Olber's Paradox only works for fields of constant density with range

[kmarinas86]

[math]x+\frac{x}{2}+\frac{x}{4}+\frac{x}{8}+\frac{x}{16}+\frac{x}{32}+\frac{x}{64}+...=2x[/math]

 

If there are x photons from r=[0,1]

If there are x/2 photons from r=[1,2]

If there are x/4 photons from r=[2,3]

If there are x/8 photons from r=[3,4]

If there are x/16 photons from r=[4,5]

If there are x/32 photons from r=[5,6]

If there are x/64 photons from r=[6,7]

Assuming that the pattern holds to +infinity:

There will be 2x photons from r=[0,+inf)

This clearly is not an infinite number of photons.

 

If a photon represents, in proportion, a figure of mass, then constant increasing of radius implies a constant rate of halving the amount of mass at that radius. If one were to determine the surface density, it would be proportional to [math]1/(r^2 2^r)[/math]. For a field of constant density, the surface density would remain constant.

 

This scenario assumes that the density of the universe decreases at larger and larger scales (does not tell us where from however).

 

Certainly, if we look further away, we see denser regions of space, because maybe we are not in a dense area of space. Certainly the Local Group is not. Could not we say the same for the spherical vicinity 1 billion lights of radius from us and claim that it is relatively matter deprived? Maybe we are located in a gap between "a rock and a hard place", or rather in the midst of a dance of black holes like in this picture:

 

[kmarinas86]

[coldcreation]

Olber's paradox is still alive amongst the old school cosmology circles. But I see not within contemporary theory. Congrats, it is impressionable to see such art (cosmology) at its highest level of creativity.

 

Question: I don't see the relation between the history of the universe as shown in the little diagram bottom left (which seems to be the standard hot big bang chart with inflation added to fix the problems) and the multiple universe (multiverse) picture. How do you relate the two illustrations? Are you saying the same scenario is repeated over and over as shown in the multiple universe illustration, each universe the same size, same age, overlapping, with the same natural laws?

 

I may be wrong, but should the universe(s) be ablaze like the surface of a star in your theory?

 

CC

[kmarinas86]

Olber's paradox is still alive amongst the old school cosmology circles. But I see not within contemporary theory. Congrats, it is impressionable to see such art (cosmology) at its highest level of creativity.

 

Question: I don't see the relation between the history of the universe as shown in the little diagram bottom left (which seems to be the standard hot big bang chart with inflation added to fix the problems) and the multiple universe (multiverse) picture. How do you relate the two illustrations?

 

The big bang charts shows what things appear to be. If you look at a small portion of the sky, what you get is it that chart. But look everywhere, at all distances observable, then things start to appear more variant (my prediction).

 

Are you saying the same scenario is repeated over and over as shown in the multiple universe illustration, each universe the same size, same age, overlapping, with the same natural laws?

 

No. These round objects can be conceptualized in 3-space (although its probably actually 4). They exist at the same time and are part of the same universe.

 

They cannot be black holes. They have to be something like Gravastars (or like dark energy stars) - which all should have similar appearances to black holes. They have to have radii exceeding 1 billion light years. If we were to see the outline of them, each of them would appear larger than our moon (according to their angular size in the sky) despite being the reason for much of the cosmic background radiation.

 

Here is the same picture, but with the Sloan Digitial Sky Survey put over it (as an example).

 

 

I may be wrong, but should the universe(s) be ablaze like the surface of a star in your theory?

 

CC

 

No, the very large objects are opaque. You cannot see through them. One must look between them to see further. Outside these collections of large (whatever) and the galaxies is truly empty space. So that a convergence of theory is possible, one may postulate an existence of a quasi-"electron cloud" surrouding this region - a part of an ultimate multiverse.

[kmarinas86]

If our eyes were sensitive to the contours of the these objects, this is something like what we would see in the sky. Stars, galaxies, and the very large objects in the distant background:

 

[coldcreation]

So what is the difference with the Linde Multiverse hypothesis?

His sounds cyclic too, in that there are big bang type universes scattered throughout the vast expanse of space (then nothing) and yet more space (then more nothing again) each with different physical laws, some areas where life can form and others not. We just happen, fortunately for us, to live in a universe where mold spores developped and evolved into creatures that could creat perfect art, intelligent, conceptual and gorgeous.

