In accelerators we shoot very high momentum particles at each other to probe the

Question

In accelerators we shoot very high momentum particles at each other to probe their structure at very small length scales. Has that anything to do with the HUP that addresses the spread of momentum and space?

Related, when we accelerate a proton at exactly, say, 1 GeV, then we know exactly its momentum. But for high momentum particles the Broglie wave length also shrinks, the particles position becomes more precise. But that would violate HUP.

What goes on with high momentum particles and their momentum spread?

thanks

Explanation / Answer

The reason accelerators increase in energy is in order to be able to probe smaller distances, the smaller the wavelength the more details as with optics.

The de Broglie wavelength does not describe the location of the particle in space time, that is the function of the wave packet, as elucidated in this note of Hans de Vries: the de Broglie wavelength is a consequence of the HUP.

Those protons in the accelerator are wave packets and do not have a unique frequency and because of HUP, it is not possible to have exactly 1GeV energy.

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