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All the physicists already know that the n-body problem reveals chaos, so that the planets around the sun should undergo deterministic chaos with a Lyapunov exponent of the order of, say, $\frac{+1}{3.5\,\text{million years}}$, [1]. This implies we cannot predict neither forward nor backward in time what was the orbital configuration of the planets around the Sun, when the prediction time goes beyond some finite time of the order of the Lyapunov exponent, [2]. Obviously when we account for any and all the celestial bodies the prediction time decrease significantly, I will say maybe to less than a few thousands of years if you ask me, [3].

Now a problem arises ... The apparent regular behavior of the celestial bodies in the sky is nothing but a short-period section of the whole chaotic picture, let say about a single point in the whole phase space. What does then, within this viewpoint, experimental evidences like "red shift" tell us? Or better to ask, what can they tell us? Does the idea behind "big bang" persist or it will lose its witnesses immediately?

(Of course you better know the distant to moon is altering, and many many other facts that all of you know better than me, the moon getting farther doesn't have anything to do with big bang and the whole universe expanding, does it?)


Edit:

@RobJeffries conducted me in his comments to an article in which a regular behavior was predicted for the solar system within periods far longer than what I had mentioned according to another reference, [1]. Meanwhile, @DirkBruere mentioned in his answer that the overall behavior of the universe can be studied independent of studying the chaotic behavior of every single celestial body in universe, just as the cases for the kinetic theory of gases. According to these two notices I sought to find some references that will describe the matter more thoroughly. These are what I can say for now:

  1. the followings are some passages collected from [4] regarding the subject:

    Celestial Mechanics was the prototype of order. The use of perturbation theories in the solar system had proved quite effective in predicting the motion of the planets, satellites and comets. Despite the fact that the perturbation series were in most cases extremely long, their effectiveness was never doubted. ... Poincare proved that most of the series of celestial mechanics are divergent. Therefore their accuracy is limited. On the other hand, it was made clear that the most important problem of celestial mechanics,the N-body problem, cannot be solved analytically. ... A completely different approach to the theory of dynamical systems was based on Statistical Mechanics. This approach dealt with the N-body problem, but from a quite different point of view. Instead of a dominant central body (the sun) and many small bodies (planets), it dealt with N-bodies of equal masses (or of masses of the same order) with N tending to infinity. Then a number of statistical assumptions were made that gave results that could be tested by experiment. ... In this approach the notion of individual orbits of particles became not only secondary, but even irrelevant. ... The most important result of ergodic theory was the proof by Sinai (1968,1970) of the basic theorem of gas dynamics for a hard sphere gas. Namely,Sinai proved that a gas composed of hard spheres moving along straight lines and colliding elastically is ergodic, and has positive metric entropy. A particularly simple case of this theorem is the motion of a point inside a square box containing a circular body. The particle moves along a straight line until it hits the boundaries of the box, or the circle. Such a motion is ergodic. After this theorem everyone was satisfied that statistical mechanics had found a sound foundation. It was thought that cases where orderly motion appeared, as in celestial mechanics, were in some sense exceptional. Yet, as we will see, the real situation is quite different. The ergodic cases of statistical mechanics and the ordered cases of celestial mechanics are both exceptions and the most general case is in between.

    What I understand according to this quotation is that the case for gases (ideal gases with such critical properties like having their molecules as rigid spheres and etc.) is in the opposing position regarding the order found in the celestial dynamics and that the general case of the many body dynamics is neither totally ergodic as in the kinetic theory of gases, nor totally ordered as perhaps for planets in the solar system. However, in the rest of the book, if I have caught the idea correctly, it is said that the case for celestial dynamics is not totally ordered or integrable, but case to being integrable with probable windows of chaos. Then solar system and some galaxies are studied for stability and things like that and most of the celestial bodies are found to be stable within their ages or within the whole age of the universe, if I am right. However, I didn't find anywhere in the book the author addressing the overall behavior of the whole universe (maybe my mistake). It is only mentioned here and there that the age of universe is the Hubble time which is about 10 billion years, like the age which is usually accounted for the universe assuming Big Bang has happened. So I conclude, that Big Bang has happened is presumed by the author and he had no doubt in it, while he doesn't strictly address the predictability of the overall behavior of the universe, specially if we know the whole universe has no ergodic behavior and thus is not like the cases for the ideal gases for which we have the kinetic theory. Now, please clarify the situation, what are the reasons for us to assume the behavior of the whole universe is predictable like in the kinetic theory of ideal gases.

