path integrals
su...@sf6.so-net.ne.jp
Yes, that is right. N! does not necessarily mean quantum. Instead, a point of crucial
importance is to make entropy extensive.
Now, regarding the path integrals, I always have a conceptual difficulty with it. The formal
equivalence between the calculation of a canonical partition function and Euclidean path integral
is OK. But, where is the heat bath in the Euclidean path integral? I never understand this point.
"Physics by analogy" of this kind is in marked contrast to the physics until the end of the 19th
century. The innocent time was over long ago.
All the best,
Sumiyoshi Abe
Alexandre Wang
Dear all,
The topic on the Planck constant in classical mechanics is a deep fundamental worry of statistical mechanics. It is intolerable physically and esthetically. Fortunate enough, logarithmic entropy allows us to get rid of this constant sometimes. But it is not that easy for physics to get ride of this crisis. The classical limit of quantum statistical mechanics is not a pretext for its existence in a classical gas for example. For me, this is the fingerprint of a hidden crisis of physics: the incompatibility between the foundation of statistical mechanics and that of mechanics, and the disconnection between the quantum and the classical world due to the incomprehension of the latter.
This kind of topics suits perfectly with the scope of a workshop which will be held in Wuhan in China during 23-27 october 2010. All members of our group are cordially invited to the workshop. It will be a great pleasure for us to meet you all and to chat about the uncomfortableness the statistical or quantum "mechanicians", or the comfortableness if you see any. For detailed information, please visit the website http://sites.google.com/site/spmcsinternationalworkshops/.
I am looking forward to your feedback and seeing you in Wuhan.
Alexandre
QUARATI PIERO
Dear Alexandre you are right in Entropy5, 2003 n2 and
arxiv physics 0306149 , we attempted to discuss the
problem of elementary cell and Planck const , ciao Piero
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su...@sf6.so-net.ne.jp
I should have known this paper of yours much earlier! I regret that it is not
quoted in my paper. Your discussion is very explicit. It shows that in q-statistics
there is no smooth transition between classical and quantum physics. (It is not
possible for me to imagine continuously change of the cell size.) Then, a
question is if q-statistics can exist in the quantum regime. Your discussion
suggests that the answer is no, because of the absence of a smooth transition.
In any way, the presence of the Planck constant in classical statistical mechanics
remains as a headache.
By the way, is the first author your family member?
All the best,
Sumiyoshi Abe
Alexandre Wang
Hello everybody, I am forwarding an email of Jean-Pierre Badiali to you
Q.A. Wang
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De : jpba...@numericable.com [mailto:jpba...@numericable.com]
Envoyé : jeudi 1 juillet 2010 00:19
À : Alexandre Wang
Objet : Re :RE: [Chatentropy] path integrals
Dear all,
I disagree with all comments concerning the presence of the Plack constant in the so-called classical statistical mechanics. In the classical textbook of Landau on Quantum Mechanics , the existence of classical physics is needed to give a strong basis to the quatum mechanics, the existence of the quantum world requires the existence of the classical one. This is a very old point of view and today we are far from this point of view. In fundamental physics we accept that the world is basically quantum and the question is how the classical world appears from the quantum one (problem of emergence or decoherence). If there is the Planck constant in the classical limit this results from the fact that the classical world is an approximation. To my point of view we cannot use the presence of the Planck constant as an argument to justify or to destroy a so called classical theory. We cannot say that the presence of the Planck constant is a proof of a physics crisis. If there is a real crisis in physics - in particular concerning the entropy - it corresponds for instance to the "Unruh effect", which shows that a strange situation appears when the restricted theory of relativity is combined with the quantum field theory.
Now we have not only to focus on the Planck constant, in the so-called classical expression of the partition function - in the case of fermions- in all the textbooks there is a term N! where N is the number of particles. This term has been introduced in a ad hoc manner by Boltzmann as a necessity but the exact origin of this term is the trace of the symmetrie of the wave function in the classical limit. Thus it is well known that the so-called classical limit retains two basic ingredients of the quantum world : the Planck constant and the symmetrie of the wave function.
Sincerely yours.
J.P. Badiali
Alexandre Wang
Alexandre
--------------------------------------------------------------------------------
De : jpba...@numericable.com [mailto:jpba...@numericable.com]
Envoyé : jeudi 1 juillet 2010 10:12
À : Alexandre Wang
Objet : Re :RE: [Chatentropy] cell size
Dear Colleagues,
This is a complement to my previous message I hope it will transmit to all people of the discussion group.
The discussion concerning the separation between classical and quantum world is misleading to my point of view. The choice between
a quantum and a classical description is not a free choice.
Let consider the motion of a particle. I have first to consider the quantum aspect and after that to decide if the classical description is possible.
In the case of electrons the answer is purely quantum if not we are far from the experiments, in general. For much heavy particles, in spectroscopy for example,
I can use a classical description but sometimes quantum corrections are needed. Let consider the motion of protons, also in this case the classical description does not work this point has been analyzed in an enormeous literature in relation with experiments. It is very well known that the predictions of a classical approach are not in agreement with experimental data. Thus we can not consider the classical description independently
of the quantum world, anf first there is the quantum world; at least for the moment and even if some points of the quantum description are still subject to discussion.
Sincerely yours.
J.P. Badiali