How the Universe Ends

[Loren Pechtel]

There is a simple way to address the paradox.

Generate a random distribution of stars in 3d. Then calculate the total energy at Earth. It is easy to create random vectors in tools like Scilab, free, or Matlab and Mathematica.

Compare to the threshold energy of the eye.

You can vary the density and distribution nd the mea Place stars beyond our limit of observation to see if stars way off in the distance have any meaningful impact on the results.

Numbers talk.

We are talking about an infinite universe. You are losing the important data in the roundoff error.

Instead:

Make your distribution exactly as you described, calculate the energy from each star but do not add them together. Lets assume your space is 1000ly across. Divide the stars up into 10 zones, 0-50ly, 50-100ly...450ly-500ly from Earth. For each shell add up the total energy that reaches the Earth. You'll find each zone contributes a similar (due to the random nature it won't be exactly the same) energy flux to the Earth.

 

[Loren Pechtel]

You must be assuming a broadly random distribution of stars. Maybe not so. Suppose all stars, the whole infinity of them is lined up along one straight line. I have to guess that we would have mostly infrared radiation all coming from two opposite directions. Black sky and deep-fry cooking? Or any situation in between. So, a paradox but not that of the bright sky at night.

True, but that's not consistent with what we see in the sky.

You may have an infinity of stars but only a finite number of them emitting energy, although in this case you may not want to call all of them "stars". And I don't know of it's at all possible for any body to emit no energy at all, except black holes and even them in a way they do (Dawkin's something).

If you have an infinity of stars but only a finite number of them emit energy then an infinitely small percentage of all stars emit energy--but when we look into the night sky that's not what we find. If there were an infinite number of black stars for every lit star we would notice it gravitationally.

(And it's Hawking radiation, not Dawkin's.)

 

[steve_bank]

There is a simple way to address the paradox.

Generate a random distribution of stars in 3d. Then calculate the total energy at Earth. It is easy to create random vectors in tools like Scilab, free, or Matlab and Mathematica.

Compare to the threshold energy of the eye.

You can vary the density and distribution nd the mea Place stars beyond our limit of observation to see if stars way off in the distance have any meaningful impact on the results.

Numbers talk.

We are talking about an infinite universe. You are losing the important data in the roundoff error.

Instead:

Make your distribution exactly as you described, calculate the energy from each star but do not add them together. Lets assume your space is 1000ly across. Divide the stars up into 10 zones, 0-50ly, 50-100ly...450ly-500ly from Earth. For each shell add up the total energy that reaches the Earth. You'll find each zone contributes a similar (due to the random nature it won't be exactly the same) energy flux to the Earth.

That is the beauty of setting up a simulation, easy to vary parameters. If I had the energy and better eyesight I'd do it. It is simple, I'd be surprised if it has not been done.

There is another possibility. In an infinite universe what we observe may be a local phenomena.

 

[Jokodo]

There is a simple way to address the paradox.

Generate a random distribution of stars in 3d. Then calculate the total energy at Earth. It is easy to create random vectors in tools like Scilab, free, or Matlab and Mathematica.

Compare to the threshold energy of the eye.

You can vary the density and distribution nd the mea Place stars beyond our limit of observation to see if stars way off in the distance have any meaningful impact on the results.

Numbers talk.

We are talking about an infinite universe. You are losing the important data in the roundoff error.

Instead:

Make your distribution exactly as you described, calculate the energy from each star but do not add them together. Lets assume your space is 1000ly across. Divide the stars up into 10 zones, 0-50ly, 50-100ly...450ly-500ly from Earth. For each shell add up the total energy that reaches the Earth. You'll find each zone contributes a similar (due to the random nature it won't be exactly the same) energy flux to the Earth.

That is the beauty of setting up a simulation, easy to vary parameters. If I had the energy and better eyesight I'd do it. It is simple, I'd be surprised if it has not been done.

A simulation set up without understanding the phenomenon studies will not lead to many insights. Rounding a very small number to zero before multiplying it by a very large number is bound to give wrong results.

