# Steven Hawkins says:

1. Feb 17, 2007

### Peter (IMC)

In http://www.hawking.org.uk/lectures/lindex.html Steven Hawkins says:

"In an infinite and everlasting universe, every line of sight would end on the surface of a star. This would mean that the night sky would have been as bright as the surface of the Sun. The only way of avoiding this problem would be if, for some reason, the stars did not shine before a certain time."

Now I am the last one to disagree with anything a man like Steven Hawkins says, but I´m having a difficult time understanding why what he says is true.

Stars don't exist for ever, so the star density is limited, (I guess in fact that real star density is much lower than visible star density because many stars we see don't exist anymore, though there are also many stars around that we haven't seen yet.) Also the brightness of the light of a star goes down with distance, eventually the brightness is so low that it is no longer detectable from the background radiation. (right?)

Adding everything up, my logic concludes that even in an infinite and ever lasting universe, the night sky doens't shine as bright as the surface of the Sun. I feel like the milky way should be shining that bright because almost every line of sight into the milkey way is ending up on a star... Especially close to the center of the milky way... but city lights are already lighting up the atmosphere so much you can't see the milkey way at all.

Where is my logic wrong?

2. Feb 18, 2007

### cesiumfrog

Isn't the point of the paradox ("everlasting") that the ancients didn't know that? Then, what can they conclude if there is no light from one direction in the sky? (And still, if the stars always existed and are distributed infinitely, is it thermodynamically possible for one to cool down?)

Last edited: Feb 18, 2007
3. Feb 18, 2007

### cristo

Staff Emeritus
4. Feb 18, 2007

### Staff: Mentor

Individual stars don't have to live forever for every line of sight to end on a star.

Star density is limited, by a number of factors, but so what? The lower the density, the further you have to look before your sight line hits a star, but remember: we're looking infinitely far in this scenario.

5. Feb 18, 2007

### hellfire

What you describe is known as Olbers paradox. It states that in a static, spatially infinite and eternal universe that contains a distribution of light sources (stars) that is homogeneous in space and in time, the night sky would be infinitely bright.

Stars do not need to exist forever for the paradox to apply. The condition is that the distribution of stars must be homogeneous in space and in time. For example, stars shall not be distributed according to some pattern in a preferred direction in space, neither there shall exist a smaller star density in past (for example).

It is correct that the brightness decreases with distance (inverse square law). However, for an uniform distribution the number of stars increases with distance (square law), in a way that the contribution of each spherical shell to the total brightness is equal and independent of the distance. Therefore, the sum of all spherical shells will lead to an infinite brightness (if the conditions for the paradox are met).

Last edited: Feb 18, 2007
6. Feb 19, 2007

### Chronos

Just a technicality - Olber's paradox does not infer an infinitely bright sky, merely one as bright as the surface of an average star [it is not infinite because the foreground stars shield us from the photons emitted by background stars]. I also find the 'Hawkin' thing distracting. Reckless reading is the first thing that crosses my mind.

7. Feb 19, 2007

### cesiumfrog

If stars keep producing photons, the intensity of the universe must keep increasing ad infinitum.

8. Feb 19, 2007

### moe darklight

wait, I thought olber's paradox was pretty much solved by the red-shift of distant stars?

my guess is that that wouldn't happen because the amount of energy available in the universe is not infinite. the stars eventually run out of energy, and much of that light energy would be absorbed/transformed into other forms of energy anyway.

Last edited: Feb 19, 2007
9. Feb 19, 2007

### turbo

Yes. Light from stars that are very distant will be red-shifted into invisibility in accordance with the Hubble distance/redshift relation. This moots Olber's "paradox" cleanly, with no additional entities, such as intervening dust (which would have to re-radiate anyway) or other blocking/absorbing material.

10. Feb 19, 2007

### hellfire

Thanks for the clarification Chronos. What I actually meant was apparent brightness or flux, which varies with the inverse of the squared distance. This would be infinite in an universe that meets the conditions for the paradox.

11. Feb 19, 2007

### turbo

This is something that seems to be lost on the folks who cite Olber's paradox as evidence for a spacially finite universe. If you look at the Hubble UDF images, you will see spaces between the galaxies, and even in a very large telescope, these galaxies are so dim as to be invisible without very long exposures to integrate the very low flux. With deeper exposures at longer wavelengths, it might be possible to see enough galaxies to provide blanket coverage of the field, but this does not mean that we humans should see a bright sky unless we develop the ability to see in deep microwave, like WMAP.

12. Feb 20, 2007

### Peter (IMC)

I´m learning a lot here,... This is great.

In the paradox, does "an infinite and everlasting universe" mean that all stars are also everlasting? If that´s assumed, I think I can see how the sky would be bright as the surface of an average star. But if stars are not ever lasting, then I don't see how the sky would be so bright.

Could the background radiation in fact be the radiation from "every line of sight"?

13. Feb 20, 2007

### moe darklight

no, stars don't last forever... stars are pretty much huge fusion machines. and the fuel eventually runs out. more massive stars last less than less massive ones.

14. Feb 20, 2007

### cesiumfrog

If the universe has always existed, then every star has already released an infinite number of photons. (And so any dust or possible dead stars should also be shining with the corresponding temperature.)

I don't think we can bring full energy conservation into this - we'd soon need to explain why we don't see nearly enough light as to condense into new stars (at the same rate old ones are burning up their material).

