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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 $x$?

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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.

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We use human-friendly units, unnatural units. In natural units $$\hbar = c = 1$$

This makes time units equal to space units ($T=L$) and it makes energy units equal to inverse space units $([E]=1/L)$.

So, in a very fundamental sense, large energies mean small distances because energy is inverse distance.

Other answers are correct, but they express the human story of understanding the laws of nature, not anything really fundamental.

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Because the de Broglie wavelength is short for high energies.

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