We usually find ourselves unable to solve most problems on topics that we have just completed reading on from physics textbooks. Postechians might blame the textbook for its insufficient explanation as a cause for their inability to solve a problem. However, textbooks do not offer a compass to follow, and you must identify an issue prior to inadequate textbooks. Which direction are you heading towards? Nothing can help a ship that does not know where it is headed.
What should we accomplish after learning physics? Paul Dirac proposed this intriguing motto: “I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it.” The motto encourages us to be more flexible and creative while doing physics. A door to freedom is opened at this epiphany: physics is not as absolute and rigid as physics students are often taught.
No one digests abstract concepts of physics by themselves independent of images, hence each textbook always adds an image-specific, subjective perspective on physics itself. Our own experiences also contribute to subjective images of physics. You would believe pictures to be objective like laws of physics themselves, but they are not. The best way to separate subjective images and objective physics is by comparing a lot of textbooks and attempting to solve the same problem using various methods. An interesting example is the magnetic field due to a finite segment of straight wire. Most university physics textbooks for freshmen implicitly lead students to solve this problem by using the Biot-Savart law, but you can try Ampere’s law and the Ampere-Maxwell law for this problem by yourself and figure out in which conditions each law is valid. Separating objective physics from subjective images is similar to sculpturing. Michelangelo once described the same pursuit: “I saw the angel in the marble and carved until I set him free,” “The best artist has that thought alone which is contained within the marble shell; only the sculptor’s hand can break the spell to free the figures.”
The angel is finally revealed from the marble shell. One can conclude that there really is nothing subjective in your understanding of physics. Now it is time to put Dirac’s motto into practice. We get the freedom to choose any image. We can construct rigorous correspondence between new images and objective laws of physics; hence, it is actually possible to solve problems with elegant intuition and simple calculation. For instance, I realized that calculations on collisions between two rigid bodies contain some quantity identical to reduced mass and succeeded in transforming the collision of two rigid bodies into the collision of two particles with effective mass that requires much easier calculations. Tractatus Logico-Philosophicus is Ludwig Wittgenstein’s project to construct objective language and one of its last conclusions is famous 6.54: “… (He must, so to speak, throw away the ladder after he has climbed up it.) He must overcome these propositions, and then he will see the world aright.” (“These propositions” mean the rules of objective language.)
Current online education platforms share the limit that they only provide a few subjective images like classical textbooks. This is an opportunity to develop a dual education system of objective knowledge similar to the Stanford Encyclopedia of Philosophy and a free network to share subjective images with each other. “Under the lead of POSTECH” is my personal wish.