particle physics - Why are high energies equivalent to short distances?

Why are the regimes in high-energy collisions called short distances?

Qualitatively I only know that the higher the given energy of the colliding particles "the smaller are the pieces yielded by cracking the collision particles". Is there a quantitative derivation of the term relating the energy $E$ and the distance $x$?

Answer

Energy is related to frequency via Planck's relationship $E=h\nu$ and frequency is related to wavelength via the speed of light $\nu=c/\lambda$. Therefore, the higher the energy the smaller the associated wavelength. This wavelength represents the resolution with which one makes an observation.