How the Universe Ends

[lpetrich]

I suspect some idiot will discover something entirely new that will throw the universe off course. ...

That is certainly possible, and the authors of that paper do indeed speculate about variations in the Universe's behavior like the "Big Rip". But that seemed too speculative for me to want to discuss it, while all the rest of the Five Ages stuff is based on well-established physics.

BTW, in the Dark Era, I ought to include neutrinos. So it's photons, electrons and positrons, and ordinary neutrinos and antineutrinos. As the Universe expands, neutrinos will become slower and slower, and they will become essentially stationary, as electrons and positrons will also be doing. They will decay to their lowest mass state, something very slow by ordinary standards, but something that will nevertheless happen because of all the time available.

 

[steve_bank]

Conservation of what? The whole idea of some balanced beginning is shot with anti-strawberry.

Then you get anti-LaPhroaig, anti-10 years. And you just went wrong.


Since symbols can point to things, and influence the outcome of events, it goes to say that to the universe, nature itself, there are certain symbols (natural ones) that naturally influence the outcome of events, even though they are not the whole thing they represent.

Maybe spacetime is the symbol of the whole to the many, and we do not see it as the symbol, but as a unified whole, because we observe it from outside the many that react as if it were the whole (it's the holiest whole according to some linguistic interpretations, but not the whole).


Naturally occurring symbols (human language being many, a blue sky another) break symmetry, even when they only exist as tiny little pieces symbolic of some greater whole.



So where, pray tell, does this idea of perfect symmetric beginnings to anything come from? From symbols, of course.

How does the one verse end? With a symbol.

Conservation of energy. If all the energy of the universe was in the initial conditions, then all the energy post BB must stay constant. Unless something ges to or comes from nothing, or there is something else we can not detect.

 

[Jokodo]

No, Energy per unit Volume is Pascals. Watts is Energy flux per unit of time, and the relevant measures for us here is Watts per unit area.


Energy flux you mean. D*T: energy density within the shell times the thickness of the. I answered that already.

D*T? Your choice of variables is confusing and inconsistent. I'd have to get out my calck book and review shells and areas. There should be a dr in there somewhere for change in radius. dE/dr energy in the shell requires an integration.

There needn't, because it cancels out. The decrease of energy from an individual star given distance takes place at the exact same rate as the increase in number of stars, given the same density.

Pascals are N/m^2.

They are. And they're also J/m³. Or in base units: 1 kilogram per meter per second squared. Those are equivalent formulations.

You have to be careful with terms like flux in photometry and radiometry.

An individual star radiates 2pi sr total power. The star and the earth form a solid angle. When you lump energy within a shell that may may be correct. Flux is what passes through an area or a volume. In spherical shells you are changing the problem, shells and discrete stars do not necessarily match.

Which does not prevent us from calculating the average flux originating from a given shell, given an average stellar density. And finding that any non-zero average density leads to Olber's paradox points to the conclusion that any non-zero average density is incompatible with a static and infinite universe.

Is this what you are looking at?

https://en.wikipedia.org/wiki/Radiant_flux

https://en.wikipedia.org/wiki/Irradiance more like it. We are, after all, trying to determine how fast we should be going up in flames.

- - - Updated - - -

We don't observe expansion, we interpret limited observation as expansion.

Sure. Feel free to come up with a better explanation

 

[Jokodo]

jokodo

What you seem to be doing is turning into a statics problem I seem to remember a textbook electrostatics problem with shells and surface charges where r cancels out.

It naturally has to cancel out wherever you multiply an x that's proportional to the surface of a sphere with radius r with a y that's inversely proportional to the surface of a sphere with radius r. This is one of those occasions.

Having concentric shells of uniform static energy density does not seem to equate to the problem. The energy density of the shell does not radiate.

I should have said power density. Better now?

Look, it's really much simpler than you make it out to be: Just think of radiation expanding from a point source. Photons moving away at c. The photons that were emitted at a given point in time t are forming a sphere of radius (now-t) * c. This is why 1/r² holds in the first place.

 

[Kharakov]

Conservation of what? The whole idea of some balanced beginning is shot with anti-strawberry.

Then you get anti-LaPhroaig, anti-10 years. And you just went wrong.


Since symbols can point to things, and influence the outcome of events, it goes to say that to the universe, nature itself, there are certain symbols (natural ones) that naturally influence the outcome of events, even though they are not the whole thing they represent.

