Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature

by Steven Weinberg

As a result of this reappraisal of the problem of infinities, we now think that the field equations of the standard model are not of the very simple type that would be renormalizable but that they actually contain every conceivable term that is consistent with the symmetries of the theory. But then we must explain why the old renormalizable quantum field theories like the simplest versions of quantum electrodynamics or the standard model worked so well. The reason, we think, can be traced to the fact that all the terms in the field equations, apart from the very simple renormalizable terms, necessarily appear in these equations divided by powers of something like the Planck energy. The effect of these terms on any observed physical process would then be proportional to powers of the ratio of the energy of the process to the Planck energy, a ratio perhaps as small as one part in a million billion. This is such a tiny number that naturally no such effect has been detected. In other words, the condition of renormalizability that guided our thinking from the quantum electrodynamics of the 1940s to the standard model of the 1960s and 1970s was for practical purposes the right condition, though it was imposed for reasons that no longer seem relevant.