[QUOTE=mathsman1963;367685]Perhaps the universe is ajar.[/QUOTE]

...or a bottle, with debates about extent and topology being especially confusing in German: "Is that klein with a 'k' or a 'K'?"

@Dave: Nice try to "make infinity your friend," but I'm gonna guess Paul will simply repeat the question with more weasel-proof wording involving "specific entropy", that is entropy per unit mass/energy. (But I don't want to put words, whether klein oder gross ones, in his mouth.)

[QUOTE=ewmayer;367826]...especially confusing in German: "Is that klein with a 'k' or a 'K'?"[/QUOTE]
Known only to a small circle of academic researchers is the fact that unfortunately, Marx died before finishing the sequel to [I]Das Kapital[/I] which was to be called [I]Der Kleinbuchstabe[/I].

[QUOTE=Batalov;367829]Known only to a small circle of academic researchers is the fact that unfortunately, Marx died before finishing the sequel to [I]Das Kapital[/I] which was to be called [I]Der Kleinbuchstabe[/I].[/QUOTE]

:)

But which Marx - Groucho or Harpo? I confess I've never seen the comedy you mention - is it available on DVD?

[QUOTE=ewmayer;367826]...or a bottle, with debates about extent and topology being especially confusing in German: "Is that klein with a 'k' or a 'K'?"

@Dave: Nice try to "make infinity your friend," but I'm gonna guess Paul will simply repeat the question with more weasel-proof wording involving "specific entropy", that is entropy per unit mass/energy. (But I don't want to put words, whether klein oder gross ones, in his mouth.)[/QUOTE]I'd already hinted at that approach when I advised davar55 to read up on how the pre-quantum theory people handled entropy in a continuous and potentially infinite spacetime.

Nice that you've given him a further hint.

[QUOTE=ewmayer;367826]
@Dave: Nice try to "make infinity your friend," but I'm gonna guess Paul will simply repeat the question with more weasel-proof wording involving "specific entropy", that is entropy per unit mass/energy. (But I don't want to put words, whether klein oder gross ones, in his mouth.)[/QUOTE]

[QUOTE=xilman;367844]I'd already hinted at that approach when I advised davar55 to read up on how the pre-quantum theory people handled entropy in a continuous and potentially infinite spacetime.

Nice that you've given him a further hint.[/QUOTE]

Yes, the universe is ajar. But then cosmology is a lever.

And infinity is indeed my friend, in fact a friend to all.
Because if not for infinity, universal entropy might actually be
constantly increasing, until thermal equilibrium, meaning a kind
of death of the universe.

There can be no actual infinity in the universe, which is how
we know space is finite and total mass-energy is finite.
Time regresses infinitely, but this is not a contradiction,
as explained in the monograph cosmo3.txt.

Before I go delving into QT on just a "hint", I think we should
get together on the basic bases of cosmology. If we can't
agree on these, the QT details won't matter.

[QUOTE=davar55;368502]Before I go delving into QT on just a "hint", I think we should get together on the basic bases of cosmology. If we can't agree on these, the QT details won't matter.[/QUOTE]For a start it's not quantum theory which we are suggesting that you do not understand well enough but classical thermodynamics --- a theory which predates quantum theory by decades.

The reason why we are making these hints is that your cosmology appears to violate simple physical principles which are now about 150 years old. If you can not resolve these apparent violations your theory is doomed, regardless of your claims about (in)finiteness, dimensionality and so forth.

[QUOTE=xilman;368580]For a start it's not quantum theory which we are suggesting that you do not understand well enough but classical thermodynamics --- a theory which predates quantum theory by decades.

The reason why we are making these hints is that your cosmology appears to violate simple physical principles which are now about 150 years old. If you can not resolve these apparent violations your theory is doomed, regardless of your claims about (in)finiteness, dimensionality and so forth.[/QUOTE]

I have no problem with defining T or conservation of Energy.
And entropy in a local closed system always non-decreasing
is reasonable, although that poses a statistical challenge
to Quantum Theory. However:

(1) Entropy as defined can increase (with extremeely low probability)
even before QT considerations. It just usually doesn't.

(2) The Universe is NOT strictly a closed system, as I explained.
It is open-closed. Hence the rule of non-decreasing entropy
doesn't stricttly apply to the Universe as a whole.

