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.
We are all waiting for the start-up of LHC foreseen for September 10th. People at CERN are working toward this goal and another success has been achieved with the first test of the clockwise injection system from the SPS to the LHC. We just report this milestone because as all physics community we are eager to see the first results flowing down from this machine. I think there will be particle physics before and after LHC and the former will be much different from the latter.
Here is the CERN news.
Attilio Cucchieri and Tereza Mendes are two researchers working in Brazil at the forefront of our understanding of the behavior of Yang-Mills theory in the infrared. They do computations on the lattice and presently they have got the record of the largest lattice ever used to compute the behavior of propagators at the low momenta limit. Attilio has also done a lot of theoretical work in the same field. They are married but I think this is not the most relevant information for this post. Today they posted on arxiv the third revision of one of their relevant work about ghost propagator. This is a continuation of another paper of them published on PRL about the gluon propagator (see here and here). In both papers they cited one of my works as also their lattice computations support my theoretical analysis.
From their work we now know that Cucchieri and Mendes are ghostbusters. They proved on the lattice that the ghost behaves like a free particle and we know that “free particle” means no coupling. The ghost has disappeared and the Gribov-Zwanzinger scenario faded away. These authors ask a serious question: What is now the confining mechanism? Indeed, there is another question to be answered: What do Gribov copies serve to? They do not seem to be relevant in any part of QCD and so this also is a question to be answered. We have lived with such ghosts for a lot of time and now time is come to give up to cope with them.
We expect new striking works form Attilio and Tereza about QCD now that they contributed so strongly to set the scenario.
In the fall of August 2001 I was in Gargnano on Garda Lake in Italy to participate at the Conference “Mysteries, Puzzles and Paradoxes in Quantum Mechanics”. This was one of a series of Conferences with the same title organized by Rodolfo Bonifacio, a former full professor at University of Milan and now retired (latest news say that he is taking sun in Brasil). These Conferences were very successful as the participants were generally the most representative in the field of quantum optics and fundamental physics. I have had also the luck to meet interesting people that are still in touch with me like Federico Casagrande, an associate professor at University of Milan currently carrying on relevant research in quantum optics and laser physics. That year there was also Vittorio Giovannetti. Vittorio took a PhD in Physics at University of Camerino with Paolo Tombesi and David Vitali that are behind an international renowned group of quantum optics and gave also to the community a number of high quality researchers. At that time Vittorio was a post-doc at MIT and was working together with Seth Lloyd and another brilliant Italian post-doc Lorenzo Maccone. This collaboration produced a lot of relevant papers, mostly in applications of quantum mechanics, that appeared on Nature, PRL and several other high impact archival journals.
Bonifacio was involved with an original idea about intrinsic decoherence. He got a paper published on Nuovo Cimento B and another, with the collaboration of Camerino’s group, on PRA. After we listened at his talk about this interesting matter I exit the room where talks were taken place and exchanged some words with Vittorio and another person. In a while I averted my attention from Vittorio and the other person and started to mumbling thinking about decoherence. Than, looking at Vittorio I said loudly: “Yes, thermodynamic limit! Classical limit can be obtained from quantum mechanics much in the same way thermodynamics is obtained from statistical mechanics!”. Vittorio stared at me and repeated “Yes, thermodynamic limit.” than kept on talking with the other person. This was the start of a lot of papers I have got published on this matter and some interesting experimental work has also been done. The question is still open. The proceedings of the Conference are here.
Today there is a lot of confusion in physics about classical limit and interpretation of quantum mechanics. Indeed, there is a lot of people accepting without critics many-world interpretation without realizing that are out of the realm of physics in this case. If a theory has no criteria to undergo an experimental check is not a theory and we have to forget about this. I have seen a lot of unprepared people talking about many-worlds without elementary cognitions of physics. This is bad and this is why we are living this times today. Mathematics is not enough to be a physicist.
Following my exchange with Lubos Motl (see here) I try to explain what an unconventional view is for people working in QCD. Of course, I agree with Lubos sight that it does not matter how unconventional is your view and so more attracting. What really counts is that this view agrees finally with experiments. But for QCD we have an important goal to reach, a goal that can hit all QFT and whatever else will follow: Our ability to manage a strongly coupled theory and this is a thing that nobody is able to do today in its full generality. This would be a large impact technology as it could possibly apply to any field of physics.
Currently, people tries to approach Yang-Mills theory with lattice computations that grant a non-perturbative solution to such a theory. From a strict theoretical point of view we know from QFT that a tower of non-perturbative equations exists to obtain n-point functions of the theory and these are Dyson-Schwinger equations and can always be obtained for any QFT. What you need here is a proper truncation of the tower and you are done. But this is the most serious difficulty with this approach as it is generally hard to evaluate how good is the chosen truncation and one can also incur in a dramatic error.