 

Albeit, his multiverse is prone to Olbers paradox too under certain conditions. Each bubble has to expand in order to justify a dark night sky.

 

cc

[Pyrotex]

[math]x+\frac{x}{2}+\frac{x}{4}+\frac{x}{8}+\frac{x}{16}+\frac{x}{32}+\frac{x}{64}+...=2x[/math]

 

If there are x photons from r=[0,1]

If there are x/2 photons from r=[1,2]

If there are x/4 photons from r=[2,3]

If there are x/8 photons from r=[3,4]...

 

Dear Kmarinas,

I checked several websites on Olber's Paradox, and I am afraid your initial equation and assumptions above, do not work. Sorry.

 

You say "there are x/2 photons from r=[1,2]", but that only from a point. Photons come not from points in a flat sky, but from spherical SHELLS that surround us. If we assume the shells are rather thin, then photons come from the AREA of the shell with radius r.

 

Actually, as the radius r increases, the area of each shell goes UP as the square of r. On the other hand, the inverse law says that the amount of radiation we recieve from an object goes DOWN as the inverse square of the distance.

 

These two principals exactly ballance each other. The areas of the shells go up as r^2 and the radiation from any given point on a shell goes DOWN as 1/r^2. A little simple calculus will combine these two principals to show that the total radiation from each shell should be the same.

 

In other words, this is how the math really works:

If there are x photons from shell with r=[0,1], then

there are x photons from shell with r=[1,2]

there are x photons from shell with r=[2,3]

there are x photons from shell with r=[3,4]

 

Therefore, if the Universe were infinite, the sky would blaze infinitely bright in all directions. Of course, this is NOT what we see.

 

Your statement that Olber's Paradox only works with uniform star density is correct, but it doesn't make the Paradox go away. We only have to calculate the AVERAGE star density for the visible Universe and use that for the radiance of each shell. We get the same result.

 

Take a look here.

[coldcreation]

Therefore, if the Universe were infinite, the sky would blaze infinitely bright in all directions. Of course, this is NOT what we see.

.

 

Olbers paradox OP is no paradox. It has nothing to do with cosmology. It has nothing to do with the night sky. It does however have to do with comicology, i.e., it's a bad joke.

 

Even in an infinite nonexpanding universe OP is nul.

In an infinite nonexpanding universe the night sky would be dark. If you don't believe it go take a look outside tonight.

Look for example in the direction of the Galaxy center, or in anyother direction, look at the Hubble deep fields.

You are looking at the sky of an infinite stationary universe.

 

Edited to add a quote from the paper linked above:

 

"...the amount of light we receive from the shell does not depend upon how far away the shell is. We receive the same amount of light from distant shells as we do from nearby shells. Hmmmmmm. So, if there are million such shells in the Universe, then we simply multiply the contribution of 1 shell by million to get the total amount of energy we receive from the Universe. Further, we should see this light at all times, even at night, since the shells completely surround us. This type of reasoning gave rise to Olbers's Paradox."

 

I agree with two things above: Hmmmmmm, and, This type of reasoning gave rise to Olbers's Paradox.

 

That "We receive the same amount of light from distant shells as we do from nearby shells" is absolutely not true.

[Pyrotex]

Olbers paradox OP is no paradox. It has nothing to do with cosmology. It has nothing to do with the night sky. It does however have to do with comicology, i.e., it's a bad joke....

No. Actually it is serious cosmology. I am sorry that you do not understand.

[coldcreation]

Olbers paradox has nothing to do with contemporary cosmology. It's a thing of the past, old school.

[Pyrotex]

...That "We receive the same amount of light from distant shells as we do from nearby shells" is absolutely not true.

What is your reasoning?

[coldcreation]

 

Olbers paradox OP is no paradox. It has nothing to do with cosmology. It has nothing to do with the night sky. It does however have to do with comicology, i.e., it's a bad joke....

 

What is your reasoning?

 

 

The light intensity from a spherical shell or point source decreases inversely proportional to the square of the distance.

 

The inverse square law.

 

Eventually, in any universe model, QSSC, Segal's chronometric cosmology, the universe according to Arp, CC or any other, expanding or not, multiple or cyclic, hot or cold, there will be a fall-off of light intensity inversely proportional to the square of the distance. Thus, a visual horizon is inevitable in any universe.

