Day One

This blog is my personal English translation of a book titles "Lecture on Physics (by Dr Yukawa)" original Japanese version 講談社学術文庫 物理講義 (ブツリコウギ).

This is a book version of the three day Lecture on Physics made by Dr Yukawa in Tokyo in 1974. I have been reading this book for more than ten years and more than 10 times since I purchased it. Every time I read it, actually a part of it, I find something new. Dr Yukawa talked about his own physics world to physics students in this lecture. The degree of understanding of the contents very much depends on a reader. Although my understanding is still very shallow and limited (I am pretty much a layperson to physics) I decided to try to translate it into English mostly because I thought and hoped that by doing this job my understanding would improve, become deeper and wider through the process of translation. Plus I may have a chance to find some people to help me understand what he said one step further and to share the physics world of Dr Yukawa with. This attempt may take a couple of years or more to be completed.

Notes (No. 1 to No. 95) are added to the book version. Since the Notes were not made by Dy Yukawa but added to help the readers I do not translate them unless otherwise I think it needed to do so. These Notes are good and helpful to understand what Dr Yukawa said in the lecture.

Some parts are redundant probably because of the nature of this somehow informal lecture as he said but I found that he tended to repeat the same thing because that is important to the listeners even it seems simple.


Lecture on Physics by Dr Yukawa

Day One

Contents

　　1.はじめに At the beginning
　　2.素粒子の世界の奇妙さ Strange world of Elementary Particles
　　3.歴史から何を学ぶか What do we lean from history ?
　　4.創造の原点に帰る Returning to the basics of creativeness
　　5.実在感のなかったニュートン像 Newton's image with scarce reality
　　6.ニュートンの物質観 Newton's view on Matters
　　7.創造の内的動機 Inner motive of creativeness
　　8.ハイゼンベルクの“中心的秩序” Hisenberg's "Central Order"
　　9.質点と剛体 Point Mass and Rigid Body
　　10.角運動量の問題 Problems of Angular Momentum　　
     11.ひずみと応力について About Strain and Stress 
　　12.物理学は“思惟の経済”か？ Is physics economy of thoughts?
　　13.遠隔力と近接力 Action-at-distance and Contact Force
　　14.マクスウェルによる解決 Solution by Maxwell


6.ニュートンの物質観 Newton's view on Matters

But in Principia there are several things which differ from those written in our ordinary text books. Not several the contents differ from the beginning. There is no Point Mass. What there are, then? They are particles or corpuscles. There are submatters these days. The question is that people at that time thought what matter was. By following Plato's "Idea"  and his materialistic view and the traditional ways of thoughts since Aristotle I do not think it strange that the thought of ether had come out in the modern age. In the very long history of physics the atomic theory had been minor and even heretic. In this sense 20th century has gone far much. There is no other science than the atomic theory in 20th century. The atomic theory has become orthodox since 19th century but there were still many other theories in 19th century, The atomic theory, in a broad sense, had become orthodox after entering the 20th century but the other theories had not totally vanished. That was "ether".
Matter can be divided, which has been the base idea of the the traditional thoughts since Aristotle. I think that this idea was a very natural way of thinking. Unless you can find any reason for giving up somewhere in the process of infinite divisions it is natural to take a position of being able to make divisions infinitely. There come out various different substances according to the stage of divisions. Some fragments of the divided matter may be big, some may be small and some may be much smaller. And the smallest substance is ether, which was the idea though roughly. The ether theory or the thought of ether was to compensate or avoid the contradiction of infinite divisions being possible.
Infinite divisions being possible means as a result that matter is continuous. Then what is coming out is that matter does not move in continuous matter. Matter just staying still does not make a physical world. To make a physical world motion is required. But to make motion is difficult as it is difficult to think of motion in the world where there is no void. That is the same difficulty as trying to change the seat where there is no empty seat. To change the seat you must immediately move to the seat where someone has just leaving and sit on. But how the first empty seat was made? The first empty seat was brought in from somewhere else.
This kind of idea will be thought out by a clever person. But Descartes had a big problem. The today's equations of continuous matter mechanics did not so easily found. Although Huygens already developed the wave theory of light and even found astonishing Huygens' principle at this time these were not successfully expressed in mathematics. So it was a problem to existence of void but in the view of no void how shall motion be treated.
What did Newton do? It is not easy to deny the ether while the advantage of atom theory is that it has void. This is very important. Void exists therefore atoms exist. Atoms exist therefore void exists. This had been the view since Democritus. I think that this was an decisive discovery. Void exists therefore an atom can move. Moving substances can be either an atom or large matter.
What the matter we think about is something which keeps its identity, not only it thinks so but the others see so as well. Well, the matter does not think but things like human being think so by themselves. "I" of yesterday is "I" of toady. "I" of ten years ago and "I"of today are linked with its identity. This is not only I think so but the others see so as well.
Matter is something which has its identity in this sense and so can be an atom. Therefore in the Newtonian mechanics somethings like matter or atoms move around in where there is nothing or void. However, the atom Newton was thinking about was Democritus' atom, which is a kind of a rigid body or something like it. Newton himself said so not in Principia but in his book on optics. He wrote many experiments in the beginning of this book and about thirty questions like questions to himself. In these self questions he wrote that this material world is made from atoms. God made this world by His order and might. So many atoms were made by God. These should be unbroken matter. Men are unable to break them no matter what men do. This is a religion. This kind of belief perhaps still exists. He believed God.



