If the observable universe was visible to the naked eye....

[rollete]

What would the Earth's night sky look like? Would our eyes see any dark spots? Is there are way to calculate such a probability?

This hypothetical is about the observable universe only. 93 billion light-years diameter, isotropic, visible light.

Not sure what's the most appropriate tag for this...

 

[Vanadium 50]

I don't understand. The observable universe is visible to the naked eye. If our eyes were more sensitive, everything would of course be brighter.

 

[andrewkirk]

I think the question could be interpreted as follows: Is there any non-degenerate cone, with apex at a point on Earth, whose intersection with the sphere that is the observable universe, contains no radiating matter?

I think some minimum threshold of radiation density to count as 'radiating matter' might need to be set because any particle can undergo nuclear decay and radiate, which would mean that one isolated particle of Hydrogen would be enough to render a cone 'occupied'.

 

[rollete]

Lets assume that all the stars, galaxies, clusters, are all magically equally bright in the night sky to our eyes.

What I'm really asking is if there would be any line of sight that wouldn't end up on the surface of a luminous object.

Let me know if I'm not making sense...

 

[russ_watters]

Lets assume that all the stars, galaxies, clusters, are all magically equally bright in the night sky to our eyes.

Does that include all frequencies or just visible ones? Because if it includes all frequencies, the cosmological microwave background would satisfy your query: it's everywhere.

What I'm really asking is if there would be any line of sight that wouldn't end up on the surface of a luminous object.

Aside from the CMB, which originated when the universe was opaque and therefore was itself a single luminous object, the answer to that is no. The best visual range idea of what the universe might look like with more powerful eyes is the Hubble [Ultra] Deep Field pictures:

Note that this is also at a magnification/resolution beyond human sight, so at human resolution this would appear to be a near uniformly bright field, a la some regions of the Milky Way.

 

[Drakkith]

It seems to me that the limited resolution of the eye would blur much of the light, so even though the HST sees a large amount of blackness, the sky would still appear nearly featureless and overwhelmingly bright.

 

[andrewkirk]

What I'm really asking is if there would be any line of sight that wouldn't end up on the surface of a luminous object.

A line of sight won't generate a dark spot. To be a spot, it needs to subtend a nonzero solid angle at the eye - hence the reference to a nontrivial cone in post 3.

 

[rollete]

Does that include all frequencies or just visible ones?

Just visible ones.

Aside from the CMB, which originated when the universe was opaque and therefore was itself a single luminous object, the answer to that is no. The best visual range idea of what the universe might look like with more powerful eyes is the Hubble [Ultra] Deep Field pictures:

Note that this is also at a magnification/resolution beyond human sight, so at human resolution this would appear to be a near uniformly bright field, a la some regions of the Milky Way.

Right, I was wondering about this image. I'm not sure about how deep into the past those galaxies are, though. Is this really the edge of our observable universe?

Yes, given the eye resolving capability it would probably look like a close to uniformly bright sky.

 

[rollete]

A line of sight won't generate a dark spot. To be a spot, it needs to subtend a nonzero solid angle at the eye - hence the reference to a nontrivial cone in post 3.

This flies over my head. But I'll read on it. Thanks.

 

[Drakkith]

Right, I was wondering about this image. I'm not sure about how deep into the past those galaxies are though. Is this really the edge of our observable universe?

No. Most of those galaxies are much closer than the edge. The tiny, deep red dots scattered about the picture are galaxies which are much, much closer to the edge. We just can't see the vast majority of them because they've been redshifted almost completely out of the visual spectrum and are incredibly dim.

 

[rollete]

No. Most of those galaxies are much closer than the edge. The tiny, deep red dots scattered about the picture are galaxies which are much, much closer to the edge. We just can't see the vast majority of them because they've been redshifted almost completely out of the visual spectrum and are incredibly dim.

I see. I was kinda imagining this exercise including all those galaxies that can only be detected outside of the visible spectrum, but as if they magically became visible to us. Like literally make all luminous objects within the observable universe visible to the naked eye.

But I guess there would still be a lot of 'empty' space between baryonic matter for lines of sight to pass through.

 

[rollete]

Because if it includes all frequencies, the cosmological microwave background would satisfy your query: it's everywhere.

Well, excluding the CMB.

 

[Vanadium 50]

Lets assume that all the stars, galaxies, clusters, are all magically equally bright in the night sky to our eyes.

To a very good approximation (not including redshift), they are. Galactic surface brightness is independent of distance, and is driven primarily by the galaxy's star density. There is a little difference related to color, but this of course averages out over any reasonably sized patch of sky.

 

[rollete]

I think the question could be interpreted as follows: Is there any non-degenerate cone, with apex at a point on Earth, whose intersection with the sphere that is the observable universe, contains no radiating matter?

I think some minimum threshold of radiation density to count as 'radiating matter' might need to be set because any particle can undergo nuclear decay and radiate, which would mean that one isolated particle of Hydrogen would be enough to render a cone 'occupied'.

Sorry, I see what you mean now. Imagine that we look through the cross section (arbitrarily small radius) of the intersection between the cone and the sphere to see if there's any 'radiating' matter inside the cone. This is exactly what I mean. (planets, comets, anything bigger than a dust particle also counts)

Galactic surface brightness is independent of distance, and is driven primarily by the galaxy's star density.

