Why Is the Night Sky Dark If the Universe Is Infinite?

[Chronos]

Show the math, Garth.

 

[jdlawlis]

Olber's paradox continued

The following website offers a different explanation, which I don't entirely agree with. It appears to explain Olber's paradox by the finite lifetime of a star rather than the finite age of the universe. While this phenomenon would certainly lower the apparent brightness in a finite age universe, it would have no effect in an infinitely old and infinitely large universe.

http://physics.uwstout.edu/deptpages/physqz/olber.htm

On a related note, let's assume that the universe was infinitely old and infinitely large, but expanding at a rate less than the speed of light. True, light from distant sources would appear to be red-shifted; however, wouldn't each distant object be receiving an infinite amount of energy, causing its own temperature and wave frequency to increase? In other words, how can you attenuate an infinite energy source? Do you see what I am driving at?

 

[kmarinas86]

The area of the sky which a star covers is inversely proportional to the square of the distance.
The brightness of a star is inversely proportional to the square of the distance.
Therefore, the brightness of a star is roughly proportional to the area of the sky it covers.
The integral of n^p from n=1 to n=infinity is finite only if p, the exponent, is less than -1.
In this case, stars would not appear in every point in the sky only if the surface area of all the stars combined at r decrease faster than 1/r, so the number of stars at this distance is proportional to distance^k, k<1.
In a star system, there remains the same number of stars (1 usually, ex. the sun) at differing radii, so k equals 0 for star systems.
In galaxies, mass is proportional to radius, so k equals 1 for galaxies.
At large scales, it is claimed by the cosmological principle that density at the largest scales is the same throughout, meaning a k that equals 2.

 

[oldman]

Olbers’ paradox and the speed of light

I suggest that there is more to Olbers paradox than met the sharp eye of Edgar Allen Poe.

For the purposes of discussion assume that Poe’s resolution of this paradox was the correct one, namely that the night sky is dark because the universe is not infinitely old.. Paul Wesson ( Paul Wesson, "Olbers' paradox and the spectral intensity of the extragalactic background light", The
Astrophysical Journal 367, pp. 399-406 (1991).) has explained this quantitatively by calculating that the amount of background light that has
reached us since the universe began, from within the particle horizon, is insufficient to dispel the darkness of the night. The expansion of the universe, he calculates, only darkens the sky by a further factor of two.

The WMAP results show that spatial sections of the universe are flat (within observational error). Deep Hubble photographs show that the observable universe is filled with luminous galaxies. Stellar age measurements show that local galaxies are roughly as old as ours. A working hypothesis consistent with these observations is that the universe is an infinite dispersion of evolving luminous objects that originated with in an event that took place some 14 billion years ago. The lambda CDM model is not in conflict with such a working hypothesis.

According to this hypothesis the physical reason for our dark night skies is the finite speed of light, c, which together with the age of the universe determines the location of the particle horizon. The quantitative darkness (or brightness) of the night sky depends on the magnitude of c. If c were larger than it is, the night sky would be brighter.

Suppose, as Joao Magueijo has argued in “Faster than the Speed of Light”, that c was much larger in the early universe than it is now. Could the “dark sky” of the early universe then be correspondingly brighter, and the early universe hotter, as the conventional resolution of Olbers paradox suggests? There is evidence that this was the case. Maybe all is not yet cut and dried with Olbers paradox.

 

[heusdens]

That is not a stupid question . . . . In fact it is one of the best questions you can ask. What it means, logically, is the universe cannot be both infinitely old and spacious at the same time.

This need not be correct.

The correct conditions for Olbers' paradox to come into play are:

A universe infinite in extend homogeniously filled with luminous matter which exist for infinite time (eternal)

So theoretically the universe can be infinitely old and infinite in extend, if we assume that either stars have not always existed (which is the assumption the Big Bang theory makes) and/or is not static (which is also postulated by the Big bang theory).

The Big bang theory of course also states that the observable universe is of finite age, but the question wether that means that time is not infinite is still open, we can only ascertain that we can not observe anything before a certain time (i think the time at which the universe became transparent to light).

Theoretically there is also the possibility that the universe has a fractal nature in such a way that the average density of lumnious matter would drop down to zero when we increase the diameter, in which case Olbers' paradox also does not arise.
Just observation shows that this is not the case in the observable universe.

 

[kmarinas86]

This need not be correct.

The correct conditions for Olbers' paradox to come into play are:

A universe infinite in extend homogeniously filled with luminous matter which exist for infinite time (eternal)

So theoretically the universe can be infinitely old and infinite in extend, if we assume that either stars have not always existed (which is the assumption the Big Bang theory makes) and/or is not static (which is also postulated by the Big bang theory).

The Big bang theory of course also states that the observable universe is of finite age, but the question wether that means that time is not infinite is still open, we can only ascertain that we can not observe anything before a certain time (i think the time at which the universe became transparent to light).

Theoretically there is also the possibility that the universe has a fractal nature in such a way that the average density of lumnious matter would drop down to zero when we increase the diameter, in which case Olbers' paradox also does not arise.
Just observation shows that this is not the case in the observable universe.

However, one musn't consider the Milky Way as the center of the universe. In fact, there is no center of the universe, but rather there are places with more gravitational pressure than others. The only way to see this fractal structure in the immediate future is to assume that the structure does not change much with time. From the timeline of the Big Bang it is deduced that the further we look back, there is greater matter and energy density. But if this matter and energy density was about the same as it appears to us right now (at about the same spot), then it would appear that we are looking down a gravitational pressure gradient, meaning that our region of the universe (nearest 1 billion light years) is located at the suburbs.

In a fractal universe, the local density is inversely proportional to the cube of the scale factor at the region. Therefore, via integration, the density of the whole would fall inversely proportional to the square of the scale factor. The density would fall fast enough - the density of the whole needs to fall at a rate faster than inversely proportional to the radius in order to avoid Olber's paradox. A decreasing scale factor then begs the question - why are we in a bubble of a higher scale factor, and where could there be even higher scale factors? It is physically unlikely that we are completely surrounded by a bubble of lower scale factor (another way to say regions of greater gravitational pressure) - as in completely closed shell.

Another possibility is that there are particular places in the sky where one could look deeply to find spaces between the regions of high gravitational pressure. After zooming even further, one may find that there are other galaxies on the other side of the regions of high gravitational pressure, proven by their low redshifts in correspondence to their anomalously small angular sizes.

But regions of higher gravitational pressure could be large in angular width (tens of degrees) making it more difficult to find the places where these very distant galaxies may be seen. However, beyond that region behind the deep gravitational wells blocking most of this, would be a scale beyond anything currently realized...

 

[gone gator]

"Why is the sky dark at night?"

A seemingly naive question that has a profound answer.
If the universe were :
1. Infinite and
2. Infinitely old i.e. eternal and
3. Static (all three being true together) then the night sky should be burning bright!

i think Kepler used this to argue there were a finite number of stars in the Universe even before Newton's fears of collapse... (and two centuries before Olber's formulation of the problem).

"Before the expansion of the universe was discovered it was generally thought by astronomers, back to the ancient Greeks, that the universe was eternal.

and a few brits continued to believe it was eternal even afterwards...

(addendum) ...when the universe is homogenous and isotropic at the large scales.

in 1907 Fournier published a nice theory solving the paradox by assuming a fractal distribution of stars.

Edgar Alan Poe was the first to propose there simply had not been enough time for the light to have gotten to us. (as well as ?one of? the first illustrations of how weather could be both chaotic and predictable [he must have been reading of LaPlace?]).