Is The Universe A Closed System?

[FissX]

If not, does the second law of thermodynamics even apply? What role would entropy play if it is not?

 

[Drakkith]

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.

 

[FissX]

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?

 

[Drakkith]

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.

 

[xAxis]

@Drakkith:
Isn't the universe closed system by definition?

 

[Ryan_m_b]

@Drakkith:
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.

 

[FissX]

Ok so, is the universe a perpetual motion machine? See where I'm going?

 

[FissX]

If the universe is a closed system, where are the boundries?

 

[Ryan_m_b]

Ok so, is the universe a perpetual motion machine? See where I'm going?

Why would it be? Even though the total amount of energy remains the same the total amount of energy available for work always decreases.

If the universe is a closed system, where are the boundries?

It doesn't have any. Likewise it has no centre.

 

[FissX]

In order for it to be a closed system, it would require boundries.

 

[Ryan_m_b]

In order for it to be a closed system, it would require boundries.

Why?

 

[FissX]

http://en.wikipedia.org/wiki/Thermodynamic_system

 

[Ryan_m_b]

http://en.wikipedia.org/wiki/Thermodynamic_system

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).

 

[Mark M]

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?

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.

 

[g.lemaitre]

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.

 

[Mark M]

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.

 

[g.lemaitre]

Virtual particles exist only to mediate interactions. They disappear before they can do anything else, so no energy conservation laws are violated.

OK, thanks

 

[g.lemaitre]

xAxis wrote:

Isn't the universe closed system by definition?

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.

 

[Drakkith]

xAxis wrote:

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.

 

[g.lemaitre]

The rest of your post makes no sense.

prove it

 

[deesquared]

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.

 

[Mordred]

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

http://arxiv.org/abs/0708.2962

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
$$t\propto a$$ 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

 

[deesquared]

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."

Any comments?

 

[Mordred]

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

https://www.physicsforums.com/showpost.php?p=3977517&postcount=3

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

Universe geometry

The origins of the universe is unknown in cosmology. The hot big bang model only covers the history of the universe from 10^-43 seconds forward. Prior to that is described as a singularity. However its important to note that the singularity is not a black hole style. Instead singularity in this case simply means a point in time where our mathematics can no longer accurately describe it. Numerous youtube videos and pop media articles would have you believe our universe exploded from some super particle. This was never predicted by the hot big bang model.

The observable universe which is the portion we can see is a finite, sphere with a radius of 46 Gly, which is equal to 46 billion light years. The 46 Gly particle horizon refers to the today's distance of objects, whose radiation emitted in the past we receive today. The overall size of the universe is not known, it could be infinite or finite. If its infinite now then it would be infinite in the past, a finite value can never become infinite. So why is geometry so important to cosmology if we know the size of the observable universe? The answer to that question lies in how geometry affects the following aspects, Light paths, rate of expansion or collapse and overall shape.

In regards to light paths and geometry a closed universe described as a sphere will have two beams of light emitted at different angles eventually converge. An open hyperbolic universe such as a saddlebag will have those same two light beams diverge. A flat universe will have parallel light paths (provided the beams at emission were parallel to begin with)
You will notice on each image there is a triangle, this triangle represents how the geometry affects our measurements. In a flat curvature the three angles of a equilateral triangle will add up to 180⁰. A positive curvature will add up to greater than 180⁰, a negative curvature will add up to less than 180⁰

Image from http://universeadventure.org

The topography of the universe is determined by a comparison of the actual density (total density) as compared to the critical density. The critical density is represented by the following formula

$\rho_{crit} = \frac{3c^2H^2}{8\pi G}$

$\rho$=energy/mass density
c=speed of light
G= gravitational constant.

density is represented by the Greek letter Omega $\Omega$ so critical density is $\Omega crit$
total density is

$\Omega$total=$\Omega$_{dark matter}+$\Omega$_baryonic+$\Omega$_radiation+$\Omega$_{relativistic radiation}+${\Omega_ \Lambda}$

$\Lambda$ or Lambda is the value of the cosmological constant often referred to as "dark energy" more accurately it is the vacuum pressure that attributes to expansion.
the subscript "₀"for $\Omega$ shown in the image above denotes time in the present.

Energy-density is the amount of energy stored per unit volume of space or region. Energy per unit volume has the same physical units as pressure, the energy or mass density to pressure relations are defined by the equations of state (Cosmology). see
http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

$\Omega=\frac{P_{total}}{P_{crit}}$
or alternately
$\Omega=\frac{\Omega_{total}}{\Omega_{crit}}$

Geometry in 2D
In developing a theory of space-time, where curvature is related to the mass-energy density, Scientists needed a way of mathematically describing curvature. Since picturing the curvature of a four-dimensional space-time is difficult to visualize. We will start by considering ways of describing the curvature of two-dimensional spaces and progress to 4 dimensional spaces.
The simplest of two-dimensional spaces is a plane, on which Euclidean geometry holds.
This is the geometry that we learned in high school: parallel lines will go off to infinity
without ever crossing; triangles have interior angles that add up to 180. Pythagoras’
theorem which relates the lengths of the sides of a right triangle also holds:
c² = a² + b²
where c is the length of the hypotenuse of the right triangle, and a and b are the
lengths of the other two sides. One can generalize the Pythagorean theorem to three dimensions as well:
c²= a² + b² + c²
see image 2.0 below On a plane, a "geodesic" is a straight line(shortest distance between two points). If a triangle is constructed on a flat 2 dimensional plane by connecting three points with geodesics. The curvature can be represented in 2D, if you establish each angle of a equilateral triangle with
$\alpha$,$\beta$,$\gamma$ for a flat geometry this follows the relation

