[HN Gopher] Olbers' Paradox
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Olbers' Paradox
Author : bookofjoe
Score : 125 points
Date : 2020-12-12 14:36 UTC (8 hours ago)
(HTM) web link (en.wikipedia.org)
(TXT) w3m dump (en.wikipedia.org)
| bjornedstrom wrote:
| That "#:~:text=" highlighter is so annoying it has made me switch
| from Google Chrome to Firefox.
| thih9 wrote:
| I don't have Chrome, could you elaborate? Where is the
| highlighter and what does it do?
| bjornedstrom wrote:
| The link points to "https://en.wikipedia.org/wiki/Olbers%27_p
| aradox#:~:text=In%2...."
|
| In case that renders as a link by Hacker News, I've added a
| space here and removed the https part:
|
| en.wikipedia.org/wiki/Olbers%27_paradox #:~:text=In%20astroph
| ysics%20and%20physical%20cosmology,infinite%20and%20eternal%2
| 0static%20universe.
|
| What it does is that it highlights that text in the page,
| with a yellow background color. Making the rest of the text
| difficult to read (your eyes are drawn to the very yellow
| highlighted part).
| mlinksva wrote:
| I love it, and have been manually creating such links every
| day since discovering the feature. One should be able to
| link to any portion of a page, and now one can, largely.
| The highlighting ought to be something a browser allows a
| user to customize, but I really wish Firefox (which I use
| about half the time) had the feature.
| Jap2-0 wrote:
| Agreed (I use Firefox), but (from being forced to use
| Chrome) you should be able to get the highlight to go away
| by clicking somewhere else on the page or by scrolling.
| Arnavion wrote:
| More details at
| https://chromestatus.com/feature/4733392803332096 and
| https://github.com/WICG/scroll-to-text-fragment/
| xingyzt wrote:
| You can click to unhighlight. I find it useful for linking to a
| section of a page without an anchor nearby.
| michaelcampbell wrote:
| That reminded me to look for extensions that automatically move
| mobile wikipedia links to desktop ones; thankfully there's one
| for both Chrome and FF.
| spixy wrote:
| yes: https://github.com/spixy/NoMoreMobile
| mlinksva wrote:
| Would love to see that rendered superfluous https://meta.wi
| kimedia.org/wiki/Community_Wishlist_Survey_20...
| tigerbelt wrote:
| Infinite is a construction, misused in this paradox. And most.
| permo-w wrote:
| "[Edward Robert] Harrison argues that the first to set out a
| satisfactory resolution of the paradox was Lord Kelvin, in a
| little known 1901 paper, and that Edgar Allan Poe's essay Eureka
| (1848) curiously anticipated some qualitative aspects of Kelvin's
| argument:
|
| Were the succession of stars endless, then the background of the
| sky would present us a uniform luminosity, like that displayed by
| the Galaxy - since there could be absolutely no point, in all
| that background, at which would not exist a star. The only mode,
| therefore, in which, under such a state of affairs, we could
| comprehend the voids which our telescopes find in innumerable
| directions, would be by supposing the distance of the invisible
| background so immense that no ray from it has yet been able to
| reach us at all."
| tigerbelt wrote:
| I love the quote, very beautiful explanation of the question !
|
| Thank you for this history and for sharing it !
|
| Sometimes while ruminating I wonder whether ,
|
| Questions which have no answers are not really questions .
|
| Does the difference matter ?
|
| To your theory of everything ?
|
| -13 HN Karma Hint:
|
| None of those words
|
| re Infinite Boundaries , Matter
|
| Interesting distractions ,
|
| If the goal is TOE ,
|
| Distractions unacceptable in TOE
|
| But wadda I know !
| narag wrote:
| What's the main piece of evidence against the hypothesis of
| "something" (a force, dark matter, dark energy, some exotic
| effect) dimming/slowing/distorting the light over very high
| distances?
| rg2004 wrote:
| 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.
| kryogen1c wrote:
| > 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.
| pdonis wrote:
| _> 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 wrote:
| 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.
