Introduction to Symmetry Breaking for "I hate math" people.
According to Dr.Youichiro Nambu, symmetry is broken in this universe.(does this mean there is one where symmetry is not
broken? Nobody knows).
In late 50's, three American physicist proposed a model to explain "super conductivity", their idea was this.
May be.. Things do exist in super-conducting area but it is "invisible". In this case, "invisible" means that, it does
not interact with anything at all, causing a piece of metal into super-conducting state. It is like a super highway without stop lights or traffic jam where cars are invisible as if they don't exist erasing each other(sounds strange. but this is what happens or what they proposed.)
But, this phenomenon was known to occur at extremely low temperature where nothing can move because it is like everything is frozen literally.
When Mr.Nambu heard about this new theory now known as BCS theory, he somehow thought like the following:
MAY BE (OUTER)SPACE ITSELF IS SUPERCONDUCTOR.
Now, I would say that probably no one can think like this unless you are like Einstein or Dr.Nambu.
According to articles I read, he was known as a living dictionary when he was in middle school(something like 7-9th grade in Japan), his classmates at the time was asked to talk about his impression, and he or she said "everone knew it is better and faster if you ask Mr.Nambu when you don't understand something. I guess people like Dr.Nambu, or Gauss(German Mathematician who created all kinds of mathematics needed for understanding of Electricity and Magnetism), or Hamilton(Anglo-Irish mathematitian, famous for inventing imaginary number) , I mean, they are like .. They probably have different kind of brain which works differently than ours.
Anyways, back to his discovery. So, after seeing presentation of the newest theory about super-conductivity, according to his auto-biography
Dr.Nambu said something like this to himself "I was very impressed with the beauty of the mechanism represented there, but I felt something is missing and I did not like (I forgot what he did not like...haha), then, he thought about it for 2 years and during that 2 years, very strange experiment was done by Dr.Wu? and Dr....I forgot,, anyways, the experiment's result was like the following.
In this experiment, no matter how many times we do this experiment, more particles rotating clockwise are observed compared to particles rotating anti-clockwise.
For about 2 years, nobody was able to figure out why such strange thing happens. It is almost like throwing a dice and you always get more odd number than even number. That's how strange this phenomena is. So, Dr.Nambu was thinking about these things and somehow suddenly realized that, according to his semi-auto-Biograhy,
"Suddenly, I realized that Gauge invariance(means symmetry not broken)does not apply in this case or new theory on super-conductivity does not follow the Gauge-invariance(symmetry not broken law), this symmetry(not broken) idea is like saying
"no matter where you go around the world, things are the same".
But, according to Dr.Nambu's calculation, new theory proposed by 3 American physicist about super-conductivity violated newly introduced principle called
gauge-invariance(not broken symmetry theory: it is like famous "they all look alike" thing..) which was proposed by Dr.Yang(from China) and Dr.Mills(American).
(actually, exact same idea was introduced before these two famous Nobel Prize winner came up with it. This forgotten man, Uchiyama, was too smart and nobody in Japan was able to understand what he is talking about. So, he was ignored for a long time. Before he died, it is known that he said something like this:
"if you are a true physicist, write a paper in your own language" (this is like saying "oh I don't like English why you guys write things in English?(I am just guessing..) . I guess he was some kind of nationalist or somewhat passionate and probably did not like Western culture. I am not sure. Maybe he was like those super-Cool Last Samurai-type guy. I like this guy, well, it is more like I like people like him who does not surrender, sort of speak. It is just amazing how he was able to stand his credit or fame not mentioned at all (if not stolen) throughout his life, not only in the Western world, but also in Japan. He probably did not talk much, so, I don't know much about him. But he wrote several textbooks for physics. may be he was ... well, I will stop here.
On the other hand, Dr.Nambu has always been "Mr. Nice Guy"and somewhat old-fashioned and liked being traditional. So, he started to think "something is wrong because old rules does not work in this case" He said something like this.
"I knew there was something wrong. Although I was very impressed by new theory by 3 American physicist, their method was violating the other newly introduced Gauge-theory(this theory is like. saying.. "we all bleed red"..sort of speak, and Dr.Nambu did not think so). So, for the next 2 years, I tried to understand what the problem was."
(I... feel somewhat ashamed of myself because I don't take things seriously or traditionally like Dr.Nambu. I guess that is why I could not make it as a professional physicist. )
Then, he started to try applying all these ideas which came out in late 50's to his mentor's theory(Yukawa theory, Yukawa theory is that .. oh boy, this is hard to explain. I will explain it later..). In his Nobel Prize paper which is like 16 pages says something like the following.
" as I have shown through numerous calculation and approximation, it is obvious that these phenomena does not follow Gauge Invariance, and it cannot explain Yukawa's theory(Yukawa theory is the first word you will find in any modern particle physics textbook, Yukawa explained that "strong-force" inside nucleus(=proton and neutron which constitues nucleus) is caused by mutual exchange of a new particle called meson(he named it mesotron, now known as meson) which acts like a super-glue(not his word, I made it up).
Now I used a word "strong force" how strong is it? Well, there is a perfect and sad example, namely, atomic bomb. Atomic Bomb is extremely powerful because it tries to break protons and neutrons connected by Yukawa's meson super-glue. This super-glue is so strong and if you try to seperate them, you get atomic bomb sized explosion. Yukawa came up with this idea in 1934 and received Nobel Prize after the WWII. When Einstein met Yukawa, Einstein told Yukawa "I am sorry" and started to cry(ture story).
