probing short distances needs high energy

You cannot feel the fine texture of a page through thick winter gloves; the gloves are too coarse a tool for the fine detail. To examine something small, you need a probe finer than the thing you are studying. In the quantum world the probe is a wave, and the rule is blunt: to see small things you need short wavelengths, and short wavelengths mean high energy. To look deep inside matter, you must hit it hard.

Here is why, in three steps. First, any beam of particles is also a wave, with a wavelength set by its momentum (the de Broglie relation): faster, more energetic particles have shorter wavelengths. Second, a wave can only resolve features comparable to or larger than its own wavelength — just as ocean swells roll past a thin pole but break on a wide breakwater. Third, putting these together, resolving structure at a tiny distance demands a wave of correspondingly tiny wavelength, which demands a particle of correspondingly high energy. To probe distances a thousand times smaller, you need roughly a thousand times the energy.

This single idea explains why particle physics is the physics of giant accelerators. Studying the inside of the proton, or searching for structure within quarks and electrons, means reaching down to distances far smaller than an atom, which forces the energy ever higher — into the millions and billions of electronvolts and beyond. It is the reason machines like the Large Hadron Collider are enormous and expensive: there is no cheap shortcut to short distances. Higher energy is, quite literally, a sharper magnifying glass.