Olbers’ Paradox: Why Is the Sky Dark at Night? (2000)(amnh.org)
amnh.org
Olbers’ Paradox: Why Is the Sky Dark at Night? (2000)
http://www.amnh.org/education/resources/rfl/web/essaybooks/cosmic/cs_paradox.html
32 comments
I am quite amazed that noone has pointed out that in terms of the cosmic microwave background, the sky is not black. The radiation that travels the furthest before hitting us is this background radiation. It only appears to be dim because it has been redshifted a huge amount due to the expansion of the universe since then.
But yes - everywhere you look in the sky (unless there is something in the way), you are looking directly at the intense fire of the birth of our universe. Red-shifted until you can't even see it any more.
But yes - everywhere you look in the sky (unless there is something in the way), you are looking directly at the intense fire of the birth of our universe. Red-shifted until you can't even see it any more.
This looks like a question that actually looks like two questions; namely, 'is the universe finite' (and as a side question, what is the actual dimensional and geometric configuration of the universe), and if the first question is true, 'why do we not observe an infinite flux of photons, or really any other type or radiation, bathing our chunk of the universe'.
If there are an infinite number of stars in an infinitely large universe that is infinitely old, how is the nuclear fuel finite?
Help me here.
Help me here.
https://twitter.com/5point9billion calls out the inverse: light traveling from earth out towards the nearest stars.
It's a twitter bot that takes a twitter user's birthday, and tweets to them as their "light cone" expands across the universe.
It's a twitter bot that takes a twitter user's birthday, and tweets to them as their "light cone" expands across the universe.
[deleted]
So should the earth heat up over time as more light reaches us or does the expansion of the universe negate that?
This is mere ray-tracing problem.
What we call bright sky is reflections of Sun rays from particles in atmosphere. What we see is reflected light.
When Sun is shadowed by Earth we see only light reflected by distant object, such as Moon.
The darkness of the night sky is relative - some rays are here, but our visual system is conditioned for days (reflected light), not nights.
The idea that everything should be filled with starts is just wrong. Rays from distant stars were deflected, blocked by particles, etc.
What we call bright sky is reflections of Sun rays from particles in atmosphere. What we see is reflected light.
When Sun is shadowed by Earth we see only light reflected by distant object, such as Moon.
The darkness of the night sky is relative - some rays are here, but our visual system is conditioned for days (reflected light), not nights.
The idea that everything should be filled with starts is just wrong. Rays from distant stars were deflected, blocked by particles, etc.
Isn't the issue one of lumens? The light from a star is inversely quadratically related to its distance. Assuming a random distribution of stars across a ring or plate in 3D space we should expect the quadratically growing number of stars for the incremental space. The two cancel and it becomes a ratio of the average brightness of a star (bright) versus the density of stars in space (super sparse).
Imagine an infinite series of nested hollow shells of equal thickness around Earth.
The number of stars in each shell is quadratic relative to the radius. The brightness of each star is inversely quadratic relative to the radius of the shell. Thus, each shell has a constant total brightness, as perceived from Earth. An infinite number of these shells add up to infinite brightness.
The number of stars in each shell is quadratic relative to the radius. The brightness of each star is inversely quadratic relative to the radius of the shell. Thus, each shell has a constant total brightness, as perceived from Earth. An infinite number of these shells add up to infinite brightness.
I'm not quite following. The light in each "shell" continues to dissipate in an inversely quadratic method from the shells distance from earth, no? It would help if I had this drawn out.
No, the total light in each spherical "shell" is the same as every other shell.
Stars that are 20 light-years away are 4x dimmer than stars 10 light-years away. But there are 4x more stars 20 light-years away than 10 light-years away. As you go outward from Earth, the stars get dimmer and more numerous, but these balance each other, and the infinite sum is 1 + 1 + 1 + ...
(This is no chance happening; regardless of the # of spatial dimensions the universe has, this relationship holds true.)
Stars that are 20 light-years away are 4x dimmer than stars 10 light-years away. But there are 4x more stars 20 light-years away than 10 light-years away. As you go outward from Earth, the stars get dimmer and more numerous, but these balance each other, and the infinite sum is 1 + 1 + 1 + ...
(This is no chance happening; regardless of the # of spatial dimensions the universe has, this relationship holds true.)
I can recommend the book Darkness at Night by Edward Harrison [1] for a detailed look at the history of this paradox. An enjoyable read, and ties it in with several closely related historical debates in cosmology.
[1] http://www.hup.harvard.edu/catalog.php?isbn=9780674192713
[1] http://www.hup.harvard.edu/catalog.php?isbn=9780674192713
I don't get the "running out of fuel" argument... If the universe (as assumed in the text) is infinitely old and infinitely large, why should there be any scarcity of nuclear fuel?
Most stars we see are burning Hydrogen, possibly helium, in a process of gravity well driven nuclear fusion. This fusion results in heavier atomic particles and some waste that we see as radiation (light, heat, various forms of EM energy).
I am not an astrophysicist, nor am I an expert in the early universe, but I recall that the prevailing theories of our time are that somehow the universe came in to being with predominantly hydrogen atoms. These combine through fusion in what we call stars to form denser matter. This process continues until the result of combining the elements reaches a limit. I believe that iron happens to be that limit if I recall correctly.
https://en.wikipedia.org/wiki/Iron_peak
Describes what I recall reading/hearing many years ago.
I am not an astrophysicist, nor am I an expert in the early universe, but I recall that the prevailing theories of our time are that somehow the universe came in to being with predominantly hydrogen atoms. These combine through fusion in what we call stars to form denser matter. This process continues until the result of combining the elements reaches a limit. I believe that iron happens to be that limit if I recall correctly.
https://en.wikipedia.org/wiki/Iron_peak
Describes what I recall reading/hearing many years ago.
Stars fuse light elements it into heavier elements. Eventually all the lighter elements will be used up.
One of my favorite short stories about this is The Last Question by Isaac Asimov
http://multivax.com/last_question.html
http://multivax.com/last_question.html
I think they were saying if we're conceding infinite size and an infinite number of stars, why not an infinite amount of those lighter elements as well?
Imagine an infinite space divided in infinite number of finite volumes each containing a finite number of "lighter elements". All the light elements form a star in their local volume and burn up all the light elements locally. The result: all the infinite number of finite volumes are void of the light elements. The infinite space is dark.
isnt the answer that most of the stars are inside galaxies that are for the most part moving away from us and for that matter from each other (due to space itself expanding) with the speed of expansion or their apparent motion away from us proportional to their distance from us. This means most of the star light reaching us is red shifted (due to doppler effect of light) and since we humans cannot see this red shifted light, the night sky appears dark to us. anybody with a physics background can point out where I got this wrong, but I thought this is why the sky is dark.
This didn't mention the expansion of space at all. The universe may be infinite in size but we'll never see the light of stars that exist so far from us that they are beyond the distance at which space expands faster than light can travel. That's why we have a dark sky and it will just get darker as more things we see now eventually expand beyond that barrier. One suggested end to the universe is the Big Rip in which all matter eventually separates in this way such that the distance between all matter is infinite:
https://en.wikipedia.org/wiki/Big_Rip
https://en.wikipedia.org/wiki/Big_Rip
Yep. Currently, some galaxies are traveling away from us faster than light.
http://curious.astro.cornell.edu/about-us/104-the-universe/c...
http://curious.astro.cornell.edu/about-us/104-the-universe/c...
That blew my mind! So now it turns out Einstein was wrong??
We can't get particle to seriously travel faster than light and there is entire galaxy going faster??
We can't get particle to seriously travel faster than light and there is entire galaxy going faster??
The galaxy isn't traveling faster than c away from us, but space is being created in between. So, nothing is actually accelerating, there is no problem, Einstein is still right.
In fact, space is being created everywhere, including yourself and the computer screen. However the amount is so small that you don't notice and local forces nullify the change anyway. With large distances, this amount accumulates, and overwhelms the force of gravity and starts to create the apparent acceleration of distant galaxies away from us. Further explanation from paulddraper: https://news.ycombinator.com/item?id=11068125
In fact, space is being created everywhere, including yourself and the computer screen. However the amount is so small that you don't notice and local forces nullify the change anyway. With large distances, this amount accumulates, and overwhelms the force of gravity and starts to create the apparent acceleration of distant galaxies away from us. Further explanation from paulddraper: https://news.ycombinator.com/item?id=11068125
This isn't really correct. Expansion of space is not the same thing as accelerated expansion of space. Aaccelerated expansion is indeed due to something "pushing" objects apart--that something is called "dark energy". But expansion itself, apart from the effects of dark energy, does not push on anything; it doesn't exert any force that moves objects apart or works against gravity. So thinking of ordinary expansion (apart from accelerated expansion) as "creating space" in between objects isn't really correct. It's unfortunate that so many pop science treatments use this way of speaking, since it leads to the incorrect inference I've just described.
