Physics

Why the Speed of Light Is Always A Constant

Ivethium

26 Jun 2025 • 10 min read

The speed of light being the same for everyone in Special Relativity was always a mystery to me.

Why should light behave so strangely compared to everything else we see in daily life?

This puzzle led me to dive deeper into Maxwell’s equations, hoping to find a satisfying explanation. While the mathematics was elegant, I wasn’t fully satisfied with just accepting the equations as fundamental truths. So I developed a mental model that helped me understand this phenomenon in a way that actually made sense.

Let’s begin with something familiar: relative speed.

If two cars are heading toward each other — one at 60 km/h and the other at 80 km/h — each sees the other approaching at 60 + 80 = 140 km/h. That’s classical motion, and it makes perfect sense.

Now imagine one of the cars turns on a flashlight. Your intuition might say: “Surely the light is coming toward the other car at c + v.”

But that’s not what happens.

No matter how fast you move, you always measure light’s speed as exactly c.

This isn’t just strange — it breaks how we’re taught to think about motion. Yet this fact lies at the heart of modern physics and the theory of Special Relativity.

So how can it possibly be true?

Two Ways to Understand Why Light’s Speed Is Always c

Maxwell’s Equations

These are four elegant equations that describe electricity and magnetism. When you combine them, they predict the existence of a wave — an electromagnetic wave — that always travels at the same speed in vacuum: c. That number isn’t guessed — it’s built into the very structure of the laws.

The Vacuum Has No Reference Frame

This is the explanation I developed to make it truly intuitive to me. The key insight is that light isn’t moving “through” something like air or water. It’s a ripple in electric and magnetic fields — and those fields exist even in empty space.

Here’s the key point:

if the vacuum had a velocity, then some observer would have to be at rest relative to empty space itself. But this would create a privileged reference frame — a special “absolute rest” frame — which contradicts the fundamental principle that all inertial frames are equivalent.

Why would the universe be so unfair as to randomly pick certain observers as “truly at rest” while condemning others to “truly moving”?

Such cosmic favoritism would make physics fundamentally unjust and arbitrary.

Let’s now explore both of these ideas, starting with the stunning depth of Maxwell’s equations.

1. Maxwell’s Equations: Light Has a Built-In Speed

In the 1860s, James Clerk Maxwell didn’t just describe electromagnetism — he revealed its internal logic. His equations feel less like observations and more like axioms — rules of the universe that space itself obeys.

Let’s break them down and see what they tell us:

Gauss’s Law (Electric Fields)

$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$

Electric charges are sources of electric fields.

Like gravity coming from mass, electric fields radiate outward (or inward) from charges. This law connects charge to field — it defines how space responds to the presence of charge.

Gauss’s Law for Magnetism

$$ \nabla \cdot \mathbf{B} = 0 $$

Magnetic field lines always form closed loops.

Unlike electric charges, magnetic “monopoles” don’t exist. There are no magnetic beginnings or ends — just continuous loops. This law encodes a deep symmetry.

Faraday’s Law of Induction

$$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} $$

Changing magnetic fields create circulating electric fields.

This is why generators work. Move a magnet near a coil, and electricity appears. Nature couples magnetism to electricity through change.

Ampère’s Law (with Maxwell’s Correction)

$$ \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} $$

Magnetic fields are caused by electric currents and by changing electric fields.

This is where Maxwell made his revolutionary addition, but first, let’s understand exactly what problem he identified.

The Specific Problem Maxwell Discovered: Consider a capacitor being charged through a wire. Current flows through the connecting wire toward the capacitor plates, but then appears to “stop” — no current flows through the empty space (or dielectric) between the plates. Now apply Ampère’s original law to find the magnetic field around this circuit using two different surfaces:

Surface S1: A flat surface that intersects the wire carrying current I. Ampère’s law gives: ∮ B · ds = μ₀I
Surface S2: A balloon-shaped surface that bulges out between the capacitor plates, avoiding the wire entirely. Since no current crosses this surface, Ampère’s law gives: ∮ B · ds = 0

But both surfaces are bounded by the exact same circular path around the wire! The magnetic field cannot depend on which surface you choose for the calculation — that would make the law inconsistent and unphysical.

Maxwell’s Physical Insight: Between the capacitor plates, although no charges flow, the electric field is rapidly changing as the capacitor charges up. Maxwell realized that this changing electric field must itself act like a current in terms of producing magnetic fields. He called this the “displacement current” — not because any charges are displaced, but because it mathematically displaces the missing current needed to make Ampère’s law consistent.

