Heat-death hypothesis thoughts

[steenpat]

Ok, I neglected the forum rules for my first post. Hopefully I got it right this time.

Here are a few ideas I have about the so-called heat-death hypothesis.
First, if we take the wikipedia entry as a description, it's inherently false. It suggests that the universe reaches maximum entropy, which implies that the second law of thermodynamics is violated. So, obviously maximum entropy will never be reached. In fact the real model suggests a limiting function that keeps coming closer but in fact never reaches it.

Or could it?

If we take into account Zeno's paradox, then things like this happen all the time. We know from calculus that theoretically I can never move exactly from one space to another due to a limiting process, but in fact this is violated all the time in nature by casual observation. In fact, if this was impossible I could not move anywhere at all. So does this mean that the second law can be violated, or that Zeno's paradox is somehow fundamentally flawed?

Other research seems to imply an 'entropy gap' which inevitably will push the system away from equilibrium. Can someone explain how that would form? I couldn't find much material on it.

 

[zhermes]

Ok, I neglected the forum rules for my first post. Hopefully I got it right this time.

Well, you've gotten some of the rules right, but you're neglecting lots of much more fundamental things to worry about...

First, if we take the wikipedia entry as a description, it's inherently false. It suggests that the universe reaches maximum entropy, which implies that the second law of thermodynamics is violated.

It implies no such thing. How does reaching a maximum imply decreasing?!

So, obviously maximum entropy will never be reached. In fact the real model suggests a limiting function that keeps coming closer but in fact never reaches it.

Oh "obviously" and "in fact" eh? What "real model" is this exactly? And how does it "suggest" an *asymptotic* function?

If we take into account Zeno's paradox

Why would we take into account an antiquated philosophical conundrum?

We know from calculus that theoretically I can never move exactly from one space to another due to a limiting process

What kind of calculus do you use? Calculus is what traverses and solves Zeno's paradox in the first place...

So does this mean that the second law can be violated, or that Zeno's paradox is somehow fundamentally flawed?

What do you know, a 2000 year old "paradox" may not be the best guide for physics.

Other research seems to imply an 'entropy gap' which inevitably will push the system away from equilibrium. Can someone explain how that would form? I couldn't find much material on it.

From the wikipedia entry on Entropy: "This results in an "entropy gap" pushing the system further away from the posited heat death equilibrium."
First off, this sentence *is* badly worded, thus I understand your confusion. The "entropy gap" is not some particular mechanism, and it wouldn't actively "push" the universe away from equilibrium.
The 'entropy gap' is simply the difference in the entropy of the universe at any given time, and the maximum possible entropy of the universe. If the former increases more slowly than the latter (like one train going slower behind another), then the distance between (the 'entropy gap') will always be increasing, and thus the system's actual state will be further and further away from the maximum possible state (called the 'equilibrium' position).

This last part was a good question. The beginning wasn't. You should try to actually learn about physics/science before you start postulating unfounded things, and more to the point, you should use these forums to learn more---not to share your own thoughts from a cursory reading of wikipedia.

 

[Chronos]

Heat death is the ultimate consequence of an eternal expansion. Eventually, all fuel available to power stars, etc., will be used up and nothing will remain save cold embers and black holes. After all the black holes evaporate [which will take a gazillion years], the temperature of the universe will be virtually absolute zero. If the universe does eventually recollapse, we will get a 'do over' [the bouncing universe model].
.

 

[steenpat]

zhermes: Thanks for destroying me. :)

I assumed the second law meant entropy always increases, but apparently it can remain static as well; so basically what I said is all wrong and the system will reach maximum entropy at some point.

Chronos:
Would the system ever reach absolute zero or would it be arbitrarily close to absolute zero?
And at this state, would quantum fluctuations start to create another big bang? According to the definition it seems that fluctuations could cause randomness at any time, but that would seem counter-intuitive to the evolution of the universe. After all, if the universe is meant to be stable until it's end (I'm assuming here), then it would seem that fluctuations are unwanted phenomena until the end is reached. Making big assumptions here, but I guess that's how my brain works.

 

[collinsmark]

Would the system ever reach absolute zero or would it be arbitrarily close to absolute zero?

Close, but not quite, perhaps. Some suspect that due to expansion, the universe is approaching what is called a de Sitter universe. De Sitter space is much like totally empty Euclidean space, except a de Sitter universe is dominated by the cosmological constant (causing expansion), complete with quantum fluctuations. The temperature of a de Sitter universe would be ever so slightly above absolute zero, where an equilibrium would be reached. (Definitely much, much colder than empty space is now though.)

And at this state, would quantum fluctuations start to create another big bang?

Here is a paper that Chalnoth pointed me to a few months ago, that describes what I'm about to discuss (paper by Sean Carroll and Jennifer Chen):
http://arxiv.org/abs/gr-qc/0505037"

Some have theorized that the quantum fluctuations in a de Sitter universe might, rarely but occasionally, create very small black holes. Of course this sort of black hole wouldn't stick around long at all due to Hawking radiation. Energy is taken from the background and then quickly given back. To a hypothetical observer, such a black hole creation/evaporation event might not even be anything to write home about (or even noticed?).

On the other hand, if the observer's mind's eye was inside such a black hole (which began not with a concentrated mass forming a singularity, but rather from an intensely warped space-time fluctuation), things might be quite different. Even though from the outside, the black hole is tiny in both size and lifetime, from the inside it is infinite in spatial dimensions and lasts forever. It also might be just the situation where an inflationary field might form, creating an inflationary expansion phase, which in turn creates loads and loads of matter in the process, at least as seen from the inside (and seemingly very low-entropy at that -- very similar to our own early universe).

[Edit: And this vast creation of matter (from inflation) as seen from the inside would not be detectable on the outside, because such matter also creates a corresponding gravitational field containing negative energy. They cancel each other out. The matter energy (E = mc²) + its corresponding negative gravitational energy = zero.]

Something out of nothing.

(Although I personally find theories/ideas such as this extremely compelling and attractive, I am a bit haunted by a "turtles all the way down" aspect of the whole thing.)