 

[Cheerful Charlie]

http://iopscience.iop.org/article/10.1088/2058-7058/15/10/27

[h=2]Abstract[/h] In his article on the most beautiful experiment in physics, Robert Crease quotes some respondents to his poll who chose reductio ad absurdum arguments, rather than real experiments (September pp19–20). These included "Olbers" paradox that the sky is not uniformly bright although it contains – to all intents and purposes – an infinite number of stars". The article goes on to say that "the paradox is resolved by the fact that the universe is expanding,which means that distant light has not yet reached us".

 

[Jokodo]

I worked on radar, electronic countermeasures, and IR systems. One of the first thing I did was verify for myself 1/r^2.

I have done open range testing of antennas. Computing energy at a distance from a source by 1.r^2 is common.

It is not simple line of sight. In radiometry a distant star and the Earth form a frustum with finite areas of the star and Earth at the ends. As an approximation a distant star light years away looks like an isotropic source. It is a theoretical point source radiating equally in all directs over 2PI steradians.

A star is not a point source. E. g. Alpha Centauri A has an apparent radius as seen from Earth of 0.007 archseconds.

You do not seem to have any understanding of applied electromagnetics and how different models are used. Computaionaly a distant star is for all practical purposes is trade like a pont source.

For most practical purposes. For the purposes of trying to understand whether there would be any black spots left on the night sky in an infinite static universe, it remains a two-dimensional source.

For the purpose of deriving whether we could live in such a universe without being incinerated, it doesn't make a difference.

Can you derive inverse square without looking it up?

Can you derive what inverse square law implies, assuming a static and infinite universe, for the sum of the light reaching us from each of several "shells", say of 0-50 lightyears, 50-ly, 10-150? For the sum of the light reaching us from shells 0-10 billion lightyears, 10-20 billion ly, 20-30 billion ly? For the sum of the light reaching us from shells 0-100 quadrillion ly, 100-200 quadrillion ly?

 

[Jokodo]

You must be assuming a broadly random distribution of stars. Maybe not so. Suppose all stars, the whole infinity of them is lined up along one straight line. I have to guess that we would have mostly infrared radiation all coming from two opposite directions. Black sky and deep-fry cooking? Or any situation in between. So, a paradox but not that of the bright sky at night.

or whether all those stars would emit at least some energy, etc. The universe could be infinite either without an infinity of stars, or with an infinity of stars spread around in a way that wouldn't light up all the sky at night

How would that work?

You may have an infinity of stars but only a finite number of them emitting energy, although in this case you may not want to call all of them "stars". And I don't know of it's at all possible for any body to emit no energy at all, except black holes and even them in a way they do (Dawkin's something).

So, broadly, for all those, I concede the point.

or with an infinity of stars but only a finite number of them emitting some energy. There could be also situations where the topology of the universe would keep the light from spreading to the whole universe. Also, the universe could be infinite but with a beginning, in which case you would only see the stars that are close enough to us consistent with our sky at night.

Indeed, but then no-one is disputing that the universe can be infinite in space. What the paradox demonstrates is that it cannot be static and infinite in space.

If by static you mean "no beginning" then I agree, at least for that point. If by static you mean currently static, with or without a beginning, then I disagree. The point is whether there's a beginning or not.

So, I'll assume your "static" implies "no beginning" and I'll agree with that.

And those who object to the Standard Model because they feel it comes too close to a universe more or less popping into existence out of nothing 13 billion years ago surely wouldn't be happy to replace it with a universe literally popping into existence as is 14 billion years ago.

Sorry, that's all lost on me.

Also, if you have an infinite universe that keep expanding, the light coming from distant stars won't ever reach us. Same result, our sky at night.

Sure, but in an expanding universe, going back in time eventually brings you to a point where it was, for all intents and purposes, infinitely dense. This is true whether it's expanding logarithmically, linearly, or exponentially.

I can conceive of a universe that's static, without a beginning, expanding at a constant rate and in a uniforme way throughout, with an infinity of stars, that would look locally as it does to us.

