Intrinsic decoherence is a scientific truth

01/10/2009

I would like to talk nicely of an initiative that helped me to find out that my view of decoherence, intrinsic decoherence, is indeed a scientific truth. Periodically, the Journal Club of Condensed Matter Physics presents an interesting selection of published papers in the area of condensed state of matter. This on-line journal was formerly started at Bell Labs and, due to its significant editorial members, contains a selection of very interesting works. This month, the first listed paper is a striking one, appeared in Physical Review Letters. It is an experimental paper and this means that the effect was indeed observed and measured. You can find this paper here but a subscription is needed to read it in full.

Let me summarize what I am claiming about this matter (see also here and here). A theorem due to Lieb and Simon says that, when the number of particles is taken to go to infinity for a quantum system with Coulomb interactions then Thomas-Fermi model is recovered. Thomas-Fermi model is a semiclassical model and so, a quantum system loses coherence and starts to behave classically. Please, note that this is a mathematical theorem. On the same ground, a beautiful theorem due to Hartmann, Mahler and Hess (see here)  shows that the decay is Gaussian when the same limit of particles going to infinity is taken. Both theorems, taken together, give a definite scenario of what happens, intrinsically, to quantum coherence of an isolated system. Can this be seen experimentally?

As I have already said, more than ten years ago, Horacio Pastawski and his group (check two papers by him here) proved, with NMR experiments, the very existence of this effect. They met a lot of difficulties to get their paper published. It was not and you can find it here. This group produces  a lot of very good physics and also this was fine as testified by a successive confirmation due to Dieter Suter and Hans Georg Krojanski appeared in Physical Review Letters. So far, it appeared as some pieces of a big jigsaw were around and nobody noticed them to make each other fit. Rather, researchers tried, in a way or another, to insert them in known matters. But this is completely new physics!

On August 8th of the last year, a paper on Physical Review Letters appeared that confirmed all this. This paper is the one I cited at the start of this post and is due to A. P. D. Love,  D. N. Krizhanovskii,  D. M. Whittaker,  R. Bouchekioua,  D. Sanvitto,  S. Al Rizeiqi,  R. Bradley,  M. S. Skolnick,  P. R. Eastham,  R. André, and Le Si Dang. I cite all of them because they did a great job and must be named. The physics relies on the behavior of polaritons. These are quasi-particles appearing in a Bose-Einstein condensate and, being bosons themselves, they condensate too. But observing such a condensate and to understand its decay it is not an easy task. Rather, this makes for an experimentalist a true challenge. Authors above accomplished this task and proved that number fluctuations are involved in the process, the decay is Gaussian and, all in all, the effect is purely intrinsic. The true signature of this effect is the dependence of the Gaussian decay on the number of particles and this is clearly seen by these authors.

All of this shows clearly that two effects are at work in producing the world we observe: an intrinsic effect that appears for a large number of interacting particles and a decay of quantum coherence produced by the interaction with the environment. For the particular case of cosmological perturbations, it is the intrinsic mechanism that induces a classical behavior (see here for an alternative view).


The question of the arrow of time

31/08/2009

A recent paper by Lorenzo Maccone on Physical Review Letters (see here) has produced some fuss around. He tries to solve the question of the arrow of time from a quantum standpoint. Lorenzo is currently a visiting researcher at MIT and, together with Vittorio Giovannetti and Seth Lloyd, he produced several important works in the area of quantum mechanics and its foundations. I have had the luck to meet him in a conference at Gargnano on the Garda lake together with Vittorio. So, it is not a surprise to see this paper of him in an attempt to solve one of the outstanding problems of physics.

The question of the arrow of time is open yet. Indeed, one can think that Boltzmann’s H-theorem closed this question definitely but this is false. This theorem has been the starting point for a question yet to be settled. Indeed, Boltzmann presented a first version of his theorem that showed one of the most beautiful laws in physics: the relation between entropy and probability. This proof was criticized by Loschmidt (see here) and this criticism was sound. Indeed, Boltzmann had to modifiy his proof by introducing the so called Stosszahlansatz or molecular chaos hypothesis introducing in this way time asymmetry by hand.  Of course, we know for certain that this theorem is true and so, also the hypothesis of molecular chaos must be true. So, the question of the arrow of time will be solved only when we will know where molecular chaos comes from. This means that we need a mechanism, a quantum one, to explain Boltzmann’s hypothesis. It is important to emphasize that, till today, a proof does not exist of the H-theorem that removes such an assumption.

Quantum mechanics is the answer to this situation and this can be so if we knew how reality forms. An important role in this direction could be given by environmental decoherence and how it relates to the question of the collapse. A collapse grants immediately asymmetry in time and here one has to cope with many-body physics with a very large number of components. In this respect there exists a beautiful theorem by Elliot Lieb and Barry Simon, two of the most prominent living mathematical-physicists, that says:

Thomas-Fermi model is the limit of quantum theory when the number of particles goes to infinity.

For a more precise statement you can look at Review of Modern Physics page 620ff. Thomas-Fermi model is just a semi-classical model and this just means that this fundamental theorem can be simply restated as saying that the limit of a very large number of particles in quantum mechanics is the classical world. In some way, there exists a large number of Hamiltonians in quantum mechanics that are not stable with  respect to such a particle limit losing quantum coherence. For certain we know that there exist other situations where quantum coherence is kept at a large extent in many-body systems. This would mean that exist situations where quantum fluctuations are not damped out with increasing number of particles.  But the very existence of this effect implied in the Lieb and Simon theorem means that quantum mechanics has an internal mechanism producing time-asymmetry. This, together with environmental decoherence (e.g. the box containing a gas is classical and so on), should grant a fully understanding of the situation at hand.

Finally, we can say that Maccone’s attempt, being on this line of thought, is a genuine way to understand from quantum mechanics the origin of time-asymmetry. I hope his ideas will meet with luck.

Update: In Cosmic Variance you will find an interesting post and worthwhile to read discussion involving Sean Carroll, Lorenzo Maccone and others on the questions opened with Lorenzo’s paper.


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