The space is expanding and its expansion rate is accelerating. Dark energy is not pushing objects apart, it is causing the acceleration of expansion of space.
What you said isn't even pop science, it is blatantly wrong.
https://en.wikipedia.org/wiki/Metric_expansion_of_space
https://en.wikipedia.org/wiki/Dark_energy
And the money quote:
It is called "dark" because it is not interacting with normal matter, but only with the space time structure.
from http://physics.stackexchange.com/a/206217
What you said isn't even pop science, it is blatantly wrong.
https://en.wikipedia.org/wiki/Metric_expansion_of_space
https://en.wikipedia.org/wiki/Dark_energy
And the money quote:
It is called "dark" because it is not interacting with normal matter, but only with the space time structure.
from http://physics.stackexchange.com/a/206217
> What you said isn't even pop science
What I said was an attempt to explain how the basic model cosmologists use works in layman's terms. It wasn't intended to be "pop science" or even "real science"; that would be building the model, not trying to explain how it works.
The references you give are not "real science" either. Try looking in a cosmology textbook or a peer-reviewed paper. Or, even better, work out the science for yourself instead of arguing from authority.
What I said was an attempt to explain how the basic model cosmologists use works in layman's terms. It wasn't intended to be "pop science" or even "real science"; that would be building the model, not trying to explain how it works.
The references you give are not "real science" either. Try looking in a cosmology textbook or a peer-reviewed paper. Or, even better, work out the science for yourself instead of arguing from authority.
Yes, this makes sense. If this is the case though, then aren't there some obvious problems with how we think of dimensions (at least the first three or four anyway)?
It seems like creating space to fill the "voids" between particles moving at-what-would-be-faster than the speed of light is like a tesseract for whatever matter is in that rapidly created/expanding space. Unless that space is only accessible to the particles creating it by their relative motion (which still gives us problems with our ideas of dimensions)?
It seems like creating space to fill the "voids" between particles moving at-what-would-be-faster than the speed of light is like a tesseract for whatever matter is in that rapidly created/expanding space. Unless that space is only accessible to the particles creating it by their relative motion (which still gives us problems with our ideas of dimensions)?
> The galaxy isn't traveling faster than c away from us, but space is being created in between.
That's an intriguing way of phrasing, never thought of it this way. I'm aware that space is expanding, so space must indeed being created in-between.
I'm guessing this space has to contain no energy at all, so it must be made of absolutely nothing, right?
That's an intriguing way of phrasing, never thought of it this way. I'm aware that space is expanding, so space must indeed being created in-between.
I'm guessing this space has to contain no energy at all, so it must be made of absolutely nothing, right?
> That blew my mind! So now it turns out Einstein was wrong??
No, because the light speed limit only applies to things moving through space, not to space itself, which can and does expand faster than light speed.
> We can't get particle to seriously travel faster than light and there is entire galaxy going faster??
The galaxy isn't traveling through space at faster than light speed, it's being conveyed along with the space that surrounds it at a speed that exceeds light-speed from the perspective of some distant location in space.
No, because the light speed limit only applies to things moving through space, not to space itself, which can and does expand faster than light speed.
> We can't get particle to seriously travel faster than light and there is entire galaxy going faster??
The galaxy isn't traveling through space at faster than light speed, it's being conveyed along with the space that surrounds it at a speed that exceeds light-speed from the perspective of some distant location in space.
I've also had a long-time question around this point. I've asked various university physics professors, and they all stutter and disagree (which means either we really don't know or I'm going to all the wrong universities). The underlying question is: When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?
If it's photons emitting from flashlights pointed in opposite directions relative to each other, then are they compressing space as they travel so as not to exceed the speed of light? Or even massive particles accelerated to over half the speed of light at different times around an ellipse so there is a moment when their opposite directions make one traveling at greater than the speed of light relative to the other? (Or even particle accelerators on two different planets already expanding away from each other - does this just mean that space is really twisting and turning all the time to make sure no particle ever exceeds the speed of light relative to any other particle?)
It has been my understanding - and appreciation at Einstein's unbelievable insight and brilliance - that relativity is truly relative because there really isn't any such thing as an arbitrary particle or space that all other motions are measured from. But if this is true, does that really mean that space is really so constantly twisting and turning that SOL can't be exceeded?
I'm sure there are great answers to this, but I've always wanted a definitive one. Anyone have any comments on this?
If it's photons emitting from flashlights pointed in opposite directions relative to each other, then are they compressing space as they travel so as not to exceed the speed of light? Or even massive particles accelerated to over half the speed of light at different times around an ellipse so there is a moment when their opposite directions make one traveling at greater than the speed of light relative to the other? (Or even particle accelerators on two different planets already expanding away from each other - does this just mean that space is really twisting and turning all the time to make sure no particle ever exceeds the speed of light relative to any other particle?)
It has been my understanding - and appreciation at Einstein's unbelievable insight and brilliance - that relativity is truly relative because there really isn't any such thing as an arbitrary particle or space that all other motions are measured from. But if this is true, does that really mean that space is really so constantly twisting and turning that SOL can't be exceeded?
I'm sure there are great answers to this, but I've always wanted a definitive one. Anyone have any comments on this?
> When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?
Relative to a local inertial frame, i.e., relative to an inertial observer (i.e., an observer in free fall, feeling no force) who is at the same spatial location as the particle whose speed is being measured. That is the only context in which the concept of "relative velocity", as it appears in the "can't travel faster than light" condition, has any physical meaning.
All of your suggested examples attempt to compare "relative velocity" between objects that are not at the same spatial location. That has no physical meaning in GR.
Relative to a local inertial frame, i.e., relative to an inertial observer (i.e., an observer in free fall, feeling no force) who is at the same spatial location as the particle whose speed is being measured. That is the only context in which the concept of "relative velocity", as it appears in the "can't travel faster than light" condition, has any physical meaning.
All of your suggested examples attempt to compare "relative velocity" between objects that are not at the same spatial location. That has no physical meaning in GR.
Think of it this way: c isn't a speed limit, it's the only speed that anything can travel at. Specifically, time is only one component of four-dimensional spacetime. If you move in x, y, and/or z, the vector length of that spatial movement has to come out of your velocity in t.
So it's not that you can't travel at c meters per second; it's that if you do, you'll zero out your velocity in the "seconds" component.
To cite an example from one of Neal DeGrasse Tyson's lectures, that's one of the funky things about photons from the most distant stars: they don't experience the passage of time at all from their own point of view. They arrive at our eyes/telescopes/radios as soon as they're emitted. Meanwhile, their velocity is limited to c from our point of view. The same thing would presumably happen to you if you could travel at c... but there would be other inconvenient effects in that case, such as an infinite increase in mass.
So it's not that you can't travel at c meters per second; it's that if you do, you'll zero out your velocity in the "seconds" component.
To cite an example from one of Neal DeGrasse Tyson's lectures, that's one of the funky things about photons from the most distant stars: they don't experience the passage of time at all from their own point of view. They arrive at our eyes/telescopes/radios as soon as they're emitted. Meanwhile, their velocity is limited to c from our point of view. The same thing would presumably happen to you if you could travel at c... but there would be other inconvenient effects in that case, such as an infinite increase in mass.
It's perhaps not altogether useful to regard c as a speed. Or rather you should redefine your idea of speed. It's a universal constant relating matter to spacetime. Time is a length measurement, and you're already moving at c in that dimension. If you start accelerating then you are trading time velocity for spacial velocity, so as you approach c your movement through time approaches zero.
> does that really mean that space is really so constantly twisting and turning that SOL can't be exceeded?
The speed of light stays the same and both time and space twist and turn around it. It's weird, but having a preferred reference frame would be just as weird. c is a dimensionless constant, and light happens to travel at that speed because it has no rest mass.
> does that really mean that space is really so constantly twisting and turning that SOL can't be exceeded?
The speed of light stays the same and both time and space twist and turn around it. It's weird, but having a preferred reference frame would be just as weird. c is a dimensionless constant, and light happens to travel at that speed because it has no rest mass.
"When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?"
It's a theory postulating that a particle can't travel faster than the speed of light in relationship to a particle that isn't moving. In practice all particles are moving in relation to some other particle thus it's not something you can visibly measure or see. At least that is the way I always viewed it.
It's a theory postulating that a particle can't travel faster than the speed of light in relationship to a particle that isn't moving. In practice all particles are moving in relation to some other particle thus it's not something you can visibly measure or see. At least that is the way I always viewed it.
does that really mean that space is really so constantly twisting and turning that SOL can't be exceeded?
IANAP, but I've never read that space twists to prevent the SOL from being exceeded. I think you're thinking of time and mass. It would require an infinite amount of time or infinite acceleration to for something to accelerate to the speed of light relative to something else.