Maybe spacetime is the symbol of the whole to the many, and we do not see it as the symbol, but as a unified whole, because we observe it from outside the many that react as if it were the whole (it's the holiest whole according to some linguistic interpretations, but not the whole).


Naturally occurring symbols (human language being many, a blue sky another) break symmetry, even when they only exist as tiny little pieces symbolic of some greater whole.



So where, pray tell, does this idea of perfect symmetric beginnings to anything come from? From symbols, of course.

How does the one verse end? With a symbol.

Conservation of energy. If all the energy of the universe was in the initial conditions, then all the energy post BB must stay constant. Unless something ges to or comes from nothing, or there is something else we can not detect.

I know conservation of energy. The point is that it doesn't explain asymmetries that exist.

 

[bilby]

Conservation of what? The whole idea of some balanced beginning is shot with anti-strawberry.

Then you get anti-LaPhroaig, anti-10 years. And you just went wrong.


Since symbols can point to things, and influence the outcome of events, it goes to say that to the universe, nature itself, there are certain symbols (natural ones) that naturally influence the outcome of events, even though they are not the whole thing they represent.

Maybe spacetime is the symbol of the whole to the many, and we do not see it as the symbol, but as a unified whole, because we observe it from outside the many that react as if it were the whole (it's the holiest whole according to some linguistic interpretations, but not the whole).


Naturally occurring symbols (human language being many, a blue sky another) break symmetry, even when they only exist as tiny little pieces symbolic of some greater whole.



So where, pray tell, does this idea of perfect symmetric beginnings to anything come from? From symbols, of course.

How does the one verse end? With a symbol.

You mean with a cymbal, right?

I don't think it's quite as cymbal as all that.

Indeed, i suspect the entire argument is an over cymblification.

 

[steve_bank]

jokodo

What you seem to be doing is turning into a statics problem I seem to remember a textbook electrostatics problem with shells and surface charges where r cancels out.

It naturally has to cancel out wherever you multiply an x that's proportional to the surface of a sphere with radius r with a y that's inversely proportional to the surface of a sphere with radius r. This is one of those occasions.

Having concentric shells of uniform static energy density does not seem to equate to the problem. The energy density of the shell does not radiate.

I should have said power density. Better now?

Look, it's really much simpler than you make it out to be: Just think of radiation expanding from a point source. Photons moving away at c. The photons that were emitted at a given point in time t are forming a sphere of radius (now-t) * c. This is why 1/r² holds in the first place.

jokodo, buddy...This is an informal discussion. It is not a win or loose debate.

If I were to look at it seriously I'd first bound the problem.

First what is the average irradiance on the surface during the day.

Second how many stars at say 10 /100/1000... ly equal to the sun would it take to be equivalent.

That, for me, bounds the problem into a manageable picture that is not open ended. Then I'd d find the total radiated power of typical galaxie in the visible spectrum. When working on a problem in a new area I need some kind of refernce point.

Then I'd work up a simulation that can vary distributions/placements of galaxies.

That is how I approach problems, one step at a time, the gestalt approach never works for me. I use incremental model building.

I am not interested in debating text book electromagnetics.

 

[Kharakov]

Conservation of what? The whole idea of some balanced beginning is shot with anti-strawberry.

Then you get anti-LaPhroaig, anti-10 years. And you just went wrong.


Since symbols can point to things, and influence the outcome of events, it goes to say that to the universe, nature itself, there are certain symbols (natural ones) that naturally influence the outcome of events, even though they are not the whole thing they represent.

Maybe spacetime is the symbol of the whole to the many, and we do not see it as the symbol, but as a unified whole, because we observe it from outside the many that react as if it were the whole (it's the holiest whole according to some linguistic interpretations, but not the whole).


Naturally occurring symbols (human language being many, a blue sky another) break symmetry, even when they only exist as tiny little pieces symbolic of some greater whole.



So where, pray tell, does this idea of perfect symmetric beginnings to anything come from? From symbols, of course.

How does the one verse end? With a symbol.

You mean with a cymbal, right?

I was thinking about Underseer's avatar.... and now I'm thinking about early Slayer.

 

[steve_bank]

The BB began with the clash of the Great Cymbal by the great Gong Spirit.

 

[Jokodo]

It naturally has to cancel out wherever you multiply an x that's proportional to the surface of a sphere with radius r with a y that's inversely proportional to the surface of a sphere with radius r. This is one of those occasions.



I should have said power density. Better now?