  2. Especially have the scientists done a statistical analysis of the the whole universe for them to predict its overall behavior during last 10 billion years? In [5] it is written that Einstein never took the Big Bang theory serious since he thought if one traces the motion of the galaxies backward in time the theory will fail. Do we have any integration of the dynamical equations for the whole universe? I mean something like what is done in the paper introduced by @RobJeffries in the comments, but instead of focusing on the solar system studying the whole universe with all its galaxies and superstructure complexes and etc.

  3. Searching Internet I found only one related study regarding the dynamics of the whole universe and chaos. Check [6] wherein it is stated that chaos came to be dominant in the dynamics of the whole universe at the very beginning of its formation from $10^{-43}\,s$ and lasted only a very brief time, like at least $10^{-36}\,s$ in duration. If this is true, then before that will be unpredictable and I saw, e.g., in [7] that a modern physicist may even use this and say Bib Bang is not necessary at all:

    I find it more satisfactory to make a cosmological model where the density and temperature are never infinite. This precludes a Big Bang and replaces it with a different picture of time where time never begins and never ends. This is in contrast with the standard cosmological model where time begins at the Big Bang and never ends during an infinite future expansion. While I cannot prove rigorously that the conventional wisdom is wrong, it does entail the singularities and concomitant breakdown of general relativity that we have mentioned. The existence of plausible alternatives now, however, makes the Big Bang idea less plausible.

  4. And last, but by no means least, a very recent paper [8] claims that if one prefers the Bohmian quantum mechanics over the Copenhagen interpretation of the quantum mechanics, then no singularity arises at all and, hence, no Big Bang singularity is predictable at all:

    Ali and Das explain in their paper that their model avoids singularities because of a key difference between classical geodesics and Bohmian trajectories. Classical geodesics eventually cross each other, and the points at which they converge are singularities. In contrast, Bohmian trajectories never cross each other, so singularities do not appear in the equations.

With all these considerations now I still have question regarding the predictability of the dynamics of the universe backward in time (general relativity is not a statistical theory), so that the red shift effect and the cosmic background radiation shouldn't be a strong justification of the Big bang idea. Do they?


[1] as for reference please check this youtube movie of Alex Maloney's McGill course on Classic Mechanics, around the minute 43

[2] as for reference for this check the page 322 of the book "Nonlinear Dynamics and Chaos" by Steve Strogatz, when he is defining and explaining the ``time horizon"

[3] This is my own intuition, so I added the expression that "if you ask me"

[4] Contopoulos, G. "Order and Chaos in Dynamical Astronomy", Springer, 2010.

[5] Javadi, H. & Javadi, A. "Physics from the Beginning upto Now, Including presentation of CPH theory", Etta Publisher, 1386 (in Farsi).

[6] After Big Bang Came Moment of Pure Chaos

[7] Frampton, P.H. "Did time begin? Will time end? Maybe the Big Bang never occurred", World Scientific, 2010

