On the arrow of time again


Lorenzo Maccone’s argument (see here)  is on the hot list yet. Today, a paper by David Jennings and Terry Rudolph (Imperial College, London) appeared (see here) claiming Maccone’s argument being incorrect. Indeed, they write down Maccone’s argument as follows

Any decrease in entropy of a system that is correlated with an observer entails a memory erasure of said observer

but this erasure is provided by quantum correlations. The key point is the link between quantum correlations and local decrease of entropy as seen by classical correlations. Jennings and Rudolph interpret Maccone’s view as the reduction of information at a quantum level entails a reduction of information at a classical level and we do not observe such events. These authors show counterexamples where this does not happen arguing that Maccone’s argument does not explain rather worsens the problem as quantum correlations can decrease while classical ones can increase.

I guess that this comment will undergo the standard procedure of Physical Review Letters for it and Lorenzo Maccone will produce a counterargument facing in this way a review process. As it stand, it appears a substantial open problem to the original Maccone’s proposal but relies in an essential way on the interpretation Jennings and Rudolph attach to it.

Being this a really exciting matter, it will be really interesting to following the way events will take place.


The question of the arrow of time


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.

Sean and Horacio


I know Sean Carroll as some years ago I read his beautiful lectures on general relativity that become a book. Some years later I started to read his blog and this I do also today. Sean touched a lot of arguments in physics during these years but the most important for me are those about arrow of time and reality forming (measurement problem in quantum mechanics). These two matters are strongly linked and their understanding represents a great achievement in physics and this explains why a lot of ink, paper and digital data have been spent around the world. Sean has written an article on this on Scientific American (see here). Contrarily to some wisdom around this problem is really deep as there is no reason on Earth to accept environmental decoherence and multi-universe interpretation as the ultimate answers that finally do not grant any answer to a simple fact. This fact was explained to me quite simply by Giorgio Careri. Careri has been a professor of mine at department of physics of “La Sapienza” in Rome. A day I was walking to the new building of the department (Fermi building) together with some other students when we met him going into the opposite direction. I do not remember the reason why we started to talk but he said something I am still here to remember:”One of the deepest question physics should answer is why, having a four dimensional space-time, we can move backward and forward and we can stop in three of these dimensions but not in time?”. Currently an answer is still lacking being at the root of our understanding of how reality forms and the way it forms.

Horacio Pastawski is a researcher working at University of Cordoba in Argentina and has carried out with his a group a lot of relevant work that can be traced back on the most important archival journals in physics and on arxiv as well. Horacio’s group has found an answer to this matter through NMR experiments. The point can be traced back to the Boltzmann and Loschmidt controversy. In order to answer to the criticism of Loschmidt claiming that as all laws of mechanics are reversible one should conclude that H-theorem is false, Boltzmann put forward the so called Stosszahlansatz (molecular chaos hypothesis) to conclude that indeed H-theorem is right. Boltzmann’s hypothesis is purely statistical and being this true Boltzmann is right. So, the understanding of arrow of time passes through an explanation of Boltzmann’s Stosszahlansatz that we currently lack. But in 1998 Horacio’s group performed an NMR experiment with a complex molecule, ferrocene and cobaltocene, where they showed that an intrinsic instability appears in the thermodynamic limit provoking irreversibility (see here). This shows that Boltzmann is right and this also explains why we observe irreversibility all around in the macroscopic limit. Of course, this result met skepticism in the community and they had severe difficulties to get their paper published on an archival journal notwithstanding no flaw is appearing in their experimental procedure. Anyway, they published their results on Molecular Physics and Physica A and so these are part of scientific literature. But their results received an unexpected confirmation on PRL quite recently in a different perspective as these authors were trying to understand decoherence in quantum computation.

We see that thermodynamic limit plays a central role in our understanding of reality and this matches fairly well with the observed fact that macroscopic objects behave classically and gives also a satisfactory understanding of Boltzmann’s hypothesis that would be completely missing accepting acritically environmental decoherence and multi-verse.

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