| theplague42 wrote:
| 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 wrote:
| 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 wrote:
| the point is 1 photon from a star seems like nothing, but 1
| photon multiplied by infinite stars is infinite photons
| blinding us
| umvi wrote:
| "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 wrote:
| 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.
| koliber wrote:
| 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.
| warent wrote:
| 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.
| maweki wrote:
| 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.
| RyanShook wrote:
| Doesn't the expansion of the universe explain this? I don't
| understand the paradox.
| GuB-42 wrote:
| It does, but at the time, we didn't know about that.
| galaxyLogic wrote:
| Let's assume the universe is not expanding but is infinite.
| At some point in time stars started lighting up. Maybe they
| even all lit up at once, long time ago. But some stars are so
| far away that the light from them has not yet reached us.
|
| Even though there are an infinite number of stars we can only
| see the light from a subset of them because the light from
| the rest of them has not reached us yet.
|
| So I think the simple resolution of the paradox is that the
| speed of light is not infinite. No?
|
| What I also never understood was what about matter that is
| not lit up? There could be many more unlit heavenly bodies
| than stars, which would block the light from the stars.
| kmm wrote:
| While it's true that the finite age of our universe and the
| expansion of space explain the paradox in the universe we live
| in, I don't think those are necessary conditions, nor is the dark
| sky proof our universe is not infinitely old.
|
| What I feel is the core of the resolution of the paradox is
| (global or local) conservation of energy. Even in an infinitely
| large eternal steady state universe, if we assume the total
| energy of the universe is conserved one cannot have an increase
| in energy density everywhere at once.
|
| If in this universe stars live forever, you'd have eternal
| "sources" of energy, and for energy to be conserved you'd need
| compensatory "sinks" draining energy out of the universe, like
| black holes which don't increase in size. In which the resolution
| of the Olbers' paradox would be that most of your lines of sight
| would end in such a black hole.
|
| If, like is usual in physics, you assume local conservation of
| energy, stars cannot live forever, so in an eternal steady state
| universe there must be a mechanism recycling the radiation back
| into a star. In this case, again every line of your sight would
| eventually hit a star, but most of the radiation would never
| reach you, being used underway to make a new star. (This is a
| blatant violation of the second law of thermodynamics of course,
| which is the actually issue with eternal steady state universes).
| DiogenesKynikos wrote:
| Energy is not conserved on the scale of the Universe. General
| Relativity has no energy conservation law (it has a stress-
| energy tensor conservation law). Two examples of this:
| expansion of the universe causes the total energy contained in
| radiation to decrease, and the total amount of dark energy to
| increase.
| vanni wrote:
| Right. Sabine Hossenfelder about it:
| https://www.youtube.com/watch?v=ZYM6HMLgIKA&t=395s
| cygx wrote:
| It depends on the way you look at things:
|
| Noether's second theorem works fine in General Relativity (in
| fact, this was the historic context of her paper). So for any
| given time-like vector field, you'll get an energy
| conservation law. In case of Friedmann cosmology and chosing
| cosmological time as said vector field, you'll get a term
| proportional to H2 which picks up the change in energy.
|
| However, you won't be able to make this into a covariant
| expression: Gravitational energy-momentum can be expressed in
| terms of pseudo-tensors at best...
| AnthonyAguirre wrote:
| Probably better not to use the term "steady state" here (even
| if pretty appropriate) in that the "steady state" cosmological
| model is/was one that is exponentially expanding, with all
| physical observables statistically time-independent. It solves
| Olber's paradox due to the radiation redshift. That model was
| observationally incorrect, but actually has pretty much been
| reborn in "eternal inflation" in which the Universe as a whole
| is in a quasi-exponential state with local regions expanding
| sub-exponentially like our observable universe.
|
| In either classic steady-state or eternal inflation case,
| energy conservation is not necessarily a problem: you can have
| vacuum energy that converts steadily into radiation, while
| being generated by the expansion.
| onlyrealcuzzo wrote:
| How does the universe expand? What is it expanding into? And
| why isn't that thing considered the universe?
