of things. If you position a computer screen on a hiltop far enough away that, on a dark night, you can just make out whether it's on or off, then your eyes are getting about 6 photons per second. It doesn't matter whether these come from a million separate pixels, or from one light-bulb of similar total brightness.