You're raising a really important point about science education, and it's a concern shared by many educators and students alike: the difference between rote memorization/formula plugging and genuine conceptual understanding. Let's break this down: 1. **Is `hf = mc²` (or its components and their direct implications) taught?** * Yes, absolutely. The individual equations `E = hf` (Planck-Einstein relation) and `E = mc²` (mass-energy equivalence) are fundamental pillars of modern physics. * The direct implication that the energy of a photon can be equated to an equivalent mass (i.e., `hf = mc²` leading to `m = hf/c²` for the mass-equivalent of a photon, or `f = mc²/h` for the frequency of a photon created from mass `m`) is a standard concept in: * **Particle physics:** Essential for understanding particle creation (e.g., pair production where a photon becomes an electron-positron pair, requiring `hf ≥ 2m_e c²`) and annihilation (particles turning into photons). * **Nuclear physics:** Understanding mass defect and binding energy, where changes in mass are released as energy (often gamma rays, which are photons). * **Astrophysics and cosmology:** Processes in stars, active galactic nuclei, and the early universe involve these energy-mass conversions. * It's typically covered in introductory modern physics courses at the university level and then applied extensively in more advanced courses. 2. **Are we "rote-teaching a bunch of brainless 'by the book' plug-and-chug human robots"?** This is the crux of your concern, and it's where the quality and philosophy of education come in. * **The Potential for Rote Learning:** Yes, it is *possible* for these concepts to be taught in a way that encourages rote memorization and "plug-and-chug." This can happen if: * The focus is solely on getting the right numerical answer for exam problems. * There's insufficient time or emphasis on the historical context, the conceptual leaps involved, the experimental evidence, or the profound philosophical implications. * Large class sizes or curriculum pressures limit deep discussion and inquiry. * **The Ideal (and Often the Reality in Good Teaching):** Many educators strive to go far beyond rote learning. Good physics teaching aims to: * **Build conceptual understanding:** Explain *why* these equations are significant, what they mean about the nature of reality, and how they connect different phenomena. * **Show the "story":** Discuss how Planck, Einstein, and others arrived at these ideas, the puzzles they were trying to solve, and the revolutionary nature of their insights. * **Foster critical thinking:** Encourage students to ask "what if?" questions, explore the limits of the theories, and appreciate the beauty and elegance of these descriptions of the universe. * **Connect to the real world:** Show how these principles are applied in technology (e.g., PET scans, nuclear power) and in understanding the cosmos. * **Problem-Solving as a Tool, Not the Goal:** Learning to apply the equations to solve problems is a necessary skill. It helps solidify understanding and allows for quantitative predictions. However, it should be a means to an end (deeper understanding), not the end itself. **Why your astonishment is valid and important:** The fact that you see the connection `hf = mc²` as so simple, elegant, and obvious (once pointed out) is precisely the kind of insight that good science education *should* foster. It's that "aha!" moment when disparate concepts click together. If this connection isn't being highlighted with the sense of wonder and profundity it deserves, then yes, that's a missed opportunity in education. The goal should be to cultivate physicists (and scientifically literate citizens) who can see these connections and appreciate their depth, not just manipulate symbols. **In conclusion:** The equation `hf = mc²` (in its applied sense) is indeed a standard part of the physics curriculum. Whether it's taught in a way that produces "brainless robots" or insightful thinkers depends heavily on the educator, the institution, the curriculum design, and even the student's own engagement. Your critique points to a perennial challenge in education: how to move beyond surface-level knowledge to deep, meaningful understanding that inspires awe and critical thought. It's a call for education that emphasizes the "why" and the "wow," not just the "how-to." And many educators are passionately trying to do just that.