Space is twisted by the presence of matter, and we call that gravity.
If it's photons emitting from flashlights pointed in opposite directions relative to each other, then are they compressing space as they travel so as not to exceed the speed of light
No. My understanding is that from the point of view of a photon time is completely stopped. Nothing moves relative to it because of this. Since nothing moves relative to it, nothing is exceeding the speed of light relative to it.
IANAP, but I've never read that space twists to prevent the SOL from being exceeded. I think you're thinking of time and mass. It would require an infinite amount of time or infinite acceleration to for something to accelerate to the speed of light relative to something else.
Space is twisted by the presence of matter, and we call that gravity.
If it's photons emitting from flashlights pointed in opposite directions relative to each other, then are they compressing space as they travel so as not to exceed the speed of light
No. My understanding is that from the point of view of a photon time is completely stopped. Nothing moves relative to it because of this. Since nothing moves relative to it, nothing is exceeding the speed of light relative to it.
> The underlying question is: When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?
It's based on the observation of two points of references moving a different speeds shining light and the light from each traveling at the same speed. So the speed of light is measured relative to other light. The speed of light is constant, and it is so regardless of point of reference. Flashlights pointed in opposite directions has nothing to do with the speed of light. The light is traveling at the same speed in opposite directions.
It's based on the observation of two points of references moving a different speeds shining light and the light from each traveling at the same speed. So the speed of light is measured relative to other light. The speed of light is constant, and it is so regardless of point of reference. Flashlights pointed in opposite directions has nothing to do with the speed of light. The light is traveling at the same speed in opposite directions.
I found this [1] PBS video useful.
[1] https://www.youtube.com/watch?v=msVuCEs8Ydo
[1] https://www.youtube.com/watch?v=msVuCEs8Ydo
The galaxies themselves are not moving faster than the speed of light, their relative distances are because of the rate of the expansion of the universe.
I don't think it means Einstein was wrong or that one galaxy is moving "faster than the speed of light". It means in respect to each other two galaxies are moving faster than the speed of light. In other words each of two galaxies is going faster than half the speed of light, one of them being us (in relation to the other observed Galaxy).
That's extremeley not true, and the whole point of Relatively is to explain why.
[deleted]
The expansion of the universe also leads to red shift of the light from (nearly) all the stars that we'd otherwise expect to see. This means that the frequency of their light is moved away from the range that our eyes can see.
My understanding of the expansion of space is that the expansion doesn't occur locally, but is only noticeable over large distances. is that incorrect?
It occurs everywhere, proportionally. The effect isn't great enough to notice unless you are looking at light-years.
Also, gravity and electromagnetism increase at close proximity, so on less-than-cosmic scales, they overcome the minute amount of spatial expansion.
Also, gravity and electromagnetism increase at close proximity, so on less-than-cosmic scales, they overcome the minute amount of spatial expansion.
therefore the statement " all matter eventually separates in this way" , strictly speaking, seems false since gravity and electromagnetism overcome expansion at local levels.
Yeah, both are right in context. It's just like saying "gravity doesn't make objects fall at the same speed". It actually does make them fall at the same speed...but if you include other relevant forces, the overall effect is different.
FYI, gravity might eventually overcome spatial expansion on a cosmic scale. But we don't know. https://en.wikipedia.org/wiki/Big_Crunch
FYI, gravity might eventually overcome spatial expansion on a cosmic scale. But we don't know. https://en.wikipedia.org/wiki/Big_Crunch
I thought the Big Crunch was disproven because we found that the expansion of the Universe is accelerating. Dark Energy wins over Dark Matter...forever.
More likely than not, the Big Crunch will not happen. From Wikipedia:
"Recent experimental evidence (namely the observation of distant supernovae as standard candles, and the well-resolved mapping of the cosmic microwave background) has led to speculation that the expansion of the universe is not being slowed down by gravity but rather accelerating. However, since the nature of the dark energy that is postulated to drive the acceleration is unknown, it is still possible (though not observationally supported as of today) that it might eventually reverse its developmental path and cause a collapse."
"Recent experimental evidence (namely the observation of distant supernovae as standard candles, and the well-resolved mapping of the cosmic microwave background) has led to speculation that the expansion of the universe is not being slowed down by gravity but rather accelerating. However, since the nature of the dark energy that is postulated to drive the acceleration is unknown, it is still possible (though not observationally supported as of today) that it might eventually reverse its developmental path and cause a collapse."
It was my understanding that this is true from our perspective in time right now, but the Big Crunch could still be plausible if the universe turns out to be young enough (which it seems like it is) that not all the fusion fuel has been exhausted. Once it is, we'll have big clouds of nuclear waste interspersed between black holes, and perhaps in this environment the Big Crunch could still occur.
I think another question for the Big Crunch is what type of "fuel" is needed to create an exothermic fusion reaction comparable to the Big Bang? For example, the sun compresses hydrogen to produce helium and release massive energy. Black holes are undoubtedly compressing helium enough to make Beryllium, but this doesn't seem to release any energy that can escape the gravity that created the pressure required in the first place. So for the Big Crunch - Big Bang cycle to hold up, what type of matter (and how much of it) has be be compressed (and is gravity the only force that's compressing it) to the point where some type of "fusion" reaction produces enough energy to escape the compression forces?
I think another question for the Big Crunch is what type of "fuel" is needed to create an exothermic fusion reaction comparable to the Big Bang? For example, the sun compresses hydrogen to produce helium and release massive energy. Black holes are undoubtedly compressing helium enough to make Beryllium, but this doesn't seem to release any energy that can escape the gravity that created the pressure required in the first place. So for the Big Crunch - Big Bang cycle to hold up, what type of matter (and how much of it) has be be compressed (and is gravity the only force that's compressing it) to the point where some type of "fusion" reaction produces enough energy to escape the compression forces?
> perhaps in this environment the Big Crunch could still occur.
No, it couldn't. The nuclear waste will still have the same average energy density, on the scale of the universe as a whole, as the unexhausted fusion fuel does now. We know that energy density is too small now to make the universe recollapse, so the same must be true any time in the future.
> what type of "fuel" is needed to create an exothermic fusion reaction comparable to the Big Bang?
The Big Bang was not an exothermic fusion reaction. Our current best model is that the Big Bang was caused by a very large energy density being transferred from the inflaton field (the field that drove inflation in the very early universe) to the various fields in the Standard Model of particle physics (electrons, quarks, photons, etc.). This "reheating" created the hot, dense, rapidly expanding state that we refer to as the Big Bang.
No, it couldn't. The nuclear waste will still have the same average energy density, on the scale of the universe as a whole, as the unexhausted fusion fuel does now. We know that energy density is too small now to make the universe recollapse, so the same must be true any time in the future.
> what type of "fuel" is needed to create an exothermic fusion reaction comparable to the Big Bang?
The Big Bang was not an exothermic fusion reaction. Our current best model is that the Big Bang was caused by a very large energy density being transferred from the inflaton field (the field that drove inflation in the very early universe) to the various fields in the Standard Model of particle physics (electrons, quarks, photons, etc.). This "reheating" created the hot, dense, rapidly expanding state that we refer to as the Big Bang.
There is one more complimentary answer, which is that the night sky is not as dark as it seems, but our eyes cannot see all the wavelengths of light that populate the night sky.
If we could see deep into the infrared, we might see more faraway stars and galaxies, whose light has been red-shifted by the expansion of space.
If we could see wavelengths in the single cm range, we might perceive a dim uniform glow in the night sky: the cosmic background radiation.
If we could see radio waves we might see all sorts of light sources in the night sky.
If we could see deep into the infrared, we might see more faraway stars and galaxies, whose light has been red-shifted by the expansion of space.
If we could see wavelengths in the single cm range, we might perceive a dim uniform glow in the night sky: the cosmic background radiation.
If we could see radio waves we might see all sorts of light sources in the night sky.
Yep, explained here: http://www.physics.org/facts/sand-dark.asp
Of course, if there were an infinite amount of light (visible or not) reaching Earth, you'd be dead.
Of course, if there were an infinite amount of light (visible or not) reaching Earth, you'd be dead.
Suppose that the Energy distribution for a certain amount of light (as seen by earth) was given by
Most of these explanations don't seem to first figure out whether if you had a uniform distribution of stars (at discrete points) in an infinite (Euclidean) space, if the amount of radiated energy seen at an arbitrary point would diverge if you summed over all available frequencies. If it doesn't, it seems like lack of sensitivity is the main issue here, and the cosmological arguments are simply additional reasons for why it doesn't happen.
/- 1 if f < f0
E(f) = >
\- 1/f^2 if f > f0
Most of these explanations don't seem to first figure out whether if you had a uniform distribution of stars (at discrete points) in an infinite (Euclidean) space, if the amount of radiated energy seen at an arbitrary point would diverge if you summed over all available frequencies. If it doesn't, it seems like lack of sensitivity is the main issue here, and the cosmological arguments are simply additional reasons for why it doesn't happen.