Look, it's really much simpler than you make it out to be: Just think of radiation expanding from a point source. Photons moving away at c. The photons that were emitted at a given point in time t are forming a sphere of radius (now-t) * c. This is why 1/r² holds in the first place.

jokodo, buddy...This is an informal discussion. It is not a win or loose debate.

If I were to look at it seriously I'd first bound the problem.

First what is the average irradiance on the surface during the day.

Second how many stars at say 10 /100/1000... ly equal to the sun would it take to be equivalent.

You will find that the number of stars it would take rises in direct proportion to the number of stars you expect to find, under the simplification of a large-scale uniform distribution. This directly leads to the conclusion that any non-zero average stellar density leads to a paradox under the assumption of a spatially and temporarily unbounded, static universe.

 

[steve_bank]

It naturally has to cancel out wherever you multiply an x that's proportional to the surface of a sphere with radius r with a y that's inversely proportional to the surface of a sphere with radius r. This is one of those occasions.



I should have said power density. Better now?

Look, it's really much simpler than you make it out to be: Just think of radiation expanding from a point source. Photons moving away at c. The photons that were emitted at a given point in time t are forming a sphere of radius (now-t) * c. This is why 1/r² holds in the first place.

jokodo, buddy...This is an informal discussion. It is not a win or loose debate.

If I were to look at it seriously I'd first bound the problem.

First what is the average irradiance on the surface during the day.

Second how many stars at say 10 /100/1000... ly equal to the sun would it take to be equivalent.

You will find that the number of stars it would take rises in direct proportion to the number of stars you expect to find, under the simplification of a large-scale uniform distribution. This directly leads to the conclusion that any non-zero average stellar density leads to a paradox under the assumption of a spatially and temporarily unbounded, static universe.

1. My approach and reasoning is...
2. My model and equations are...
3. Results of calculations are...
4. Conclusion based on 3 is...



Take a look at ibetrich's posts on math. Most of his theoretical stiuf is beyond me but his clarity stands out..

 

[Jokodo]

You will find that the number of stars it would take rises in direct proportion to the number of stars you expect to find, under the simplification of a large-scale uniform distribution. This directly leads to the conclusion that any non-zero average stellar density leads to a paradox under the assumption of a spatially and temporarily unbounded, static universe.

1. My approach and reasoning is...
2. My model and equations are...
3. Results of calculations are...
4. Conclusion based on 3 is...

You ignored it when I did that before...

 

[steve_bank]

You will find that the number of stars it would take rises in direct proportion to the number of stars you expect to find, under the simplification of a large-scale uniform distribution. This directly leads to the conclusion that any non-zero average stellar density leads to a paradox under the assumption of a spatially and temporarily unbounded, static universe.

1. My approach and reasoning is...
2. My model and equations are...
3. Results of calculations are...
4. Conclusion based on 3 is...

You ignored it when I did that before...

Seriously. This is not a classroom and I am not a teacher. That being said your posts are fuzzy. I am sure it may be clear to you in your head but it does not come through to me . I have not seen you yet make a coherent persuasive argument.\\The math you posted here was problematic. You posted a mix of top level variables and the base dimensions, in capitals for some reason. Threw me for a bit. The use of Pascals to measure EM energy in space claiming it applied to a volume..

What I see is someone with a science background without a lot of experience problem solving in unfamiliar ground. We all do the same thing, a little research, try a solution. A little more research and a better solution. The 'scientific method' Even seemingly simple problems can take a lot of work to go all the way to runn8ing calculations and validating the model.

Nobody usually jumps to a solution without prior experience. Most EEs use incremental model building at some level of complexity. Start off small and validate as you go.

Take it for what you will. We all go through a practical learning curve in new situations. It is not a shortcoming, it is us human beings.

 

[Jokodo]

You ignored it when I did that before...

Seriously. This is not a classroom and I am not a teacher. That being said your posts are fuzzy. I am sure it may be clear to you in your head but it does not come through to me . I have not seen you yet make a coherent persuasive argument.\\The math you posted here was problematic. You posted a mix of top level variables and the base dimensions, in capitals for some reason. Threw me for a bit. The use of Pascals to measure EM energy in space claiming it applied to a volume..

What I see is someone with a science background without a lot of experience problem solving in unfamiliar ground. We all do the same thing, a little research, try a solution. A little more research and a better solution. The 'scientific method' Even seemingly simple problems can take a lot of work to go all the way to runn8ing calculations and validating the model.