7.創造の内的動機 Inner motive of creativeness

The above Newton's thought is considered to be strange seeing from the modern age. But I think this is very important to understand Newton. I do not think it unnecessary to learn mechanics. Rather Newton so devoted himself to study shown in the episodes I introduced before. He did so for seeking God. God exist. Without thinking that God exist one cannot be so devoted. God was something he relied on.
The next story is purely my imagination so please do not think it true.
His father passed away he was born. In a few years later his mother re-married someone and went away. He was alone. Nobody seemed to help him. He started his life without help. He was not very healthy. He however became a great physics master, which is rare and a very slight possibility. If he had grown up normally and studied is it possible that he could become even greater? (laughter) This is a question of the result. Then I think that he lost his father at the start of his life he sought God. What is God as father? On this issue he wrote in Principia that where there is God who govern every thing there must be those governed.
"There must be those governed" meant special to Newton. Newton had no child. He had no father, no child. Then he brought God in. He wanted to become a child of God, a child governed by the governor. This is a similar to the case of a student who wants to have a teacher who occasionally scold him. However the teachers of these days do not much concerned about students. As a teacher rarely scolds students the students to pretend to become naughty. Even becoming naughty the teacher does not scold them and then the students get frustrated. And then there will be many possible things. (laughter)
Newton then thought that God as a father govern the universe. God is the law maker and creator of the world which is governed by the order. God govern the ways how things and machines should move. Newton states that he would try to find the ways how things and machines should move or make them re-occur.
This is the outline of my imagination about the thought of Newton. Men do not work very hard without inner motive. There must be some reason why you study physics. There actually will be many different motives. But there are some motives you cannot notice by yourself. People study physics because it seems interesting. But the reasons why they become interested in physics vary with each person and they may not be so aware of why.

  
8.ハイゼンベルクの“中心的秩序” Hisenberg's "Central Order"







9.質点と剛体 Point Mass and Rigid Body

Then I will be back to the story of Newton now. Newton also had a similar way of thinking. I think we can always say that when we try some very difficult things very hard we look for a sort of central order. Einstein was a typical one. We will talk about Einstein later. In case of Newton we can refer to the Democritean atom theory while there was the ether theory as well. Since this is very crucial so Newton did not say Point Mass. He did not think that atom is Point Mass.
When you open Principia you will find many unclear things written. What are written? You may know that this book begins with the definition - Mass is the product of Density and Volume. But this is preposterous. Density is defined as Volume divided by Mass. It is strange that Density is used to define Mass. How should Density be defined. But this is not strange at all if you think that his thought was based on atom theory. Density is to count how many atoms are in a unit volume. Apart from the technical method how to count atoms there is no other simpler way than this. When there are 100 atoms in a unit volume the density is 100 and when there are 1,000 atoms in unit volume the density is 1,000.
This means that an atom has a volume, the smallest limit of volume or something which is very small but has a certain volume anyway. What are the differences between the thing which has volume and that which does not have ? There are many differences. Point mass has the three (3) degrees of freedom (Note 13). The concept of degree of freedom was gradually introduced after Newton. Unlike Point Mass somehow extended matters have higher degrees of freedom. Among these extended matters one simple matter is a rigid body or Perfect Elastic Body, which has a very high elastic modulus. So when two rigid bodies of very high elastic modulus collide they rebound each other with no deformation. The extreme is Perfect Elastic Body, which we could also call a rigid body. Both Point Mass and Perfect Elastic Body are the result of the limit concept.
In our real world any large scale bodies are neither Point Mass nor Perfect Elastic Body, which are just the result of the limit concept. However, when we look into a micro world like that of atoms, there is a problem, which of Point Mass or Perfect Elastic Body is more close to Matters which constitute the nature. More strange things may constitute the nature and much more highly likely strange things will do. Rigid Body has the six degrees of freedom as it has the freedom of rotation. Newton then thought about the matters like Rigid Body. However he did not do much about Rigid Body mechanics.
What we learn about Rigid Body mechanics is that made by Euler. We have Euler's equations of motion (Note 14). As you have learned well you may know the Euler's equations. This was a great shift from the past. Why so great? This is because Euler proposed the two coordinates - one is fixed with Rigid Body and the other fixed with the earth, for instance. A spinning top has two axises - one fixed with the top itself and the other fixed with the earth. Euler though out Eulier's Angles (Note 15) or even more difficult idea like the modern spinor (Note 67). Euler did not invented the very complicated idea of spinor but he brought out Euler's equations by using Eulier's angles. Newton did not go far this. Some more advance of calculus were needed to reach Euler's Equations. At the same time Fluid mechanics was born. Euler studied Fluid mechanics, ie Continuum Mechanics.