Going back in time doesn't make any difference with this one.

How so? If the universe is expanding without matter being added to it, it was denser before than it was now. And before that it was denser still. There comes a point where it's too dense for atoms and molecules to form. That's not what I call a static universe.

Maybe it's against the implicit rule of the "Standard Model" but in this case the paradox is that of the standard Model, not that of an infinite universe with an infinity of stars.

Of any model in which the first law of thermodynamics holds.

And that just is the standard model. The standard model does not preclude the possibility that it's infinite in space (if anything, most cosmologists seem to prefer this possibility). What it precludes is a universe that's borderless and static.

* "borderless" is a better terminology than "infinite". If space bends in on itself so we have a finite yet borderless universe (think: the 3-d version of a sphere's surface), the paradox still arises.

If "static" also exclude expansion then I agree.
EB

Static excludes expansion because a universe that's expanding doesn't remain in the same state for long.

 

[steve_bank]

You do not seem to have any understanding of applied electromagnetics and how different models are used. Computaionaly a distant star is for all practical purposes is trade like a pont source.

For most practical purposes. For the purposes of trying to understand whether there would be any black spots left on the night sky in an infinite static universe, it remains a two-dimensional source.

For the purpose of deriving whether we could live in such a universe without being incinerated, it doesn't make a difference.

Can you derive inverse square without looking it up?

Can you derive what inverse square law implies, assuming a static and infinite universe, for the sum of the light reaching us from each of several "shells", say of 0-50 lightyears, 50-ly, 10-150? For the sum of the light reaching us from shells 0-10 billion lightyears, 10-20 billion ly, 20-30 billion ly? For the sum of the light reaching us from shells 0-100 quadrillion ly, 100-200 quadrillion ly?

I already explained it. All you need is trigonometry, geometry, the definition of an isotropic radiator, and conservation of energy to derive 1/r^2. I leave it as an exercise for the student. . On a problem like this I'd go to a white board and sketch a picture to start. Or you can just google inverse square law.

Reread my post. I won't repeat it.

 

[Jokodo]

For most practical purposes. For the purposes of trying to understand whether there would be any black spots left on the night sky in an infinite static universe, it remains a two-dimensional source.

For the purpose of deriving whether we could live in such a universe without being incinerated, it doesn't make a difference.



Can you derive what inverse square law implies, assuming a static and infinite universe, for the sum of the light reaching us from each of several "shells", say of 0-50 lightyears, 50-ly, 10-150? For the sum of the light reaching us from shells 0-10 billion lightyears, 10-20 billion ly, 20-30 billion ly? For the sum of the light reaching us from shells 0-100 quadrillion ly, 100-200 quadrillion ly?

I already explained it. All you need is trigonometry, geometry, the definition of an isotropic radiator, and conservation of energy to derive 1/r^2. I leave it as an exercise for the student. . On a problem like this I'd go to a white board and sketch a picture to start. Or you can just google inverse square law.

Reread my post. I won't repeat it.

You did not explain anything that was under dispute. 1/r^2 is not under dispute. What appears to be under dispute is that r^2 * 1/r^2 = 1, and you're the one disputing it.

If you imagine space as sliced into multiple concentric shells of equal thickness, a bit like an onion, with earth at the center, then the volume of those shells is (in the limit of a shell with 0 thickness, but it gets close very quickly) proportional to the surface of a sphere - thus to r^2. So is the number of stars and the sum of their radiation in absolute terms, at least roughly on grand scales. Since the apparent magnitude, or the amount of light energy reaching earth, is proportional to 1/r^2, this means that the amount of light reaching us from each shell will be roughly the same because r^2 * 1/r^2 = r^2/r^2 = 1.

The only thing that can help you to avoid a linear growth in proportion to distance of the total light reaching is the fact that some nearer stars will be occluding more distant stars (that's unless you declare stars as point sources, in which case this won't help either). And even so, the percentage of sky predicted to be black approaches 0 rather quickly in an asymptotic manner - by the distance for which the linear model with point stars derives 100% coverage, it's already 1 - 1/e for the more realistic model with stars as 2-dimensional light sources. More then enough to evaporate every rock in the universe.