[kmarinas86]

Dear Kmarinas,

I checked several websites on Olber's Paradox, and I am afraid your initial equation and assumptions above, do not work. Sorry.

 

You say "there are x/2 photons from r=[1,2]", but that only from a point. Photons come not from points in a flat sky, but from spherical SHELLS that surround us. If we assume the shells are rather thin, then photons come from the AREA of the shell with radius r.

 

Actually, as the radius r increases, the area of each shell goes UP as the square of r. On the other hand, the inverse law says that the amount of radiation we recieve from an object goes DOWN as the inverse square of the distance.

 

These two principals exactly ballance each other. The areas of the shells go up as r^2 and the radiation from any given point on a shell goes DOWN as 1/r^2. A little simple calculus will combine these two principals to show that the total radiation from each shell should be the same.

 

In other words, this is how the math really works:

If there are x photons from shell with r=[0,1], then

there are x photons from shell with r=[1,2]

there are x photons from shell with r=[2,3]

there are x photons from shell with r=[3,4]

 

Therefore, if the Universe were infinite, the sky would blaze infinitely bright in all directions. Of course, this is NOT what we see.

 

Your statement that Olber's Paradox only works with uniform star density is correct, but it doesn't make the Paradox go away. We only have to calculate the AVERAGE star density for the visible Universe and use that for the radiance of each shell. We get the same result.

 

Take a look here.

 

The cosmological principle is not assumed in the opening post (OP). Rather, a decreasing density is assumed as distance from greater clusters increases.

 

If we throw the cosmological principle into the trash bin, it is possible to get an infinite universe that is not infinitely bright.

 

If you take the integral of 1/r from r=1 to r=infinity, you'll get infinity.

 

But if you take the integral of 1/r^2 from r=1 to r=infinity, you'll get 1.

 

In general, integrating 1/r^2 from r=a to r=b gives us 1/b - 1/a.

 

If the density drops with distance at a sufficient rate, then you won't have infinite brightness. In this case, the brightness provided by each radii must be 1/r^a ... where a is number greater than 1. In this way, what we end up with is a finite brightness.

 

When integrated from r=1 to r=infinity, the integral of 1/r^p is finite as long as p>1.

 

If p=2, starting from the sun (its distance from earth), the brightness by other stars would that of 1 sun.

If p=1.5, starting from the sun (its distance from earth), the brightness by other stars would that of 2 suns.

If p=1.25, starting from the sun (its distance from earth), the brightness by other stars would that of 4 suns.

If p=1.2, starting from the sun (its distance from earth), the brightness by other stars would that of 5 suns.

If p=1.1, starting from the sun (its distance from earth), the brightness by other stars would that of 10 suns.

If p=1.01, starting from the sun (its distance from earth), the brightness by other stars would that of 100 suns.

etc.

 

For brightness to drop with the square of the distance, overall density at a particular radii must drop with the square of the distance. The mass at each radii in this case would be a "constant" as the derivative of volume increases with the square of the radius - i.e. M is proportional to R so that additional brightness added is inversely proportional to the square of the distance. This is the case with galaxies with flat rotation curves, as a result of having M proportional to R for significant ranges of R. If a galaxy were infinite in size but having the same 1/r^2 density gradient, some parts of the sky would be dark, depending which way we looked. And for very small r, we have black holes, which are not necessarily bright as long they are not taking in large amounts of matter.

 

It is by theories such as the big bang which make it possible to see immediate regions of the universe of having a density [math](a_{now}/a_{then})^3[/math] times greater than more far off regions of the universe.

 

Olbers' paradox - Wikipedia, the free encyclopedia

 

A different resolution, which does not rely on the Big Bang theory, was offered by Benoît Mandelbrot. He postulated that if the stars in the universe were fractally distributed (e.g. like a Cantor dust), it would not be necessary to rely on the Big Bang theory to explain Olbers' Paradox. This model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred. This is merely a demonstration of the consequences of fractal theory, rather than a serious resolution of this paradox. Astronomical observers have found no evidence to support a fractal distribution of the stars.

 

The idea of a hierarchical cosmology - what would now be called a fractal cosmology - had been proposed in 1908 by Carl Charlier.

[kmarinas86]

The light intensity from a spherical shell or point source decreases inversely proportional to the square of the distance.

 

The inverse square law.