10.角運動量の問題 Problems of Angular Momentum

What I am concerned about differs from what I have just said. To consider Point Mass as reducing the size of a rigid body to the limit differs from to consider Point Mass from the beginning. When reducing the size of a rigid body to the limit where the three degrees of freedom (out of six degree of freedom) gone ? On the contrary Point Mass does not have these additional three degrees of freedom from the beginning and therefore has only the original three degrees of freedom. This differs from reducing the size of a rigid body to the limit and considering where the three degree of freedom have gone ? This problem exists from the beginning. This is a matter of interpretation and a matter of how to take the limit.
Angular momentum is a very important quantity. Since the advent of quantum physics it has become even more important as it leads to spin. Spin is, as you know well,  Planck constant h divided by 2π and multiplied by an integer or 1/2. Angular momentum comes out as an important quantity when dealing with multiple Point Masses and Rigid Body.
Angular momentum (L) is, to speak simply, when for instance a thing like a ball (Rigid Body) rotates around an axis (Note 17), L = mvr, where m = mass, v = velocity, r = radius. And v/r = ω (angular velocity). At the same time Rigid Body spins itself. Its angular momentum (L) is L = I ω, where I (moment of inertia) = mr², then L = mr²ω. Then reducing "r" of the both equations. For L = mvr (orbital rotation), when "r" reduces to the limit or zero L becomes zero as well. No rotation ? But for L = mr²ω (spinning), when "r" reduces to the limit or zero ω increases to the maximum. But it depends on how ω reaches the maximum. If  "v"(of v/r = ω) has a certain limit L becomes zero. When "v" increases without limit, then L, as the result of L = mr²ω, will become zero. This is one interpretation.
After the advent of Quantum Mechanics, an electron is treated as it has spin in itself. I do not know whether electron is a point particle or not but as it is treated so then an electron has spin though it is a point particle (Note 18). Ninety-nine persons out of 100 think that though it is a point particle it has spin. Dirac equation is remarkably well made up and a mans who doubts will be a fool. This is one way of thinking.

(My internal Note: this part (Angular momentum and spin) is repeated in Day Two 2 < ニュートン力学における空間 Space of Newton Mechanics> again in more simple or clear way.)

But it is not a bad thing that one out of 100 people would think that there may be some relation between the problem of this (an electron has spin though it is a point particle) and and a problem handled by Classic Mechanics. As the situations have changed much in Quantum Mechanics it is not so meaningful to talk about it from a point of view of the Newton's stage. Nonetheless what I want to emphasize here is that the concept of Point Mass has many issues to consider.

If you always think about this kind of things you will fail all the examinations so it is very inefficient. When I was young I did not think about these things very much. If you always think about this kind of things you are not able to go up to Relative Theory and Quantum Theory. For some certain practical purpose or the principal of the minimum required effect for achievement or whatever I thought about these things only to some extent because catching up the front line of the latest physics was important.

However when I become a professor at a university I must have made a lecture. I am not making a lecture as a university professor today. This is not a lecture. I do not know exactly how to call what I am doing now, just I talk as I like. Anyway as a professor I must have made a lecture. I started with my lecture with Mechanics. Not Newton's Mechanics which I have been talking about but I made lectures on Elastic Body and Fluid Body by following the typical Mechanics shown in the text books.

