Is Terry wrong?


I am a great estimator of Terry Tao and a reader of his blog. Tao is a Fields medalist and one of the greatest living mathematicians. Relying on such a giant authority may give someone the feeling of being a kind of dwarf trying to be listened around. Anyhow I will try. Terry come out with an intervention in Wikipedia here claiming:

“It may be relevant to point out that one of the references cited in the disputed section [3] has a significant error in it, despite being published. Namely, in the proof of Theorem 1, the author is assuming that an extremum A for the Yang-Mills action for a special class of connections (namely those in which A^1_1=A^2_2=A^3_3 and all other components vanish) is necessarily an extremum for the Yang-Mills action for all other connections also, but this is not the case (just because YM(A) \geq YM(A'), for instance, for A’ of this special form, does not imply that YM(A) \geq YM(A') for general A’). Since one needs to be an extremiser (or critical point) in the space of all connections in order to be a solution to the Yang-Mills equations, the mapping provided in Theorem 1 has not been shown to actually produce solutions to the Yang-Mills equation (and I suspect that if one actually checks the Yang-Mills equation for this mapping, that one will not in fact get such a solution). Terry (talk) 20:32, 28 February 2009 (UTC)”

This claim of mistake by my side contains a misinterpretation of the mapping theorem. If the theorem would claim that this is true for all connections, as Terry says, it would be istantaneously false. I cannot map a scalar field on all the Y-M connections (think of chaotic solutions). The theorem simply states that there exists a class of solutions of the quartic scalar field that are also solution for the Yang-Mills equations and this can be easily proved by substitution (check Smilga’s book) and Tao is proved istantaneously wrong. So now, what is the point? I have a class of Yang-Mills solutions that Tao is claiming are not. But whoever can check by herself that I am right. So, is Terry wrong?


Physicists and finance


Just to point out an interesting article in the New York Times (see here) about physicists working for financial markets. I have known some years ago a physicist that took this decision rather than keeping on living as a postdoc with very few bucks to maintain his family. I have never seen him again but I think he did not regret his choice.

The article is interesting as points out as a physicist working for certainties can become a scientist on uncertainties. Looking at their salaries you should interchange above adjectives.

Ballentine and the decoherence program


A problem that I have treated in this blog is the question of the quantum-classical transition. This question is hotly debated by people working in quantum optics, quantum computation and wherever foundations of quantum mechanics may enter. Of course, this problem today appears far from being settled and is a heavy burden left us by the fathers of quantum mechanics. Something has been acquired as environmental decoherence. Fighting this effect is a problem experimentalists have today in their everyday activity. But we know that this cannot be all the story.

Some time ago Wojciech Hubert Zurek, one of the main contributors to environmental decoherence, claimed that Hyperion, a Saturn’s moon, behaves classically in its motion just for environmental decoherence otherwise we would observe a macroscopic quantum object splashed in its orbit as happens to electrons in an atom. Of course some people contested these conclusions and come out with a sound explanation of classicality of Hyperion’s motion without the need of environmental decoherence. One of these authors is Leslie Ballentine. I think that a lot of people have read his beautiful book about quantum mechanics. Ballentine and Nathan Wiebe wrote a paper (see here), that went published on Physical Review A (see here), where they soundly proved that Hyperion behaves classically without recurring to any kind of external agent. In some way they gave an hint of an intrinsic emerging of classicality for macroscopic objects (“for all practical purposes” as John Bell taught us). This means that classicality may be an emerging property of quantum objects.

Of course, defenders of environmental decoherence tried to attack Ballentine and Wiebe view (see here). Ballentine’s answer is here. This gives a lucid view of the present criticisms to environmental decoherence, that I would like to recall it is a true observed effect, claiming an intrinsic decoherence effect for isolated quantum systems. The last word has not been said yet. Future experiments will say.

Most of the supporters of environmental decoherence share Ballentine’s views as are well aware of the limitations of this approach. This is part of the truth. I think that here is in view some new deep understanding of how reality forms. Some subtlities are implied and this can explain difficulties researchers have currently met.

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