Exploring the Expansion of the Universe and Heat Death

[SpaceTiger]

The proper distance to the particle horizon is not DPH = ct0. Rather, it is the proper distance to the most distant object we can observe, and is therefore related to how much the universe has expanded, i.e. how far away the emitting object has become, since the beginning of time. In general this is ~ 3ct0. The relationship between the particle horizon and light travel time arises because the comoving coordinate of the most distant object we can see is determined by the comoving distance light has traveled during the lifetime of the universe.

The important thing to note is in that last sentence: "...the comoving coordinate of the most distant object we can see is determined by the comoving distance light has traveled during the lifetime of the universe." It implies that the comoving distance to the most distant object we can see depends on how old the universe is (i.e. changes with time). This is shown more explicitly in the bottom panel of Figure 1, where the dashed line shows how the particle horizon has changed throughout cosmic history.

 

[Chronos]

I interpretted [misinterpretted?] that to mean we have always been able to observe light emitted by any object that has ever, or will ever, be within our particle horizon since the beginning of time. I thought figure 1 depicted the spatial displacement of the particle horizon over time. The temporal displacement was always T[now] minus T0. Your patience is appreciated.

 

[SpaceTiger]

I interpretted [misinterpretted?] that to mean we have always been able to observe light emitted by any object that has ever, or will ever, be within our particle horizon since the beginning of time. I thought figure 1 depicted the spatial displacement of the particle horizon over time.

Actually, that section from which you quoted is trying to make exactly that distinction. It's saying that the plot depicts a changing particle horizon with time instead of the worldline of a single particle horizon. The plot is in comoving coordinates, so it follows the expansion, in a manner of speaking. If the horizon moves from one set of comoving coordinates to another, then it will be surrounded by a different set of galaxies, clusters, etc. Likewise, if the comoving radius of our particle horizon is increasing, then that means it encloses more objects with time.

Does that make sense? If comoving coordinates are a point of confusion then I will happily elaborate.

 

[Mike2]

I noticed that you didn't answer my question, so I'll assume you're not familiar with the different possible definitions of "universe":

1. All that we can observe at this moment in time.
2. All that has had a causal influence on us since the beginning of time.
3. All that has or will have a causal influence on us.
4. All that could have a causal influence on us.

I was suggesting that the cosmological event horizon was restricting and reducing entropy so that complex forms such as life came into existence. Since entropy is a description of the whole state, it does not matter how fast the particles are or how heavy they are. This means that it must be the size of the whole universe itself, everything that now exists whether observable or not, that would cause complexity to emerge to compensate for dissipation. If it exists, this would be a very strong restriction and would be implemented with high probability since there would be no alternative but that this balance be maintained. So I suppose that this kind of balance to entropy would give rise to more solid objects such as particles themselves. It may be that as the universe as a whole expands and the curvature of space decreases, that this dissipation is compensated for by the curvature involved with dense energy of particles at those points.

But the cosmological horizon is much smaller than the size of the entire universe. And since objects there redshift and slow just as with a black hole event horizon, I also speculated that the calculation for the entropy of a black hole is applicable to the entropy inside the cosmological event horizon. Thus, if the cosmological event horizon is shrinking, then the restriction of entropy inside become more restricted. As I recall from the paper I read that it may be that the restriction on entropy inside the event horizon has not yet become smaller than the entropy inside. But they may not have taken into account the entropy of space itself or of dark matter or dark energy, etc. But if the horizon's restriction of entropy inside does not actually cause complexity to start to arise, then perhaps the expansion of the universe may be limited so that the entropy of the horizon never becomes smaller than the entropy inside. Or since the cosmological event horizon is not a topological property, its entropy may not require a topological compensation, such as a particle, but my require only a softer response of just the configuration of particles on the average with possibly some delay.

 

[Chronos]

Bear with me a bit longer, ST, I'm trying to wrap my head around this. From page 9-10 of the Lineweaver paper:

The particle horizon has traditionally been depicted as the worldline or comoving coordinate of the most distant particle that we have ever been able to see (Rindler, 1956; Ellis & Rothman, 1993). The only information this gives is contained in a single point: the current distance of the particle horizon, and this indicates the current radius of the observable universe. The rest of the worldline can be misleading as it does not represent a boundary between events we can see and events we cannot see, nor does it represent the distance to the particle horizon at different times.

I'm reading this to mean the observable universe only changes in size, not observable content over time. The paragraph that follows appears to support this interpretation:

An alternative way to represent the particle horizon is to plot the distance to the particle horizon as a function of time (Kiang, 1991). The particle horizon at any particular time defines a unique distance which appears as a single point on a spacetime diagram. Connecting the points gives the distance to the particle horizon vs time. It is this time dependent series of particle horizons that we plot in Fig. 1. (Rindler (1956) calls this the boundary of our creation light cone – a future light cone starting at the big bang.) Drawn this way, one can read from the spacetime diagram the distance to the particle horizon at any time. There is no need to draw another worldline.

