If not, does the second law of thermodynamics even apply? What role would entropy play if it is not?
To our knowledge it is. At minimum you could count the observable universe as a closed system because anything outside it will not have had time to affect you locally due to the finite speed of light.
We once assumed that we would fall off the edge of the earth too. When you say "observable universe" you refer to technology constraints. If all assumptions are based on limits in technological capability, what is the point in exploration and creative thought?
No, I refer to the actual observable universe in visible light or neutrinos (The latter is not actually possible at the moment). Before about 300,000 years after the universe started, it was too hot and too dense for light to move freely throughout the universe. Once it cooled off enough for nuclei to permanently combine with free electrons the universe became transparent to EM radiation, aka light, and the CMB (cosmic microwave background) was created at this time. So the furthest we can look back using light is to about 300,000 years after the creation of the universe as we know it. (I purposely don't use the term "big bang" because it inherently creates incorrect views on what happened) Prior to 300,000 years neutrinos were able to move freely since they interact very weakly with other matter, but we cannot observe them very well currently. Still, this puts a limit on how far back in time, or in distance we can see in either case.
The distance at which the original space that emitted the current CMB is believed to be about 14 billion parsecs, or 45.7 billion light years. The edge of the actual observable universe, with ANY form of radiation, is believed to be about 14.3 billion parsecs, 46.6 billion light years. (So the diameter of the observable universe is currently about 93.2 billion light years) Past this point we cannot see, even in principle, as nothing has had time to reach us yet.
Isn't the universe closed system by definition?
In this context the discussion alludes to a multiverse. In that case AFAIK the word universe reduces from it's definition of everything.
Ok so, is the universe a perpetual motion machine? See where I'm going?
If the universe is a closed system, where are the boundries?
Why would it be? Even though the total amount of energy remains the same the total amount of energy available for work always decreases.
It doesn't have any. Likewise it has no centre.
In order for it to be a closed system, it would require boundries.
That only applies if there is both a surrounding and a system but the universe has no surrounding. If it is infinite then the reason is obvious and even if it was finite it would wrap around itself (like how in the old fashioned video game asteroids if the player drove off through the right wall they would come out of the left).
Nope. The solution to the Einstein field equations for an expanding space-time is the FLRW metric. This space-time is spatially symmetric.
Another consequence of the FLRW space-time is that, as Ryan points out, it has no boundaries. It could be infinite. If it is finite, it's either a simply connected surface or a non-simply connected surface.
As Darkkith explained, because of the rate at which the universe expands, we can approximate our observable universe to be a closed system. So yes, it obeys the second law.
What about virtual particles? Wouldn't the existence of virtual particles imply that the universe is not closed? Virtual particles seem to come from outside of the universe and appear inside it.
Virtual particles exist only to mediate interactions. They disappear before they can do anything else, so no energy conservation laws are violated.
I think he's on to something. The universe by definition contains all there is. So if we were to witness something that appeared to emerge from nowhere, we would just say that it emerged from some other unknown place that is part of our universe. We would say that it popped out of a wormhole whose other side was in some other part of the universe. We would employ the same tactic Wolfgang Pauli used when he explained what happened to the missing energy in certain particle collisions, ie, it was carried away by a neutrino, though he used the word neutron. We wouldn't give up the principle of the conservation of matter we would invent some desperate loophole to save the theory.
In a way, that the universe is a closed system can become a useless tautology. Let's rename universe "everything" and let's replace the predicate: is a closed system with contains everything. After all, if something contains everything then beyond its borders is nothing. (though you could make the argument that speaking of the universe's borders is not sensible but you know what I mean) So now if you put the new subject and predicate together you get a useless tautology: everything contains everything.
Obviously if we witnessed a violation of one of the conservation laws and saw something appear from nothing we would have to change our science. The rest of your post makes no sense.
I am also struggling with whether the universe is an open or closed system in the thermodynamic sense, and how to include gravitational effects. If matter tells space-time how to curve, and space-time tells matter how to move, then there seems to be an interaction between matter and the space-time metric. Therefore we would need to include the thermodynamic properties of space-time if we wanted to consider the universe as a closed system. If we do not include the thermodynamics of space-time, or if it makes no sense to apply the notions of statistical physics to space-time, then the universe would seem to be open. Landau & Lifshitz discusses this briefly on p.30 in section 8 of "Statistical Physics" (3rd edition) in relation to the 2nd law of thermodynamics. I am stumped.
in the thermodynamic sense, the observable universe is treated as a closed system, as there is no outside influences. In localized phenomena, describing a region of thermodynamic measurements. Such as say the accretion disk layers of a BH. The treatments can vary, they can either be treated as a closed or open system, depending on the thermodynamic process under study. Ideal gas law treatments describing thermodynamics in cosmology can get fairly intense, however the equations of state in cosmology greatly simplify numerous calculations.
For example you can model the CMB with the appropriate equations of state, or you can apply the Bose-Einstein and fermi-dirac distributions/statistics.
here is a good article using the latter method
http://www.wiese.itp.unibe.ch/lectures/universe.pdf :" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis
its a textbook style article and the metrics is similar to Scott Dodelssons "Modern Cosmology" 2nd edition
here is an example using the equations of state to describe thermodynamic history of the universe, keep in mind the article is a comparison of the between the equations of state and Gibbs law
its handy as it shows both methodologies. As thermodynamics at best is an approximation, the method used is also an approximation. The first method would be a tighter approximation, Gibbs law according to the last paper is a tighter approximation compared to the
[tex]t\propto a[/tex] relation a is the scale factor.
The number of processes you account for, ie particle species, chemical reactions, entropy density, phase transitions etc will invariably give you a tighter approximation
Thanks for the references...you are right...intense!
The Landau and Lifshitz reference discusses why the present Universe is so far from equilibrium and why it should not be considered as a closed system, which led to my original post. Maybe I should include it here:
..."when large regions of the Universe are considered, the gravitational fields present become important. These fields are just changes in the space-time metric. When the statistical properties of bodies are discussed, the metric properties of space-time may in a sense be regarded as "external conditions" to which the bodies are subject. The statement that a closed system must, over a sufficiently long time, reach a state of equilibrium, applies of course only to a system in steady external conditions. On the other hand, the general cosmological expansion of the Universe means that the space-time metric depends essentially on time, so that the "external conditions" are by no means steady in this case. Here it is important that the gravitational field cannot itself be included in a closed system, since the conservation laws which are, as we have seen, the foundation of statistical physics, would then reduce to identities (not sure what they mean here). For this reason, in the general theory of relativity, the Universe as a whole must be regarded not as a closed system, but as a system in a variable gravitational field. Consequently the application of the law of increase of entropy does not prove that statistical equilibrium must necessarily exist."
sorry I don't own that textbook, though I do own quite a few lol. You'll have to post the metrics. If your unfamiliar with how to post latex here is the instructions
make sure any statements copied from it are referenced see global guidelines
this textbook however is a free and official free for distribution release may help
http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde
my signature has a link where you can find numerous articles covering the spacetime relations of the FLRW metric or the Einstein field equations. Think of cosmology as a perfect fluid matter as positive pressure with a correlating equation of state, dark energy or the cosmological constant as the negative pressure (vacuum). here is an article covering in a simple metric form the relations. These relations also apply to thermodynamics
this doesn't cover the temperature but does help understand the pressure relations
I put the original L&L quote in my previous post. Thanks again for the references...my copies of GR and Cosmology books are pre-"Dark Energy" and needed to be updated...I just ordered the Dodelson book.
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