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Molecules, crystals and quantum statistics
I
Nuclear
Physics
A91 (19671 697-699;
@
North-Holland
Publishing
Co., Amsterdam
BOOK REVIEWS H. RICHTER,Wahrscheinlichkeitstheorie, xii-462 p. DM 68)
2. neubearbeitete
Auflage
(Springer
Verlag,
Berlin,
1966.
Recent contributions to the inexhaustible theme of the misunderstandings to which the epistemological aspects of quantum mechanics can give rise (usually described as “objections to the Copenhagen interpretation”) have revealed the surprising fact that the field of these misunderstandings is not limited to the proper quanta1 effects, but extends to the very foundations of the theory of probability. It is fortunate, therefore, that a new edition of Richter’s masterly treatise should just now become available: this is precisely the kind of book to which serious students should be referred for the elucidation of the doubts and obscurities left in their mind by a first contact with an admittedly difficult subject. Indeed, what distinguishes Richter’s book is the painstaking treatment given to the epistemological problems of the theory. These problems have long been discussed without the help of adequate mathematical methods. Now, thanks to the beautiful theories of measure and integration created by the genius of Lebesgue and the penetrating analysis of the statistical concepts by Kolmogoroff, the whole framework of the theory of probability can be exhibited with perfect rigour in a form exquisitely adapted to physical applications. It is just in such a form that the subject is presented in Richter’s book, and this makes it invaluable for the physicist wishing to explore it in depth. This exposition has the great advantage of being conceived as a whole “aus einem Guss“ - by a mathematician keenly aware of the double aspect of the theory, as an abstract logical system, but also as a tool for the analysis of concrete situations. After a chapter introducing the reader to the basic concepts of the theory of sets, the author immediately passes to a thorough discussion, occupying a whole chapter, of the epistemological aspect of the probability concept. Then follows an exposition, remodelled according to modem ideas and methods, of the “classical” theory ofprobability, as a preparation to the development of the fully-fledged modern theory to which the following chapters are devoted. The first of these presents with admirable concision all that the physicist needs to know of the theories of measure and integration. The exposition of the theory is divided into three chapters, of which the last is especially remarkable for its sharp and lucid analysis of the different forms of convergence of stochastic sequences utilized in probability theory. The theory of stochastic processes is not treated, because other textbooks are available for this special subject (e.g. the smaller treatise by K. Krickeberg, reviewed earlier in this journal 48 (1963) 527). All advanced students in physics aspiring to more than the ability to participate in the current mass production of “research” papers ought at least once in their life acquire knowledge of the matters dealt with in the book under review, and they hardly could do better than to take this book as their guide. L.R. E. FERMI,Molecules, $13.50)
crystals
and quantum
statistics
(Benjamin,
New York,
1966. xiv-300
p. cloth
In its original conception (1934), this treatise was a contribution to acomprehensivecollectivework (never completed) which aimed at acquainting the Italian students with the (then) modern developments of atomic physics. This origin accounts not only for the rather elementary level of exposition, but also for the somewhat heterogeneous contents. The publication of an American translation after thirty years partakes perhaps more of piety to Fermi’s memory than of the urge to fulfil a real need. However, even this slender work possesses those admirable didactic qualities which confer all Fermi’s writings a perennial value, and it may well be offered to the present-day students as a model of simple, lucid and elegant presentation of physical theories. To the original text, which has wisely been translated without alteration, Dr. L. Motz has added appendices dealing with recent developments as well as a list of references. These additions will give the student useful guidance to further reading. L.R. 697
Nuclear
Physics
A91 (19671 697-699;
@
North-Holland
Publishing
Co., Amsterdam
BOOK REVIEWS H. RICHTER,Wahrscheinlichkeitstheorie, xii-462 p. DM 68)
2. neubearbeitete
Auflage
(Springer
Verlag,
Berlin,
1966.
Recent contributions to the inexhaustible theme of the misunderstandings to which the epistemological aspects of quantum mechanics can give rise (usually described as “objections to the Copenhagen interpretation”) have revealed the surprising fact that the field of these misunderstandings is not limited to the proper quanta1 effects, but extends to the very foundations of the theory of probability. It is fortunate, therefore, that a new edition of Richter’s masterly treatise should just now become available: this is precisely the kind of book to which serious students should be referred for the elucidation of the doubts and obscurities left in their mind by a first contact with an admittedly difficult subject. Indeed, what distinguishes Richter’s book is the painstaking treatment given to the epistemological problems of the theory. These problems have long been discussed without the help of adequate mathematical methods. Now, thanks to the beautiful theories of measure and integration created by the genius of Lebesgue and the penetrating analysis of the statistical concepts by Kolmogoroff, the whole framework of the theory of probability can be exhibited with perfect rigour in a form exquisitely adapted to physical applications. It is just in such a form that the subject is presented in Richter’s book, and this makes it invaluable for the physicist wishing to explore it in depth. This exposition has the great advantage of being conceived as a whole “aus einem Guss“ - by a mathematician keenly aware of the double aspect of the theory, as an abstract logical system, but also as a tool for the analysis of concrete situations. After a chapter introducing the reader to the basic concepts of the theory of sets, the author immediately passes to a thorough discussion, occupying a whole chapter, of the epistemological aspect of the probability concept. Then follows an exposition, remodelled according to modem ideas and methods, of the “classical” theory ofprobability, as a preparation to the development of the fully-fledged modern theory to which the following chapters are devoted. The first of these presents with admirable concision all that the physicist needs to know of the theories of measure and integration. The exposition of the theory is divided into three chapters, of which the last is especially remarkable for its sharp and lucid analysis of the different forms of convergence of stochastic sequences utilized in probability theory. The theory of stochastic processes is not treated, because other textbooks are available for this special subject (e.g. the smaller treatise by K. Krickeberg, reviewed earlier in this journal 48 (1963) 527). All advanced students in physics aspiring to more than the ability to participate in the current mass production of “research” papers ought at least once in their life acquire knowledge of the matters dealt with in the book under review, and they hardly could do better than to take this book as their guide. L.R. E. FERMI,Molecules, $13.50)
crystals
and quantum
statistics
(Benjamin,
New York,
1966. xiv-300
p. cloth
In its original conception (1934), this treatise was a contribution to acomprehensivecollectivework (never completed) which aimed at acquainting the Italian students with the (then) modern developments of atomic physics. This origin accounts not only for the rather elementary level of exposition, but also for the somewhat heterogeneous contents. The publication of an American translation after thirty years partakes perhaps more of piety to Fermi’s memory than of the urge to fulfil a real need. However, even this slender work possesses those admirable didactic qualities which confer all Fermi’s writings a perennial value, and it may well be offered to the present-day students as a model of simple, lucid and elegant presentation of physical theories. To the original text, which has wisely been translated without alteration, Dr. L. Motz has added appendices dealing with recent developments as well as a list of references. These additions will give the student useful guidance to further reading. L.R. 697