What is making a lecture ? If you do not understand what you are taking about, you cannot make a lecture. There seems some techniques to make a lecture on the things which you do not understand well. This kind of techniques should be used as less as possible though occasionally could be used. The principal problem is that people do not understand well or are not well sure about what they talk by themselves. When I read "Principia" I come across many strange writings. Then I found that while we learn somethings already well organized the original creators who made these were very concerned about in many points. These concerns are natural. For instance, when I come to Tokyo I see higher and higher buildings each time I come. These high buildings are supposed to be sure by using new technologies like flexible structure. But those who designed and built these high building should have been very concerned and even feared as it would be a serious problem if the building fell down soon after built. They worried about even those which should not have been worried. Newton was concerned about many things. As a result he did not go further to Point Mass and Rigid Body either.


11.ひずみと応力について About Strain and Stress


Then, I am going to talk about further on Continuum Body which I mentioned earlier. Newton also did something on Continuum Body but at his time this was too difficult. Then there comes a story of strain and stress of Elastic Body. We face a similar difficulty with this again. What is difficult is that when considering that matter is continuum we find at the same time that matter is made by atoms or atomic structure or crystal-like lattice structure. Then Elasticity must be thought differently from that of Continuum Body. Cauchy and other physicists studied these but as these are very difficult so these are seldom lectured. There will be many restrictions about Elasticity and Elastic Modulus coming out. This is not a big issue we discuss now, however.
Apart from what kind of structure the matter has in a very micro state, what I am always concerned about is that there are many crystal-like lattice cubes alined side by side . There are many atoms, then people may think the matter be continuous. Then stresses act and react each other on the surface. The strains are created accordingly. Strain is symmetric tensor, which may be OK. That is it. That can be. Furthermore stress is also symmetric tensor.
I do not understand this argument well. This seems a reasonable story. But we face a similar problem coming out to the one we just encountered about the difference between Point Mass and Rigid Body and also about Problems of Angular Momentum. How it comes out is that when there is a small matter what is wrong with that being spinning very rapidly. A different spinning way make a different matter. When considering strain non-symmetry parts are cut off. Unless cutting off non-symmetry parts it does not become symmetrical. If there is some spinning there is a non-symmetry part. Stress also has
a non-symmetry part by some way of taking a limit, which relates with some spinning. However, non-symmetry parts are simply cut off by common methods.






13.遠隔力と近接力 Action-at-distance and "Near Force" (*)

Then what I am talking about next is, of course, the remaining problem. Force and Motion. I do not like to restore Force very simply to some other things. What did Newton found is not the definition of Force, I think. What he found was  the correct relationship between Force and Motion.
Then it is certain that Force become clear. Before this Newton's discovery Force had used for and had many different things. Even in19th century, for instance Helmholtz a very big thesis on Conservation Law of Energy. In this thesis he did nor use Energy. He used "Karft" (force in German) and Erhaltung (conservation in English). The word Force (Kraft) was not very clear even in the time of Helmholtz. The word Energy was made, probably by an English man Lord Kevin, and then Energy was differentiated from Force.
Setting these historical things aside, I think that it was Newton who first discovered and dentified Force and Acceleration, which used to be different things.
And then what Force is ? There were two, one was 遠隔力(Enkaku-Ryoku, literally "distant force") and 近接力(kinsetsu-Ryoku, literally "near force"). Action at distance is Fernwirkung in German. And 近接力(kinsetsu-Ryoku) was Nahewirkung in Germany. There is no English for this. It is not a serious problem even there is no English for this, but it is better to have the both Forces.
Force is principally "Near Force", of course. Like I strike a desk, like you push or are pushed, these are
Nahewirkung. Friction and Resistance are also Nahewirkung. A thing contacts anther thin, where Force occurs. What is Action-at-distance then ? This used to be mysterious. Something works at a far distance. To wink, for instance. To wink is Fernwirkung when you think it naively. This has a physics' element. Light arrives. When there is some obstacle the light reflect and returns to yourself. If there is no obstacle by its inspiration some effect works, This is in fact Action-at-distance.
In old days people thought Action-at-distance mysterious. They thought that Action-at-distance should be restored to "Near Force". This was an old days and period. This was a natural way of thought. When you try to restore Action-at-distance to "Near Force" there must exist something. For instance taking a light transmission, there exists something like ether which exist between one to the other, then light is considered to travel like a wave by the effect of either itself working side by side each other. Besides this, of course, light is considered as particles. Although this relates deeply with Action-at-distance, light as being particles does not work under Action-at-distance. Light emit from somewhere and travels very fast and makes some effect at the destination, which is considered as a kind of  "Near Force".
Meanwhile the most important force at the time of Newton was Universal Gravity. This is decisively important. Gravity is Action-at-distance. To say instantly there is a force between two things. Not from one thing to the other, force instantly exists between them. If force transfer, it does unlimitedly fast. There is nothing in between. Someone says there may be ether. The atomic stand point of view allows the existence of void, nothingness. Vacuum exists. And force makes effect in there. Force works directly between the two things. This is very mysterious. You may not think it mysterious but it used to be very mysterious before.
Then, I do not know very well but Leibniz, for instance, stated that Action-at-distance was nonsense. To this
Leibniz opinion the Newtonians (the followers of Newton in Britain) tried to protect the Newton theory, by saying that it is useless and unnecessary to think of ether and "Near Force" and Action-at-distance itself explains well the laws of mechanics, which finally won and there we now study the standard classic mechanics.
Time entered the end of 19th century without thinking unnecessary things like ether and "Near Force".  However, how about Newton himself. He himself was thinking of some way to restore Action-at-distance to
"Near Force". This was how Newton differed. He was thinking of matter like ether. At that time it was very difficult to rewrite Action-at-distance by using "Near Force". Then who made this ? Before talking this though Newton himself was thinking of some way to restore Action-at-distance to
"Near Force". The Newton followers made a period by saying that Action-at-distance itself explains well the laws of mechanics. There was a period. But Newton did not have period. As Newton was very careful and did not express what was uncertain and did not talk abut ether publicly, which was a true story. 

