Thermodynamics and The Universe

You just change a sign in the metric, the object that describes how distances work in spacetime, and it all follows (after a little while). Points 2 and 3 in the list above are almost immediately obvious after you do this.It's often interesting to tweak things a bit and see what stuff "could" have been like.

must be the extra time on their hands ... ducks behind desk ...

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Yeah, literally. It's a interesting look at how PDEs behave in alternative metrics, plus it shows you how special 3 + 1 is. A paper by Tegmark, I think, kind of said most of what has been said so far.
It's not researched or anything really, most of the main results can be shown on a few A4 sheets.

Philosophers' Playground: Time Times Two

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There is an interesting paper, On the Dimensionality of Spacetime, on this by MIT physicist Max Tegmark where he argues that the only stable dimensional set up is one in which there are three spatial and one temporal dimension.

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It is a wonderful paper. But, be careful, Tegmark does have a philosophical ax to grind here. He is one who has a soft spot for the Anthropic Principle, the cosmological version of Intelligent Design.

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link in original is to
http://space.mit.edu/home/tegmark/dimensions.pdf

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Abstract. Some superstring theories have more than one effective low-energy limit corresponding to classical spacetimes with different dimensionalities. We argue that all but the (3+1)-dimensional one might correspond to ”dead worlds’, devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a (3+1)-dimensional spacetime. With more or less than one time dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions. In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures. A space with less than three dimensions allows no gravitational force and may be too simple and barren to contain observers.

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So there could be a number of strung together sub universes but only in the 3+1t sectors(s) would life exist.

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Well the idea of two time dimensions,(outside F-theory, I don't know String Theory so I don't understand it in that context) I would have thought is just kind of an interesting look at what happens to SR and Particle interactions when you change a few things. I think somebody would be going out on a limb if they started talking about life in such a place.Plus, it isn't a cosmological model. There would be no coherent way of saying those other worlds exist, all you can say is "This is what a world with Special Relativity left intact, but with another time dimension would look like".
This is the way I would have understoof it in a purely SR and simple particle physics stuff.However, Tegmark doesn't do this the way I'm familiar with it. He actually uses String Theory, so I can't really comment on his paper.
Although he still seems to say the same basic consequences.Except to say: The Anthropic Principle hasn't got anything to do with intelligent design, in fact it's a lazy link to make. I think Tegmark's just saying why String Theorists might not have to explain 3+1 dimensionality. The Anthropic Principle is sort of a modification to the Copernican Principle.
i.e., Your position isn't special, up to the fact of your existence.Anyway I should probably stop talking about this, Tegmark's paper is a mix of stuff I know and stuff I don't.I only ever heard of the paper (wasn't on arxiv and I never specifically wanted it, so I didn't go through Quantum & Classical Gravity), so thanks for the link.Edited by Son Goku, : Additions

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It is a wonderful paper. But, be careful, Tegmark does have a philosophical ax to grind here. He is one who has a soft spot for the Anthropic Principle, the cosmological version of Intelligent Design.

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As SG has pointed out, complete nonsense Admittedly the AP has a hierarchy of versions, the higher of which are certainly meta-physical... but nothing to do with ID - pantheistic if anything. But the Weak AP, used here, is simple common sense. To quote again from that article

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The idea is that the universe and its constants are so perfectly picked that the universe as a stable enough place to support matter, much less life, is evidence of Divine Creation

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is not the AP in any of its forms. That is just classic design argument.Edited by cavediver, : changed quote style

Now that takes me back Simple idea really - just gives you an extra dynamic of compactification from 12D (10+2) down to 10D (9+1)c.f. low energy M-theory in 11D (10+1) down to 10D (9+1) Exactly - when we used to play with it, it was looking at the reflection/transmission at a pseudo-Riemannian/Kleinian boundary (3+1 space time/2+2 space-time for the readers)Tegmark's overall idea is similar to mine - reality is simply a necessary aspect of logic/mathematics.

