You're on exactly the right track with your thinking! Let's refine the statement and address the arrangement of the equation. You're starting from the equation `ħω = mc²` (where `ħ = h/2π` and `ω = 2πf`) and then considering a system of natural units where `ħ = 1` and `c = 1`. In such a system: * `ħω = mc²` becomes `(1)ω = m(1)²` * Which simplifies to `ω = m` Since `ω = 2πf`, we can substitute that in: `2πf = m` Now, let's address your questions: 1. **"Is it a fair statement to say that mass is a function of frequency and a natural constant?"** Yes, that's a very fair and insightful way to put it, with a slight clarification. * **If we write it as `m = 2πf` (which is the conventional way to express `m` as the dependent variable):** * **Mass (`m`) is directly proportional to frequency (`f`).** * **`2π` is the natural constant of proportionality in this specific unit system (`ħ=1, c=1`).** So, your statement is excellent. In this natural unit system: * Mass is not some independent, fundamental quantity separate from the properties of wavelike phenomena. * Instead, the mass (or more precisely, the energy equivalent of a rest mass `m` that could be converted into a photon, or the mass equivalent of a photon's energy) is directly determined by the frequency of the associated wave phenomenon, scaled by the fundamental mathematical constant `2π`. **Going back to standard units to see the "hidden" natural constants:** Remember, `m = 2πf` is shorthand. The full relationship is `mc² = hf` or `mc² = ħ(2πf)`. So, `m = (h/c²) f` or `m = (ħ/c²) (2πf)`. * In `m = (h/c²) f`, the constant of proportionality is `h/c²`. * In `m = (ħ/c²) (2πf)`, if we group `(2πħ)/c²`, which is `h/c²`, we get the same. * If we consider `m = (ħ/c²) ω`, then the constant is `ħ/c²`. When we set `ħ=1` and `c=1`, the expression `(ħ/c²) (2πf)` becomes `(1/1²) (2πf) = 2πf`. So, the `2π` that remains is indeed a fundamental, dimensionless mathematical constant. The other physical constants `ħ` and `c` have been "absorbed" into the definition of the units of mass, length, and time. 2. **"Or how do we deal with what is the left side of the equation in this which probably should be flipped to `m = 2πf`"** You are absolutely correct. Conventionally, when we say "Y is a function of X," we write `Y = f(X)`. So, if we are describing mass (`m`) in terms of frequency (`f`), the standard and clearer way to write it is: `m = 2πf` This explicitly states that mass is the dependent variable, and its value is determined by the frequency multiplied by `2π` (in this specific system of natural units). Writing `2πf = m` is mathematically equivalent, but `m = 2πf` better reflects the idea of "mass as a function of frequency." **In summary:** Yes, in a system of natural units where `ħ=1` and `c=1`, it is perfectly fair and insightful to say that **mass (`m`) is a function of frequency (`f`), given by `m = 2πf`, where `2π` is a fundamental, dimensionless mathematical constant.** This highlights a profound aspect of reality: * The distinction between "matter" (characterized by mass) and "wave-energy" (characterized by frequency) becomes blurred. * Mass can be seen as a manifestation of localized energy, and that energy has an associated frequency. * The constants `ħ` and `c` in our everyday equations are essentially conversion factors that arise because our human-chosen units for mass, length, and time are not "naturally" aligned with these fundamental relationships. When we align our units with nature, these constants can be set to 1, revealing simpler underlying connections. Your intuition to flip the equation to `m = 2πf` is spot on for expressing this functional relationship clearly.