Basis Lab

Answers · The physics underneath

How can light travel through empty space if there's nothing to wave?

In shortLight is a self-sustaining ripple of electric and magnetic fields, each one creating the other, so it needs no material to travel through.

Light travels through empty space because it is not a waving of any material. It is an oscillation of two fields, electric and magnetic, each one generated by the change in the other, so the disturbance carries itself. Sound needs air because air is the stuff being pushed. Light needs nothing because the two rules that govern the fields never mention any stuff.

∇×E=−∂B∂t∇×B=μ0ε0∂E∂t\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} \qquad\qquad \nabla \times \mathbf{B} = \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}

The feedback loop

Read each rule as a sentence about a small loop in space. The left side is how much one field circulates around the loop. The right side is how fast the other field is changing through that loop. So a changing magnetic field is encircled by an electric field, and a changing electric field is encircled by a magnetic field. The minus sign in the first rule makes the induced electric field oppose the change in the magnetic field, and that opposition is what turns a one-way push into an oscillation. Start with a magnetic field that is growing. It drives an electric field looping around it. That electric field is itself changing, so it drives a magnetic field. By then the original magnetic field is falling, so the electric field reverses, and the cycle repeats. No charge and no material appear in the rules. The loop closes between the two fields alone.

FIG 1Each field is the source of the other
The cycle has no material in it. Once a disturbance exists, the two rules keep it going.

The speed is not a separate measurement

The two constants in the rules are the only numbers in them. μ0\mu_0 is measured by hanging two current-carrying wires side by side and weighing the force between them. ε0\varepsilon_0 is measured by charging two plates and weighing the force between them. Neither experiment uses light. Put the two measured values into the relation below and the speed of the disturbance follows.

c2=1μ0ε0c^2 = \frac{1}{\mu_0 \varepsilon_0}

Take μ0=1.2566×10−6\mu_0 = 1.2566\times10^{-6} and ε0=8.8542×10−12\varepsilon_0 = 8.8542\times10^{-12} in SI units. Their product is 1.1127×10−171.1127\times10^{-17}. The reciprocal is 8.988×10168.988\times10^{16}, and its square root is 2.998×1082.998\times10^{8} metres per second. That number was already on record as the speed of light, which is what identified light as this wave.

Why the sound analogy misleads

The natural guess is that every wave must be a pattern in some substance, because every wave met before light was. That guess fails here because the two rules are not statements about displacements of a substance. They are statements about how a field loops around a region where the other field is changing. A field is not a material, and its change is not a movement of material. The loop closes on itself, so there is nothing missing when the air is pumped out. The guess assumes that a wave must be a shape taken by matter, and light is a shape taken by the fields themselves.

In a material, the fields push charges and the wave slows. The vacuum description is the clean case with no charges present. The classical rules also do not say what a field is made of; they say how it behaves. That is a gap in the description of fields, not a missing material for the wave. The rules remain true in a vacuum, and the speed that comes out of them is the speed in a vacuum.

Worth keeping

  • A changing magnetic field produces a looping electric field, and a changing electric field produces a looping magnetic field, with a sign that makes the pair oscillate rather than run away.
  • The speed of that oscillation is set by two constants measurable with wires and plates, and the number comes out at about 300 million metres per second.
  • Nothing in the two rules refers to a material, so the wave survives when the material is removed.

Where this goes next

This question is one step of Waves, Modes and Frequency, a course that works through its subject from the beginning. The page that teaches this part of it is Charges, Loops and a Wave With Nothing to Wave, and it reads the whole way through whether or not you have an account.

What an account changes is the practice: problems standing under every idea, marked with a reason rather than a tick, in a copy of the course that is yours.

Read that pageThe whole course

Other questions people ask about this

  1. How can you predict the shape of a plucked string a moment after you let go?Write the starting corner as a sum of the string's allowed standing shapes, let each shape oscillate at its own rate, then add them back together.
  2. Why does pushing a swing at just the right moment make it go much higher?A swing goes higher when each push arrives in step with the motion already there, so many small pushes add up instead of cancelling.
  3. Why does a wave on a string travel at the same speed no matter how hard you pluck it?A harder pluck makes a bigger wave, but the speed of the wave is fixed by the string's tension and mass per length, so amplitude does not change it.
  4. Why do two waves moving in opposite directions make a standing wave that doesn't go anywhere?Two travelling waves going opposite ways add point by point; where one rises the other falls they cancel permanently, so the pattern stays put even though both waves keep moving through it.
  5. Why is momentum conserved in a collision when kinetic energy is not?Momentum is conserved because the internal pushes in a collision cancel in pairs, while kinetic energy can be turned into heat and deformation.
  6. Why does a planet speed up when it gets closer to the Sun?A planet speeds up near the Sun because its fixed angular momentum forces its sideways speed up as its distance falls, and gravity does work as it falls inward.

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