Steven Hawking: Exploring the Limitless Universe

[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?

 

[cesiumfrog]

Stars don't exist for ever,

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?)

 

[cristo]

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

I presume you mean "Stephen Hawking" ?

 

[russ_watters]

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.

 

[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 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.)

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).

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?)

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).

 

[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.

 

[cesiumfrog]

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

 

[moe darklight]

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

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

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.

 

[turbo]

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

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.

 

[hellfire]

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.

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.

 

[turbo]

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.

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.

 

[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"?

 

[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.

 

[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.

 

[turbo]

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.)

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

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.

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.

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.

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.

 

[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.

 

[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.

 

[Physics-Learner]

If the universe has always existed,

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.

 

[heusdens]

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.

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.

 

[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 can't 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.

 

[Chronos]

Any stuff external to the observable universe is not a very useful platform for doing science.

 

[hellfire]

assuming that the bb is correct, we have no knowledge of anything before the bb, and never will.

This is surely not something that follows from the big-bang theory. There are theories of quantum cosmology that postulate classical regimes beyond the big-bang and these theories should be or will be testable. For some discussion about this see this thread.

 

[Physics-Learner]

hi hellfire,

it is all philosophy, just like my answers to it. none of it follows from the big bang theory.

i am familiar with the oscillating universe theory. but then what caused the first oscillation ? and we aint a going to prove that these oscillations are occurring, even if they were.

we can not think, without the concept of time, space and matter. just like my question above about the first oscillation. the use of the word "first" infers the existence of time.

we just can not make conclusions about what is beyond this universe from knowledge that we have in this universe. we can simply choose to have philosophies.

if we believe in the bb, all that is, was, and ever will be is in this universe after the big bang. nothing about what is in this universe can tell us about what came before the big bang.

we don't know that space, time, and matter even exist outside of this universe. we surely are not going to be able to prove it.

i think there is a point when we become too open-minded, such that we will allow anything in as a possibility.

one problem that scientists have is the inability to admit to the possibility that there are certain things that can not be discovered. i think one reason this is so, is that it makes them feel less important.

 

[hellfire]

if we believe in the bb, all that is, was, and ever will be is in this universe after the big bang. nothing about what is in this universe can tell us about what came before the big bang.

we don't know that space, time, and matter even exist outside of this universe. we surely are not going to be able to prove it.

I do not see or understand how your conclusion follows. If you read my contribution to the thread I have mentioned you will see that there are quantum cosmological models that can be tested.

For example, the loop quantum cosmology model predicts a semiclassical phase that sets the initial conditions for inflation and should provide an imprint in the CMB spectrum. This phase starts after the "discrete phase" that solves the classical singularity and acts as a transition between two classical regimes in the model. You can search for yourself for information about this and verify my claims.

Nevertheless, if you still insist in claiming that we can't say anything about a possible phase before the big-bang, I assume that you have some technical argument against testable quantum cosmological models in general. Please feel free to expand about it, I would be very interested because this issue is far from trivial and simple.

 

[Peter (IMC)]

If everything is relative, how come we can say the universe is expanding?

Observer A that stays on Earth will think that time slowed down for Observer B that went on a 40 year round trip at light speed. Observer B however, is convinced that time went a lot faster for Observer A.

Who's right? They both are I'd say.

Could there be a place/situation where another observer would actually see the universe contracting? And still we and that observer would both be right?

 

[Physics-Learner]

hi hellfire,

below is a site about quantum cosmological models.

http://arxiv.org/PS_cache/gr-qc/pdf/0412/0412026.pdf

i haven't attempted to keep up my calculus or physics at anywhere near that level of detail. so from your perspective, i am probably someone who does not know enough to really have a conversation with. and i would agree with you, from your perspective.

but from my perspective, scientists are a bit delusional to really think that they can figure out what came before the big bang (assuming the bb is actually real). i figure they have as much chance of doing that as they do to prove that god exists.

of course, they will always have theories - and 99.9999999999999 % of the people would have no way of debating with them, because they don't have that sort of knowledge. that tends to bolster their self-image, if nothing else.

i don't believe in string theory, either. and even many mainstream scientists believe it is and will always be a philosophy, because they can never test it. but the one thing about string theory that begs to be answered - what makes up strings. by its very definition, a string is made up of points. so i see no way for these strings to be the actual constituents of matter, even if they were proven to exist at some point. if and when proven, some group of physicists would be developing theories as to what makes up the strings.