You don't get to deny that by running a simulation in which you ignore floating point imprecision.

 

[Loren Pechtel]

There is a simple way to address the paradox.

Generate a random distribution of stars in 3d. Then calculate the total energy at Earth. It is easy to create random vectors in tools like Scilab, free, or Matlab and Mathematica.

Compare to the threshold energy of the eye.

You can vary the density and distribution nd the mea Place stars beyond our limit of observation to see if stars way off in the distance have any meaningful impact on the results.

Numbers talk.

We are talking about an infinite universe. You are losing the important data in the roundoff error.

Instead:

Make your distribution exactly as you described, calculate the energy from each star but do not add them together. Lets assume your space is 1000ly across. Divide the stars up into 10 zones, 0-50ly, 50-100ly...450ly-500ly from Earth. For each shell add up the total energy that reaches the Earth. You'll find each zone contributes a similar (due to the random nature it won't be exactly the same) energy flux to the Earth.

That is the beauty of setting up a simulation, easy to vary parameters. If I had the energy and better eyesight I'd do it. It is simple, I'd be surprised if it has not been done.

There is another possibility. In an infinite universe what we observe may be a local phenomena.

I see nothing in your answer addressing the roundoff problem. Sometimes brute force doesn't produce useful answers.

In this case we have energy dropping off at distance^2 but the volume, and thus the number of stars, going up at distance^2. (These are two sides of the same coin, not a coincidence.) Thus the energy per shell remains constant and a constant * infinity = infinity. The only way to avoid frying is if the energy per shell is zero.

 

[Loren Pechtel]

For most practical purposes. For the purposes of trying to understand whether there would be any black spots left on the night sky in an infinite static universe, it remains a two-dimensional source.

For the purpose of deriving whether we could live in such a universe without being incinerated, it doesn't make a difference.



Can you derive what inverse square law implies, assuming a static and infinite universe, for the sum of the light reaching us from each of several "shells", say of 0-50 lightyears, 50-ly, 10-150? For the sum of the light reaching us from shells 0-10 billion lightyears, 10-20 billion ly, 20-30 billion ly? For the sum of the light reaching us from shells 0-100 quadrillion ly, 100-200 quadrillion ly?

I already explained it. All you need is trigonometry, geometry, the definition of an isotropic radiator, and conservation of energy to derive 1/r^2. I leave it as an exercise for the student. . On a problem like this I'd go to a white board and sketch a picture to start. Or you can just google inverse square law.

Reread my post. I won't repeat it.

We understand 1/r^2. We also understand it's only half the issue.

 

[Loren Pechtel]

You don't get to deny that by running a simulation in which you ignore floating point imprecision.

So many engineering types don't get it about imprecision.

10 X = 3000000
20 X = X + 1
30 If X + 1 > X GOTO 20
40 Print "X = X + 1"

The entire department believed this would never terminate.

(The seed value is simply to make the termination come faster. This was on an ancient, interpreted system that executed at roughly 1ms per line.)

 

[steve_bank]

That is the beauty of setting up a simulation, easy to vary parameters. If I had the energy and better eyesight I'd do it. It is simple, I'd be surprised if it has not been done.

There is another possibility. In an infinite universe what we observe may be a local phenomena.

I see nothing in your answer addressing the roundoff problem. Sometimes brute force doesn't produce useful answers.

In this case we have energy dropping off at distance^2 but the volume, and thus the number of stars, going up at distance^2. (These are two sides of the same coin, not a coincidence.) Thus the energy per shell remains constant and a constant * infinity = infinity. The only way to avoid frying is if the energy per shell is zero.

Don't know what you mean by round off and precision here.