[8] No Big Bang? Quantum equation predicts universe has no beginning

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    $\begingroup$ Where do you get your information from? Stability analyses for the solar system work over very considerably longer timescales than you suggest. $\endgroup$ – Rob Jeffries Mar 22 '15 at 12:20
  • $\begingroup$ @RobJeffries, references added. Meanwhile, please explain more about the stability analysis you mention, does it take into account all the planets together? what about the other celestial bodies? What about the stability analysis of the whole universe? After all, the question is regarding Big Bang and not actually about the solar system. Thanks for your time. $\endgroup$ – owari Mar 22 '15 at 17:30
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    $\begingroup$ I am no expert, but it appears that the Lyupanov timescale is not really the determining factor as far as solar system stability goes. adsabs.harvard.edu/abs/2008ApJ...683.1207B arxiv.org/abs/1411.5066 $\endgroup$ – Rob Jeffries Mar 22 '15 at 18:28
  • $\begingroup$ I do not see the connection between orbital motions and the big bang. $\endgroup$ – Kyle Kanos Mar 23 '15 at 2:36
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    $\begingroup$ Regarding [8], we already have a question indicating that the claims made there are...rather overconfident. $\endgroup$ – ACuriousMind Mar 31 '15 at 18:07
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You seem to be misunderstanding the depth of the prediction we've made of the past in saying that the Big Bang happened. You do make a very valid point that chaotic systems even with as few elements as the solar system are practically impossible to past-predict (I'm going to start using the word "postdict"1 because it makes me feel better). I'm more than willing to admit that we have no way of knowing where Earth was around the Sun 4.5 billion years ago. However, I'm sure you would agree that what we can say is that Earth was in orbit of the Sun 4.5 billion years ago. Earth is orbiting the Sun now, there is no evidence that it is an extrasolar capture, and we estimate its age at about 4.6 billion years. Therefore, we can say it was orbiting the Sun 4.5 billion years ago.

This may not seem like much of a postdiction, but if, before now, we had absolutely no idea where Earth was at that time, then this statement would become a major breakthrough in our understanding of the history of our solar system. In a similar manner, saying the Big Bang happened is just as deep. We don't know the exact conditions or the distribution of energy at the Big Bang (not yet anyway), but we have the evidence that it happened. We know that space is expanding and that galaxies and other celestial bodies are all moving away from us. We also know that the universe is cooling. We can determine the recessional velocity of objects at different distances and use that to determine the expansion history. Then we can trace this backwards and say that everything must have been contained in an incredibly hot and dense point at about 13.8 billion years in the past. This is our Big Bang era. We aren't saying exactly where things were and how much and what they were doing. Like saying Earth was in orbit of the Sun 4.5 billion years ago, we are saying the universe was a hot, dense, and incredibly small in scale 13.8 billion years ago.

Many models and theories exist that speculate on the initial conditions of the universe or try to establish more of the specifics during the Big Bang era, and can you blame us for being thorough?

I'll try to address as many of your follow up points as I can:

Both (1) and (2) are based on the idea that we are making postdictions that are too specific for a chaotic system to allow. I've attempted to explain how that is not the case in my above writings. If I have succeeded, then I don't think anything more is necessary for these points. If I haven't succeeded, then I'm not sure what reservations you have, so I'll wait to tackle these points.

Your point (3) is getting into chaotic inflation. Inflationary theories in general only exist to solve problems in the old Big Bang theory. But all inflation theories admit the Big Bang era occurs after inflation, and they also allow for the Big Bang moment before inflation (that is, the curvature singularity). The Big Bang era is the era of a hot, dense universe that is radiation/matter dominated and ends at about the time of recombination. Everyone agrees this happened just like they agree Earth orbited the Sun. Inflation itself (not just chaotic inflation) is a period of rapid expansion, but most physicists agree that there was probably a curvature singularity beforehand.2 There are theories and physicists like the one you quote that say a curvature singularity is unnecessary; that the universe needn't ever have been a point, but that doesn't mean they don't think the Big Bang era or expansion in general was non-existent.

Point (4) is not something to put a lot of weight on yet. In another of my answers I specifically addressed this exact paper and detailed how it was too insufficient to to take seriously.

All in all, the present evidence for the Big Bang is very compelling evidence and the theories involving the Big Bang have made some remarkable predictions that fit the available data very well. It may be true that we cannot postdict the exact state of the universe 13.8 billion years ago. We may even be off in the age by a few billion years, but I maintain that we can say the Big Bang era occurred as surely as we can say that Earth was in orbit of the Sun 4.5 billion years ago.


1I looked it up and apparently "postdict" is a word that means exactly what I was hoping it did. Hooray for consistency of prefixes!