often tests are positive because the tester was actually looking for a particular result, which sometimes influences the test itself.

i can recall being a physics student in college. at that time, whatever the teacher said, i believed. i was simply learning whatever i could. who was i to challenge the physics community.

while my math and physics are no longer as good as they once might have been, i have something today that i did not have then - LIFE EXPERIENCE.

as we go backwards in history, we basically see theories about physics that were later proven wrong. Newton's equations seemed to be able to show what gravity was. einstein's bible about gravity explains it very differently.

so i have learned not to put a lot of credence in these theories, just because someone with more knowledge about physics than myself is telling me that it is so. many, if not most, things that were once so, are no longer so.

i wasnt interested enough to read much of the article, as i don't like that sort of detail any more.

but when one refers to quantum cosmological models - are we basically talking about the possibility that there was some sort of quantum mechanic effects in the singularity ? and scientists are attempting to theorize what these effects were ?

 

[moe darklight]

If everything is relative, how come we can say the universe is expanding?

well... everything is relatively relative is a better way to describe relativity I think.

 

[Chronos]

good pointl

 

[hellfire]

Physics-Learner, IMHO you should use your skepticism to drive your curiosity and not to dismiss the work of others. Anyway, I have no problem with that.

but when one refers to quantum cosmological models - are we basically talking about the possibility that there was some sort of quantum mechanic effects in the singularity ? and scientists are attempting to theorize what these effects were ?

Right. It is assumed that quantum mechanical effects of the gravitational field are important at singularities. The theories that describe this are known as quantum gravity theories. And the models or theories that are based on them and try to describe the origins of the universe are known as quantum cosmology. For example, about loop quantum cosmology, you may want to take a look to the semi-popular articles of Abhay Ashtekar in this page.

 

[Physics-Learner]

hi hf,

i will look at the page.

i don't want you to think i am dismissing the work of others. as i said in a previous post, either galileo or Newton was supposed to have said that his accomplishments came from having strong shoulders to stand on.

where i tend to differ with scientists is that my suspicions or intuition tells me that there are many things that are not within our capacity to ever understand. i don't know this for sure - i just suspect it. i also don't place the same level of confidence in theories that scientists do. most will more than likely be proven to be wrong, eventually. but that does not mean they weren't important. we can't very well learn to run, until we start to walk. and even though i feel there are block walls that we can not break down, it doesn't mean that i think we should give up. we don't know for sure where these block walls are.

thanks for your contributions. even if i don't necessarily take it as certainty, i appreciate having someone capable of explaining what these theories are.

i enjoy reading about physics, but not at the calculus-level. maybe that is physics for dummies. LOL.

 

[Sojourner01]

On the subject of star lifetimes:

No, a star does not have to be infinitely long-lived. Suppose it exists for a long time then dies - what then?

Well, since your line of sight extends infinitely far in this model, the probability that there will be an active star somewhere behind the space the first star used to fill will tend towards 1.

In fact, if your line of sight is truly infinite and the universe is homogenous, your line of sight will always extent through an infinite number of active stars.

Even more damning evidence against this model, I'd say.

 

[Chronos]

Fascinating, PL. It appears you are asserting 'math' is irrelevant in your odel of the universe.

 

[Peter (IMC)]

On the subject of star lifetimes:

No, a star does not have to be infinitely long-lived. Suppose it exists for a long time then dies - what then?

Well, since your line of sight extends infinitely far in this model, the probability that there will be an active star somewhere behind the space the first star used to fill will tend towards 1.

In fact, if your line of sight is truly infinite and the universe is homogenous, your line of sight will always extent through an infinite number of active stars.

Even more damning evidence against this model, I'd say.

well.. I´m not going to say that this model should be proven correct. I´m just trying to understand why its wrong... :)

Suppose the life time of a star is 1 year. But star density is the same as it is now. Stars keep popping up and dying out all the time, natural process I guess.

Intuitively, I feel like the average life span of a star in this model determines how bright the nigh sky lights up (also star density is a factor I guess). Now, I know intuition is not always your best friend in science, but sometimes it's all you have,. :)

I don't see how the star's light/radiation continues to move for ever. Perhaps mathematically it does, but a at a certain point it's not practical anymore.

Has there never been done any calculation on the relation between star density, average star life span and the brightness of the night sky? (in an infinite universe, or even in "our" finite big bang universe)