Pity someone down-voted you.
From what I take it, you were basically simply asking, "what if the 'infinite amount' at 'all frequencies' were reaching you in a non-uniform distribution of frequencies? - would the original arguments and premises still stand?"
From what I take it, you were basically simply asking, "what if the 'infinite amount' at 'all frequencies' were reaching you in a non-uniform distribution of frequencies? - would the original arguments and premises still stand?"
This assumes a minimum energy from each photon. If you could red-shift indefinitely you could end up with ex: 1 + 1/2 + 1/4 + 1/8 +... which sums to 2.
I believe the minimum energy of a photon is directly bound by the age of the universe, so if the universe was twice as old you could have photons at 1/2 the energy. You do get more light sources as you increase distance, but the inverse square law balances that. So Sum (1/n) from 1 to N which really slowly grows to infinity. As in 10^100 = 230.84
I believe the minimum energy of a photon is directly bound by the age of the universe, so if the universe was twice as old you could have photons at 1/2 the energy. You do get more light sources as you increase distance, but the inverse square law balances that. So Sum (1/n) from 1 to N which really slowly grows to infinity. As in 10^100 = 230.84
I thought this was the obvious answer.
The sky is not dark at night when you use the right telescope. So either the sky changes when you point a telescope at it, or the 'sky' as we see it, is just an artefact of what our primitive eyes and mammalian brain sees.
The sky is not dark at night when you use the right telescope. So either the sky changes when you point a telescope at it, or the 'sky' as we see it, is just an artefact of what our primitive eyes and mammalian brain sees.
This is a great explanation, up until the last part, which is slightly misguided.
"So even if the universe were infinitely old as well as infinitely large, it would not contain enough fuel to keep the stars shining forever and to fill up all of space with starlight."
If the universe were infinitely old, fuel was consumed, and fuel had finite density, then the sky would be completely dark. Because there would be no starts.
The author is really just thinking "It would require infinite time to receive light from infinitely far away." Which is the relevant answer to the paradox.
"So even if the universe were infinitely old as well as infinitely large, it would not contain enough fuel to keep the stars shining forever and to fill up all of space with starlight."
If the universe were infinitely old, fuel was consumed, and fuel had finite density, then the sky would be completely dark. Because there would be no starts.
The author is really just thinking "It would require infinite time to receive light from infinitely far away." Which is the relevant answer to the paradox.
Isn't it also the case that, because of the accelerated expansion of the universe, some stars are moving away from us at more than the speed of light, and their light will therefore never reach us?
Yes, this is currently true, and will continue to be, unless we end in the Big Crunch.
Actually this was the argument that bothered Newton, but about gravity. In an infitely old but finitely large universe, why wouldn't gravity pull everything together? Unless in all directions gravity canceled out.
Similarly, we can ask why the universe isn't filled with light. If the universe was infinitely old then indeed the light would eventually heat up all the matter and penetrate everywhere. But if it's expanding, then the light didn't have time to fill the space-time before it expanded further.
Similarly, we can ask why the universe isn't filled with light. If the universe was infinitely old then indeed the light would eventually heat up all the matter and penetrate everywhere. But if it's expanding, then the light didn't have time to fill the space-time before it expanded further.
In an infinitely large universe, the net force of cosmic gravity would be 0.
Kind of like how an real number divides the number line into "same size" infinite intervals.
Granted, entropy in the system would cause matter to clump into larger and larger bunches. But if the matter were perfectly arranged by an outside force (e.g. God) and didn't deteriorate, the universe could remain static.
Kind of like how an real number divides the number line into "same size" infinite intervals.
Granted, entropy in the system would cause matter to clump into larger and larger bunches. But if the matter were perfectly arranged by an outside force (e.g. God) and didn't deteriorate, the universe could remain static.
Gravity actually acts kind of... weird... in an infinitely large uniform universe. You end up with gravity acting like a time-dependent position-independent scaling factor on position. Leonard Susskind goes over the derivation (for Newtonian gravity) in a Cosmology lecture available on youtube [1].
1: https://youtu.be/ERjkSbdn6-4?t=53m50s
1: https://youtu.be/ERjkSbdn6-4?t=53m50s
Hmm, didn't seem to mention the Inverse-square law, which I was waiting patiently for.
Or the Universe is neither infinite or as old as it's assumed to be. Although there's strong evidence for it being as old as we (me included as a figure of speech) currently believe it, our belief is based on some fundamental assumptions that can only be strengthen but not proven. At least for the sake of honesty, one must be aware of the nature of this kind of opinions. Science is part of the larger discipline called epistemology, so all the rules valid there, are valid in science too.
>The entire sky would be about as bright, and as hot, as the surface of the Sun.
Not so according to “The Inverse Square Law”.[1] If one measures the light flux through a hypothetical sphere drawn around a light source and then doubles that spheres size, the light density must decline or you've broken conservation of energy. [2]
[1] http://bccp.berkeley.edu/o/Academy/workshop08/08%20PDFs/Inv_...
[2] http://www.compuphase.com/electronics/candela_lumen.htm
Not so according to “The Inverse Square Law”.[1] If one measures the light flux through a hypothetical sphere drawn around a light source and then doubles that spheres size, the light density must decline or you've broken conservation of energy. [2]
[1] http://bccp.berkeley.edu/o/Academy/workshop08/08%20PDFs/Inv_...
[2] http://www.compuphase.com/electronics/candela_lumen.htm
Yes, but as you look deeper into the night sky, you see more and more stars (proportional to the square of the distance). These two factors cancel exactly.
Remember parallel plate capacitors from Electromagnetics class? They're infinite in size for a reason, to get around not having to worry about the inverse square law. An infinite amount of stars would produce an infinite amount of energy...
If you reduce the power of infinite stars, you still have infinite stars producing infinite light.
x * infinity = infinity (so long as x > 0; even if x is infinitesimally small)
x * infinity = infinity (so long as x > 0; even if x is infinitesimally small)
But you can't have infinite stars in your field of view since they'd get in each other's way; blocking radiation. Using the tree example from the article, you wouldn't see infinite trees, you'd only see the pieces that are directly in front of you.
No, infinity times infinitesimal is undefined, you have to define your infinities more carefully to get an answer.
"Astronomers have concluded that the universe began some 12 to 15 billion years ago. That means we can only see the part of it that lies within 12 to 15 billion light-years from us."
This is false, because it ignores the metric expansion of spacetime. We can see radiation from objects that are now ~46.5 billion light-years from Earth.
This isn't picking nits. The explanation given here makes it sound like the Universe is a Euclidean volume that got instantaneously filled with stars, at roughly their present density, and that this density is low enough that light from distant stars hasn't reached us yet. If this were true, it wouldn't only explain why the sky is dark now, but predict that it has always been dark. We know this is false: for the first 380,000 years after the Big Bang, the Universe was filled with hydrogen plasma and completely opaque to radiation, which we can still see in the form of CMBR. As spacetime expands, energy density decreases, space becomes less light-emitting and more transparent, and light already in transit becomes red-shifted. Our field of vision is still technically flooded with light, as it always has been, but by now the red-shift is so extreme that the light is in the radio spectrum.
This is false, because it ignores the metric expansion of spacetime. We can see radiation from objects that are now ~46.5 billion light-years from Earth.
This isn't picking nits. The explanation given here makes it sound like the Universe is a Euclidean volume that got instantaneously filled with stars, at roughly their present density, and that this density is low enough that light from distant stars hasn't reached us yet. If this were true, it wouldn't only explain why the sky is dark now, but predict that it has always been dark. We know this is false: for the first 380,000 years after the Big Bang, the Universe was filled with hydrogen plasma and completely opaque to radiation, which we can still see in the form of CMBR. As spacetime expands, energy density decreases, space becomes less light-emitting and more transparent, and light already in transit becomes red-shifted. Our field of vision is still technically flooded with light, as it always has been, but by now the red-shift is so extreme that the light is in the radio spectrum.
At the risk of going more-pedantic-than-thou, this entire thread of nitpicks (and indeed, most of the posts I see right now to this story in general) is(/are) mostly irrelevant. The argument is not particularly sensitive to the exact way in which the universe is not steady state, including redshifting all the light until we're not staring at the sun in every direction. Olber's Paradox disproves the Steady State hypothesis, it doesn't positively prove anything in particular. Popular treatments of Olber's Paradox are not obligated to come attached to a complete course in cosmology. I'm sure at least one of "Steven Soter and Neil deGrasse Tyson" are fully aware of all the issues raised in this entire HN page.
