PX156 - E5 - scales

why are high energy colliders used to study the physics of small particles?
classical optics: in order to image something on a given length scale, a probe of the same scale needs to be used
ie: to resolve very small scales, very small wavelengths are needed
the de broglie wavelength of other particles is used to 'image' due to wave-particle duality:

λ = \frac{h}{p}

to observe very small details, high momentum/energy particle are needed
high energy colliders create a probe of the right composition and momentum in order to visualize a target of a specific size
eg: what electron accelerating voltage is needed to observe a particle of diameter $10^{- 15} m$ ?

\begin{aligned} λ & = 10^{- 15} m \\ ⟹ p & = 6.63 \times 10^{- 19} \\ \approx 1 G e V / c \\ e V & = \frac{p^{2}}{2 m} \\ ∴ V & \approx 1.5 T e V \end{aligned}

particle physics is just optics at a small length scales

the rayleigh criterion

Δ = 1.22 λ

an object is just resolvable if the central maxima from one slit aligns with the first minima from the other
microscopy scales:
- optical: $λ = 500 n m$ - microorganisms
- AFM: $λ = 1 n m$ - molecules
- STM: $λ = .1 n m$ - atoms
- STM: $λ = .01 n m$ - inside atoms
an object $\sim 1.5 m$
molecules $\sim 10^{- 7} m$
atoms $\sim 10^{-} 15 m$
quark $\sim ?$