The idea of setting `c = 1` can seem arbitrary or even nonsensical if you're used to thinking of `c` as having a specific, large numerical value like `299,792,458 m/s`. The key is to understand that setting `c = 1` is not a statement that the speed of light *is literally* "one meter per second" or "one mile per hour." Instead, it's a **choice of units** or a **redefinition of our measurement system** to make the equations of physics (especially relativity) look simpler and more elegant. Here's the breakdown: 1. **The Value of `c` Depends on Our Units:** * The number `299,792,458` is tied to our human-defined units of **meters** and **seconds**. * If we measured distance in "light-seconds" (the distance light travels in one second) and time in seconds, then the speed of light would be `1 light-second per second`. * If we measured distance in "light-years" and time in years, the speed of light would be `1 light-year per year`. 2. **What "Setting `c = 1`" Means:** When physicists (especially theoretical physicists) say they are "setting `c = 1`," they are adopting a system of **natural units** where: * **The unit of speed is defined as the speed of light itself.** * This means that distances and times are no longer measured in independent units (like meters and seconds). Instead, they are measured in units that are intrinsically linked by the speed of light. 3. **How it Works (The Implication for Units):** * We know `speed = distance / time`. * If we set `c = 1` (where `c` is the speed of light), then `1 = distance / time`. * This implies `distance = time` (numerically, in these new units). * This doesn't mean distance *is* time. It means that in this unit system, **1 unit of time is equivalent to the distance light travels in that 1 unit of time.** * For example: * If our unit of time is the **second**, then our unit of distance becomes the **light-second** (approx. `2.998 x 10⁸ meters`). * If our unit of time is the **year**, then our unit of distance becomes the **light-year**. * In this system, time and distance are measured in the same fundamental unit (e.g., you could measure time in "meters of light travel time" or distance in "seconds of light travel time"). 4. **Why Do It? The Advantages:** * **Simplicity of Equations:** This is the main reason. Look at `E = mc²`. If `c = 1`, it becomes `E = m`. * This beautifully highlights the fundamental equivalence of mass and energy. They are the same thing, just measured in different conventional units. When `c=1`, mass *is* energy. * Other relativistic equations also simplify: * The Lorentz factor `γ = 1 / √(1 - v²/c²) ` becomes `γ = 1 / √(1 - v²)`. Here, `v` is also a fraction of `c`, so it's a dimensionless speed between 0 and 1. * The energy-momentum relation `E² = (pc)² + (m₀c²)²` becomes `E² = p² + m₀²`. * **Focus on Fundamental Relationships:** By removing `c` (and often `ħ`, Planck's constant, by setting `ħ = 1`), physicists can focus on the core relationships between physical quantities without being cluttered by conversion factors that depend on arbitrary human units. * **Natural Scales:** It aligns measurements with the fundamental constants of nature, suggesting that these constants define the "natural" scales of the universe. 5. **Getting Back to Standard Units:** When physicists using `c=1` want to communicate their results to engineers or experimentalists who use SI units (meters, seconds, kilograms), they simply reinsert the factors of `c` (and `ħ`, etc.) based on dimensional analysis to get the correct numerical values and units. * For example, if they derive an energy `E_natural` in their `c=1` system, and they know energy should have units of `mass * speed²`, they would write `E_SI = E_natural * c²` to convert back to Joules (if `E_natural` was in kg-equivalent). **Analogy:** Imagine you're a baker. You could measure flour in grams and sugar in grams. Or, you could define a "baker's unit" where, for a particular recipe, 1 unit of sugar is always used with 2 units of flour. You could then just say "use 1 sugar and 2 flour." You've effectively set the ratio to 1:2. If someone else wants to use your recipe with grams, you tell them "my '1 sugar' is 100g, and my '1 flour' is 50g" (so 100g sugar, 100g flour). Setting `c=1` is like saying, "Let's define our unit of distance such that it's numerically equal to our unit of time when we're talking about the speed of light." **In summary:** Setting `c=1` is not denying the measured value of the speed of light in meters per second. It's a **convention** to simplify theoretical work by choosing a system of units where the numerical value of the speed of light is 1. This is achieved by making the unit of length and the unit of time interdependent, linked by `c`. It helps reveal the underlying structure of physical laws more clearly.