Why another website explaining physics? Many books and many websites explain physics for laymen. They try to convey to you what physics is and what physics is about by explaining through words, without any mathematical formulas. As a consequence, they tend to lack any exposition of physics with mathematical formulas.
Of course, laymen cannot understand mathematical formulas. This might be the reason why none of the websites try to explain physics with mathematical formulas. Nevertheless, you cannot truly understand physics without mathematics. You may have read hundreds of books on physics aimed at laymen, yet you may not truly understand physics if you haven’t studied math. Prof. Andrew Strominger at Harvard University once noted that explaining physics without mathematics is like explaining how beautiful particular scenery is without a photograph; you can only truly appreciate the beauty of the scenery when you see the photograph of it. Likewise, you can only truly appreciate physics when you know mathematics. A Chinese proverb emphasizes this point. “百聞不如一見” “Hearing something one hundred times is not as good as seeing it once.”
As it would be hard to explain all the math necessary to understand physics, I began with science and engineering college students. If you are one of these students, you know something about basic math which may enable you to understand basic physics, even though you are not majoring in physics.
From this observation, I wrote a couple of articles introducing the basic ideas of quantum mechanics to science and engineering college students on a Korean website http://kin.naver.com Many people commented that my articles were impressive. After all, science and engineering college students do not usually learn quantum mechanics unless they are physics majors, and even if they are, they have to wait until junior year to learn it. On the other hand, my article was targeted for sophomores who have already learned basic math such as calculus and linear algebra in their freshmen year. So, it must have been a striking experience for them since they would not normally have a chance to understand what quantum mechanics is about.
Then, I began to think, “Why stop here?” So, I wrote more articles at Naver and began writing them in English to upload on my homepage as well. After all, I found many concepts, observations, laws, formulas, and relations in math and physics very interesting, and found it unfortunate that many of them are not accessible to science and engineering students. This is not because they are particularly hard, but because they are rather written in unfamiliar languages.
What do I mean by unfamiliar languages? “Too mathematical” language could be one example. If physics is written in “too mathematical” language, it can hinder the understanding of physics, especially for the beginners. Given that I have so far emphasized the importance of learning physics with math, this statement may sound paradoxical, but let me put it this way. Suppose you are a first grader and learn the addition. You learn some important properties of the addition, such as its commutative property and its associative property. These properties tell you that the order doesn’t matter in the addition. The commutative property of addition means a+b=b+a, and the associative property of addition means (a+b)+c=a+(b+c). If you learn why the addition must follow such properties through some diagrams, you will be satisfied.
However, modern mathematicians are not satisfied by such explanations. They first define natural numbers. Natural numbers are the simplest numbers such as 1, 2, 3, 4, and so on. Then, they define the addition mathematically rigorously, then from all these definitions, they prove that the addition so defined must satisfy the commutative property and the associativity property. It is important that mathematics be always put on such a firm, rigorous foundation so that there is no gap in the logic, and no possibility that mathematical results based on this foundation are wrong.
Then, is it a good idea to teach the first graders the definitions of natural numbers and addition and the proof that the addition so defined has the commutative and associative properties? No. Can we say that the first graders who properly learned such properties of addition through diagrams only do not have a true understanding of why the addition has such properties, because they didn’t learn the mathematically rigorous proof? No. Even more, it often happens that the first graders who learned the commutative and associative properties of the addition through diagram have a better understanding of such properties than those ones (if there are any) who learned them only through mathematical proofs. If something is written in an unfamiliar language, and you are not fluent in reading it, you often lose track of what is going on.
I am sure that you can correctly guess why I bring up this example. Some physics books are written in such an unfamiliar, too mathematical language. It’s like teaching the first graders the definition of natural numbers and addition, instead of teaching them how to count and how to add, first. It’s like teaching the first graders the proof why the addition satisfies such properties instead of showing them diagrams and giving them examples. This is especially true for many general relativity textbooks, many loop quantum gravity textbooks and some quantum mechanics textbooks. Of course, if you are going to deal with physics in a rigorous setting as some mathematicians do, or if you need to read physics papers written by mathematicians, you need to learn all these foundations. Nevertheless, you can always learn the definition of natural number and addition, after you get used to counting and adding. That’s the way I tried to write my articles here. Physics should be learned with mathematical formulas but without too much mathematical language.
Furthermore, it suddenly struck me that I had been lucky enough to read a good series on mathematics when I was young. The series was written by the Japanese mathematician Koji Shiga (志賀浩二) and was translated into Korean with the title “혼자서 크는 수학” (“Mathematics you grow on your own”). The series was composed of six books, each of which was designed to be covered for a week. It started out with very basic mathematics usually covered in elementary school, and by the end of the sixth week you were supposed to master calculus at the level of single variable calculus for advanced high school students. Even though it eventually took longer than six weeks to finish this book, I enjoyed it very much.
Then, I began to think that I wanted to write such books. A book that starts out from scratch and builds higher and higher on to advanced math and physics.
Much later, I came across a good book on Einstein’s theory of relativity aimed at laymen. It explains successfully not only special relativity, but also general relativity, which is a topic usually covered in graduate school. This encouraged my hope that it will be possible to write such a book as I envision, a book that can explain hard physics with all mathematical formulas to laymen.
Whenever I read physics and math books, I get stuck in a lot of places. Sometimes I don’t understand the explanation or the logic of authors, sometimes I cannot follow the mathematical derivations. Then, I need help from someone else. Therefore, I tried to write articles here as clearly and kindly as possible, so that readers do not need to turn to others to get help to understand my articles. Also, I tried to convey the beauty of physics and math in my articles. There are many different ways to present the same explanation of physics and math concepts. I tried to present the clearest ones and the ones which show the beauty of physics and math most manifestly. Some of these ways to present are my own, the others I selected from my reference.
My previous aim of writing physics and math articles for my homepage was introducing the basics of physics to science and engineering college students. Now, I have made these articles accessible to laymen by writing more introductory physics and math articles. These articles can serve as the prerequisites for the articles that are aimed at science and engineering college students. Also, I have gone further and have written more articles about more advanced topics and subjects in physics. My final aim of these articles is that you understand loop quantum gravity. Normally, you would get to understand loop quantum gravity only after getting an undergraduate degree in physics and studying for a couple of years as a graduate student in physics. This would be about six years after you enter college. Nevertheless, as I presented the physical and mathematical concepts in pedagogical and accessible manners, I believe that it will take less time for you. This is an ambitious plan, but I dare try. Go ahead, and enjoy my articles!