Entropy of Static and Perpetually Old Universe

[quantumtopology]

I think you keep getting hung up on the idea of infinity.

Maybe not any more hung up than you seem to keep getting on the idea of homogeneity or expansion :hihi:

Probably not a good idea to get hung up on any idea, not even on this one ;)

 

 

If space is static and our area of space has always had low entropy (for a perpetually long amount of time) then it will have always been importing useful energy from one area of bordering space and always exporting entropy to another area of bordering space.

 

That is the antithesis of homogeneity, and it makes no difference if the universe is spatially infinite.

 

 

Well not exactly the antithesis, but I just said that I don't need the assumption of perfect homogeneity, consider for instance a fractal structure.

I guess now you don't have any "entropic" objection with a non-expanding universe.

 

By the way, it is with a sense of irony that you have now objected to my objection for the following two reasons:

 

• You cannot consider the past to be infinitely long.

• Space is infinitely large.

 

I don't have a clue where this comment comes from. Probably , what we've got here is failure to communicate. :doh:

[Turtle]

Yes you are right, just notice that the calculated probabilities of the quoted events are many orders of magnitude below the unlikeliness usually considered in Black swan theory, which is more related to psychologically neglected, apparently low probability events ("outside the realm of regular expectations").

 

Regards

Qtop

 

mmmm...well, i will reserve definitive comment until i read the book; i am probably going to hunt it down & buy it this week. :hihi:

 

nonetheless, i think the idea of "the most unlikely thing you can imagine" is at the crux of black swans and so your "orders of magnitude below" is redundant if not trivial. moreover, since it is only us humans pondering all this, what else could it be related to other than psychological phenonema?

 

well, off to the bookseller's at a turtle's pace. (i'd go just now, but just now i have deen brinking. ;)). . . . . :doh:

[modest]

I think you keep getting hung up on the idea of infinity.

Maybe not any more hung up than you seem to keep getting on the idea of homogeneity or expansion :)

Probably not a good idea to get hung up on any idea, not even on this one

 

True enough, but I think you were the one asserting the 'perfect cosmological principle'. You should accuse me of being hung up on entropy. In this thread, that would definitely be true

 

but I just said that I don't need the assumption of perfect homogeneity, consider for instance a fractal structure.

I guess now you don't have any "entropic" objection with a non-expanding universe.

 

That is correct. By abandoning homogeneity you can assert perpetually low entropy in the local (observable) universe.

 

As an analogy, the surface of the earth has a higher temperature than space (mostly because it is heated by the sun). Earth's biosphere sits between the surface of the earth and space. Because we sit in a temperature gradient, earth's biosphere can keep constant (or even lower) entropy. Useful work can be done.

 

If the earth stayed perpetually warmer than space then the biosphere could persist indefinitely. Likewise, if the local (observable) universe sat on a temperature gradient then it could persist with a relatively low entropy indefinitely. One direction of the cosmos would be warmer than the other direction. If the two directions were infinitely large then the state of low entropy could persist indefinitely.

 

~modest

[quantumtopology]

True enough, but I think you were the one asserting the 'perfect cosmological principle'. You should accuse me of being hung up on entropy. In this thread, that would definitely be true :)

 

That is correct. By abandoning homogeneity you can assert perpetually low entropy in the local (observable) universe.

 

Fair enough. I should have been more rigorous when I set up the premise of the perfect cosmological principle but my understanding of homogeneity was more like a tendency or a limit at infinity (current last observations are not able to reach the scale of homogeneity not even in the 200 Mpcs volume) .And like I said, this is a "work in progress" hypothesis and your help is welcome to shape it.

 

Regards

Qtop

[Qfwfq]

i'll leave off where i did there with no further comment until or unless i actually read taleb's book. thnx for taking note. :)

I did read it some time ago, because it had been given to me (so it wasn't a waste of my money). No doubt the guy has a very big sense of humour (so it wasn't a total waste of my time). He hashes together a lot of obvious things about human obtusity and well-known scientific culture. Sometimes he messes them, like insisting that it's the Lorentz butterfly's wings flapping that actually cause the hurricane. However, he says a lot of true things in a very humourous manner and suggests an amusing logical trick about induction and the white swan example. In the end, I didn't find all that much of great interest, despite the guy's credentials. And wait till he finally gives the long promised advice, toward the end of the book.

 

The idea that the whole visible universe is a black swain is kind of thought provoking too.

