Chapter 571 Witness the Miracle! (Part 2)

The answer is simple: Although D’Alembert once developed a one-dimensional wave equation, his solution was merely the initial solution for traveling waves. This solution is also called the general solution, but it’s actually very, very different from the later wave equations. The one Xu Yun has written out this time is the general solution from 1865, so there’s no "bug" of ’the wave equation hasn’t been derived in this world line yet’. Not to mention, just the Fourier transformation thinking needed for the classical wave equation wouldn’t even be published by Fourier in The Analytical Theory of Heat until 1822. The narrative returns to reality. At this moment, Wheat looks like an enthusiastic warrior of pure love, huffing and puffing as he works out calculations on paper: "Take the curl on both sides..." "▽·E=0..." Swish, swish, swish—as the tip of the pen dances. The simplified data appears line by line on the paper. Along with these expressions, the breathing of many great figures present grows heavier and heavier. Except for William Whewell and Prince Albert, only Wheat, the one solving the problem, hasn’t realized the gravity of the situation. After all, he is still just a mathematics student, yet to formally touch upon electromagnetism, lacking sufficient physical sensitivity. He is simply simplifying and calculating the formulas from a mathematical perspective, and doesn’t have enough mental capacity to ponder the question of ’meaning’. But as the calculations near the final stage, right before the answer is about to be written down, even the dullest person ought to react. The Scottish youth calculated and calculated, and suddenly his pen tip paused. Surprised, he looked up at Xu Yun, his face slightly flushed: "Mr. Luo Feng, this... doesn’t this formula mean..." Xu Yun nodded slightly at him, sighed, and said, "Yes, finish writing it. Some things have come to the time for the seal to be broken." Gulp—Wheat dryly swallowed a mouthful of saliva, his gaze quickly scanning the classroom. Faraday, Thomson, Weber, Joule, Stokes... At this moment, these giants who would later fill one-third the thickness of high school physics textbooks, all stared intently at Wheat’s pen tip, their expressions grave. Weber’s lips were faintly trembling, Faraday clenched a small bottle in his hand, Stokes’ fists quietly tightened... Even the reflectiveness of Joule’s big bald head seemed brighter... They were waiting. Waiting for a mathematical miracle to be witnessed. "Phew..." Wheat puffed out his cheeks, took a deep breath, and worked out the last calculations on the paper. "μ0 and ε0 are constants, so the right side naturally becomes the second partial derivative of the electric field E..." "And reorganize the negative sign, finally..." A few minutes later, a final term appears on the parchment: ▽2B=μ0ε0（?2B/?t2）. ▽2E=μ0ε0（?2E/?t2）. The former is the equation for the electric field intensity E, the latter is the independent equation for the magnetic induction intensity B. As the expressions are written out, the classroom instantly becomes dead silent. Faraday is breathing heavily, trembling as he again takes out nitroglycerin, placing it under his tongue... Looking at a few excited bigshots, who seem almost like Parkinson’s patients, William Whewell glances at Prince Albert, asks: "Um... esteemed professors, may I ask, what is the significance of these expressions?" Only then does Stokes realize there are a few unfamiliar faces present, and turns to explain to Whewell: "Mr. Whewell, you are an authority in philosophy, so perhaps there is some... well, barrier when it comes to professional knowledge of the natural sciences." Saying this, he pointed to the classic wave equation derived earlier by Xu Yun, continuing: "First, we know that Student Luo Feng—or rather, Mr. Feiyu—he derived this classical wave equation, which is mathematically absolutely valid." "That is, wherever a place fits this mathematical formula, a wave must exist there." Upon hearing this, Xu Yun looked at his nose, his nose at his mouth, his mouth at his heart, not correcting Stokes’ mistake—after all, nobody knew about the concept of quanta at this point. Stokes continued: "Then, Student Luo Feng introduced the concepts of electric field and magnetic field, and after calculations, the expression still holds. Think about what that means?" William Whewell paused for a moment, now somewhat understanding Stokes’ meaning: "So, you mean, both in the electric and magnetic fields... there are waves?" Faraday, now breathing more evenly, nodded weightily and added: "To be precise, it’s mathematically verified that both electric and magnetic fields propagate in space in the form of waves. Within the field, there exists a kind of wave that has never been discovered before..." "Never been discovered..." At the end, Faraday’s tone was almost a murmur. By now, he finally understood what Xu Yun meant by "the seal is broken": in the electromagnetic field he had studied for decades, there was actually an unknown wave! Such an important thing, and he had known nothing about it up until now... Looking at the vacillating expressions of Faraday, Xu Yun couldn’t help but feel moved himself. When he was in high school, he happened to read an article. The article was called "Faraday’s Regret." Of course, this article wasn’t some chicken soup published in Reader or Yilin. It was a short piece serialized in Xu Yun’s frequently-read academic paper called Xuexibao. That kind of newspaper cost about fifty yuan per semester.