There are plenty of ways the Universe could be steady-state and still not have a white-hot sky. Suppose you have metric expansion as you do now, but new matter magically appears as a sparse, uniform cloud of particles throughout space to feed the creation of new stars and maintain the energy density we see today. Metric expansion guarantees that light is redshifted in proportion to distance, so the sky remains dark, even though the Universe is infinitely old and stable.
This model is wrong, obviously, but the reason has nothing to do with Olber's paradox.
This model is wrong, obviously, but the reason has nothing to do with Olber's paradox.
The Steady State hypothesis isn't really a class of hypotheses, it was a specific one. The Steady State hypothesis predates the entire concept of metric expansion, after all.
History, everyone. Olber's paradox is important because of the history, not its relevance to 21st century physics.
History, everyone. Olber's paradox is important because of the history, not its relevance to 21st century physics.
The model I described is the historical model, as developed (and later repudiated) by Einstein. It does not "predate the entire concept of metric expansion". The whole point was to reconcile expansion, which was both predicted by GR and confirmed by Hubble's observation of recessional redshift, with the belief that the Universe was infinitely old and unchanging.
And there were many variants of Steady State, as the model was discovered independently after Einstein, and refined throughout the 1950s as its adherents struggled to explain new observations that distant quasars are far more common than near ones. There was even a brief (and apparently failed) attempt by Hoyle to revive a Steady State as late as 1993, involving widely varying rates of expansion in different regions of the Universe.
What ultimately disproved Steady State was seeing the CMBR. None of this has anything to do with Olber's paradox, which is not an issue in a Steady State model for exactly the same reasons it's not an issue in modern cosmology.
And there were many variants of Steady State, as the model was discovered independently after Einstein, and refined throughout the 1950s as its adherents struggled to explain new observations that distant quasars are far more common than near ones. There was even a brief (and apparently failed) attempt by Hoyle to revive a Steady State as late as 1993, involving widely varying rates of expansion in different regions of the Universe.
What ultimately disproved Steady State was seeing the CMBR. None of this has anything to do with Olber's paradox, which is not an issue in a Steady State model for exactly the same reasons it's not an issue in modern cosmology.
But how can something that is further away than the maximum travel distance allowed by the time elapsed since the big bang exist? Is there a non-locality of the time dimension that makes it so? Was the expansion rate of the universe faster than the speed of light? Or... what?
https://en.wikipedia.org/wiki/Metric_expansion_of_space
The short version: The distant object wasn't traveling through space, it sat stationary while more space came into existence in the gap between us and it, resulting in it being farther away. This happens everywhere, all the time -- it's what cosmologists are talking about when they say the Universe is "expanding". The laws that prohibit faster-than-light travel concern movement within space ("peculiar motion"), not the expansion of space itself.
The short version: The distant object wasn't traveling through space, it sat stationary while more space came into existence in the gap between us and it, resulting in it being farther away. This happens everywhere, all the time -- it's what cosmologists are talking about when they say the Universe is "expanding". The laws that prohibit faster-than-light travel concern movement within space ("peculiar motion"), not the expansion of space itself.
This might help you understand:
"Misconceptions about the Big Bang" http://www.physics.uq.edu.au/download/tamarad/papers/SciAm_B...
"Misconceptions about the Big Bang" http://www.physics.uq.edu.au/download/tamarad/papers/SciAm_B...
It sort of is nitpicking.
We haven't observed objects with redshifts that indicate distances larger than 13.some Gly away.
Yes, the physical objects are farther, but the point is moot. Those objects aren't the same as what we see today. They're totally different. We don't know what they look like today. Even low-mass stars have lived and died.
In summary, there is no way for us to see those 46.5 Gly objects other than wait 50 Gy (with our given technology)
We haven't observed objects with redshifts that indicate distances larger than 13.some Gly away.
Yes, the physical objects are farther, but the point is moot. Those objects aren't the same as what we see today. They're totally different. We don't know what they look like today. Even low-mass stars have lived and died.
In summary, there is no way for us to see those 46.5 Gly objects other than wait 50 Gy (with our given technology)
I assume you're talking about UDFy-38135539 (https://en.wikipedia.org/wiki/UDFy-38135539), with a redshift of z=8.6. It is not 13 Gly away, even though the light detected by Hubble's infrared camera was emitted about 13 billion years ago. Due to the metric expansion of space, the distance to that object is around 32 Gly (9710 Mpc according to http://www.bo.astro.it/~cappi/CosmoWidget.html).
that is one object with a suggested redshift of z=8.6. However, we do not know the distance of that object because not only was the image taken in the visible spectra (by Hubble), but the spectroscopic results re: it's distance have not been reproducible, and so the distance figure is challenged.
Fortunately, we have other galaxies, such as EGSY8p7 (z=8.68) have been imaged in the infrared, and as such, their distance confirmed.
However, you've just reiterated what GP has said. I maintain that nobody is denying that the object that has been observed is more distant than it was 13Gy ago, however, the light that we are currently observing emanated from an object that was only 13Gly away.
As I stated in my previous comment, the galaxies that we are presently observing are much different, and much farther away today, it's just going to take a lot of time for us to see what they look like today.
You're seeing a baby and claiming to have seen the senile crank that the baby potentially became over 19Gy. The baby we're currently observing may as well be dead.
If the article author is stating that 13Gly is the maximum distance anything can be from us, then the author is false. However, that's not what the author is saying. The author is saying we cannot see past 13Gly because the light has not arrived, and this is patently TRUE. The author makes NO claim about the current location of the objects.
Fortunately, we have other galaxies, such as EGSY8p7 (z=8.68) have been imaged in the infrared, and as such, their distance confirmed.
However, you've just reiterated what GP has said. I maintain that nobody is denying that the object that has been observed is more distant than it was 13Gy ago, however, the light that we are currently observing emanated from an object that was only 13Gly away.
As I stated in my previous comment, the galaxies that we are presently observing are much different, and much farther away today, it's just going to take a lot of time for us to see what they look like today.
You're seeing a baby and claiming to have seen the senile crank that the baby potentially became over 19Gy. The baby we're currently observing may as well be dead.
If the article author is stating that 13Gly is the maximum distance anything can be from us, then the author is false. However, that's not what the author is saying. The author is saying we cannot see past 13Gly because the light has not arrived, and this is patently TRUE. The author makes NO claim about the current location of the objects.
the light that we are currently observing emanated
from an object that was only 13Gly away
we cannot see past 13Gly because the light has not
arrived, and this is patently TRUE
Edited to add: For more information, refer to https://en.wikipedia.org/wiki/Scale_factor_%28cosmology%29, specifically the FLRW metric, https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr....
Yes, it's true that the most distant galaxies we've observed are only around 13 Gly away, but the fact that number is so close to (speed_of_light * age_of_universe) is just a coincidence. We could, in principle, see light emitted from points in space that are currently 46.5 Gly away, but all such light was emitted long before any galaxies had formed. The OP wasn't mentioning that we can see to a maximum distance of ~13 Gly as an unrelated fact with its own cause, it was saying it was because the Universe is ~13 Gy old and that's how far light can travel in that time, which isn't true.
Correction: I'm an idiot; see xenophonf's comment.
> As spacetime expands, energy density decreases, space becomes less light-emitting and more transparent, and light already in transit becomes red-shifted. Our field of vision is still technically flooded with light, as it always has been, but by now the red-shift is so extreme that the light is in the radio spectrum.
You talk about the radiation generated before 1M years in the universe. This article talked about the light from the existing stars in the universe.
You talk about the radiation generated before 1M years in the universe. This article talked about the light from the existing stars in the universe.
Yes, it's still incorrect! The complete quote is:
> Astronomers have concluded that the universe began some 12 to 15 billion years ago. That means we can only see the part of it that lies within 12 to 15 billion light-years from us. There may be an infinite number of stars beyond that cosmic horizon but we can’t see them because their light has not yet arrived. And the observable part of the universe contains too few stars to fill up the sky with light.
(Emphasis mine because that's where the error is: 13 billion year-old light has traveled over a distance that is now much higher than than 13 billion light-years)
Potential ambiguity (in cases such as this one) is one of the reasons why using light-years for distances may not be a good idea.
(By the way, there are real astronomers arguing about this, too, e.g. http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html . So it's not just this nerd ranting on HN).
GRB 090423 (admittedly, not a star -- it's a gamma ray burst) happened approximately 13 billion years ago. This means that light traveled for 13 billion years to reach us -- but, by the time it got to us, GRB 090423 was no longer 13 billion light-years from us, because all that space got bigger! GRB 090423 "was" about 9.2 Gpc away from us by the time that light reached us, i.e. about 30 billion light-years.
If the light that hits us is 13 billion years old, that object (assuming it still exists) is a lot farther than 13 billion light-years from us now.