(3) If Space is considered the net of open-balls of a given radius,
and the closure of each open-ball is considered a system, with
each system's entropy non-decreasing, and the Universe finite,
then by taking the sum of the entropies of the open-balls
as the net-radius goes to zero, the sum of the entropies
approaches infinity. Hence I defined the eentropy of the
Univererse as infinity. Hence it can increase but stay the same.

That post should read:

(1) Entropy as defined can decrease (with extremely low probability)
even before QT considerations. It just usually doesn't.

[QUOTE=davar55;368608]That post should read:

(1) Entropy as defined can decrease (with extremely low probability)
even before QT considerations. It just usually doesn't.[/QUOTE]

So what? Do you even have a sense of how rapidly the odds of appreciable 2nd-law violation decrease for a simple model system like "n pointlike ideal gas atoms in a finite 2-D box symmetric about the y-axis, with all atoms in the right half of the box (x > 0) at some initial time t0"? Unless you have a clue of how the odds of "all atoms again having x > 0 at some later time t, after enough time for quasi-equilibration to have occurred" vary with n increasing, it's ludicrous to invoke statistical thermodynamics as in any way supportive of your conjectured whole-universe 2nd law violation. I mean, one would have at least hoped for some speculative "low-entropy-biased quantum particle generation" scenario in a similar vein to that proposed in the steady-state model most-commonly associated with Fred Hoyle - more on that below.

==============

Related note: It is standard- in fact required, and for good reasons - practice in science that before presenting what one claims is a novel conjectured scenario, one should demonstrate in-depth understanding of "the literature", that is the history and mechanics of conjectures-long-similar-lines.

Along these lines, this was posted recently in the Science News thread - nothing new in terms of the physics, but notes that Einstein had also considered a theory similar to Fred Hoyle's before deeming it untenable in the face of the astronomical evidence:

[url=www.nature.com/news/einstein-s-lost-theory-uncovered-1.14767]Einstein’s lost theory uncovered[/url]: [i]Physicist explored the idea of a steady-state Universe in 1931.[/i]

The OP needs to understand and cogently explain why his pet scenario improves - and I mean in a manner consistent with known data - on the scenarios considered by the above luminaries. In other words, "what makes you think you understand this stuff better than Eintein and Hoyle?" For example, here is a brief cogent speculation by Hoyle which at least leads to testable predictions:
[quote]But, from the late 1940s, Hoyle argued that space could be expanding eternally and keeping a roughly constant density. It could do this by continually adding new matter, with elementary particles spontaneously popping up from space, Hoyle said. Particles would then coalesce to form galaxies and stars, and these would appear at just the right rate to take up the extra room created by the expansion of space. Hoyle’s Universe was always infinite, so its size did not change as it expanded. It was in a ‘steady state’.[/quote]
No magical agents (beyond quantum weirdness as understood at the time), no "I just know it is so" quasi-religious hubris - and more plausible-sounding scientific hypothesizing than I have seen from the OP in the entirety of this mega-thread.

[QUOTE=ewmayer;368624]Related note: It is standard- in fact required, and for good reasons - practice in science that before presenting what one claims is a novel conjectured scenario, one should demonstrate in-depth understanding of "the literature", that is the history and mechanics of conjectures-long-similar-lines.[/QUOTE]Perhaps a bit unfair here. The (current) thread title allows for the current situation. As long as the OP will capitulate at some point and understands whatever wrongness has been demonstrated then I think we are all good here.

[QUOTE=retina;368632]Perhaps a bit unfair here. The (current) thread title allows for the current situation. As long as the OP will capitulate at some point and understands whatever wrongness has been demonstrated then I think we are all good here.[/QUOTE]

Hoyle thought the Universe was increasing in size of Space because
he believed the Red Shift did indeed imply an expanding Universe, and
he was left with matter creation and constant density to explain his
steady-state universe. I on the other hand, by positing a fourth
spatial dimension of a certain kind, can explain the Red Shift et. al.
without requiring, and in fact disproving, an expansion. This negates
the astronomical data supporting big bang and supports my thesis.

Hence I demonstrate the fixed finiteness of the Universe as being
more fundamental than the entropy issue, which then is explained
in my earlier post but has not been commented on.

I must stand by my monograph, with the additions in my posts,
because the questions here have not challenged any of the
"new" ideas it contains. The particular "old" ideas that I was
able to "borrow" (such as steady-state) I had to modify based
on the "discovery-to-be" of the skin.