Thanks again for your indulgence [amateurs can be thick skulled].

 

[Garth]

I was suggesting that the cosmological event horizon was restricting and reducing entropy so that complex forms such as life came into existence.

There are two discussions going on here, one about various horizons and the other about entropy and 'information'.

May I 'fly a kite' about entropy?
The concept of entropy arose from the Second Law of Thermodynamics which itself arose from the study of heat engines and the behaviour of hot gas under pressure in a closed system. Molecules of such a pressurized gas tended to 'fly apart' and thus increase the disorder of that system.

This vague concept was given mathematical precision in the definition of entropy S:

$$dS=\frac{dQ}{T}$$
where dQ is the change in heat absorbed/lost by a system at temperature T.

However when considering the entropy of the universe, and the problem of how order arose from an original disordered state, there are two recognised questions and a third one that I have always pondered about but never resolved.

Perhaps you may enlighten me.

The first question in cosmological entropy is whether the universe can be considered as a closed system, if not the 2nd Law does not apply.

The second is whether the very fact of the expansion of the universe increases the number of possible states available for physical systems within it and that itself reduces the entropy.

But my question is whether the 2nd Law applies in the first place to a gravitating system, such as the universe, in which particles tend to 'fly together', rather than apart. In this case, when gravitation is the dominant force, may it be seen as a natural entropy-reducing and order-producing agency working in opposition to the Second Law of Thermodynamics?

Just a thought.

Garth

 

[SpaceTiger]

But my question is whether the 2nd Law applies in the first place to a gravitating system, such as the universe, in which particles tend to 'fly together', rather than apart. In this case, when gravitation is the dominant force, may it be seen as a natural entropy-reducing and order-producing agency working in opposition to the Second Law of Thermodynamics?

There's an interesting discussion of this here. In short, a system collapsing under the influence of gravity will experience a decrease in entropy, as one might intuitively expect, but it also loses energy. If it loses energy, then that means that something is leaving the system, "carrying away" entropy with it. Most of the time, this something will be light.

 

[SpaceTiger]

The particle horizon has traditionally been depicted as the worldline or comoving coordinate of the most distant particle that we have ever been able to see (Rindler, 1956; Ellis & Rothman, 1993).

Yes, this is our current particle horizon. The "worldline" of an object at this distance will bring it, in physical coordinates, further and further from us with time, but if viewed in comoving coordinates the distance is a constant. However, this is only for the current particle horizon, as is described in the next few sentences:

The only information this gives is contained in a single point: the current distance of the particle horizon, and this indicates the current radius of the observable universe. The rest of the worldline can be misleading as it does not represent a boundary between events we can see and events we cannot see, nor does it represent the distance to the particle horizon at different times.

That last sentence is key. It says that the worldline of the current particle horizon does not represent the particle horizon at different times. This is another way of saying that the comoving radius of the observable universe changes with time, which is another way of saying that the contents of the observable universe change with time.

 

[Garth]

There's an interesting discussion of this here. In short, a system collapsing under the influence of gravity will experience a decrease in entropy, as one might intuitively expect, but it also loses energy. If it loses energy, then that means that something is leaving the system, "carrying away" entropy with it. Most of the time, this something will be light.

Yes thank you - the system is radiating away energy.

I was actually thinking about a dust cloud collapsing under its own gravity - a cloud of non-interacting particles. (sounds familiar?)

BTW I'm interested that Baez recommended the book "F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, 1965", it's sitting on my bookshelf. It was our textbook at BSc level and I bought it at huge expense, but then at MSc level we were told not to use it because it is basically mistaken! I never got to the bottom of that!

Garth

 

[SpaceTiger]

I was actually thinking about a dust cloud collapsing under its own gravity - a cloud of non-interacting particles. (sounds familiar?)

That's a bit trickier, since non-interacting particles cannot reach eqilibrium, but I assure you the second law still applies. The gravitational force is time-reversible, meaning the fluctuation theorem would apply to it as well as to the other forces.

 

[Mike2]

That's a bit trickier, since non-interacting particles cannot reach eqilibrium, but I assure you the second law still applies. The gravitational force is time-reversible, meaning the fluctuation theorem would apply to it as well as to the other forces.

Do you have a link to a more mathematically complete explanation of the Fluctuation theorem. Thanks.

