Let p be a prime number, and let f be any complex valued function on the cyclic group Z/pZ. Denote by f^ the Fourier transform of f. The usual Heisenberg uncertainty principle states that

|support(f)| |support(f^)| \geq p.

Tao's new additive uncertainty principle states that

|support(f)| + |support(f^)| \geq p+1.

We will sketch a proof of this result, and show how this implies the Cauchy-Davenport theorem in additive number theory.