2 See another question and answer of mine for more information on definitions of the Big Bang as before and/or after inflation.

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  • $\begingroup$ Many thanks for the time you spent on your answer. Actually, I was thinking of the Earth being captured in the gravity of sun as one probable scenario if we really have chaos here. I guess, the stability analysis of the trajectories of the planets would support your point, but I doubt whether this stability analysis considers also nonlinear instabilities as well or not. Considering other celestial bodies beside the solar system in calculations the occurring of a large instability seems not to be safely unbelievable. One may consider solar system alone and find trajectories that never existed? $\endgroup$ – owari Apr 1 '15 at 0:20
  • $\begingroup$ Meanwhile, it's a very good idea that if when we look deep at the sky we are looking at the history of universe, then we can safely claim that the universe has had always expanded and this trend has not been chaotic, so that predictability is proved in this regard and the red shift alone is sufficient for the Big Bang theory or a theory close to it to be relevant. Good idea, indeed, and I guess you and all the other great physicists would easily accept it, however, I'm not an expert and things come to my sight rather messy. $\endgroup$ – owari Apr 1 '15 at 0:26
  • $\begingroup$ In particular, once I was studying the distance measurement in astronomy and the distance ladder for some problems that I had with some remarks in it, a great share in the knowledge we have about the distances come from luminosity of the stars, the speed of light and that light travels a straight line far enough from the huge massive bodies, but what if the inter-stellar space has more matter that we usually consider, density gradients and etc.? (actually I had some personal reasons to doubt such, not a totally blind guess but not also an acceptable reasoning for the scientific community) $\endgroup$ – owari Apr 1 '15 at 0:41
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    $\begingroup$ @owari I'm not entirely sure what you are saying. But for what I could follow; we are sure Earth is not an extrasolar capture because it has approximately the same composition as the other terrestrial planets and it's orbit is too close to a perfect circle. The continued expansion of the universe is an observation, not a claim. We can see that objects further from us are receding faster, meaning expansion must have been present in the past as well. $\endgroup$ – Jim Apr 1 '15 at 12:38
  • $\begingroup$ Actually, I still have doubt about the relevance of the evidences for the expansion of the universe and the accuracy of the distance ladder and, thus, how redshift would be understood, but aside from that I accepted your answer as it seems to be the best and the ultimate answer that the present community of physics would give. Thank you for the time and effort you put in your answer. $\endgroup$ – owari Apr 2 '15 at 18:24
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The problem is analogous to the physics of gases. Do we need to describe the chaotic motion of every molecule before we can determine overall properties? No.

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    $\begingroup$ Well, before I read your answer I thought overall prediction in gas dynamics is possible but is not possible for turbulence because of the nonlinearity of the equations governing the latter, missing in the former ... this is what is commonly said ... but reading your answer I suspect and seek Internet for a better explanation and eventually it seems to have something found. Let me take a look at two books just found before to judge your answer. $\endgroup$ – owari Mar 23 '15 at 10:10
  • $\begingroup$ Please check the update provided for the question, thanks $\endgroup$ – owari Mar 31 '15 at 12:47
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I'm not sure if that touches your question, but the universe is thought to be non-chaotic in the long term behaviour because of some anisotropy in the initial conditions (at least this is the general opinion). I watched a cool vid about that a couple of days ago.

The point for which I agree with you, is that if looking at a certain situation, in general one cannot deduce the cause of that situation, since this is an inverse problem usually ill-posed (e.g. calculating matter distribution due to potential measurments). In this context, the big-bang-model is a good guess of the intial-conditions which may evolve into the current situations, but there is no certainty, that this is the only model able to do this.