Something I don't understand. If time reversible processes mathematically lead to entropy, then doesn't the mathematics equally say that entropy leads to reversible processes, in otherwords, entropy influences the particle physics? What I don't understand is how math can prove one thing, but that thing does not prove the one. In logic one has material implication where one thing can prove the second but the second does not prove the first. But in math we're dealing with equivalences where if one thing equals another, than that means the other thing equals the first. So how did material implication enter the process of proving the Fluctuation theorem?

 

[SpaceTiger]

Do you have a link to a more mathematically complete explanation of the Fluctuation theorem. Thanks.

http://prola.aps.org/abstract/PRL/v71/i15/p2401_1?qid=57a56940f9ccff67&qseq=2&show=10

 

[Gold Barz]

Sorry ST, but could you reply to the question I PM'd you about this specific topic please?

Thanks.

 

[SpaceTiger]

Sorry ST, but could you reply to the question I PM'd you about this specific topic please?

Perhaps you should start asking your questions on the forum. After all, that was its original intent.

 

[Gold Barz]

What do you guys think of quantum fluctuations/virtual particles being able to inflate as universes during/after heat death?...maybe that is how universes are born? maybe that's how inflation happens...is it a cuckoo theory or a pretty reasonable one?

 

[Mike2]

What do you guys think of quantum fluctuations/virtual particles being able to inflate as universes during/after heat death?...maybe that is how universes are born? maybe that's how inflation happens...is it a cuckoo theory or a pretty reasonable one?

If that were true, then we could not know how old or how big our present universe is. This would push the cause of the universe so far in the past that we would never be able to discern how the universe came into being to begin with.

 

[Gold Barz]

Isnt this how inflation theory works though, each "bubble" is a universe in its own right?

 

[Chronos]

I think not. Inflation is more complicated than that. You must work out the Friedmann models before you can even consider the alternatives. I don't mean to be hard on you, Gold, but I assure you it's complicated. I barely grasp the basics.

 

[Gold Barz]

But doesn't the "creator" of the inflation theory suggest that with inflation comes multiple universes? and it makes sense too, if this inflation happened it could have happened more than once and could still be happening. Plus, the wikipedia article seems to suggest that it does come with multiple universes.

 

[Gold Barz]

Is the description of Inflation as stated in this link right?

http://www.pbs.org/wgbh/nova/universe/howbig.html

It states that our visible universe might just be a fraction of a patch of the entire universe BUT they said inflation could have happened and could still be happening so there might be other universes...wow...is this how inflation really works

 

[Garth]

It states that our visible universe might just be a fraction of a patch of the entire universe

True.

BUT they said inflation could have happened and could still be happening so there might be other universes

Show me one.

...wow...is this how inflation really works

I'm afraid so, it depends on a scalar field mediated by the Higgs boson, a fundamental particle predicted by theory yet undiscovered in laboratory physics after 20 years of trying, and leads to speculation of other universes, each one a 'bubble' in an eternally inflating foam, that can never be observed. Neat eh!

Garth

 

[JesseM]

BUT they said inflation could have happened and could still be happening so there might be other universes

Show me one.

I think he's referring to the idea of "chaotic inflation", which is discussed here:

In October 1981, there was an international meeting in Moscow, where inflation was a major talking point. Stephen Hawking presented a paper claiming that inflation could not be made to work at all, but the Russian cosmologist Andrei Linde presented an improved version, called "new inflation", which got around the difficulties with Guth's model. Ironically, Linde was the official translator for Hawking's talk, and had the embarrassing task of offering the audience the counter-argument to his own work! But after the formal presentations Hawking was persuaded that Linde was right, and inflation might be made to work after all. Within a few months, the new inflationary scenario was also published by Andreas Albrecht and Paul Steinhardt, of the University of Pennsylvania, and by the end of 1982 inflation was well established. Linde has been involved in most of the significant developments with the theory since then. The next step forward came with the realization that there need not be anything special about the Planck- sized region of spacetime that expanded to become our Universe. If that was part of some larger region of spacetime in which all kinds of scalar fields were at work, then only the regions in which those fields produced inflation could lead to the emergence of a large universe like our own. Linde called this "chaotic inflation", because the scalar fields can have any value at different places in the early super-universe; it is the standard version of inflation today, and can be regarded as an example of the kind of reasoning associated with the anthropic principle (but note that this use of the term "chaos" is like the everyday meaning implying a complicated mess, and has nothing to do with the mathematical subject known as "chaos theory").

The idea of chaotic inflation led to what is (so far) the ultimate development of the inflationary scenario. The great unanswered question in standard Big Bang cosmology is what came "before" the singularity. It is often said that the question is meaningless, since time itself began at the singularity. But chaotic inflation suggests that our Universe grew out of a quantum fluctuation in some pre-existing region of spacetime, and that exactly equivalent processes can create regions of inflation within our own Universe. In effect, new universes bud off from our Universe, and our Universe may itself have budded off from another universe, in a process which had no beginning and will have no end. A variation on this theme suggests that the "budding" process takes place through black holes, and that every time a black hole collapses into a singularity it "bounces" out into another set of spacetime dimensions, creating a new inflationary universe -- this is called the baby universe scenario.