Why This Exact Mathematical Form: Maxwell needed a term that would:

Make the divergence of both sides of Ampère’s law equal (to satisfy current conservation)
Have the same units as current density
Equal the actual current in wires to maintain consistency

For a charging capacitor:

$J = \frac{I}{A}$ (current density in the wire)

and

$$ \frac{\partial \mathbf{E}}{\partial t} = \frac{I}{\epsilon_0 A} $$

(rate of electric field change between plates).

Therefore,

$$ \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} = \frac{I}{A} = J $$

This means

$$ \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} $$

exactly replaces the missing current density between the plates.

The Profound Symmetry Maxwell Completed:

Faraday’s law: Changing magnetic fields → electric fields
Maxwell’s addition: Changing electric fields → magnetic fields

This wasn’t just a mathematical patch — it revealed that electricity and magnetism are two aspects of a unified electromagnetic field, capable of self-propagation as waves.

What Makes These Equations Feel So Foundational?

They describe not just forces, but how fields exist and evolve in space and time.
They work in vacuum — without needing any particles.
They are invariant — the same for all observers in inertial frames.
They predict phenomena like electromagnetic waves without ever assuming them.
They don’t describe electricity and magnetism separately — they reveal that the two are aspects of one unified field theory.

Now here’s the beautiful part: these equations not only describe fields — they predict light.

Deriving the Speed of Light from Maxwell’s Equations

Note: The following derivation uses the ∇ (nabla) operator, which might be unfamiliar to some readers. If you’re not comfortable with vector calculus operations like divergence and curl, don’t worry — we’ll cover an intuitive understanding of the ∇ operator and what it physically represents in another article.

Let’s take the equations in vacuum, where:

ρ = 0 (no charge)
J = 0 (no current)

They simplify to:
$$ \nabla \cdot \mathbf{E} = 0, \quad \nabla \cdot \mathbf{B} = 0 $$
$$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}, \quad \nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} $$

Take the curl of Faraday’s law and substitute Ampère’s law:
$$ \nabla \times (\nabla \times \mathbf{E}) = -\frac{\partial}{\partial t} (\nabla \times \mathbf{B}) = -\mu_0 \epsilon_0 \frac{\partial^2 \mathbf{E}}{\partial t^2} $$

Using the identity $\nabla \times (\nabla \times \mathbf{E}) = \nabla(\nabla \cdot \mathbf{E}) - \nabla^2 \mathbf{E}$ and $\nabla \cdot \mathbf{E} = 0$,

We get:
$$ \nabla^2 \mathbf{E} = \mu_0 \epsilon_0 \frac{\partial^2 \mathbf{E}}{\partial t^2} $$

That’s the wave equation. And the speed of wave propagation is:

Note: If you’re wondering why this mathematical form necessarily represents a wave and how we can immediately identify the propagation speed, we’ll explore the general structure of wave equations and why they always take this form in a future article.

c = 1/√(μ₀ε₀)

Plug in the constants:

μ₀ = 4π × 10⁻⁷ N/A²
ε₀ = 8.854 × 10⁻¹² F/m

You get: c ≈ 299,792,458 m/s

The equations literally build the speed of light into the fabric of the theory.

What Are Permeability and Permittivity?

Permittivity ε₀: How resistant the vacuum is to forming electric fields.

Permeability μ₀: How easily magnetic fields can form in the vacuum.

These are not arbitrary. They tell us how “stiff” or “responsive” space is to electric and magnetic phenomena — and together, they control how fast a ripple in those fields (i.e., light) can travel.

2. The Vacuum Has No Speed — So Light Has No Relative Speed

Even with all that math, your intuition might still rebel. Why doesn’t motion affect how we observe light’s speed?

Because assigning a velocity to the vacuum would create a privileged reference frame — and physics forbids this.

The Right Mental Model for Empty Space:

The vacuum is not a substance with properties like velocity. It’s the absolute absence of anything.

When we say empty space is empty, we mean it’s so fundamentally empty that you can’t even reasonably overlay an imaginary Cartesian coordinate system on it and define motion — because there’s no physical entity to serve as a reference for that coordinate system. There are no invisible grid lines, no hidden scaffolding, no ethereal framework. It’s emptiness so complete that the very concept of “moving through it” becomes meaningless.

Light is a self-propagating disturbance in the electromagnetic field, and this field exists equally in all reference frames — not because it’s attached to some invisible substrate, but because the field is a fundamental property of spacetime itself, not dependent on any medium.

In classical physics, waves travel through a medium: sound through air, water waves through water. The medium defines a natural reference frame. If you’re moving with the air, sound behaves differently than if you’re moving against it.