Where's this from? It's not something I've ever really considered... is there still a thermodynamic arrow of time?I forgot to mention, Kleinian space-time also rears up in Humphrey's cosmology! That's part of its pathological behaviour

IDologists do use the anthropic principle to show that the universe is designed for us - the typical post hoc ergo propter hoc logical fallacy approach. I thought it was rather an ad hominum to attack him on it and then say the paper made no mention of it. It's kind of like saying "yeah but he's _______, so he has an agenda" (fill in blank with favorite derogatory epithet).My impression of string theory is that it hypothesizes this uber universe with side eddies where some of the dimensions disappear (and we would be in one with (3+1) OR one where the extra dimensions were tangled into small eddies in the uber universe leaving us with (3+1) in the observable. Topologically these are the same.It trades a universe full of dark stuffs for one of dark dimensions ...

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I don't know. I should probably make clear that I was saying that the linear conception of time is still there to a single observer. That is they have a time orientable worldline.
The reason I pointed it out is that alot of people, when they hear of two time dimensions, initially think that instead of having a timeline, you'd have a "time area", if you catch my drift. Really? How so?

Wouldn't that be the area of possibilities, but objects would still have vectors within that area that would be indistinguishable from passage of time in a single time universe (except for objects on a line tx=-ty)?In other words, how would one know there is only one time dimension? I think of the possible perceptions of the denizens of "Flatland" ...

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I,ve been away for awhile (I am a shift worker). I'd just like to thank everyone for helping me put all of this together in terms that I can understand. The paper on superluminal expansion was also key.
Cheers

Strictly logically speaking as an observing layman, the more I read about QM and other somewhat mysterious and illogical aspects of science the more I get the notion that the significance of the basic three TD laws of the universe which is so obvious in our daily living observations are being undermined by complicated illogical mathmatical mechanisms utilized to accomodate theories which on the surface appear to go counter to the basics of the three laws.There are so many absolute necessary factors which must be precisely in place for so many billions of intricate processes to produce a prolific earth planet packed with complexity in a solar system of lifeless other planets spinning around the same star, all following the more logical ways of the three laws which naturally effect precious little entropic decrease.

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BUZSAW B 4 U 2 C Y BUZ SAW ---- Jesus said, "When these things begin to come to pass, then look up, and lift up your heads, for your redemption draws near." Luke 21:28

Hrm. Then I'd suggest you read a little further, because the impression you should be getting is that the apparently-deterministic rules that apply at our scale of existence, like the laws of thermodynamics, are actually just the statistical, stochiastic outcomes of a large number of random processes.But, hey. Stick with your conspiracy theory about scientists purposefully trying to suborn reason and logic for unspecificed purposes if that's what it takes to come to terms with observing people who know more than you about something. And we're all on the edge of our seats waiting for your completely logical, deterministic explanation for the two-slit experiment.

How does QM go against the Laws of Thermodynamics?In fact the third law, Entropy tends to zero as temperture tends to zero kelvin (Which has the immediate consequence that specific heat decreases as you lower temperture), can only be explained by Quantum Mechanics.I don't understand how QM contradicts thermodynamics, when you derive the third law using QM.As for the Zeroth Law, "If two systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other." That is unaltered.The First Law:
"An equilibrium macrostate of a system can be characterized by a quantity E(called internal energy) which has the property that for an isolated system,
E= constant

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If the system is allowed to interact and thus goes from one macrostate to another, the resulting change in E can be written in the form:
E = -W + Q

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where W is the macroscopic work done by the system as a result of the system's change in external parameters. The quantity Q being defined by the above relation, is called the "heat absorbed by the system".

On a cursory examination you would expect QM not to make to much of a difference, since the definition makes heavy use of the word macrostate. In fact it doesn't. I can give a detailed explanation of why it does not.The Second Law:
An equilibrium macrostate of a system can be characterized by a quantity S (called entropy), which has the properties that:
(a)In a nay process in which a thermal isolated system goes from one macrostate to another, the entropy tends to increase, i.e.,
S >= 0

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(b)If the system is not isolated and undergoes a quasi-static infintesimal process in which it absorbs heat Q, then:

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dS = Q/T

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where T is a quantity characteristic of the macrostate of the system. (T is called the "absolute temperture" of the system.)Again heavy use of the word macrostate, implying that this is a statement about the dynamics of bulk systems. Again something QM doesn't modify.I fail to see how QM undermines the laws of thermodynamics if it leaves three of them unchanged and is used to derive the third.All definitions taken from Federick Reif "Fundamentals of Statistical and Thermal Physics" (1965).