In order to see it this way, there would have to have been some situation of instability. It wouldn't make sense to say "that nobody noticed" or "that everybody neglected" or the likes. I don't think the Black Swan catch phrase is much use in pondering the nature of the Big Bang. They might look similar at a glance, but I'd say the BB isn't quite the same thing as BS...

[Turtle]

i'll leave off where i did there with no further comment until or unless i actually read taleb's book. thnx for taking note.

I did read it some time ago, because it had been given to me (so it wasn't a waste of my money). No doubt the guy has a very big sense of humour (so it wasn't a total waste of my time). He hashes together a lot of obvious things about human obtusity and well-known scientific culture. Sometimes he messes them, like insisting that it's the Lorentz butterfly's wings flapping that actually cause the hurricane. However, he says a lot of true things in a very humourous manner and suggests an amusing logical trick about induction and the white swan example. In the end, I didn't find all that much of great interest, despite the guy's credentials. And wait till he finally gives the long promised advice, toward the end of the book.

 

nice review. :) i think i saw something on the advice. authors; can't live with 'em, can't feed 'em to barrracuda.

 

The idea that the whole visible universe is a black swain is kind of thought provoking too.

In order to see it this way, there would have to have been some situation of instability. It wouldn't make sense to say "that nobody noticed" or "that everybody neglected" or the likes. I don't think the Black Swan catch phrase is much use in pondering the nature of the Big Bang. They might look similar at a glance, but I'd say the BB isn't quite the same thing as BS...

 

someone earlier suggestted it was bass ackwards, so maybe an inverse symmetry or some such a matter. :) anyway, i already lost one, more humorous , post to the aether so i'm outy. hope i haven't dragged the topic too far off base and caused a disturbance in the entropy of our universe by all this flapping of my gums. addio!! . . . . .

 

ps bs.... you crack me up q. :lol:

[coldcreation]

A Perpetually Old Universe?

 

An infinite spatiotemporal universe has no age. So the the term "old" is a misnomer. Qtop is correct on this point.

 

Oh, and there's no problem associated with the second law of thermodynamics in a static universe, where homogeneity is consistent with the standard cosmological principle (no need for the perfect cosmological principle).

 

 

CC B)

[modest]

A Perpetually Old Universe?

 

I mean a universe that has no beginning. The past continues uninterrupted. "Old" may not have been the best word, but I figured the meaning would be clear.

 

An infinite spatiotemporal universe has no age.

 

I wouldn't consider that necessarily true. If the universe began 4 years ago and it is eternal (meaning it will persist forever) then it is temporally infinite. If it is also spatially infinite then it is, as you say, "an infinite spatiotemporal universe". Having begun 4 years ago it would have an age. It is possible, then, for an infinite spatiotemporal universe to have an age.

 

Truthfully, that's why I wrote "perpetually old" in the title rather than "eternal". The word 'eternal' and the phrase 'temporally infinite' don't necessarily imply a perpetually long past.

 

Oh, and there's no problem associated with the second law of thermodynamics in a static universe, where homogeneity is consistent with the standard cosmological principle (no need for the perfect cosmological principle).

 

 

CC B)

 

The problem is summarized by Hawking here,

 

...On the other hand, the German physicist, Boltzmann, discovered the so-called Second Law of Thermodynamics. It states that the total amount of disorder in the universe (which is measured by a quantity called entropy), always increases with time. This, like the argument about human progress, suggests that the universe can have been going only for a finite time. Otherwise, the universe would by now have degenerated into a state of complete disorder, in which everything would be at the same temperature.

Origin of the Universe (Hawking speech)

 

And, wiki,

 

Unless an external event intervenes (thus breaking the definition of a closed system), the room is destined to remain in the same condition for all eternity. Therefore, following the same reasoning but considering the whole universe as our "room", we reach a similar conclusion: that, at a certain point in the distant future, the whole universe will be a uniform, isothermic and inert body of matter, in which there will be no available energy to do work.

Entropy - Wikipedia, the free encyclopedia

 

~modest

[quantumtopology]

I wouldn't consider that necessarily true. If the universe began 4 years ago and it is eternal (meaning it will persist forever) then it is temporally infinite. If it is also spatially infinite then it is, as you say, "an infinite spatiotemporal universe". Having begun 4 years ago it would have an age. It is possible, then, for an infinite spatiotemporal universe to have an age.