The total energy output of stars and other objects are measured using orbital parallax to estimate distance, triangulation which has a limited range. This crates astronomical candles that can be used to estimate distance to objects beyond the range of parallax. The are a number of errors and uncertainties involved in estimated energy and distance to distant objects. There are instrument uncertainties and uncertainties of the Earth's orbit for parallax for example.

We can accurately measure the energy output of the sun. It falls into a class of stars at a point on the main sequence. A distant star similar to the type and stage of our star can have distance approximated by received energy.

LOT does not necessarily apply in an infinite universe. Infinite means unmeasureable.

A simulation or experiment always trumps philosophizing and conjecture.

Put you ideas into a set of equations.

 

[steve_bank]

You don't get to deny that by running a simulation in which you ignore floating point imprecision.

So many engineering types don't get it about imprecision.

10 X = 3000000
20 X = X + 1
30 If X + 1 > X GOTO 20
40 Print "X = X + 1"

The entire department believed this would never terminate.

(The seed value is simply to make the termination come faster. This was on an ancient, interpreted system that executed at roughly 1ms per line.)

Obviously we can simulate to infinity. What I said was you can add stars out beyond our visual range in varying distributions until you start to see the effect or you do not. You could set up a sr erase and take a limit to infinity and see what the radiation at Earth would be.

It is a mathematically testable hypothesis.

 

[steve_bank]

For most practical purposes. For the purposes of trying to understand whether there would be any black spots left on the night sky in an infinite static universe, it remains a two-dimensional source.

For the purpose of deriving whether we could live in such a universe without being incinerated, it doesn't make a difference.



Can you derive what inverse square law implies, assuming a static and infinite universe, for the sum of the light reaching us from each of several "shells", say of 0-50 lightyears, 50-ly, 10-150? For the sum of the light reaching us from shells 0-10 billion lightyears, 10-20 billion ly, 20-30 billion ly? For the sum of the light reaching us from shells 0-100 quadrillion ly, 100-200 quadrillion ly?

I already explained it. All you need is trigonometry, geometry, the definition of an isotropic radiator, and conservation of energy to derive 1/r^2. I leave it as an exercise for the student. . On a problem like this I'd go to a white board and sketch a picture to start. Or you can just google inverse square law.

Reread my post. I won't repeat it.

You did not explain anything that was under dispute. 1/r^2 is not under dispute. What appears to be under dispute is that r^2 * 1/r^2 = 1, and you're the one disputing it.

If you imagine space as sliced into multiple concentric shells of equal thickness, a bit like an onion, with earth at the center, then the volume of those shells is (in the limit of a shell with 0 thickness, but it gets close very quickly) proportional to the surface of a sphere - thus to r^2. So is the number of stars and the sum of their radiation in absolute terms, at least roughly on grand scales. Since the apparent magnitude, or the amount of light energy reaching earth, is proportional to 1/r^2, this means that the amount of light reaching us from each shell will be roughly the same because r^2 * 1/r^2 = r^2/r^2 = 1.

The only thing that can help you to avoid a linear growth in proportion to distance of the total light reaching is the fact that some nearer stars will be occluding more distant stars (that's unless you declare stars as point sources, in which case this won't help either). And even so, the percentage of sky predicted to be black approaches 0 rather quickly in an asymptotic manner - by the distance for which the linear model with point stars derives 100% coverage, it's already 1 - 1/e for the more realistic model with stars as 2-dimensional light sources. More then enough to evaporate every rock in the universe.

You don't get to deny that by running a simulation in which you ignore floating point imprecision.

It will not be the same. 1/r^2 applies to a small finite source, a star. Energy density goes down with r. The frater away the less energy. In the limit to infinity the energy density from a star goes to zero. Using shells filled witrh constant average nergy is not the same. Look at observable galaxies. Lots of space between stars and galaxies. Astronomy says that unuiverse tends to look the same in all directions, but that does not get you anywhere. Shells have a finite thickness ans as sux ch stars at each boundary have different results at Earth. The universe in all dorections is not homogenious shells.

If I were to try your approach I would set it up use spherical coordinates with Earth at the center. You would end up with dE/dr at Earth. Change in energy versus radios.

