Tuesday, October 20, 2009

Can entropy decrease in a Big Crunch - without defying the Second Law of Thermodynamics?

The Universe, we're told,  is expanding, and has been from the beginning of time - reckoned to be some 13.6 billion years ago. Extrapolate back, and the Universe must have started as something incredibly small, hot and dense - a singularity. Something caused that singularity to explode, in a Big Bang.  So far, I'm telling you nothing you have not already heard or read many times.

Will the Universe go on expanding for ever? If you believe in Dark Matter and Dark Energy, then the answer is probably yes.  But so far, neither of those hypothetical entities has yet been detected. 

So there's another scenario that cannot be dismissed - that expansion will slow, and the Universe will cease expanding and then start collapsing  back on itself, ending in a Big Crunch.

 Some, myself included, are attracted to this idea, especially as it makes possible the idea of a new Big Bang, indeed, a never-ending series of Bangs and Crunches.

But some objections, or at any rate difficulties, have been raised with the idea of a Big Crunch. One of them is to do with entropy (eg  link to Yahoo forum) , and the Second Law of Thermodynamics, which is the one I intend to discuss briefly here today and tomorrow.

The essential idea conveyed by the Second Law is that while energy is never created or destroyed, energy is gradually dispersed, becoming less and less useful.  Engines use concentrated energy - fuel - to operate. The end product is waste heat - too dispersed for it to be recaptured and re-used. Indeed, the very act of trying to do that would be self-defeating, incurring a greater energy cost than that recouped.  Entropy - the spontaneous tendency for systems to become chaotic, more dispersed, has been successfully analysed statistically in terms of order/disorder, more specifically to do with numbers of possible arrangements. The example I used to give students was this. Imagine you have a neat and tidy bedroom, and there's a strong gust of wind through an open window. Papers get scattered, things fall off shelves etc.  Suppose one started with a disordered bedroom, and there was a gust of wind. You would be very surprised if you ended with a tidy bedroom.  The probability of a chance event - in this case the wind - producing disorder is hugely greater than that of producing order. Why?   Because there are relatively few ordered arrangements compared  to the number of disordered ones.

What's all this got to do with cosmology you may ask?  Well, we see entropy increase around us on a daily basis - eg salt dissolves in water. The ordered structure of a crystal is replaced with the chaos of dispersed ions in solution.  If entropy is steadily increasing, in accordance with the Second Law, then the entropy of the initial singularity must presumably have been minimal, possibly zero - a maximally-ordered  system it would seem.

There's a problem, then, with the idea of contraction back to a singularity - the Big Crunch. Why ? Because if the end result is the same singularity, then entropy would decrease steadily during the contraction. But that would be contrary to the Second Law, would it not?  Other objections have been raised. If we lived in a contracting universe, salt would presumably still dissolve in water, so we would still be seeing the Second  Law in action.

Some have tried to get round the conundrum by introducing the variable of time. It then gets very counter-intuitive, especially the concept of negative time, even history running in reverse!  Let's not go there. 

I believe there is a way of reconciling the concept of a Big Crunch with entropy and the Second Law.

I shall be posting it  here tomorrow!

Wed 21 Oct: Well, tomorrow has arrived, so here's the rest of the story.

It's all to do with the size of the Universe, and its fitness or otherwise to act as an entropy-increasing heat sink. While the Universe is expanding, there is abundant space in which heat can dissipate, or other forms of disorder can occur - eg dilution of gaseous end products etc. In the initial stages of contraction, things would continue much the same while there are still light-years between galaxies, or light-minutes between planets and their nearest neighbours, or even light-seconds between a planet and its moon with intervening space.

But imagine the process of contraction occurring continuously. There will finally come a time when one's perception of nature will change. Galaxies will collide for a start, but let's focus on events at a more local level. Previously there was almost limitless space for heat to dissipate. That will no longer be the case - for two reasons. First there is less space for any new heat to dissipate. Secondly, and more importantly, all the previous heat dissipated into the Universe - which is still out there- will become progressively concentrated. (Reminder; it's not just the contents of space that disappear into a black hole vortex - but the fabric of space-time itself- represented by the mesh in the graphic).

