Formula for speed of light, and why it is a constant
What is the formula for the speed of light? Why is it considered a constant if there is a formula?
Great question! Let’s unpack it step by step:
1. The formula for the speed of light
In physics, the speed of light in a vacuum is given by a relationship between two fundamental electromagnetic constants:
c=1μ0 ε0c = \frac{1}{\sqrt{\mu_{0}\,\varepsilon_{0}}}
where:
- cc = speed of light in vacuum (~ 3.00×108 m/s3.00 \times 10^8 \,\text{m/s})
- μ0\mu_{0} = magnetic constant (permeability of free space)
- ε0\varepsilon_{0} = electric constant (permittivity of free space)
This comes directly from Maxwell’s equations for electromagnetism.
2. Why is it considered a constant if it comes from a formula?
- The formula shows that cc is determined by fundamental properties of space itself: how electric and magnetic fields interact.
- μ0\mu_0 and ε0\varepsilon_0 are constants of nature, so their combination gives a fixed value for cc.
- In fact, since 1983, the metre is defined using the speed of light. The value of cc is exactly:
c=299,792,458 m/sc = 299,792,458 \,\text{m/s}
This is not “measured” anymore; instead, our definition of a metre is based on this constant.
3. Subtlety: constant vs. variable
- Constant in vacuum: Light always travels at cc in a vacuum, no matter what.
- Slower in materials: In glass, water, or air, light travels slower because photons interact with matter. This is described by the refractive index nn:
v=cnv = \frac{c}{n}
- But nothing can exceed cc in vacuum, making it the universal speed limit.
✅ In summary:
The formula expresses cc in terms of deeper constants of nature, but because those constants are fixed, the value of cc is fixed. It’s “constant” in the sense that it is the same everywhere in the universe (in vacuum), independent of observer, time, or motion.