So it was natural to think light moved through something too — an “aether.” If this aether existed, then whoever was at rest relative to it would be in a special, privileged frame. Everyone else would be moving through the aether and would measure different speeds for light depending on their motion.

But no experiment ever found evidence for such a privileged frame. The Michelson–Morley experiment tried to detect our motion through the aether by comparing light speeds in different directions as Earth moved through space. The result? Nothing. Always c. No matter what.

The Deeper Problem with Aether:

If the vacuum could have a velocity, then there would be observers who are “truly at rest” — at rest relative to empty space itself.

This would mean the universe arbitrarily chose certain observers as special.

Why should someone floating in one particular region of space be granted the cosmic privilege of being “absolutely at rest” while everyone else is deemed “absolutely moving”? What makes their reference frame fundamentally superior to yours or mine?

The universe would essentially be playing favorites — randomly blessing some observers with a special status for no discernible reason. This kind of cosmic bias seems not just wrong, but deeply unfair.

Why This Solves the Problem:

Since there’s no medium and no privileged frame, light’s speed cannot depend on the observer’s motion.

Every observer, regardless of their velocity, must measure the same speed c. This isn’t just a quirk — it’s a fundamental requirement for the universe to treat all observers fairly. The constancy of light speed is nature’s way of ensuring that no reference frame gets special treatment. It’s the universe’s commitment to fundamental fairness and democracy among all observers.

Simple Thinking Points

The Right Mental Model for Empty Space:

Empty space is so fundamentally empty that you can’t even overlay imaginary coordinate systems on it
There are no invisible grid lines, hidden scaffolding, or ethereal frameworks to define motion relative to
The concept of “moving through” such absolute emptiness becomes meaningless

No Privileged Observers:

If vacuum had velocity, some observers would be “truly at rest” while others are “truly moving”
This would mean the universe arbitrarily grants cosmic privilege to certain observers
Physics demands that all inertial frames be equivalent — no observer gets special treatment

Light as a Property of Spacetime Itself:

Light is a self-propagating disturbance in electromagnetic fields that are fundamental to spacetime
Since every observer gets the same empty space (because empty space is just empty space), every observer must get the same light speed
Just as emptiness is equally empty for everyone, light speed must be equally constant for everyone

Maxwell’s Equations Lead to the Same Conclusion:

Even if we view Maxwell’s equations as fundamental observations rather than derived principles
They predict electromagnetic waves that travel at a speed built into the structure of spacetime itself
This speed cannot depend on the observer because the equations work identically in all inertial frames
Both approaches — the emptiness of space and the universality of Maxwell’s equations — lead to the same inescapable result: c is constant for all observers

Why I Find the “True Emptiness” Intuition More Compelling

While Maxwell’s equations provide a mathematical foundation for light’s constant speed, I personally find the “true emptiness of vacuum” argument more philosophically satisfying. There’s something deeply intuitive about the idea that absolute emptiness cannot have properties like velocity or provide reference frames for motion.

When you really grasp that empty space is so fundamentally empty that even imaginary coordinate grids become meaningless, the constancy of light speed stops feeling like a strange quirk and starts feeling inevitable. How could light’s speed depend on your motion when there’s literally nothing for you to be moving relative to?

This perspective makes me more willing to accept that our everyday assumptions about space and time might need revision. If we take the true emptiness of vacuum seriously, then we must accept that:

Everyone measures the same light speed c
But we observe relative motion between objects
Something has to give way to resolve this apparent contradiction

The natural candidates are our vague, everyday assumptions about length and time being absolute and universal. These concepts feel solid and unchanging in daily life, but they’re really just approximations based on our limited experience with slow speeds.

I find it philosophically more satisfying to preserve the elegant truth of empty space’s true nature and allow our intuitions about space and time to be flexible. After all, why should the universe conform to human intuitions developed by observing relatively slow-moving objects?

The Road to Special Relativity

This understanding of light’s constant speed — whether derived from Maxwell’s equations or from the true emptiness of vacuum — leads directly to the principles of Special Relativity:

If light speed is constant for all observers
And we observe that objects can have relative motion
Then measurements of space and time intervals must depend on the observer’s motion

In our next blog post, we’ll derive exactly how space and time must transform to preserve the constancy of light speed. We’ll discover that:

Time dilates (moving clocks run slow)
Length contracts (moving objects shrink)
Simultaneity becomes relative (events that are simultaneous for one observer aren’t for another)
Mass and energy become equivalent through E = mc²

All of these seemingly bizarre effects will emerge naturally from the simple requirement that everyone must measure the same speed for light. The constancy of c isn’t just a strange fact about light — it’s the key that unlocks the true nature of space and time themselves.