| ben_w wrote:
| > What is it expanding into?
|
| The future, literally. To _grossly_ oversimplify: if all of
| space is east-west, and time is north-south, the Big Bang
| is the north pole. Only the universe is the map rather than
| the globe, and the globe doesn't have to exist for the map
| to exist and to have the same expansion in space (
| /longitude) with respect to time (/latitude).
|
| Also there may or may not be a Big Crunch/south pole, this
| is all just a way to get into the nature of the geometry by
| way of a convenient frame of reference.
| saurik wrote:
| 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.
| jessermeyer wrote:
| The Hubble was pointed at what appeared to be a black void of
| space, and revealed lush fields of stars and galaxies.
|
| So at one degree of perception, we have an empty void, and at
| another, a bright flush of light and activity.
| avian wrote:
| There is still plenty of space between the individual stars in
| the Hubble Deep Field image. From that point of view it just
| confirms the paradox - even with a powerful telescope stars
| don't fill up your entire field of view.
|
| I think a more fitting example of "an empty void yet a bright
| flush of light" would be the microwave background. With eyes
| sensitive to longer wavelengths the entire sky is indeed
| bright.
| jessermeyer wrote:
| > even with a powerful telescope stars don't fill up your
| entire field of view.
|
| Suppose the experiment is repeated on a black pixel from the
| Deep Field image, and another swell of stars are observed,
| hinting at a kind of fractal distribution.
|
| Were the universe eternal and static, why could this pattern
| not repeat indefinitely in infinite time, space and matter?
| The paradox seems to assume a kind of infinite level of
| sensitivity of the observer.
| avian wrote:
| No, the paradox as described in the Wikipedia article
| doesn't assume the infinite level of sensitivity.
|
| The figure explains it visually - the further away you go
| from the observer, the more stars you capture in your
| camera's field of view and the apparent brightness stays
| the same. The 1/r^2 term for light intensity is cancelled
| by the r^2 for the number of stars.
|
| It's interesting think what an experimental result you
| describe would imply. It either contradicts the nature of
| light or that we're in the center of a cloud of stars where
| the density of stars falls with distance from us.
| jessermeyer wrote:
| Thanks for spelling it out. Makes more sense now.
| [deleted]
| csours wrote:
| As I understand it, in the galactic core where stars are more
| densely packed, it would be bright all the time. I wonder if
| there's a photorealistic render of this.
| gameswithgo wrote:
| the game Elite Dangerous simulates it. not sure how realistic
| but it is fun to explore
| synn wrote:
| You can watch it there : https://youtu.be/mj09iR6Tjd8
| pontus wrote:
| 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 be dark.
| cambalache wrote:
| No. At no distance "R" from the earth does a start becomes a
| point. A point does not have a surface area, a star does (even
| if it is very far away).
| colanderman wrote:
| 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
| should come into play.
| pontus wrote:
| 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.
| pdonis wrote:
| _> 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.
| oconnor663 wrote:
| I don't think this is an issue. A star isn't a single point,
| and each one maps to a small-but-not-infinitessimal area on the
| unit sphere.
| pontus wrote:
| 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_0^\infty P(f) df = P_total.
|
| For each frequency then, we have a total of P(f)/(hf) photon
| emitted per second. The total number of photons emitted per
| second by the star is then \int_0^\infty df P(f)/hf which is a
| finite number.
|
| The total number of photons received per unit area a distance r
| away from the star would then be
|
| \frac{1}{4\pi r^2} \int_0^\infty df P(f)/hf
|
| If your detector has an area A (e.g. your retina or some other
| device), you'd expect to see
|
| \frac{A}{4\pi r^2} \int_0^\infty df P(f)/hf
|
| photons per second from the star. As r gets really large, you'd
| see this drop arbitrarily low. Conversely, the amount of time
| you'd need to wait to see a single photon from that star then
| grows, making the star dark.
| pdonis wrote:
| _> 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.
| pontus wrote:
| 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.
| pdonis wrote:
| _> 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.
| 4ad wrote:
| No, the rational numbers are dense.
| [deleted]
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