 

Eventually, in any universe model, QSSC, Segal's chronometric cosmology, the universe according to Arp, CC or any other, expanding or not, multiple or cyclic, hot or cold, there will be a fall-off of light intensity inversely proportional to the square of the distance. Thus, a visual horizon is inevitable in any universe.

 

This is not true.

 

Assume the cosmological principle in a non-expanding universe.

 

Assume 1 star per unit volume.

 

[math]Number\ of\ stars \propto \frac{4}{3}\pi r^3[/math], where r is the range of observation.

 

The new stars at each radii corresponds to the derivative of the volume or [math]4 \pi r^2[/math].

 

The brightness of each star is related to their distance, or rather, inversely proportional to the square of its distance from the basic observation region. Therefore, the photons recieved by each shell is the same (the same as what pyrotex said).

 

If you integrate r from r=1 to r=infinity, you get infinite value ... not good for our eyes!

 

So unless if we have a finite horizon or sufficiently decreasing density with distance, there is no explanation for the dark sky that I am aware of.

 

Pryotex disagreed with me because he started off with the cosmological principle, and using it, his reasoning determines that my formulation is wrong. But my point is that if the cosmological principle is abandoned in favor of a universe with fractally distributed density, it is not necessary for the sky with infinite range of sight to be infinitely bright if density decreases at a rate that leads to a finite limit of brightness, which was the whole point of using the equation:

 

[math]x+\frac{x}{2}+\frac{x}{4}+\frac{x}{8}+\frac{x}{16}+\frac{x}{32}+\frac{x}{64}+...=2x[/math]

 

Note: The equation above is only "similar" to the integral of [math]\frac{x}{2^n}[/math] from n=0 to n=infinity.

[coldcreation]

...the photons recieved by each shell is the same....

 

If you integrate r from r=1 to r=infinity, you get infinite value ... ...

 

So unless if we have a finite horizon or sufficiently decreasing density with distance, there is no explanation for the dark sky that I am aware of.

 

I do not agree with the above reasoning.

 

Spherical shells consists of point sources. The intensity of light from each source diminishes with a very specific value (inverse square law). So the volume calculation does not follow.

[kmarinas86]

I do not agree with the above reasoning.

 

Spherical shells consists of point sources. The intensity of light from each source diminishes with a very specific value (inverse square law). So the volume calculation does not follow.

 

But the number of stars at each radii increases to make up for that decrease in brightness:

 

At r=1, you have 1 for brightness (x stars)

At r=2, you have 1/4 + 1/4 + 1/4 + 1/4 for brightness (4x stars)

At r=3, you have 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 + 1/9 for brightness (9x stars)

At r=4, you have 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 for brightness (16x stars)

 

etc.

 

The surface area of a sphere is proportional to the square of its radius. And constant density (cosmological principle) implies constant surface density at any defined 2D surface. These are the reasons which explain why there are rational people who believe Olber's Paradox.

 

Of course, the reason why the Milky Way is not infinitely bright is because its density decreases with distance to the point where it does not extend infinitely. That's good news for our eyes.

 

If the cosmological principle were imposed on our solar system, we would be in a living hell right now.

[kmarinas86]

So what is the difference with the Linde Multiverse hypothesis?

 

My idea intends to link super galactic with the subatomic. In this idea, the basis of branching of universes has to be parallel to the formation of fermions and bosons in the nucleus.

 

His sounds cyclic too, in that there are big bang type universes scattered throughout the vast expanse of space (then nothing) and yet more space (then more nothing again) each with different physical laws, some areas where life can form and others not.

 

My idea does not posit different universes with different physical laws, but does not rule them out. Under my idea, undiscovered physical laws, but moreso new cosmological objects, are meant for larger distances. My hypothesis rests on the assumption of the break down of the cosmological principle for objects greater than 1 billion light years in diameter.

 

 

We just happen, fortunately for us, to live in a universe where mold spores developped and evolved into creatures that could creat perfect art, intelligent, conceptual and gorgeous.

 

Albeit, his multiverse is prone to Olbers paradox too under certain conditions. Each bubble has to expand in order to justify a dark night sky.

 

My hypothesis ditches the cosmological principle to the point where densities decrease with distance at a suffienctly steeping gradient such that our observable universe is largely finite, as is the atomic nucleus in the center of an atom which is relatively compact compared to the surrounding electron cloud. But in the same sense that an atomic nucleus is not alone in the universe, our "immediate" universe is not alone either.

 

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