So, unconventional views here are those that evade both approaches given above and are able to recover lattice results. I would like to cite the work of Sorella et al. ( see their latest preprint) where they consider an extended Yang-Mills Lagrangian to recover lattice results. Other works have been put forward e.g. by Cornwall as in a pioneering paper to be found here and this produced several interesting works by Aguilar, Natale and Papavassiliou that, numerically solving Dyson-Schwinger equations, are trying to support Cornwall’s view. Finally, I have modified Bender et al. approach that did not work changing it into a gradient expansion recovering straightforwardly lattice results. I apologize for any missing contribution but anyhow I would appreciate whoever would help me to enlarge this list and I will be happy to do it.
What is the most valued of these approaches? Surely one would appreciate the most general ones, those that are not just fitted for the specific aims but that can expand to a large extent to all fields of physics and this possibility exists. So, the stake is high and lattice computations defined the aims. Next years we will see what physicists creativity deserves to us.
Some months ago a paper of mine was rejected by an editor of JHEP in a few minutes as this person pretended that my choice of the initial solution of Yang-Mills theory to build a strong coupled QFT was “ad hoc”. The point is that I assumed that the work of George Savvidy and Sergei Matinyan was universally known. These authors proved without any doubt that Yang-Mills mechanics is generally chaotic and so, if I would like to use a gradient expansion to build a QFT I am in a serious difficulty as a QFT built on chaotic solutions cannot exist.
Matinyan summed up most of these results here and was kind enough to cite a paper of mine. So, we all known that for small perturbations one can use free particle solutions but what one can do for the strong coupling case, what are the solutions to start from?
In this post I showed that a non chaotic classical solution exists that has the property to manifest a massive dispersion relation. This classical solution is obtained when one takes all the components of the Yang-Mills to be equal (see here). This is a kind of “replica trick”, that is, we replicate a massless scalar field a number of times enough to solve exactly Yang-Mills equations of motion. So, if we want the quantum theory to produce a mass gap, this is the only choice we have. A QFT can be straightforwardly built and we can manage strong interactions in the strong coupling limit.
So, aside from rejection records, there are serious reasons for satisfaction as a meaningful theory exists that is general enough to treat a quantum field in the strong coupling limit due also to the relevant contribution of Matinyan and Savvidy. The starting point is anyhow a gradient expansion. We will have more to say about in future posts.
Tommaso Dorigo is shocking us in these days with a striking post after another. Today he posted this one where there is evidence that the Higgs is light indeed being between 115-135 GeV and there are reasons to regret. The most severe of these is the shutdown of LEP that Luciano Maiani was forced to order to start LHC construction. More time would have been given to this people and surely now we would not stay still waiting. But this was not Maiani’s fault. Luciano Maiani is a great physicist and has been my professor at “La Sapienza” where he tried to teach me quantum mechanics. Today I cannot say if he succeeded but I can hide myself behind Feynman’s view to be safe… Maiani was just forced to close LEP to respect scheduling and, I can guess, for the allocated budget at that time. This was the only logical choice. Now a great window is surely open for Fermilab to anticipate the discovery. We are eager to see. Meantime we can say that Lubos Motl is half right, we hope for the other half…
Update: For some guess about what to expect at LHC, Sean Carroll has posted this. We are all eager to see. Bets are on…
As promised in my preceding post I said that a classical spontaneously broken scalar theory can be exactly solved. This is true as I will show. Consider the equation
You can check by yourself that the exact solution is given by
being the v.e.v. of the field and an elliptical Jacobi function. As always the following dispersion relation must be true
giving a consistent classical solution. When one goes to see the spectrum of the theory, the Fourier series of the Jacobi dn function has a zero mass excitation, the Goldstone boson.
Update: A proper full solution is given by
being an integration constant.
I am starting my vacations. This will last for about three weeks and so lower throughput should be expected in the next days.
I will keep on following web activity but I do not expect to see Higgs discover in these next days. Anyhow I will do a lot of work on Yang-Mills and more generally QCD and I hope to give some interesting news here on the blog.
All newspapers today give this beautiful news: There is ice on Mars and this was the results of analysis by NASA Phoenix Mars Lander.
Mars as seen by Phoenix Mars Lander
I have read this article from New York Times and I think next step would be the search for life, very elementary life. Indeed, looking at pictures from Mars it does not come as a surprise that water existed in liquid form on the planet time ago and Mars should have had a very different aspect. But it is also possible that life existed at that time and now it is completely disappeared. There has been a temporal window inside which some kind of evolution took place but all depends on the width of the window to define the complexity of such organisms. Anyhow, having such a large reservoir of water should make a manned mission on Mars easier in the future.
Due to the large success and to a wide availability of resources, NASA planned to extend this mission further. Please, folks do not give up the good work!