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«KomTO-UeHTp» 

MocKBa 
2004 

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ISBN 5-89353-056-X 

Y,.IJ;K 530.1 
EEK 22.3 

© <DJK.B1rnbcp, 2004 

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4 

Fallacies of Theoretical Physics 

Contents 

Preface. 

The Dirac monopole 
l. Introduction 
2. Necessary digression 
2.1. About the dimensions of the physical quantities 
2.2. The notion of solitary magnetic pole 
3. Do the monopoles have right to the existence ? 
4. About the compatibility of the existence of a point monopole 
with the representations of the classical electrodynamics 

The diamagnetic response of the substance 
1. Introduction 
2. The van Leeven theorem and the Bohr theorem 
3. The diamagnetic response of a free electron collective 
in the framework of the quantum mechanics 
4. The insulator model 
5. The diamagnetic response of a free electron collective 
in the framework of the non-quantum mechanics 
6. A little digression from topic 
7. The diamagnetic response of a normal metal 

7.1. A week diamagnetic response 
7.2. A stong diamagnetic response 
7.3. The two electron groupings in a normal metal 
8. The diamagnetic response of a superconductor 

The EPR paradox 
l. The source of the paradox 
2. An alternative proposed by EPR 
3. The commutative and non-commutative operators 
4. Comments concerning the EPR alternative 
5. The two particles interacting with each other 

5.1. Specialization of the problem 
5.2. The EPR method of measurement of the value of a physical quantity 
6. Measurements of the values of the momentum and the co-ordinate of a free 
point particle which moves along the X-axis eternally 

5 

7. The statement of EPR concerning the measurements 
8. About the probability of ..• 

The Ehrenfest theorem 
1. Introduction 
2. Mathematical aspects of the Ehrenfest article 
3. Physical problems 
3.1. General reasoning 
3.2. The continuity equation 
4. About "the co-ordinate probability" and "the average value 
of co-ordinate" 
5. The change of the particle state in the course of time 
6. Essence of he Ehrenfest theorem 
7. Conclusions 
8. Epilogue 

The Lorentz invariance of the Dirac equation 
1. Introduction 
2. Traditional method of checking the Dirac equation for Lorentz invariance 
3. The truly Lorentz invariant equation 
4. The interpretation of the Dirac equation 

6 

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10 

МОНОПОЛЬ ДИРАКА 

1. Введение.

В 1931 году Поль Дирак, анализируя проблему “неинтегрируемой 
фазы волновой функции частицы ”, пришел к следующему выводу.
“Полный поток магнитного поля, пересекающий малую замкну­
тую 
поверхность, 
окружающую 
одну 
из таких 
точек, равен 

h ’C
АпФ = 2п • п • -— , где 
п -  характеристика узловой линии, которая

оканчивается там, или сумма характеристик всех узловых линий, окан­
чивающихся внутри поверхности, если их более чем одна. Таким обра­
зом, в конечной точке существует магнитный полюс с зарядом (надо

1 
/Z'C
полагать -  магнитным, -  Ф .В.) DJl=—n  
” 
(Здесь h , q , с  -  постоянная
2 
q
Планка, заряд электрона, скорость света).
Хотя из приведенной цитаты трудно понять (мне, по крайней ме­
ре), усматривал ли Дирак разницу между магнитным потоком и магнит-
1 
h ’C
ным зарядом, именно на основании выражения Ш=—п 
Дирак при-
2 
q
шел к выводу, что помимо уже известных ко времени написания его 
статьи элементарных частиц, вполне возможно, существуют еще и дру­
гие элементарные частицы -  носители не электрического, а магнитного 
заряда (очевидно, напоминающие собой изолированные -  уединенные -  
магнитные полюса). Позднее такие частицы стали называть монополя­
ми. Поиски монополей ведутся, по-видимому, с начала 60-х годов XX 
века и, судя по научной литературе, уверенность ряда авторитетнейших

я  привел цитату из основополагающей статьи Дирака. Целое число п он называет ха­
рактеристикой линии. Что касается “там” {“которая оканчивается т а м так это “в 
точке, в которой заканчивается линия ”. Что же касается "'точек ”, то в статье Дирака 
речь шла о линии (в пространстве), в точках которой “волновая функция частицы равна 
нулю ”. Такую линию Дирак назвал узловой. На всякий случай напомню, что смысл даже 
самых обычных терминов, присутствующих в научной статье (не предназначенной, на 
самом деле, ни для кого, кроме узких специалистов), очень часто можно понять только 
при тщательном изучении статьи и сопутствующей по тематике литературы. Заглядывать 
в толковый словарь русского языка бесполезно.
Основополагающие статьи Дирака, а также статьи других теоретиков и эксперимента­
торов представлены в сборнике “Монополь Дирака”, из-во “МИР”, М.:, 1970.

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