Nobody usually jumps to a solution without prior experience. Most EEs use incremental model building at some level of complexity. Start off small and validate as you go.

Take it for what you will. We all go through a practical learning curve in new situations. It is not a shortcoming, it is us human beings.

Indeed it's not a classroom, and I'm not your teacher either.

OK, let's try it stepwise. If the universe is a) infinite in space, b) does not have a (recent) beginning in time, c) does not expand, and d) the visible part of it is not an extreme outlier, then we can derive the following:

The 'local', as in averaged over galaxy clusters and void over several hundred megaparsec from home, luminosity density is about 190 Million solar luminosities per megaparsec cubed (here or here). For some reason, astronomers are behind the rest of the world when it comes to using SI units, and while this can easily be converted to Watts per cubic meter, I'll stick with their units for the time being.

Let's for the moment ignore our own galaxy and the Local Group and pretend we're isolated by a void of 100 Mpc from the nearest galaxy, and from their assume that average density quoted above, and calculate the power output and irradiance at earth per shell, starting at 100 Mpc from home and with a thickness of 1 Mpc per shell. In effect, we're thus pretending that our closest neighbors are at 100 Mpc from home; this can of course only lead to an underestimation of the irradiance.

The total volume of the first such shell is 4/3 * pi * (101Mpc)³ - 4/3 * pi * (100Mpc)³, i. e. the volume of the sphere circumscribed by its outer limit less the volume of the sphere circumscribed by its inner limit, as given by the volume of a sphere as 4/3 * pi * r³. This comes out as 126925 Mpc^3. This volume can equivalently be derived by using the formula for the surface of a sphere with r=the (logarithmic) average of its distance, times its thickness: The volume increases in proportion to the square of its (average) distance.

The total power output of that volume of space is given by multiplying it with the luminosity power density of 190 million suns/cubic Megaparsec: we get 2.4 * 10^13 solar luminosities or 9.28×10^39 W total output from that one shell. With a uniform distribution of galaxies, the power output increases with volume, and since volume increases with the square of average distance for shells of equal thickness, (absolute) power output per shell increases with the square of the distance.

We can derive a lower bound by the irradiance of the stars and galaxy within that shell at Earth's surface by pretending that they're all concentrated along its outer limit, i.e. 101 Mpc away, with your 1/(r²). The result is just under 1nW per square meter. Since the (absolute) luminosity per shell increases with r² and the relative luminosity as a function of absolute luminosity decreases with r², we expect each shell to contribute a roughly equal amount of irradiation. But let's do an explicit check for this (next paragraph).

Time for a quick sanity check: let's replace all mentions of 100Mpc or 101Mpc with 1000/1001Mpc to verify that the sum of the apparent luminosity / energy flux at earth's surface per shell indeed is constant: The result is actually slightly higher than before. That's expected because we're calculating a lower bound by pretending that the galaxies are concentrated along the outer rim of the shell, instead of being uniformly distributed. The error this introduces grows smaller with distance.

So, how much is one nanowatt per square meter? Not a whole lot.  Sunlight is up to 1050 W/m² on a cloudless noon in the tropics when the sun's at zenith. So we'd need over a trillion such shells to equal the irradiance of a tropical noon, and a couple orders of magnitude more to get a sky almost every corner of which that's glaring as bright as the average star. At 1Mpc per shell, that's just over a trillion megaparsecs or 3.553×10^18 ly - or around 38 million times the diameter of the visible universe. But you know what's the cool thing about an infinite universe? It barely starts at 3.553×10^18 ly radius.

Please tell me where you disagree, if you do!

 

[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.



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.

I don't assume any such thing. I only assume that the universe-wide density of stars is (a) non-zero

Huh? How do you figure that's a different assumption from assuming the recursive clustering pattern ends? What do you think the universe-wide density of stars is if the distribution pattern is a fractal with clustering at all scales?

I guess you're right. One problem, however, is that with such a structure, we'd expect to see much larger anisotropies than we do (except if we're close to the centre of our local billions-of-lightyear-scale super-super-cluster.

and (b) higher than the density of black holes, measured in terms of, loosely, volume, not mass.

I'm not clear on how black holes would help. If the universe were static, wouldn't the black holes have to be collectively emitting as much Hawking radiation as the light falling into them?

Black holes help if Hawking radiation doesn't exist. As far as I know, it is still a (well-reasoned) theoretical construct that seems to follow from what we know about the world, but without direct empirical confirmation. If we're willing to throw everything we think we know about the world out the window, why keep Hawking radiation?