 

[Garth]

I think he's referring to the idea of "chaotic inflation", which is discussed here:

Yes, sometimes referred to as 'eternal inflation' Langevin Analysis of Eternal Inflation but my challenge was "Show me one - one of these other universes!"

Garth

 

[Gold Barz]

They said quantum fluctuations are the reason for these universes, is it the same type of quantum fluctuations that happen normally in our universe or is it different? do these virtual particles "inflate"? the same virtual particles we see near black holes?

 

[Gold Barz]

I read somewhere that the creator of the theory, the brilliant, Dr. Alan Guth says inflation forces the multiple universes scenario on us...

"In fact, Dr. Guth said, "Inflation pretty much forces the idea of multiple universes upon us."

from here - http://courses.washington.edu/phys55x/A%20New%20View%20of%20Our%20Universe%20Only%20One%20of%20Many.htm

 

[Garth]

They said quantum fluctuations are the reason for these universes, is it the same type of quantum fluctuations that happen normally in our universe or is it different? do these virtual particles "inflate"? the same virtual particles we see near black holes?

Quantum fluctuations in what?
Some pre-existent quantum foam has to be assumed, can we observe such or unambiguously test for it? I think not.
It is not like the Hawking radiation around a BH because there was no BH, the BH Hawking radiation is based on the spherically symmetric Schwarzschild solution embedded in a flat space-time, but there is no space-time 'outside' any 'yet-to-be-created' universes.

Just a thought.

Garth

 

[Chronos]

I object to the notion of inflation forcing acceptance of multiverses - albeit less strenuously than say, a week ago. Recent discussions with more qualified experts give me pause to reexamine my position... i.e., I might be wrong. Shocking.

 

[hellfire]

They said quantum fluctuations are the reason for these universes, is it the same type of quantum fluctuations that happen normally in our universe or is it different? do these virtual particles "inflate"?

As far as I know they are the same, at least in that framework. In my opinion there is, however, an important difference in the theoretical treatment of the subject. When treating quantum fluctuations of any field in any classical background, no backreaction of the fluctuations on the background spacetime is considered. For eternal inflation to work, the backreaction of the fluctuations on the metric has to be considered: some of the fluctuations of the field responsible for inflation can start to inflate space as they have the properties to do so. However, in order to successfully explain the quantum effects of matter on spacetime one should consider the fluctuations of the metric itself (the quantum effects of spacetime). This is not possible without going into wild speculations, as there is no successful quantum gravity yet. The model of eternal inflation (leading to separated universes or bubbles) relies on this heuristic argument which seams not to be completely rigorous. This is just my personal opinion.

 

[Chronos]

That's a bit wordy for my taste, hellfire, but I like the way you think. My only concern is we might need to relax our parameters when it comes to the fluctuation thing. Your objection on the basis of back-reactions is well founded [there have been numerous papers to that effect]. But I have nagging doubts if it works all the way back to the quantum level. But, hell, I have nagging doubts about everything on that level. So don't let it stop you, just fear what happens in between. I know it scares me.

 

[SpaceTiger]

Quantum fluctuations in what?
Some pre-existent quantum foam has to be assumed, can we observe such or unambiguously test for it? I think not.

I'm going to agree with Garth on this one. We should try to obtain a more complete understanding of our own universe before indulging in wild speculation about multiverses. If it's possible to test for them, then I'm sure it's many, many years off.

 

[Gold Barz]

But the current inflation theory seems to suggest the existence of other "bubbles"...like I said before the creator of the theory said it himself that inflation forces the idea of multiple universes or bubbles on us, but as ST and Garth said there is no way we can test this and we do not even know if it is possible to test for it, and there will be NO communication between bubbles, so when its all said and done it might as well be only one universe, even if there are others.

Also, I have read many times that most scientists do not doubt inflation, is this really true?

 

[SpaceTiger]

Also, I have read many times that most scientists do not doubt inflation, is this really true?

Eh, it's true that most astronomers/physicists favor inflation over all competing theories, but I wouldn't go as far as to say they don't doubt it. If we detect B-mode polarization of the CMB at the predicted levels, then it may attain the status of "beyond reasonable doubt" in the minds of most scientists, but we still lack direct evidence.

 

[Gold Barz]

So in the most current inflationary theory, these pocket universes are suggested right?

 

[Chronos]

I yield to the graduate student.. but still disagree... much fun!

 

[Gold Barz]

Who's the graduate student?, disagree with what point?...I'm lost lol