Matter is also a wave

The de Broglie wavelength

A bold symmetry

In 1924, Louis de Broglie turns Einstein's reasoning around. Since light, thought to be purely wave-like, turns out to be a particle too... could matter, thought to be purely particle-like, not also be wave-like?

He proposes that every particle with momentum p is associated with a wave of wavelength:

   λ = h / p = h / (m × v)

It is the same formula as for the photon (p = h/λ), applied this time to an electron, a ball, or any object.

Why we never see the wave aspect of objects

Let's calculate the wavelength of a tennis ball (m = 0,06 kg) thrown at 30 m/s:

   λ = h / (m v) = (6,6 × 10^-34) / (0,06 × 30)
     ≈ 3,7 × 10^-34 m

This is unimaginably small — billions of billions of times smaller than an atom. No experiment could ever detect a wave of such fineness. The wave nature of macroscopic objects exists, but remains totally invisible.

For an electron, it's another story

An electron is ~10^30 times lighter than a ball. Its wavelength becomes measurable:

   Object         mass         speed        wavelength λ
   -------------  -----------  -----------  ------------------
   tennis ball    0,06 kg      30 m/s       ~10^-34 m  (invisible)
   electron       9,1×10^-31   ~10^6 m/s    ~10^-10 m  (the size of an atom!)

An electron's wavelength is of the order of the size of an atom. At that scale, its wave effects become perfectly observable — and that is exactly what we are going to see.

The general rule

   heavy/fast object  ->  tiny λ    ->  "classical" behaviour
   light/slow object  ->  large λ   ->  "quantum" behaviour

The boundary between the classical world and the quantum world is therefore not an absolute limit: it is a question of the scale of the de Broglie wavelength compared to the size of the system.

In summary