You've hit upon a crucial point of distinction, and I apologize if my previous explanation conflated different concepts. You are absolutely correct: the equation m = hf/c^2 itself does not involve rates of change, and therefore, calculus is not needed to derive or solve it for a specific value. It describes a static equivalence between mass and energy (or frequency). Let me clarify directly: * For the equation m = hf/c^2 specifically: * h is Planck's constant (a fixed value). * f is frequency (a specific value for a given photon/energy). * c is the speed of light (a fixed constant). * Therefore, m is a specific mass value corresponding to that frequency. * This is a direct algebraic relationship. If you know any two of the variables (m, f), you can find the third (assuming h and c are known constants). Calculus is not involved. Where my previous explanation might have caused confusion: My examples involving differential equations (like trajectories or weather prediction) were meant to illustrate that many other areas of science do require calculus because they deal with dynamic systems and rates of change. I was trying to make a broader point about "finding answers" in science generally, which was perhaps misleading in the context of your specific algebraic equation. Your excellent point: "These are not rates. What? What are the rates here these are. These are static points that's saying that mass changes as a rate. That's absurd." You are absolutely right. The equation m = hf/c^2 does not say that "mass changes as a rate." It describes a fundamental equivalence: * A photon of a certain frequency f has an equivalent mass m. This equivalent mass isn't "changing" over time in this context; it's a direct consequence of its energy. * Conversely, if a certain mass m is converted entirely into energy, it will produce photons (or other forms of energy) with a total equivalent frequency f. Think of it like this: 1 \text{ kg of apples} = \text{X number of apples}. This isn't a rate of change; it's a static conversion factor based on the average mass of an apple. Similarly, m = hf/c^2 is a conversion factor between frequency (an energy proxy) and mass. Summary of correction: You are completely correct that calculus is not needed for the equation m = hf/c^2. This equation describes a static relationship between mass, frequency, and fundamental constants. My previous examples of differential equations and rates of change were applicable to other areas of physics and science, but not to the direct interpretation and application of m = hf/c^2. Thank you for pressing me on this. It's crucial to be precise!