Back in Berkeley, Weinberg reconsiders how we understand some of the theories of physics, that is, why they actually are true. He begins teaching a general relativity course starting from physical principles, rather than the usual geometric approach. These course notes later became the basis for his book Gravitation and Cosmology. Around this time, Louise was pregnant, so Weinberg avoided opportunities to travel to spend more time at home. He begins working on functional analysis, but discovers the Russian Faddeev has already done foundational work in this area. Weinberg then reexamines what he knows about quantum field theory, and jettisons the Heisenberg–Pauli canonical formalism, taking particles as his starting point. This led him to a clearer understaning of antimatter. He embarks on a series of papers about massless particles. in 1964, he is promoted to full professor. Louise applied to Harvard Law School, prompting a move to Cambridge, Mass.

The relation between local spacetime curvature and matter energy density is given by the Einstein equation – it is the field equation of general relativity in the way that Maxwell’s equations are the field equations of electromagnetism. Maxwell’s equations relate the electromagnetic field to its sources – charges and currents. Einstein’s equation relates spacetime curvature to its source – the mass-energy of matter. This chapter gives a very brief introduction to the Einstein equation; we consider the equation in the absence of matter sources (the vacuum Einstein equation) and will include matter sources in Chapter 22. Even the vacuum Einstein equation has important implications. Just as the field of a static point charge and electromagnetic waves are solutions of the source-free Maxwell’s equations, the Schwarzschild geometry and gravitational waves are solutions of the vacuum Einstein equation.