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  • $\begingroup$ I think I can understand your point, please bear with me if I am wrong. You mean if there arise a preferred direction at the great blast, then this direction will be the source of a long-term order if we ignore the chaotic details, am I right? Meanwhile, I'm not an expert in this field, but read somewhere that the anisotropy was in the form of expansion (red shift) in two directions and contraction (blue shift) in the third one, and I guess the preferred direction has its root in quantum fluctuations, right? $\endgroup$ – owari Apr 1 '15 at 0:07
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    $\begingroup$ @owari: Yes this is the idea behind it. However, for details on how this anisotropy is modeled in BB-theory, I might not be the right one to ask. $\endgroup$ – image Apr 1 '15 at 0:43
  • $\begingroup$ Your answer is very good, indeed, but I am going to accept @Jimnosperm's answer, as your answer justifies why Big Bang can be a good idea, but it doesn't conclude that the present state of the universe has necessarily triggered by a Big Bang or a anything close to it. There might be several other ideas that can prove to be good as well. $\endgroup$ – owari Apr 2 '15 at 17:52
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    $\begingroup$ @owari: Yes, no problem. In the end, I might be more a sceptic than a believer ;) For an illustrative historcal description of the bing bang model, I suggest you reading this book. It's no "hard" science book, though it's quite enjoyable to read. $\endgroup$ – image Apr 2 '15 at 18:39
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The problem with this question is in the premise that where dynamical chaos is applicable nothing is predictable or can be extrapolated to the past. This is a wrong premise.

Take this demonstration of a chaotic system. Note that it is computer simulation and of course it fits real data. Computer simulations are time symmetric, so the individual points can be taken back with accuracies related to computer capabilities. If you take this double pendulum simulation and stopped it at one point you could not extrapolate to the vector of its beginning, with pencil and paper, but a computer, with all the values and the boundary condition can. It is the complexity of the problem and the simplicity of some descriptions that make dynamical chaos theory useful. I stress the "dynamical" because :

Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect.

Dynamical clarifies that equations exist, chaos shows that the complexity is high and collective behavior is examined.

The same is true about the solar system, where the chaotic study applies too. The existence of planetariums uses the dynamical equations to extrapolate positions of planets, despite that the system is considered dynamically chaotic.

In a different framework, given a gas and infinite computing power the dynamical equations are known and given the initial boundary conditions and all the constants each individual molecule could be followed. Its position is truly chaotic as far as we are concerned but the principle tells us that we could determine it backwards and forwards in time. Fortunately we developed statistical mechanics, and before that , thermodynamics to have predictive and postdictive knowledge of a system as a whole.

Now the Big Bang hypothesis is not chaotic.

big bang

General Relativity is a dynamical system which sets the framework, the coordinates, on which the primordial soup of energy is developing in time. The soup is classical thermodynamic after a certain point in the expansion of the coordinates and as in a gas, the individual component, lets say protons neutrons electrons locations are irrelevant and fitted statistically after the first three minutes . The chaotic behavior is irrelevant to the overall development in time.

Before the 3minute point a lot of nuclear and particle and special relativity behaviors enter in the modeling, and quantum mechanics is paramount, again with dynamical equations. The inflationary period was introduced to explain the isotropy in the microwave background radiation. Homogenization could not be attributed to classical thermodynamics as the regions of space could not interact with each other classically . Quantum fluctuations have been successful in modeling the data.

So chaos is not the everyday meaning of chaos and is not applicable in physics wherever there exists complexity. Tools have been developed to model the data of the observed universe and they are very successful at the moment.

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  • $\begingroup$ Sorry @annav, as far as I can say, humbly, you have not fully understood my question and, actually, I know what I mean by chaos! Predictability that you claim to be infinitely possible is not possible in the real world. You can always solve an equation by integrating it forward or backward, but if the system behaves chaotically then there would be a horizon time after which the result is not reliable. If you read my question I already talked about the positive Lyapunov exponent and I should add that the planetarium example is irrelevant. Meanwhile, thank you very much for trying to be helpful. $\endgroup$ – owari Apr 2 '15 at 17:31
  • $\begingroup$ My basic statement is that dynamical chaos is a way of describing complexity, but not all complexities are describable by dynamical chaos. Thermodynamics is a way of describing complexity too, overall "order out of confusion" . $\endgroup$ – anna v Apr 2 '15 at 18:21

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