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6.1: Prelude to the Fundamental Forces

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  • The fundamental forces are normally divided in four groups, of the four so-called “fundamental” forces. These are often naturally classified with respect to a dimensionless measure of their strength. To set these dimensions we use \(\hbar\), \(c\) and the mass of the proton, \(m_p\). The natural classification is then given in Table \(\PageIndex{1}\). Another important property is their range: the distance to which the interaction can be felt, and the type of quantity they couple to. Let me look a little closer at each of these in turn.

    Table \(\PageIndex{1}\): A summary of the four fundamental forces
    Force Range Strength Acts on
    Gravity \(\infty\) \(G_N\approx 6\, 10^{-39}\) All particles (mass and energy)
    Weak Force \(<10^{-18}\)m \(G_{F}\approx 1\, 10^{-5}\) Leptons, Hadrons
    Electromagnetism \(\infty\) \(\alpha \approx 1/137\) All charged particles
    Strong Force \(\approx 10^{-15}\)m \(g^{2}\approx 1\) Hadrons

    In order to set the scale we need to express everything in a natural set of units. Three scales are provided by \(\hbar\) and \(c\) and \(e\) – actually one usually works in units where these two quantities are 1 in high energy physics. For the scale of mass we use the mass of the proton. In summary (for \(e=1\) we use electron volt as natural unit of energy)

    \[\begin{align*} \hbar &= 6.58 \times 10^{-22} \text{ MeV s}\\ \hbar c & = 1.97 \times 10^{-13} \text{ MeV m}\\ m_{\mathrm{p}} & = 938 \text{ MeV}/c^2\end{align*}\]

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