(My internal Note: "Near Force" can be translated as Contact Force.)


14.マクスウェルによる解決 Solution by Maxwell

Then how the problem of "Near Force" and Action-at-distance went on. Those who solve this problem in a certain way were Faraday and Maxwell and Maxwell was the person who completed this. However, this was about Electromagnetic Force, not Gravitational Force. These days everything starts with a story of Electromagnetic Field and "Near Force" and not a story of Action-at-distance. But first we learn
Electromagnetic we study and see some tiny pieces of paper being attracted by a rubber bar or something rubbed. This is Action-at-distance where Coulomb's Law works. The key equation of this electrostatic force is of the same form as that of the gravitational force. Since then there came our many thoughts which I will talk abut later, like Biot-Savart law, etc, people were taking Action-at-distance explanation. 
Action-at-distance explanation was taken in the continent. In 19th century mainly German scholars took the
Action-at-distance explanation, which seems a development of Newtonian mechanics. There is a substance and it has the force due to the only substance (that is, due to the mass). Thus substance happens to have a charge, which brings forth another force than gravity. The force due to the charge was thought to be understood like gravity or Action-at-distance,
Then after the story had become more and more complicated Maxwell came in. His famous book on Electromagnetism, Treaties on Electricity and Magnetism, 1873 is a very thick book. I have not read much and those who have read are few, I suppose. A very interesting thing is written in the preface of this book. Generally a book having a poor preface is not a good book. There is no exception, I think. At least one thing very striking a cord should be written in the preface, otherwise the book is not a good book. What Maxwell wrote in the preface is that he takes a standpoint of  "Near Force" like Faraday. And by this he thoroughly explained the then Electromagnetic theory based on Action-at-distance in terms of  "Near Force", plus he drew a conclusion the light being Electromagnetic phenomenon. This is written in this book. This story is just an opposite direction of the development of mechanics. Thus was what actually happened.

(My internal Note:

The title of another and shorter Maxwell's book is A Dynamical Theory of the Electromagnetic Field first published in 1865. Please note the word Field is used. Please also refer to the following chapters:


Day Two

10. “場”とは何か What  is "Field"?
11. 相対論における場 Field in Theory of Relativity
12. 特殊相対論による場の制約 Limitation of Field by Theory of Special Relativity

Day Three

2. 波動ということ――エーテルから場へ Wave - From Ether to Field
8.量子力学の完成――場の量子論 Completion of Quantum Mechanics - Quantum Theory of Field
9.量子力学と特殊相対論 Quantum Mechanics and Theory of Special Relativity

As I talked about force today and will continue it tomorrow. And I briefly mentioned space but almost all remains untouched so I will do it tomorrow. This is the end of the lecture today.


(End of Day One)