Put it into a set of equations that can be evaluated.

 

[Loren Pechtel]

That is the beauty of setting up a simulation, easy to vary parameters. If I had the energy and better eyesight I'd do it. It is simple, I'd be surprised if it has not been done.

There is another possibility. In an infinite universe what we observe may be a local phenomena.

I see nothing in your answer addressing the roundoff problem. Sometimes brute force doesn't produce useful answers.

In this case we have energy dropping off at distance^2 but the volume, and thus the number of stars, going up at distance^2. (These are two sides of the same coin, not a coincidence.) Thus the energy per shell remains constant and a constant * infinity = infinity. The only way to avoid frying is if the energy per shell is zero.

Don't know what you mean by round off and precision here.

The total energy output of stars and other objects are measured using orbital parallax to estimate distance, triangulation which has a limited range. This crates astronomical candles that can be used to estimate distance to objects beyond the range of parallax. The are a number of errors and uncertainties involved in estimated energy and distance to distant objects. There are instrument uncertainties and uncertainties of the Earth's orbit for parallax for example.

We can accurately measure the energy output of the sun. It falls into a class of stars at a point on the main sequence. A distant star similar to the type and stage of our star can have distance approximated by received energy.

LOT does not necessarily apply in an infinite universe. Infinite means unmeasureable.

A simulation or experiment always trumps philosophizing and conjecture.

Put you ideas into a set of equations.

The logic has been explained multiple times already. You're looking at the energy per star and discarding small values, never mind that they're multiplied by big values.

 

[Loren Pechtel]

You did not explain anything that was under dispute. 1/r^2 is not under dispute. What appears to be under dispute is that r^2 * 1/r^2 = 1, and you're the one disputing it.

If you imagine space as sliced into multiple concentric shells of equal thickness, a bit like an onion, with earth at the center, then the volume of those shells is (in the limit of a shell with 0 thickness, but it gets close very quickly) proportional to the surface of a sphere - thus to r^2. So is the number of stars and the sum of their radiation in absolute terms, at least roughly on grand scales. Since the apparent magnitude, or the amount of light energy reaching earth, is proportional to 1/r^2, this means that the amount of light reaching us from each shell will be roughly the same because r^2 * 1/r^2 = r^2/r^2 = 1.

The only thing that can help you to avoid a linear growth in proportion to distance of the total light reaching is the fact that some nearer stars will be occluding more distant stars (that's unless you declare stars as point sources, in which case this won't help either). And even so, the percentage of sky predicted to be black approaches 0 rather quickly in an asymptotic manner - by the distance for which the linear model with point stars derives 100% coverage, it's already 1 - 1/e for the more realistic model with stars as 2-dimensional light sources. More then enough to evaporate every rock in the universe.

You don't get to deny that by running a simulation in which you ignore floating point imprecision.

It will not be the same. 1/r^2 applies to a small finite source, a star. Energy density goes down with r. The frater away the less energy. In the limit to infinity the energy density from a star goes to zero. Using shells filled witrh constant average nergy is not the same. Look at observable galaxies. Lots of space between stars and galaxies. Astronomy says that unuiverse tends to look the same in all directions, but that does not get you anywhere. Shells have a finite thickness ans as sux ch stars at each boundary have different results at Earth. The universe in all dorections is not homogenious shells.

If I were to try your approach I would set it up use spherical coordinates with Earth at the center. You would end up with dE/dr at Earth. Change in energy versus radios.

Put it into a set of equations that can be evaluated.

The same argument applies to galaxies--and at a large scale evenly distributed.

 

[steve_bank]

OK you win Lauren. An infinite universe is in no way shape or form is possible. And in other news Trump made another tweet.

 

[Bomb#20]

Very broadly, yes, but actually any non-zero average density leads to the paradox.

and more generally whether all lines of sight would be occupied by stars,

All lines of sights being occupied by stars is a consequence, not a premise.