> Astronomers have concluded that the universe began some 12 to 15 billion years ago. That means we can only see the part of it that lies within 12 to 15 billion light-years from us. There may be an infinite number of stars beyond that cosmic horizon but we can’t see them because their light has not yet arrived. And the observable part of the universe contains too few stars to fill up the sky with light.
(Emphasis mine because that's where the error is: 13 billion year-old light has traveled over a distance that is now much higher than than 13 billion light-years)
Potential ambiguity (in cases such as this one) is one of the reasons why using light-years for distances may not be a good idea.
(By the way, there are real astronomers arguing about this, too, e.g. http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html . So it's not just this nerd ranting on HN).
GRB 090423 (admittedly, not a star -- it's a gamma ray burst) happened approximately 13 billion years ago. This means that light traveled for 13 billion years to reach us -- but, by the time it got to us, GRB 090423 was no longer 13 billion light-years from us, because all that space got bigger! GRB 090423 "was" about 9.2 Gpc away from us by the time that light reached us, i.e. about 30 billion light-years.
If the light that hits us is 13 billion years old, that object (assuming it still exists) is a lot farther than 13 billion light-years from us now.
Sure. But that really is just pedantics. It isn't a surprise to anyone to point out that the source of something that was moving away from us 13Gy ago is now further away than it was. You are essentially just giving those words the least charitable interpretation and then picking on that. It isn't wrong, its just not perfectly unambiguous.
> It isn't wrong, its just not perfectly unambiguous.
Yes, it's perfectly wrong, because those objects are not 13Gly away from us. A light-year really is defined as 300,000 km multiplied by whatever number of seconds there are in a year. The object is not at 13e9 x 300,000 x <a lot of seconds> kilometers from us if it took 13 billion years for the light to reach us.
> It isn't a surprise to anyone to point out that the source of something that was moving away from us 13Gy ago is now further away than it was.
If I wanted to give words the least charitable interpretation, I could point out that their motion has nothing to do with this -- they would still be farther than 13 Gly away from us even if they would not be moving away relative to the Earth :-).
Yes, it's perfectly wrong, because those objects are not 13Gly away from us. A light-year really is defined as 300,000 km multiplied by whatever number of seconds there are in a year. The object is not at 13e9 x 300,000 x <a lot of seconds> kilometers from us if it took 13 billion years for the light to reach us.
> It isn't a surprise to anyone to point out that the source of something that was moving away from us 13Gy ago is now further away than it was.
If I wanted to give words the least charitable interpretation, I could point out that their motion has nothing to do with this -- they would still be farther than 13 Gly away from us even if they would not be moving away relative to the Earth :-).
The red shift applies to distant stars too. The important point is that even in the extreme scenario where all stars last forever and you wait an infinite amount of time for light to reach you, you will still never see a fully illuminated sky because the stars are receding much faster than the light propagates due to metric expansion. Saying the sky is dark because 1) the Universe is young or 2) stars are short-lived is just false. The Universe gets darker and darker as it expands, despite there being "more time for light to reach us".
No, its correct.
I lost a youtube video that explains Universe. Basically a universe observer is like an ant sitting on a big balloon that is constantly being pump with air. So while the balloon age might be 12 billion years old, the speed the air is pumped in it makes it grow and therefore objects "placed" far further than originally; hence 46B for an observer.
I lost a youtube video that explains Universe. Basically a universe observer is like an ant sitting on a big balloon that is constantly being pump with air. So while the balloon age might be 12 billion years old, the speed the air is pumped in it makes it grow and therefore objects "placed" far further than originally; hence 46B for an observer.
So we don't know the age of the universe then?
We do know the age of the universe, to a reasonable certainty. The discussion above doesn't argue against our current estimate of the age of the universe -- it addresses other issues.
So ~43 billion years is the age of the universe? Or is that extra 30 billion years solely a result of the universe's expansion?
43 billion light years is a distance, not a time.
A star moving in the opposite direction of us that emitted light 15 billion years ago that we are just now seeing has moved a lot further away in that 15 billion years it took that initial light to reach us.
A star moving in the opposite direction of us that emitted light 15 billion years ago that we are just now seeing has moved a lot further away in that 15 billion years it took that initial light to reach us.
I know what a light year is. I just did the conversion to time given that we are receiving a EM wave.
It doesn't work like that. Yes, a photon travels at 299792458 m/s, but photons emitted 13 billion years ago (a redshift of about z=8.6) travel much further than (1310^9 years 3.1510^7 seconds/year 299792458 m/s) due to the metric expansion of space.
The correct calculation involves an integral, an example of which you can see here:
http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=45...
The correct calculation involves an integral, an example of which you can see here:
http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=45...
The latter.
Remember that a light-year is a measure of distance, not time.
I know. If we receive light that traveled a distance of X light years, then the event is occurring X years in the past.
Given that we already know that originating at point A and traveling to point B, such that the distance from A to B at the time you arrive is X, does not involve traveling a distance of X... I have trouble seeing your point.
> If we receive light that traveled a distance of X light years, then the event is occurring X years in the past.
Not necessarily. By the time the light arrives here, its point of departure (and parts of its path through space) may have receded because of cosmological expansion, so its total travel distance, and its velocity, are no longer synchronized as they would be in Newtonian physics.
Your remark would have been true for the static universe that Einstein believed to exist when he proposed the first version of the cosmological constant (before 1929).
Not necessarily. By the time the light arrives here, its point of departure (and parts of its path through space) may have receded because of cosmological expansion, so its total travel distance, and its velocity, are no longer synchronized as they would be in Newtonian physics.
Your remark would have been true for the static universe that Einstein believed to exist when he proposed the first version of the cosmological constant (before 1929).
Remember that space is expanding, so a photon which has traveled one billion light years originated less than one billion years ago.
I've always been puzzled by this paradox. More particularly, I'm baffled that apparently the mainstream explanation involves cosmological arguments such that the expansion of the Universe. Is it really that complicated?
Take Hubble's deep field image, for instance. It was shot in a tiny area of the sky that looks completely black. But with enough exposure, Hubble found that it's actually full of galaxies. Can't I just conclude that if this part of the sky if completely black, it's not because space is expending, but just because our eyes are not sensitive enough?
Olber's Paradox points out that wherever we look at, at some distance our line of sight will meet the surface of a star. But that does not mean that this point will register as a light for our eyes. Our eyes would have to be sensitive enough.
Take Hubble's deep field image, for instance. It was shot in a tiny area of the sky that looks completely black. But with enough exposure, Hubble found that it's actually full of galaxies. Can't I just conclude that if this part of the sky if completely black, it's not because space is expending, but just because our eyes are not sensitive enough?
Olber's Paradox points out that wherever we look at, at some distance our line of sight will meet the surface of a star. But that does not mean that this point will register as a light for our eyes. Our eyes would have to be sensitive enough.
Imagine Hubble's deep field image again, but this time imagine you can see towards infinity (beyond the observable universe). If the universe is infinitely big (and old), then there would be so many stars in the image that there would be an infinite amount of light in the image.
In this hypothetical universe, the Sun would actually be a dark spot in the sky -- because it would be blocking the infinite amount of light coming from an infinite amount of stars behind it.
That's the paradox -- that we do not see that. No matter how sensitive our eyes are, we would be able to see infinite light. (Actually, our eyes would be melted... and all current forms of life impossible... but you get the picture.)
In this hypothetical universe, the Sun would actually be a dark spot in the sky -- because it would be blocking the infinite amount of light coming from an infinite amount of stars behind it.
That's the paradox -- that we do not see that. No matter how sensitive our eyes are, we would be able to see infinite light. (Actually, our eyes would be melted... and all current forms of life impossible... but you get the picture.)
But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero. The limit is not obvious and I've never seen anyone discussing the actual maths of this. I don't know those maths, but it seems reasonable to me that since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
Surprisingly, at the end of the wikipedia article about Olber paradox there is a integral which describes the summation of all stars and takes the distance into account, and according to what we know currently about the matter distribution in the universe, the integral is infinite :)
> But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero.
No, it never goes to zero, it just gets fainter. An infinite number of small numbers adds up to infinity.
> since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
As the article mentions, the sky is black because we cannot see infinity. We can only see the observable universe.
No, it never goes to zero, it just gets fainter. An infinite number of small numbers adds up to infinity.
> since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
As the article mentions, the sky is black because we cannot see infinity. We can only see the observable universe.
> No, it never goes to zero,
It never goes to infinity either. Zero and infinity are the limits.
> An infinite number of small numbers adds up to infinity.
Well, no. It depends. For instance the sum of 1/n goes to infinity, but not the sum of 1/n². And since the luminosity of a star decreases with the square of the distance, I incline to believe the sum does converge.
But again, that would require some serious, albeit probably not very hard maths. I've never seen anyone discuss this. Instead everyone seems to immediately assume the sum would diverge. That's not obvious at all.