$\alpha$+$\beta$+$\gamma$=$\pi$.

image 1.0

On a plane, (shown above) we can set up a cartesian coordinate system, and assign to every point a coordinate (x; y). On a plane, the distance ds between points (dx and dy) is given by the relation
$d{s^2}=d{x^2}+d{y^2}$

If a triangle is constructed on the surface of the sphere by connecting the angles will obey the relation

$\alpha$+$\beta$+$\gamma$=$\pi+{AR^2}$

image 1.1
where A is the area of the triangle, and R is the radius of the sphere. All spaces in which
$\alpha$+$\beta$+$\gamma$>$\pi$ are called positively curved" spaces. It is a space where the curvature is homogeneous and isotropic; no matter where you draw a triangle on the surface of a sphere, or how you orient it, it must always satisfy the above equation.
"On the surface of a sphere, we can set up polar coordinates "north pole" and "south pole" and by picking a geodesic from the north to south pole to be the "prime meridian". If r is the distance from the north pole, and $\theta$ is the azimuthal. angle measured relative to the prime meridian,"⁽¹⁾ then the distance ds between a point (r; $\theta$) and another nearby point (r+dr+$\theta$+d$\theta$) is given by the relation

${ds^2} = {dr^2} + {R^2} {sin^2}(r/R)d\theta^2$

"An example of a negatively curved two-dimensional space is the hyperboloid, or saddle-shape. A surface of constant negative curvature. The saddle-shape has constant curvature only in the central region, near the "seat" of the saddle."⁽¹⁾. David Hilbert proved that a constant negative curvature cannot be constructed in a Euclidean 3D space. Consider a two-dimensional surface of constant negative curvature, with radius of curvature R. If a triangle is constructed on this surface by connecting three points with geodesics, the angles at its vertices $\alpha$
$\beta$,$\gamma$ obey the relation $\alpha$+$\beta$+$\gamma$=$\pi-{AR^2}$.

${ds^2} = {dr^2} + {R^2} {sinH^2}(r/R)d\theta^2$

image 1.2

A negative curvature is an open topography

If a two-dimensional space has curvature or flat which is homogeneous and isotropic, its geometry can
be specified by two quantities k, and R. The number k, called the curvature constant, R is the radius

k = 0 for a flat space,
k = +1 for a positively curved space,
k = -1 for a negatively curved space

Geometry in 3D
A two dimensional space can be extended to a three-dimensional space, if its curvature is homogeneous and isotropic, must be flat, or have uniform positive curvature, or have uniform negative curvature.

The 3 possible metrics for homogeneous and isotropic 3D geometries can be represented in the form ds²=dr²=S_k(r)²dΩ²

where
dΩ²=dθ²=sin²d$\phi$²$$S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}$$

If a three-dimensional space is flat (k = 0), it
has the metric

ds² = dx² + dy² + dz² ;

expressed in cartesian coordinates or

${ds^2} = {dr^2} +{r^2}[d\theta^2 + {sin^2} d\phi^2]$

If a three-dimensional space has uniform positive curvature (k = +1), its
metric is

${ds^2} = {dr^2} +{R^2}{sin^2}(r/R)[d\theta^2 + {sin^2}\theta d\phi^2]$

A negative curvature in the uniform portion has the metric (k=-1)

${ds^2} = {dr^2} +{R^2}{sinH^2}(r/R)[d\theta^2 + {sin^2}\theta d\phi^2]$

Geometry in 4D

Thus far we have discussed the 2 and 3 dimensional components. The Friedmann-Lemaitre-Robertson-Walker metric (FLRW) can be used to describe the 4D dimensions with the use of a(t). a(t) is the scale factor. See the redshift and expansion article for more information or the cosmocalc.
http://cosmology101.wikidot.com/redshift-and-expansion
http://cosmocalc.wikidot.com/start

Scale factor in a homogeneous and isotropic universe describes how the universe expands or contracts with time.
The FLRW metric can be written in the form

$d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]$

references
(1)"Introductory to Cosmology" Barbera Ryden"
images 1.0,1.1 and 1.2 (see (1))
(2)"Modern Cosmology" Scott Dodelson
(3)"lecture notes, Introductory to Cosmology" Dr. Ka Chan Lu

 

[deesquared]

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.

 

[Mordred]

Now as far as the second law of thermodynamics there are numerous treatments

keep in mind some of these articles are model specific to show different studies using entropy.
however they do show the metrics involved.

"Generalized Second Law in Cosmology From Causal Boundary Entropy
http://arxiv.org/pdf/gr-qc/9904061v2.pdf

http://cosmos.asu.edu/sites/default/files/publication_files/cosmological_horizons_and_the_generalized_second_law_of_thermodynamics.pdf

http://faculty.ksu.edu.sa/djdou/SMNotes/TSM8.pdf

as I mentioned the articles I posted including the first article does go into the second law,
this should give you enough to work from for the time being

 

[Mordred]

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.

gotcha, You'll like Dodelson's book another to consider for introductory level is Barbera Ryden's
Introduction to cosmology

http://www.amazon.com/dp/0805389121/?tag=pfamazon01-20

her metrics on single -multi component universes is masterful