I should have said all with equal apparent magnitude. Sorry for the confusion. The question of visibility is one point that is likely cleared out. The other is the cone intersection (arbitrarily small cross section, so pretty much a 'line'), which andrewkirk understood right away.

My bad for not formulating this right.

 

[russ_watters]

I should have said all with equal apparent magnitude. Sorry for the confusion. The question of visibility is one point that is likely cleared out. The other is the cone intersection (arbitrarily small cross section, so pretty much a 'line'), which andrewkirk understood right away.

@Vanadium 50 was more on point than you realized. The brightness of point sources of light falls with the square of distance, but galaxies are not point sources, they are extended objects. And their apparent size also gets smaller with the square of distance, making the intensity of the light from that smaller area roughly the same. That's the reason the HUDF can detect galaxies of vastly different distances in the same exposure; their surface brightnesses are similar.

The caveat of redshift means that in particular with the HUDF pictures, some galaxies become redshifted out of the frequency range of the detector.

In any case, my understanding is that the HUDF does not miss a large fraction of the galaxies in our observable universe, but I don't have a ready link to a source for that. I'm going to take a somewhat of a guess and say it can see about half.

 

[Drakkith]

In any case, my understanding is that the HUDF does not miss a large fraction of the galaxies in our observable universe, but I don't have a ready link to a source for that. I'm going to take a somewhat of a guess and say it can see about half.

Sounds like a reasonable guess.

 

[andrewkirk]

The point of @russ_watters and @Vanadium 50 about apparent brightness of galaxies per unit solid angle being broadly constant makes me feel that the answer to the question must be Yes - there would be dark spots (empty cones). Otherwise we would have a solid white night sky, like a scaled-down version of Olbers' paradox.

The only thing that might prevent that conclusion is the red shift issue. My guess is that, if we exclude the CMBR then, even if we count all sources within the observable universe, regardless of the frequency at which their light would arrive here, there would still be plenty of dark spots - ie cones from which the only incoming radiation is from the CMBR. But that is just a guess. Maybe the amount of incoming radiation at very low frequencies is so much more than that in the visible range that it fills in all the holes.

 

[rootone]

What I'm really asking is if there would be any line of sight that wouldn't end up on the surface of a luminous object

This is Olber's Paradox
https://en.wikipedia.org/wiki/Olbers'_paradox
While there are plausible explanations it remains a paradox ( I think).
Some would use this as an argument that the Universe in totally cannot be infinite.

 

[Drakkith]

While there are plausible explanations it remains a paradox ( I think).

The resolution of the paradox lies in the fact that light has a finite speed and the universe has a finite age. Light simply hasn't had time to travel from every conceivable portion of the universe to get to Earth.

 

[rollete]

@Vanadium 50 was more on point than you realized. The brightness of point sources of light falls with the square of distance, but galaxies are not point sources, they are extended objects. And their apparent size also gets smaller with the square of distance, making the intensity of the light from that smaller area roughly the same. That's the reason the HUDF can detect galaxies of vastly different distances in the same exposure; their surface brightnesses are similar.

The caveat of redshift means that in particular with the HUDF pictures, some galaxies become redshifted out of the frequency range of the detector.

In any case, my understanding is that the HUDF does not miss a large fraction of the galaxies in our observable universe, but I don't have a ready link to a source for that. I'm going to take a somewhat of a guess and say it can see about half.

The point of @russ_watters and @Vanadium 50 about apparent brightness of galaxies per unit solid angle being broadly constant makes me feel that the answer to the question must be Yes - there would be dark spots (empty cones). Otherwise we would have a solid white night sky, like a scaled-down version of Olbers' paradox.

The only thing that might prevent that conclusion is the red shift issue. My guess is that, if we exclude the CMBR then, even if we count all sources within the observable universe, regardless of the frequency at which their light would arrive here, there would still be plenty of dark spots - ie cones from which the only incoming radiation is from the CMBR. But that is just a guess. Maybe the amount of incoming radiation at very low frequencies is so much more than that in the visible range that it fills in all the holes.

Makes sense, thanks.

 

[rollete]

This is Olber's Paradox
https://en.wikipedia.org/wiki/Olbers'_paradox

I was picturing something like that.

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There's a lot to find out yet.

 

[russ_watters]

I was picturing something like that.

---------------------------------

There's a lot to find out yet.

That's a cool graphic. Note though that the scale is sort of logarithmic. If the HUDF covers everything back to 95% of the age of the universe, then it it probably covers most of what is out there at least in the visible universe (but not 95%, again due to the inverse square law and higher density of the early universe).

 

[diogenesNY]

Just to add a bit of scale and perspective:

If we imagine the Earth to be de-textured, i.e. a sphere with a solid surface at 'sea level' at any given point, further assuming ideal viewing conditions, a sharp eyed human, standing on the surface of the Earth could resolve maybe Sixty five hundred (6500) distinct items - mostly stars. Maybe a total of three thousand (3000) from any given place. Real world figures are actually pretty close to that, but modded up and down given altitude, viewing conditions, etc.

diogenesNY

 

[1oldman2]

Just to add a bit of scale and perspective:

This works pretty well also. http://www.numbersleuth.org/universe/