Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Olbers' Paradox

en.wikipedia.org

Post reply on HN
Print view View original

41–50 of 86 posts

Re: Olbers' Paradox

#41

Post by kryogen1c »

rg2004 wrote: post #33

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.

> 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.

Re: Olbers' Paradox

#42

Post by pdonis »

pontus wrote: post #15
pontus wrote: post #11

Isn't this just an issue of comparing a countable and uncountable infinity? The number of points on the unit sphere is uncountable, but the number of stars is countable. As such there are in some sense more points on the sphere than there are stars, even though there are an infinite number of each. Take this together with the fact that intensity falls off as the square of the distance and it seems like the sky should…

I guess the fall-off is even worse. At the beginning the intensity falls off as 1/r^2, but eventually the intensity becomes so small that you're talking about individual photons. At some point the intensity will then fall from a single photon to zero. So, after some critical distance the intensity will actually drop to zero. More formally, each star emits some amount of power in each frequency band: P(f) so that \int…

> after some critical distance the intensity will actually drop to zero.

No, it won't. If you're going to use a quantum model of light (which you have to to use the concept of "photon"), then you have to use the quantum interpretation of "intensity". The quantum interpretation of "intensity" is the probability of detecting a photon; and this is a continuous quantity which can get smaller and smaller indefinitely without ever dropping to zero.

Re: Olbers' Paradox

#43

Post by pdonis »

pontus wrote: post #28
colanderman wrote: post #22

Earlier quoted context omitted.

Fall-off of light intensity does not factor in: while the amount of light reaching an observer from any given star does indeed fall off with the square of the distance, so does the apparent size of that star; its apparent surface brightness thus does not change with distance. (Think of day-to-day experience: people who walk away from you do not darken!) I agree that countability vs. uncountability seems like it shoul…

Great point, thanks! Makes perfect sense. Turns out though that the intensity actually falls off faster than 1/r^2 toward the end due to quantization effects. Feels silly to include quantization, but I guess when were talking about stars that may be arbitrarily far away this would need to be part of the story.

> Turns out though that the intensity actually falls off faster than 1/r^2 toward the end due to quantization effects.

No, it doesn't. See my other post in response to you upthread.

Re: Olbers' Paradox

#44

Post by pdonis »

rg2004 wrote: post #33

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.

> 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.

Re: Olbers' Paradox

#45

Post by koliber »

Imagine an infinitely long hallway in a hotel, as a mental exercise. And imagine every room is filled , and each light is on. And imagine looking at this hotel for a long distance. It will look like a continuous line.

And now imagine every other room is uccupied. Still an infinite number of rooms are occupied, but this line, from a distance, will be half as dim.

Now imagine ever millionth room is occupied. Still, we have an infinite number of occupied rooms. And now, depending on the distance from which you are viewing this hotel, you may notice points of light instead of a dim continuum.

Re: Olbers' Paradox

#46

Post by pontus »

pdonis wrote: post #42
pontus wrote: post #15

Earlier quoted context omitted.

I guess the fall-off is even worse. At the beginning the intensity falls off as 1/r^2, but eventually the intensity becomes so small that you're talking about individual photons. At some point the intensity will then fall from a single photon to zero. So, after some critical distance the intensity will actually drop to zero. More formally, each star emits some amount of power in each frequency band: P(f) so that \int…

> after some critical distance the intensity will actually drop to zero. No, it won't. If you're going to use a quantum model of light (which you have to to use the concept of "photon"), then you have to use the quantum interpretation of "intensity". The quantum interpretation of "intensity" is the probability of detecting a photon; and this is a continuous quantity which can get smaller and smaller indefinitely with…

The probability can then get arbitrarily small, meaning that the expected amount of time needed before the probability of having observed a photon would get progressively larger.

My argument above is semi-classical, but it shouldn't change with a full quantum mechanical approach.

Re: Olbers' Paradox

#47

Post by warent »

koliber wrote: post #45

Imagine an infinitely long hallway in a hotel, as a mental exercise. And imagine every room is filled , and each light is on. And imagine looking at this hotel for a long distance. It will look like a continuous line. And now imagine every other room is uccupied. Still an infinite number of rooms are occupied, but this line, from a distance, will be half as dim. Now imagine ever millionth room is occupied. Still, we…

In the first example, theres an infinite line of lights. In the last example, it's the same infinite line divided by a million, which is still an infinite line. They'll look identical when the photons reach your eyes.

Re: Olbers' Paradox

#48

Post by saurik »

I headed to the "Explanation" section, expecting some opining from physicists, and was somewhat confused that it started with a concrete "suggestion" from Edgar Allan Poe.

Re: Olbers' Paradox

#49

Post by maweki »

koliber wrote: post #45

Imagine an infinitely long hallway in a hotel, as a mental exercise. And imagine every room is filled , and each light is on. And imagine looking at this hotel for a long distance. It will look like a continuous line. And now imagine every other room is uccupied. Still an infinite number of rooms are occupied, but this line, from a distance, will be half as dim. Now imagine ever millionth room is occupied. Still, we…

But in the paradox it is stated that through uniformity and the shells of the virtual spheres being 2d, there are four times as many stars twice as far away and since they are only a fourth in brightness, they are as bright as a near one.

In your example, the number of doors is linear with distance but light falls of quadratically.

Re: Olbers' Paradox

#50

Post by pdonis »

pontus wrote: post #46
pdonis wrote: post #42

Earlier quoted context omitted.

> after some critical distance the intensity will actually drop to zero. No, it won't. If you're going to use a quantum model of light (which you have to to use the concept of "photon"), then you have to use the quantum interpretation of "intensity". The quantum interpretation of "intensity" is the probability of detecting a photon; and this is a continuous quantity which can get smaller and smaller indefinitely with…

The probability can then get arbitrarily small, meaning that the expected amount of time needed before the probability of having observed a photon would get progressively larger. My argument above is semi-classical, but it shouldn't change with a full quantum mechanical approach.

> The probability can then get arbitrarily small, meaning that the expected amount of time needed before the probability of having observed a photon would get progressively larger.

Yes, but the probability is never zero, and the expected time is never infinite. So saying "the intensity drops to zero" is never correct.

Post reply on HN