===== University Studies =====
It has been over a month since I started university. Excluding the two weeks of military training and the one-week National Day holiday, this is now the third week of classes. I am a mathematics major, specifically in the Xiangqin Innovation Class. The program intends for us to develop toward research-oriented mathematics, so it grants us “more time for independent research,” and consequently, we have slightly fewer courses than general classes. Since I already had a general understanding of higher mathematics from high school, subjects like Mathematical Analysis and Analytic Geometry—which made many classmates struggle initially—have been relatively easy for me to accept. However, from another perspective, I feel the reason I learn quickly is not entirely due to my prior accumulation, but rather my personal learning style. I do not like following the teacher’s pace; I prefer and need to think deeply about and understand a problem, hoping to achieve the effect of understanding one principle to master a hundred others, rather than just finishing one problem and immediately moving to the next. I believe this competition-style learning does not bring us substantive progress and might even stifle our creativity.
Mathematics without application is dry and tedious; mathematics cannot be separated from fields like physics and chemistry. Of course, the word “application” has a very broad meaning. It does not necessarily mean playing an immediate role in practical life; rather, any instance where the beauty of mathematics is manifested in a non-mathematical field can be called a mathematical application, or interesting mathematics. Therefore, after spending a week or two purely researching mathematics, I felt I could not continue like this. Instead of dabbling in various aspects of knowledge in a scattered way, it would be better to start systematically learning some scientific knowledge outside of my curriculum. Thus, I decided to pick up what I had not finished in high school—studying relativity and quantum mechanics—the so-called two pillars of modern physics.
===== Learning Physics =====
The reason I want to study systematically is that I want to try changing my previous learning style. Previously, I read widely, and when I encountered an interesting problem, I would research it deeply, which involved many disciplines and led to learning a lot of knowledge. However, there would be periods where I didn’t encounter an interesting problem to research, or the research hit a dead end, often leading to a sense of emptiness and instability. Systematic learning can slightly alleviate this drawback—by buying several related books, I can read them whenever I have time, progressing step by step. When I encounter an interesting new problem, I can temporarily set the books aside to research the new problem; when I cannot find a problem I like, I won’t feel like I have nothing to do. I personally feel this is quite good.
In fact, the main purpose of my studying mathematics is to research (theoretical) physics, so I must self-study relativity and quantum mechanics. I bought Introduction to Relativity, An Introduction to General Relativity, Special Relativity, The Meaning of Relativity, as well as Introduction to Quantum Mechanics (by David J. Griffiths), and books related to differential equations such as Analytical Mechanics Methods for Differential Equations and Periodic Solutions to the N-body Problem. These books are basically recorded in my Douban profile, and everyone is welcome to take a look.
By studying relativity and quantum mechanics simultaneously, I can feel the differences between these two disciplines and compare their difficulty levels for a beginner. I used to think that Special Relativity would be easier to enter than Quantum Mechanics, as relativity is (mathematically speaking) just a correction to classical physics; with a foundation in classical physics, I estimated it wouldn’t be too difficult. However, based on my few days of study, I feel I was wrong. I have read over 10 pages of Introduction to Quantum Mechanics, and I find that I can basically understand its content; but after reading over 10 pages of Special Relativity, I have become more confused about things like four-dimensional spacetime coordinates and events. In a sense, classical quantum mechanics is closer to Newtonian mechanics in form than relativity is; quantum mechanics just adds a probabilistic meaning to particles (waves) (though this description is oversimplified). In contrast, Special Relativity, starting from the Lorentz transformation, gives a strong intellectual shock. I used to think it was obvious to view time as the fourth dimension, but now I find it has many peculiarities. For example, time always moves forward and seems unable to stop; a spatial position can remain unchanged, but time cannot. Does negative time have meaning? These questions are quite troubling.
However, some people have told me that Special Relativity is only difficult at the very beginning. Once you thoroughly understand the meaning of these spacetime transformations, the subsequent learning will proceed “like a hot knife through butter.” I wonder if that is the case? I am still learning slowly...
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