It doesn't matter if the visible universe is an unusually dense region, a super-super-cluster if you will, separated by a sea of nothingness stretching a good sextillion light years wide from the such island, as long as there's infinitely many such islands, the same problems arise.

Show your work. I.e., show that you aren't implicitly assuming that the cluster after the cluster a sextillion light years away from us is only another sextillion light years beyond that. If the spacing goes sextillion, septillion, octillion..., how do you figure the same problems arise?

I guess you're right there, but, as above, we'd expect a background radiation far less uniform than what's observed unless we're in some kind of special place, right?

 

[steve_bank]

Don't know how the universe ends, this thread seems to be infinitely expanding.

 

[Kharakov]

Don't know how the universe ends, this thread seems to be infinitely expanding.

Q
Queue untermensche.

 

[Bomb#20]

I don't assume any such thing. I only assume that the universe-wide density of stars is (a) non-zero

Huh? How do you figure that's a different assumption from assuming the recursive clustering pattern ends? What do you think the universe-wide density of stars is if the distribution pattern is a fractal with clustering at all scales?

I guess you're right. One problem, however, is that with such a structure, we'd expect to see much larger anisotropies than we do (except if we're close to the centre of our local billions-of-lightyear-scale super-super-cluster.

Hey, I'm not proposing to overturn big-bang cosmology; I'm just rescuing Speakpigeon's "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 or with an infinity of stars but only a finite number of them emitting some energy." argument from your "But that's the whole point: to show that an infinitely old and infinitely vast universe leads to contradictions." critique. There are plenty of good observational reasons going back to Hubble for rejecting the old static universe model in favor of a big bang; I just don't think Olber's Paradox is one of them.

It doesn't matter if the visible universe is an unusually dense region, a super-super-cluster if you will, separated by a sea of nothingness stretching a good sextillion light years wide from the such island, as long as there's infinitely many such islands, the same problems arise.

Show your work. I.e., show that you aren't implicitly assuming that the cluster after the cluster a sextillion light years away from us is only another sextillion light years beyond that. If the spacing goes sextillion, septillion, octillion..., how do you figure the same problems arise?

I guess you're right there, but, as above, we'd expect a background radiation far less uniform than what's observed unless we're in some kind of special place, right?

Yes, probably so. IIRC the background radiation was the smoking gun that convinced most astronomers to get on board the big bang theory. But playing devil's advocate for a moment, maybe there's a way out. We wouldn't expect a static infinitely old universe to be gravitationally stable anyway, right? Einstein had to invent a cosmological constant to allow for it, but even that didn't really help, since any slight local variation from uniform density would throw off the balance and grow exponentially, so all the stars in above-average-density regions would rush in on one another. Trying to allow for a static universe by foreshadowing dark energy is like trying to stand a pencil on its point.

And yet here we are, in a fourteen billion year old universe, and the stars around us are keeping their distance pretty constant (statistically) without any such contrivances. Why haven't they collapsed on us even though the local stellar density is way more than enough to make them do it? Simple: the Milky Way's rotation. Centrifugal force is keeping them from landing on us -- and it's self-adjusting so it's way more effective at delivering stability than a cosmological constant ever could be.

So the obvious hypothesis to explain apparent uniformity in a (counterfactual, no Hubble's law) infinite static universe would be that the entire visible portion of the universe, with all the superclusters we can see, is just a segment of a hundred-billion-parsec super-galaxy, rotating around a core too far away for our best telescopes to spot. The background radiation would be just the collective emissions of stars too far away in the super-galaxy to see, uniform much like our blue sky because it's been scattered by intergalactic dust.

 

[Cheerful Charlie]

Sighhhhhh. Again. The Universe is expanding. Really expanding, that is space is increasing at galactic scales. Because of that for an observer, there is a limit beyond which anything observable, like photons would have to travel faster than light to reach said observer. So nothing beyond a certain distance can ever be observed. We can have infinite stars but we can never see but a paltry sample of them. Not even in principle.

 

[steve_bank]

Sighhhhhh. Again. The Universe is expanding. Really expanding, that is space is increasing at galactic scales. Because of that for an observer, there is a limit beyond which anything observable, like photons would have to travel faster than light to reach said observer. So nothing beyond a certain distance can ever be observed. We can have infinite stars but we can never see but a paltry sample of them. Not even in principle.

Is space expanding or is C changing? There is no way to know.