You must be assuming a broadly random distribution of stars. Maybe not so. Suppose all stars, the whole infinity of them is lined up along one straight line. I have to guess that we would have mostly infrared radiation all coming from two opposite directions. Black sky and deep-fry cooking? Or any situation in between. So, a paradox but not that of the bright sky at night.

or whether all those stars would emit at least some energy, etc. The universe could be infinite either without an infinity of stars, or with an infinity of stars spread around in a way that wouldn't light up all the sky at night

How would that work?

You may have an infinity of stars but only a finite number of them emitting energy, although in this case you may not want to call all of them "stars". And I don't know of it's at all possible for any body to emit no energy at all, except black holes and even them in a way they do (Dawkin's something).

So, broadly, for all those, I concede the point.

You're throwing in the towel too early -- there's still a way to make this work. To have an infinity of stars, all emitting energy in a static universe, without lighting up all the sky, you need a fractal distribution. As you noted, Jokodo's assuming a broadly random distribution of stars. But we already know stars aren't distributed randomly. They're in galaxies. Galaxies come in clusters. Clusters come in superclusters. Consequently, as you get further from here along a typical line the probability of hitting a star goes down and down. Jokodo's calculation assumes this process bottoms out with a non-zero asymptote -- that when you get far enough away from here the recursive clustering pattern ends, there's a largest scale for superclusters, and beyond that distance the distribution of superclusters becomes random. How we're supposed to either deduce or obtain observational evidence for such an assumption in a by-hypothesis infinite universe is, well, puzzling.

Indeed, but then no-one is disputing that the universe can be infinite in space. What the paradox demonstrates is that it cannot be static and infinite in space.

If by static you mean "no beginning" then I agree, at least for that point. If by static you mean currently static, with or without a beginning, then I disagree. The point is whether there's a beginning or not.

So, I'll assume your "static" implies "no beginning" and I'll agree with that.
...

Also, if you have an infinite universe that keep expanding, the light coming from distant stars won't ever reach us. Same result, our sky at night.

Sure, but in an expanding universe, going back in time eventually brings you to a point where it was, for all intents and purposes, infinitely dense. This is true whether it's expanding logarithmically, linearly, or exponentially.

I can conceive of a universe that's static, without a beginning, expanding at a constant rate and in a uniforme way throughout, with an infinity of stars, that would look locally as it does to us.

Going back in time doesn't make any difference with this one.

This is what the old "Steady State" theory was supposed to accomplish -- an expanding universe that doesn't retrodict an infinitely dense point and doesn't lead to Olber's Paradox because light from distant galaxies is redshifted to lower energy than 1/r². It does require new matter to be generated, which violates conservation laws; but who are we to make a stink about that detail when we're prepared to accept "Dark Energy"? To my mind the more serious sticking point is "would look locally as it does to us". If the overall state of the universe doesn't evolve while new matter forms at a steady pace, then why do all the galaxies look like they're the same age (adjusted for speed-of-light delay)? Shouldn't there be a few up-close quasars? Perhaps some galaxies where all the stars have burned out except the red dwarfs?

 

[steve_bank]

Correct me if I am wrong, planets are falling into the sun. Work is done by the sun's gravity on the planetary masses.

Same I would assume for a galaxy If the BB is correct, all the energy in the initial conditions must equal total energy in the universe. Unless conservation does not hold. If the universe is expanding in some fusion then the energetic density per unit volume of space must decrees, analogous to the inverse square law.

For the BB to be true for an infinitly expanding universe the expansion will run out of gas, the potential differences will be too small to do much.

In an infinite universe with infinite energy that is not a problem.

For a finite bounded universe there is no way to loose energy. It could end up as a perpetual motion machine in effect.

The BB was constructed to match what we see today from particles to galaxies. It does not explain where the initial conditions came from, a hot soup. A one time event forever expanding makes no sense without explaining initial conditions.

All conjecture from BB has no solid foundation. Conservation of energy must always hold, unless you accept something from nothing. Energy in the universe must be constant or infinite, unquantifiable.