 Temperatures in deep space, presently a few degree above absolute zero, will start to increase. The so-called microwave background radiation,  a left-over from the Big Bang - will gradually shift and start to shorten in wavelength - first to normal radio frequencies, and then into the infra-red region. That's when things start to get interesting. Engines will no longer run so efficiently, because as background temperatures rise, they will find it progressively harder to dissipate exhaust heat.

Let's now look at the salt/water system. Yes, salt will continue to dissolve in water, suggesting that all is well - that the Second Law is still operating.  But as background temperatures increase, the water gets hotter, and if there were still observers around, a point would be reached when the water was no longer liquid at normal temperatures and pressures. In other words, salt could not dissolve in water - if there were no liquid water still in existence!

So there would in fact be a gradual violation of the Second Law as we know it, were the Universe to implode towards a Big Crunch, due to increasing difficulty in dissipating waste heat against a background of rising temperature.  In the final stages, the temperatures would become so great that no heat could be dissipated at all. In that situation, one has returned to a state of minimum entropy, but hugely elevated temperatures.

Had a classical thermodynamicist such as Carnot (of eponymous cycle fame) been born into a contracting Universe he would have enunciated the Second Law of Thermodynamics differently, methinks.  Quite how it would have been worded I would not care to speculate, except to say it would need to have been heavily qualified re differences between open and closed systems. Could a contracting Universe even be described as "open". Only when the system under study was small, with a sizeable temperature difference between it and everything else "out there"?

What then?  See my earlier ideas in the margin (scroll down) which have now been appeared in the MSM - so far with no serious objections being raised. I do not believe that the Big Crunch continues indefinitely. There comes a point when, through frictional forces, the plasma reaches the maximum possible temperature - when its constituent particles (strings?) then  moving/vibrating so rapidly that they reach the speed of light,  and then transform into massless photons. When that occurs,  the system ceases to be a superblack hole, and spectacularly flies apart, creating a new Big Bang...

Update 16th Dec 2014 (5 years later!)

It's temperature that is the key to the conundrum, and the kind of world it creates for those seeking evidence of order/disorder.

In our relatively low temperature world (relying on radiated heat from a single sun that is 92 million miles away) we see lots of evidence of order, notably as the presence of substances as liquids and solids, when at higher temperatures (say in the laboratory) they becomes gases, and at thousands or millions of degrees would be in the plasma state.

But the latter are the temperatures that attain when a Universe contracts down to a black hole,  and then singularity, hypothetically or otherwise. So it's useless to go looking for the kind of ordered, low entropy signatures that we are accustomed to. We have to ask ourselves what the signatures are when temperatures are hugely elevated, such that subatomic particles are travelling at speeds close to those of light, and colliding with each other. Those collisions break down the order of associations, but progressively a simplified plasma emerges in which there are the ultimate particles only, whatever they happen to be, all crushed together. The  original translational energy across sizeable distances now becomes progressively constrained to vibrations about fixed positions (as in a classical earthly solid), obviously with enormous oscillation frequencies. Thus a kind of high-temperature/highly ordered/low entropy state does  (paradoxically perhaps) become finally achievable, but through initial fragmentation, rather than clumping association. In other words, there's more than one route to a low entropy state, depending on temperature.


sami dahan said...

very useful posts, which agree with my instincts on the matter. but why does hawking disagree that a big crunch brings about lower entropy? in a brief history of time, he insists that entropy increases during a crunch, which i do not get. how can more order or heat not be the outcome of a crunch?

Robert Sarracino said...

Penrose explains this very well in his book "The Road to Reality". Entropy due to the gravitational field increases as matter clumps. The maximum possible entropy the universe could attain, would occur if all matter in the universe were to clump into a single black hole.

At the birth of the universe matter was uniform throughout the physical space -- the universe was born in a state of minimum entropy of the gravitational field. Matter at the moment of the Big Crunch would not be so uniformly distributed. It would be clumped into black holes (presumably), and would be in a state of phenomenally higher entropy.

Unknown said...

What is the difference between Big Bang followed by Big Crunch and initial Big Bang? I think it's the same Big Bang! Entropy would be decreased by force in Big Crunch!