[rg2004]

This doesn't make sense to me. They're assuming that brightness is a continuous function that you can keep dividing in half over and over and result in a real number, but brightness is not continuous, at a certain point you only have one photon left. It stops being a question of how many photons per second and becomes a question of how many seconds between a photon.

[pdonis]

> brightness is not continuous, at a certain point you only have one photon left

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.

[at_a_remove]

Well, QM didn't exist yet. Instead, you had competing concepts of light as a wave and light as a particle. As a wave, it would seem perfectly reasonable that you could keep dividing and that it was a continuous function. We have the benefit of QM in hindsight.

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.

[kryogen1c]

> This doesn't make sense to me.

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.

[theplague42]

The point is that any decrease is offset by the increase in the number of stars. Also your distinction between >1 photon per second and <1 photon per second is meaningless.

[fractionalhare]

Can you elaborate a bit more? I don't understand how this responds to the commenter's critique. Under the hypothesis, almost all stars in the universe would be so far from Earth that we would see at most one photon from their light by the time it reached us, for whatever the applicable time interval is. Would that single photon be sufficient to register the star's existence?

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.

[warent]

the point is 1 photon from a star seems like nothing, but 1 photon multiplied by infinite stars is infinite photons blinding us

[umvi]

"at most one". As you get further away zero protons are reaching you on most cases, and zero photons times infinite stars is zero, which would appear to be darkness

[andy-x]

Zero multiplied by infinity does not have to be zero, it can be anything between zero and infinity. Refresh your https://en.wikipedia.org/wiki/Calculus.

[fractionalhare]

How does calculus relate to the context of this discussion though? Photons are discrete, not continuous, so I don't see how calculus applies.