It never goes to infinity either. Zero and infinity are the limits.
> An infinite number of small numbers adds up to infinity.
Well, no. It depends. For instance the sum of 1/n goes to infinity, but not the sum of 1/n². And since the luminosity of a star decreases with the square of the distance, I incline to believe the sum does converge.
But again, that would require some serious, albeit probably not very hard maths. I've never seen anyone discuss this. Instead everyone seems to immediately assume the sum would diverge. That's not obvious at all.
An infinite number of small numbers does not always add up to infinity! Since the apparent brightness of a star is an inverse-square law, if you assume there are an infinite number of stars, each 1 light year further away from you in a line and all the same brightness, you end up with that area being only 64%[1] brighter than it would seem with only the first star. Seems like a pretty simple resolution to this paradox to me.
[1] https://en.wikipedia.org/wiki/Particular_values_of_Riemann_z...
[1] https://en.wikipedia.org/wiki/Particular_values_of_Riemann_z...
I am going to guess that physicists have considered your resolution and it is incorrect in the face of current measurements and models.
The part that grandparent is overlooking is that while luminosity decreases as to the square of the distance, the number of stars in a given angular diameter of space increases as to the square of the distance. The two effects cancel each other out and so Olbers Paradox can't be resolved by that method.
I'm missing something here and would so happy if someone explained to me. I am sorry if I'm making false assumptions as my knowledge on the subject is very limited.
If the universe started from a single point in space and time (i.e., Big Bang), and no matter moves faster than the speed of light, how could ANY star be more distant from us than light could have traveled in the same time frame?
(I'm assuming no matter is travelling at v > c/2, otherwise my argument would only be valid for things traveling in the same hemisphere of the expansion as Earth)
If the universe started from a single point in space and time (i.e., Big Bang), and no matter moves faster than the speed of light, how could ANY star be more distant from us than light could have traveled in the same time frame?
(I'm assuming no matter is travelling at v > c/2, otherwise my argument would only be valid for things traveling in the same hemisphere of the expansion as Earth)
The matter isn't moving. Space is expanding, ie, space is being inserted in-between all bits of matter.
Edit: To elaborate further: Since all the newly expanded space also expands, the distance to travel continuously increases as the light travels, to the point where over a certain distance the light never completes the journey.
So, the net effect is that the two objects become further apart faster than c, even though neither of them are moving.
Edit: To elaborate further: Since all the newly expanded space also expands, the distance to travel continuously increases as the light travels, to the point where over a certain distance the light never completes the journey.
So, the net effect is that the two objects become further apart faster than c, even though neither of them are moving.
Expansion of space allows for the distance of two objects to increase such that it appears that one is moving away from the other at a speed greater than c/2. I think it is possible for this to even be greater than c because it is the expansion of space and not objects movement contributing to the increase in distance.
This is an important concept to understand: https://en.wikipedia.org/wiki/Comoving_distance
Space itself might be able to expand faster than the speed of light.
what about all the light that doesn't hit us.
An easy explanation is here: https://www.youtube.com/watch?v=gxJ4M7tyLRE
I find it odd that so many people seem to have trouble accepting this explanation. Light travels at a finite speed, ergo anything far enough away(adjusted for expansion of space) is invisible, because we've only existed for a dozen billion years. If the universe were infinitely old, then we'd have something interesting to talk about.
One answer to this problem is that the night sky isn't dark at all. It's just less bright than during the day. Hear me out. As a species that evolved on this planet under it's particular conditions we perceive day to be bright and night to be dark because of the particular range of light sensitivity of our eyes. Too often science leaves the human observer out of the equation. It lets us feel like gods presiding over our universe but is a big mistake.
All that said it's not unreasonable to question why the night sky is not brighter than it is.
>Too often science leaves the human observer out of the equation.
It seems this problem may have come full circle with the Measurement Problem. But yes, human beings themselves emit light, however that light resonates on a frequency that our eyes have not evolved to see, so we invented infrared optics.
It seems this problem may have come full circle with the Measurement Problem. But yes, human beings themselves emit light, however that light resonates on a frequency that our eyes have not evolved to see, so we invented infrared optics.
A mathematical explanation would involve a comparison of the density of stars throughout the universe with the inverse-square drop-off in light intensity from each.
If you assume for the sake of argument that all stars are as bright as the sun, and that stars have a uniform density throughout the universe (either a finite-but-huge or infinite universe, it makes little difference here), then you could solve for the mean intensity of light throughout, or in our case, "how bright the sky is at night."
The article makes a classic (and really hard to escape! I've seen this sort of thing called a "paradox" on many occasions.) mistake of examining two infinite quantities (infinite stars, up to an infinite distance away) and assuming that they must cancel each other out, that infinity/infinity=1. But not all infinities are the same, and infinity/infinity can work out to 0, or to 0.1, or to pi, or to infinity (as in the case of "# real numbers"/"# integers"), or to anything else; you have to look at the details -- what kind of infinity is it? -- and figure out how they compare.
If you assume for the sake of argument that all stars are as bright as the sun, and that stars have a uniform density throughout the universe (either a finite-but-huge or infinite universe, it makes little difference here), then you could solve for the mean intensity of light throughout, or in our case, "how bright the sky is at night."
The article makes a classic (and really hard to escape! I've seen this sort of thing called a "paradox" on many occasions.) mistake of examining two infinite quantities (infinite stars, up to an infinite distance away) and assuming that they must cancel each other out, that infinity/infinity=1. But not all infinities are the same, and infinity/infinity can work out to 0, or to 0.1, or to pi, or to infinity (as in the case of "# real numbers"/"# integers"), or to anything else; you have to look at the details -- what kind of infinity is it? -- and figure out how they compare.
The article makes no mistake, it just doesn't go into enough detail.
To determine the amount of energy reaching us, we need to integrate over the energy density divided by the square of the distance over the whole 3d space. As any physicist can tell you, an integral over the whole space will diverge unless the kernel falls off faster than 1/r^2.
This means that one of the following must be true
a) either the universe is finite, ie. the density falls off
b) we don't integrate over the whole space (we can't see far enough due to age of universe)
Which is exactly the argument this article is making
Edit: in other words, infinite or finite-but-huge is an important difference when integrating over constant density; the former integral will diverge, the latter will not
To determine the amount of energy reaching us, we need to integrate over the energy density divided by the square of the distance over the whole 3d space. As any physicist can tell you, an integral over the whole space will diverge unless the kernel falls off faster than 1/r^2.
This means that one of the following must be true
a) either the universe is finite, ie. the density falls off
b) we don't integrate over the whole space (we can't see far enough due to age of universe)
Which is exactly the argument this article is making
Edit: in other words, infinite or finite-but-huge is an important difference when integrating over constant density; the former integral will diverge, the latter will not
As is often the case, this explanation fails to take cosmological expansion into account. An expanding universe is a cooling one. The explanation is correct as far as it goes, but failing to take expansion into account either dates the explanation or fails to evaluate a factor that's a bit more complex than relying on the finite age of the universe.
Subsequent edit: Assuming the universe is infinite, is where the problem begins. There is no reason to assume that.
Original comment: Is this really not obvious to people? It's about subtended angles - simple geometry. As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky." Assuming radiation does indeed proceed radially and in straight lines, at increasing distance the Earth is capable of catching a decreasing portion of that star's radiation. As the distance approaches infinity, the subtended angle approaches zero and the amount of light reaching us approaches zero. The star is just as bright, but most of its radiation goes somewhere else besides Earth.
Imagine building a giant spherical shell around a star. Its radius equals the distance between earth and the star. It catches 100% of that star's radiated energy. Now paint the Earth on the inside of the shell, actual size. It looks, to someone standing on the surface of that star, like the real earth, i.e. a tiny dot. Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches. Assuming zero degradation across space.
So imagine you're in a forest of trees the closest of which are 800 miles away from you. You'd see the goddamned sky just fine.
Original comment: Is this really not obvious to people? It's about subtended angles - simple geometry. As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky." Assuming radiation does indeed proceed radially and in straight lines, at increasing distance the Earth is capable of catching a decreasing portion of that star's radiation. As the distance approaches infinity, the subtended angle approaches zero and the amount of light reaching us approaches zero. The star is just as bright, but most of its radiation goes somewhere else besides Earth.
Imagine building a giant spherical shell around a star. Its radius equals the distance between earth and the star. It catches 100% of that star's radiated energy. Now paint the Earth on the inside of the shell, actual size. It looks, to someone standing on the surface of that star, like the real earth, i.e. a tiny dot. Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches. Assuming zero degradation across space.
So imagine you're in a forest of trees the closest of which are 800 miles away from you. You'd see the goddamned sky just fine.
> As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky."
But the number of stars at a given distance increases as the distance increases, and this increase exactly cancels out the decrease in the amount of light from a given star that reaches the Earth. So your argument does not explain why the night sky is dark.
> Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches.
Now do it the other way: draw a sphere around the Earth with some radius r. Calculate how many stars are on that sphere. The number increases as r^2; and, as you have shown, the amount of light reaching Earth from a given star decreases as r^2. So, as I said above, the increase in the number of stars exactly cancels out the decrease in the amount of light from each star that reaches the Earth; thus, the total starlight reaching Earth from a given radius r is a constant, independent of r.
But the number of stars at a given distance increases as the distance increases, and this increase exactly cancels out the decrease in the amount of light from a given star that reaches the Earth. So your argument does not explain why the night sky is dark.
> Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches.
Now do it the other way: draw a sphere around the Earth with some radius r. Calculate how many stars are on that sphere. The number increases as r^2; and, as you have shown, the amount of light reaching Earth from a given star decreases as r^2. So, as I said above, the increase in the number of stars exactly cancels out the decrease in the amount of light from each star that reaches the Earth; thus, the total starlight reaching Earth from a given radius r is a constant, independent of r.
There's no reason to believe the universe is infinite nor that stars are evenly distributed throughout its volume. So "the number of stars increases as r^2" is the part that doesn't hold and is causing the paradox.
This is Kepler's theory, and it gets into philosophical trouble, as cosmologists generally take it as axiomatic that the laws of physics are the same everywhere, and so don't have much time for theories that depend on us being in a special place in the universe. A universe having a lower density of stars everywhere above some radius from Earth does put us in a special place, is hard to reconcile with universal laws, and there is no empirical evidence for it. An explanation that derives from the universe evolving over time, however, has none of the philosophical problems and does have supporting empirical evidence.
> There's no reason to believe the universe is infinite nor that stars are evenly distributed throughout its volume.
There is if you believe General Relativity is correct as applied to the universe as a whole. And if you don't, you have no model at all with which to make any predictions about what we should observe, so there's no reason to believe anything.
There is if you believe General Relativity is correct as applied to the universe as a whole. And if you don't, you have no model at all with which to make any predictions about what we should observe, so there's no reason to believe anything.
Nope.
A ball of radius R around Earth contains R^3 stars. The angular size of Earth as seen from each star is 1/R^2 or more. So the total light coming to Earth is proportional to R. As R goes to infinity, you get Olbers paradox.
If you insist on talking about trees, in an infinite forest of trees that are 800 miles apart and 1mm thick, you wouldn't see the sky.
A ball of radius R around Earth contains R^3 stars. The angular size of Earth as seen from each star is 1/R^2 or more. So the total light coming to Earth is proportional to R. As R goes to infinity, you get Olbers paradox.
If you insist on talking about trees, in an infinite forest of trees that are 800 miles apart and 1mm thick, you wouldn't see the sky.
Yup. The universe was declared infinite not because it is, but because it repeatedly defied our hubris. "If we can't find the end of it, it must be endless!" Kind of like "If she doesn't like me she must be a lesbian!"
> Is this really not obvious to people? It's about subtended angles - simple geometry.
If the universe is infinite and filled uniformly with stars, the 1/r^2 falloff in the radiation captured from each star is cancelled by r^2 dependence on the number of stars at radius r. So as you integrate r from 0 to ∞, you accumulate an infinite amount of radiation.
Is this really not obvious to you? It's all about infinitesimals - simple calculus.
If the universe is infinite and filled uniformly with stars, the 1/r^2 falloff in the radiation captured from each star is cancelled by r^2 dependence on the number of stars at radius r. So as you integrate r from 0 to ∞, you accumulate an infinite amount of radiation.
Is this really not obvious to you? It's all about infinitesimals - simple calculus.
As with others here, your problems start with "if the universe is infinite."
Yes, we are all aware of that. Nobody is saying that Olbers's paradox is unsolved; we are saying that your comment doesn't make sense. Olbers's paradox assumes from the outset that the universe is infinite. You cannot solve the paradox by invoking the inverse-square law.
You cannot solve Olbers' paradox at all, because it is a malformed question, that leads to a paradox.
Correct. Now could you please edit your top-level comment some more, so that it actually makes sense?
First you fake incredulity about how people aren't finding it "obvious", although it's unclear exactly what you think is obvious (the paradox? its resolution? modern cosmology?).
Then you launch into an explanation of the inverse-square law for a single point source. What's your intention here? By itself it doesn't demonstrate how to resolve the paradox. (As you say, the resolution is that the universe is not infinite. Thanks for adding that in the edit.)
Overall, your top-level comment was incomprehensible, as evidenced by the large number of people who thought you were trying to use the inverse-square law to resolve the paradox.
First you fake incredulity about how people aren't finding it "obvious", although it's unclear exactly what you think is obvious (the paradox? its resolution? modern cosmology?).
Then you launch into an explanation of the inverse-square law for a single point source. What's your intention here? By itself it doesn't demonstrate how to resolve the paradox. (As you say, the resolution is that the universe is not infinite. Thanks for adding that in the edit.)
Overall, your top-level comment was incomprehensible, as evidenced by the large number of people who thought you were trying to use the inverse-square law to resolve the paradox.
You are correct in your geometry, but you forgot one thing. The earth receives a smaller portion of light for stars that further away, but the number of stars at that radius goes up by the exact same amount. So from any shell the amount of light we get is the same. If the shells go out to infinity, the light becomes infinite (well, according to the naive argument).
The nearest star is the Sun. With a giant Sun nearest to Earth, it's impossible for the number of stars to go up proportionally as distance to Earth increases. There isn't 4 suns at 2 AU, and at 100000 light years wide, with 63000 AUs per light year, the milky way does't contain (63000 * 100000)^2 stars. There needs to be 4 billion times more stars in the milk way for there to be proportionally as many stars as in our solar system. You can fill the entire sky with AA battery torches and they won't be as bright as the one stuck right up to your eye.
The night sky is dark, but it doesn't mean it isn't full of rays of lights heading our way. It's darker than the day sky due to the Sun being so close, yes, but the night sky is full of light, everywhere we look. It's only because the way our minds perceive relatives, we call the night sky "dark".
The night sky is dark, but it doesn't mean it isn't full of rays of lights heading our way. It's darker than the day sky due to the Sun being so close, yes, but the night sky is full of light, everywhere we look. It's only because the way our minds perceive relatives, we call the night sky "dark".
Your explanation is correct for individual stars, but it doesn't take universal expansion into account, which independently reduces the energy available from distant sources (apart from the 1/r^2 law). The reason? Same energy, more space, so a reduction in energy per unit of volume.
Also, setting aside the issue of expansion and redshift, if you imagine a sphere with a uniformly illuminated interior (imagine a surface composed of so many stars that counting them individually makes no sense) and an observation point at the center, if you increase the radius of the sphere, there's no change in the energy received at the center.
This idea works for an infinite plane as well, and is a bit easier to grasp. Imagine an infinite plane with a fixed optical brightness, and an observation point at some distance d. Now double the distance -- no change in received energy because the plane is infinite in extent.
Also, setting aside the issue of expansion and redshift, if you imagine a sphere with a uniformly illuminated interior (imagine a surface composed of so many stars that counting them individually makes no sense) and an observation point at the center, if you increase the radius of the sphere, there's no change in the energy received at the center.
This idea works for an infinite plane as well, and is a bit easier to grasp. Imagine an infinite plane with a fixed optical brightness, and an observation point at some distance d. Now double the distance -- no change in received energy because the plane is infinite in extent.
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BTW that's (4)(pi)(a gazillion light-years ^ 2) in case the point wasn't obvious!
Is was an amazing conceptual comment - thank you
Stab in the dark:
Inverse Square Law + The number of stars in your field of vision can't be infinite.
This one's easy. The first, foundational, assumtion is way easy to knock down, via all the accumulated evidence that we erupted from a singularity 13-some billion years ago. So.. no infinite time.
But we could probably get by with, even with an infinite universe, if we just assume a universal speed, which is most definitely supported by current academic consensus. This is because of the concept of the light cone, which says that you can't be illuminated by things that lie outside your temporal and spacial vicinity, as defined by how long it takes light in a vacuum to reach you. That's a stronger statement than just how bright the sky is... it applies to any conceivable mechanism of information transfer, and it's universally supported by any experiments that we've tried (note: wormholes... possible, super crazy loop hole here... maybe an infinite universe has infinitely many wormholes to pump radiation into our light cone, so basicly multiverse, but we've already talked about the universe having an age).
I see no paradox here, but then again the Big Bang and Special Relativity are pretty new as ideas and we all benefit from the shoulders of the giants we stand on.
Edit: On further reflection, a truly infinite universe probably would park an infinite number of unstable wormholes on top of our neighborhood, but in that case the the fact that our sky is in fact dark just adds more evidence to the pile that we already have that it's not.