High energy need indeed

credit: CERN

The Large Hadron Collider (LHC) at CERN has its own cable to the energy supplier. Dunno, maybe it even generates its own energy. No luxury, you can guess.

Why do these machines need so much energy to see such small particles?
‘Watching’ elementary particles acting like waves is achieved by ‘hitting’ or ‘measuring’ it with a ray of light or other electromagnetic radiation. Because the photon, the carrier of electromagnetic radiation, as a measuring device has its own wavelength and characteristic, its wavelength must be shorter than the wavelength of the particle it needs to observe. If not, it simply passes the other particle without ‘seeing’ it. The shorter the wavelength, the more vibrations per second, and thus the more energy is needed. Let’s see.

We know what the energy of any photon at any wavelength must be, namely (given the Planck-Einstein relation)

    \[E=hf\]

with h as the Planck-constant and f the frequency of the photon. And as we also know that

    \[\lambda=\frac{c}{f}\]

with \lambda the wavelength and c the speed of light (speed divided by frequency is wavelength), and thus

    \[f=\frac{c}{\lambda}\]

from which follows that

    \[E=\frac{hc}{\lambda}\]

As h and c are constant, the shorter the wavelength, the smaller the denominator and the higher the energy needed. Eventually, with ever smaller wavelengths, the energy will skyrocket towards infinity. If it becomes large enough in such a small volume, and as energy and mass are equivalent (remember E=mc^2), the energy within the Schwarzschild radius will become large enough to create a (mini) black hole.

And that’s where the observation stops. No observation for you!