Now back to Dr.Nambu who was a loyal follower of Yukawa's philosophy or theory, he tried to apply his new idea to Yukawa-super-glue meson theory, and he concluded:
new and beautiful theory introduced by Dr.Yang and Dr.Mills called "Gauge invariance(things must be the same everywhere theory, sort of) does not apply in this case and it should mean (not broken) symmetry theory no longer holds in this case, because symmetry and Gauge invariance always come in pair.
This idea where you link symmetry and some kind of invariance(meaning it does not change if not it should be the same everywhere) was introduced by a female German physicist named Nether and it is well known as Nether's theorem(it is like saying "symmetry is almighty", sort of speak, or "all kinds of law of physics exist because our universe is full of symmetry everywhere. Her theory is like.. very beautiful or somewhat idealistic, reminds me of Leonardo Da Vinchi who was the master of symmetry in everyway).
Dr. Nambu did not agree with famous Ms or Madam Nether, Dr.Nambu must have been extremely bold to challenge such authority at the time. Basically, he was saying "all of you are wrong(but I know how to fix it)."
So, he published a paper which explains how symmetry is broken(in the paper he uses a word "Gamma5 invariance"(means symmetry) does not apply(means broken)".
It is probably either himself or some American physicist who renamed his idea as "symmetry breaking" in order to make it easier to remember or understand. By the time famous physicists started to understand his idea, he was already onto next topic........ now known as Quantum ChromoDynamics(QCD) where he introduced 3 different states of quarks which was introduced by Gell-Man(but a similar theory called "Sakata Model" already existed, but Gell-Mann was smart enough to make it somewhat more elegant if not artistic).
but these new ideas were.. again... way ahead of time and too difficult to understand for even professional physicist. So, Jewish American physicist Gell-mann named Dr.Nambu's idea as "color charge", renaming 3 different states as blue, green, and red.
Gell-mann was good at naming things. There is something called Nakajima invariance where some quantity remains the same, it is like whether if some particle is "upwards" or "downwards" sort of speak. But this idea was way ahead of time and it was hard to understand, so, Gell-man renamed this new quantity as "strangeness", very strange naming but easy to remember. So, you can say something like this.
Today, my body's strangeness did not change like always. In fact, it has never changed since I was born except in subatomic scale.
Dr. Nambu once explained Dr.Gell-man like this:
This man is what you call prodigy and he had extremely wide range of knowledge and he was the one who "Americanized" these ideas which I came up with or Dr.Nakajima came up with, naming them as "strangeness" or "color" so that people can remember it or understand it.
As he's always been, he was onto next topic when others were trying to figure out what he said 5 years ago or 40 years ago in some cases. But the following story is still about his 1961 paper which is the first paper on his "symmetry breaking theory".
This is the hardest part of his theory, but I will try my best for "I hate math" people. After he published his paper on symmetry breaking, people who used his idea won many Nobel Prizes but he did not say anything at all. It is hard to believe that he did not receive Noble Prize until last year(2008, 88 years old).
While others were busy and famous receiving Nobel Prize using his idea, Dr.Nambu was busy trying to figure out origin of mass(weight in our world). It seems like he came to realize that"mass(or weight)" changes its value when symmetry is broken.
I think he came to this conclusion because he firmly believed that invariance theory should be applicable although he showed that it does not work through numerous examples. So what does this mean? What he did is like saying "you guys are wrong in this case, but I've got a great idea which can explain this without changing old idea and new idea. it is called symmetry breaking".
Thus, his idea was born. In his paper, he says
"In other words, the masses and the coupling constants are not fixed parameters, but rather dynamical quantities which are subject to transformation when the representation is changed".
Now, this is what I call "deep and profound". What this short paragraph means is that
mass(weight in our world) either can change or in some cases, can even be newly-created if "representation is changed=symmetry is broken."
It says it all. That is symmerty breaking. After I heard the headline news about him getting Nobel Prize, I started to study his idea for the first time since 1992 when I gave up becoming a physicist.
When I was younger, I was "I wanna be Einstein"! boy. but as I grew older, it was definetely, "Dr. Nambu is the coolest guy without honor". These memories from early 90's came back to me and I re-started my study on physics from scratch. I spent almost entire firtst 3 months of this year studying it until I gave up failing to understand something called Ward=Takahashi inequality, which is like basic rule you cannot violate if you use Richard Feymann way of representing Quantum Electro Dynamic theory=QED (theory by Dyson, Shwinger, Tomonaga, and Feynmann). The following story is about how excited I was before I gave up and surrendered to Ward-Takahashi inequality theorem..
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And one day, I took a shower and suddenly, came to a conclusion with enthusiasm thinking....
"oh! my God! oh my god! I think I got it! it should be that feeling I felt when I came out from my shower room or bathing, more like when I was in the bathtub, blood stream or something flowing in my body was symmetrical(meaning same everywhere, unifrom), but.. as I came out of bathtub, and getting colder, I no longer feel symmetrical. This is the only way I can explain this. What I am trying to say is something like this.
Uniform=symmetry(when you are bathing)
not uniform=symmetry is "spontaneously broken".(when you come out of shower room)
May be you can say something like this.
Oh my! I always feel like my symmetry is not broken when I take a shower and it feels great because fluids in my body create harmony "throughout=everywhere in "my body when I take shower!
But, when I wake up next morning, especially after nightmare, I feel my symmetry is completely broken in my brain. But when I sleep well, I feel like symmetry is perfect inside my brain.
-----------------I will stop here. I may or may not write Part II if this is Part I depending on my condition which is very unstable-------------------------
Gosh this is so difficult and I am too tired and sleepy I am no longer able to tell what I am writing makes sense to me. But I am trying hard.