 

Truthfully, that's why I wrote "perpetually old" in the title rather than "eternal". The word 'eternal' and the phrase 'temporally infinite' don't necessarily imply a perpetually long past.

 

Maybe thera are some semantic confusions. I have always understood the words "temporally infinite" and "eternal" in a strict interpretation as meaning without beginning and without end, actually I think this is the only logically consistent meaning of the concept "infinite" when speaking of time, if that is not the case It would be interesting to differentiate the symetric and asymetric form of infinitines if only to avoid confusion.

I know the asymetric form is commonly used by standard model mainstreamers, but still I think it would be useful to acknowledge the other form, more logical and truer to the concept IMO of the concept "temporally infinite".

 

 

Originally posted by coldcreation:

An infinite spatiotemporal universe has no age...(no need for the perfect cosmological principle)

 

Hi CC , one thing, I believe if you use the word spatiotemporal you are implying the perfect cosmological principle, the cosmological principle was defined to deal only with the spatial component, wich is rather artificial if you think of it, since relativity theory is devoted to treat space and time together, remember also the famous phrase by Minkowski :"Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

But historically, after Friedmann and Lemaitre proposed the spatially expanding universe and Hubble found the redshift-distance linear relationship, there was a departure from that spacetime geometrically unifying concept of Einstein, wich was only natural since the expansion only affects space. Therefore the Cosmologicical principle that was originally thouht in spatiotemporal terms, was popularized by Milne in the early 30's as being an spatial principle "only". It was later that to differentiate it from this "spatial only" principle, Hoyle and company recovered the original spatiotemporal sense in the "perfect" principle.

Too bad they maintained expansion in their theory and therefore had to invent perpetual creation of matter, completely dooming their proposal.

 

 

As for homogeneity,after some discussion with Modest. I've concluded that is a trickier concept than I originally thought, and there might be more than one meaning of the concept, again if we take a strict interpretation a non-expanding might not be strictly homogenous.

 

Let's remember that FRW metric is just one way to express GR, as the Einstein equations

are covariant and admit any arbitrary coordenates and therefore other metrics, FRW is just more convenient for a homogenous, expanding universe. or as the wiki says:

"The FLRW metric starts with the assumption of homogeneity and isotropy of space. It also assumes that the spatial component of the metric can be time dependent."

We can also assume(if we concluded by other evidences that there is no expansion) that the spatial component is not time dependent, and write the metric without the scale factor, and we'd have a perfectly valid metric.

We can realize this in a more practical way if we consider that the scale factor function in the present time is given the value of unity, therefore any operation with the FRW metric for the present gives the same result as if the scale factor was absent.

So the scale factor is more like a conceptual term in the line element for present time calculations.

It is important to make this assesments because I have found too often stated that expansion is derived directly from Einstein GR, this is false, you have to add several assumptions to Einstein equations to derive expansion.

 

Regards

Qtop

[modest]

Maybe thera are some semantic confusions. I have always understood the words "temporally infinite" and "eternal" in a strict interpretation as meaning without beginning and without end

 

"Eternal" is 'Lasting forever; unending'

"temporally infinite" just means an infinite amount of time.

 

Neither imply 'no beginning' by any reasoning I can figure.

 

actually I think this is the only logically consistent meaning of the concept "infinite" when speaking of time

 

If time has a beginning then it can be labeled with the natural numbers. The passing of the first year (or any other arbitrary unit of time) would be t=1 followed by t=2, t=3 and so on. To prove that time with a beginning can be infinite consider the set of natural numbers, [math]\mathbb{N}_0 = \{0, 1, 2, 3, \ldots \}[/math], starts at zero with infinite cardinality.

 

~modest

[quantumtopology]

"Eternal" is 'Lasting forever; unending'

"temporally infinite" just means an infinite amount of time.

 

Neither imply 'no beginning' by any reasoning I can figure.

When speaking of infinite amounts, the end is not distinguisable from the beguinning except to signal where we arbitrarily choose to start counting.

 

If time has a beginning then it can be labeled with the natural numbers. The passing of the first year (or any other arbitrary unit of time) would be t=1 followed by t=2, t=3 and so on. To prove that time with a beginning can be infinite consider the set of natural numbers, [math]\mathbb{N}_0 = \{0, 1, 2, 3, \ldots \}[/math], starts at zero with infinite cardinality.