Spatially infinite universe implies here that there is a star in every possible direction (barring unfathomable cosmic coincidences). So (by conservation of surface brightness, after accounting for redshift) the entire sky should look as the sun.

I don't think redshift really solves Olber's paradox. In the example of the hubble deep field, is the dimness of distant galaxies due more to relative velocity or just the fact of such small angular size (noting galaxies have low average surface brightness to begin with)? With infinite stars, it isn't obvious whether the redshift is sufficient for total energy flux to converge. And regardless, doesn't expansion automatically violate the concept of the universe having always been in steady state?

OTOH, turbo is right in that nobody would "cite Olber's paradox as evidence for a spacially finite universe" if they already assume the universe had a beginning.

15. Feb 20, 2007

### turbo

Only if you believe that every star has an infinite life-time. That is not a reasonable assumption.

Not true. We are already at a point where light from distant galaxies is so severely redshifted that we need to advance from Hubble to Webb (enhanced IR sensitivity) in order to see further, at least with any kind of resolution. The notion that we should see all visible frequencies from all stars, no matter what their remove (look like the Sun) is not supportable.

Olber's paradox cannot survive the Hubble relationship, nor the luminosity/distance (reduction as a square of separation) flux diminution, even in a spacially and temporally infinite universe. Light from sufficiently distant sources will be redshifted into lower and lower frequencies, such that at sufficient distance, the EM will not be recognizable as such, and will join the ground state of observable space, much the same as the way that sufficiently low-frequency AC would be indistinguishable from DC.

16. Feb 21, 2007

### hellfire

You do not need to assume that stars have an infinite life-time for the paradox to hold. The assumption is that the distribution of stars is homogeneous in space and in time. If stars die, new have to born in order to mantain this condition.

Moreover, let's see how dropping the assumption of static space solves the paradox.

Consider that the density of stars in the present is $\rho$. The density in a spherical shell at a redshift related to the scale factor $a$ is:

$$dn = \frac{\rho}{a^3} 4 \pi r^2 a^3 dr = \rho 4 \pi r^2 dr$$

The electromagnetic flux coming from redshift $z$ at distance $r$ in an expanding space:

$$f = \frac{L}{4 \pi r^2 (1+z)^2}$$

The contribution of each spherical shell to the flux in an infinite space:

$$f = \int_0^{\infty} fdn = \int_0^{\infty} \frac{L}{4 \pi r^2 (1+z)^2} \rho 4 \pi r^2 dr = \int_0^{\infty} \frac{\rho L}{(1+z)^2} dr$$

To solve the integral one has to postulate a relation between $r$ and $z$. This is usually non analytic for a general cosmological model, but we are interested in a special cosmological model, namely a model that is eternal. This is because we want to drop only the assumption of static space whilst retaining all others.

The only homogeneous cosmological model that does not contain a singularity in its past and is therefore eternal is the de-Sitter model, for which the distance-redshift relation is $z = Hr$ (with $c = 1$) with a constant Hubble parameter. Thus:

$$f = \int_0^{\infty} \frac{\rho L}{(1+Hr)^2} dr = \frac{\rho L}{H}}$$

Which is finite.

Last edited: Feb 21, 2007
17. Feb 21, 2007

### Chronos

No one [AFAIK] has made any credible suggestion stars are infinitely long lived - which would qualify as a terminal case of ATM. Olber's paradox does not predict an infinitely bright sky, merely one about as bright as the surface of your average star. How bright is less important than the inescapable conclusion [by physics as we know it] that 2.7K is way too low. The finite BB model is 'only a mother could love' ugly, but remains far more plausible than an infinitely old, spacious universe homogenously populated by an infinite number of stars. At very least, such a universe must leak energy like a sieve into 'extra dimensions' to resemble what is observed. I might rethink this position if energy starts disappearing in LHC experiments.

18. Feb 21, 2007

### Physics-Learner

does anyone seriously think that the universe has always existed ? with the way that "time" has manifested itself, the only way that the universe could have always existed is if everything in the universe has always existed, as well.

19. Feb 23, 2007

### heusdens

Quite strongly, yes. That is because matter itself is eternal.

And this does not contradict this Olber's paradox, because the (visible) universe was born a finite time ago in the Big Bang, but before that there was eternal inflation. Inflation lasted a finite amount of time in our time perception, but inflation goes on outside of our universe bubble, and in that sense, the universe can be thought to be eternal and infinite.

20. Feb 23, 2007

### Physics-Learner

accdording to the big bang theory, this is when and how our universe was created. assuming that the bb is correct, we have no knowledge of anything before the bb, and never will.

i am not saying that you are wrong. simply saying that it is impossible to prove anything about it. i do tend to believe in god, but certainly know that i cant prove it.

here is what i think can be shown. we exist today. by seeing how "time" has manifested itself within our universe, the universe can not be eternal without all the objects in it being eternal, as well. since things are not eternal, it follows that the universe is not eternal.

this universe follows a cause-effect system. to say that the universe was able to create itself from nothingness disobeys this cause and effect.

therefore, i conclude that something does exist outside of this universe(that is responsible for its creation), but that is as far as we can go. our minds can not think without the concepts of space, time, and matter. however, we do not know that any of these concepts have any validity outside this universe. we do not know, or will never know anything at all about outside this universe, while we are in this universe.