It follows from what I said above, one thing is the amount of time , which in case we consider it infinite, we can choose arbitrarily any of its elements to start the infinite count, but we must be aware that one thing is the infinite amount and other thing how we label it or count it, if we want to count something, be it finite or infinite, obviously we must start somewhere, that we arbitrarily call start, or beguinning. There is no other way to count. If you use the naturals you might wanna start with 0 or 1 or any other natural number, it doesn't matter. You say that because we are able to start counting something with natural numbers, an infinite amount of something has a beguinning. Well only in the trivial sense that in order to count something you must start doing it.

That only means that the act of counting has a beguinning not that the infinite amount of something has a beguinning any more than it has an end.

 

But in the end I think you contradict yourself, in our previous discussions, when we talked about an infinite time universe, you kept on calling it perpetually old, in other words with no beguinning.

But I could have made up a bizarre argument "a la BBT" to justify a beguinning for the static universe, and according to your current definition of infinite time with beguinning but no end, it would be valid.

 

Regards

Qtop

[quantumtopology]

To further clarify the concepts of my last post, it is interesting to think in geometrical terms,

the geometrical line could be thought of as a timeline, as we know a line has no beguinning nor end, it extends infinitely in both directions. But we can arbitrariliy choose a point fron this line and say the line start there, whichever the direction we wish to coose. Now we have an object called Ray, that extends infinitely only in one direction, curiously enough, the startin point is called the endpoint.

Now, we must agree that the ray is a part of the Line, we know something that is infinite like the line or like time, can contain infinite parts that are themselves infinite like rays, or like the infinite set of the naturals, that will only depend on our arbitrary choice of a starting point or endpoint in the case of the ray, where we start counting or place a dot in the line.

 

Regards

Qtop

[coldcreation]

The problem is summarized by Hawking here,

 

...the universe can have been going only for a finite time. Otherwise, the universe would by now have degenerated into a state of complete disorder, in which everything would be at the same temperature.

 

This line of reasoning is entirely fallacious. It assumes that things in an infinite spatiotemporal universe have been here forever. There is no reason why that should be the case. Things change. Stuff evolves, often very slowly. So the conclusion that entropy should have reached it's peak by now is nonsensical as it is absurd.

 

Hawking's assertion above is just as nonsensical as his claim that Olber's paradox refutes an infinite universe. In the latter claim he simply neglected the possibility that the geometric structure of the universe may not be Euclidean.

 

CC

[Qfwfq]

Things change. Stuff evolves, often very slowly.

In derogation of the 2nd principle of thermodynamics?

 

Hawking's assertion above is just as nonsensical as his claim that Olber's paradox refutes an infinite universe. In the latter claim he simply neglected the possibility that the geometric structure of the universe may not be Euclidean.

Actually, a simpler alternative for an expanding universe is that it could be an alternative explanation of the CMB, it was consred in the past at least.

[quantumtopology]

Actually, a simpler alternative for an expanding universe is that it could be an alternative explanation of the CMB, it was consred in the past at least.

Hi Qfwfq

This is a bit cryptic, or at least I can't figure out what you refer to, can you elaborate on it?

 

Regards

Qtop

[quantumtopology]

Hawking's assertion above is just as nonsensical as his claim that Olber's paradox refutes an infinite universe. In the latter claim he simply neglected the possibility that the geometric structure of the universe may not be Euclidean.

 

Exactly, for instance, a hyperbolic geometry universe (that actually is locally Euclidean and differences from a euclidean scenario only appear at huge radial distances) solves the paradox since it demands skies to be dark due to the simple fact that EM radiation decreases in intensity and frequency with distance in a static setting which mimics the effect that a recessional velocity in a expanding universe would show.

 

It is a pity that nobody in mainstream physics ever mentions this puzzling coincidence even though is a plain and simple fact derived from applying a hyperbolic geometry rather than an Euclidean to EM radiation. Actually in the mathematical environments concepts like horospherical wavefronts are commonly used.

 

You only need some notions of Non-euclidean geometry and rudimentary knowledge of Electromagnetic theory, but non-euclidean geometry is rarely taught nowadays in Physics programs.(differential geometry is what gets closer but it is taught basically in relation with GR and is much more about calculus and algebra than about descriptive geometry).

 

Regards

Qtop

[modest]

This line of reasoning is entirely fallacious. It assumes that things in an infinite spatiotemporal universe have been here forever.

 

The first law of thermodynamics would assert that.

 

~modest