Becoming real

Carl M. Bender, Hugh F Jones

The coupling of non-Hermitian -symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models. It is found that in all cases the energy remains real for small values of the coupling constant, but becomes complex if the coupling becomes stronger than some critical value. For a quadratic non-Hermitian -symmetric Hamiltonian coupled to an arbitrary real Hermitian -symmetric Hamiltonian, the reality of the ground-state energy for small enough coupling constant is established up to second order in perturbation theory.

Mark I. Alpert

Philip Ball

Tim Beardsley

Gracia, Jose

It was time to make Quantum Mechanics real. Once we do, the theory stops whispering and starts speaking plainly. This chapter shows what happens when we take that step. By treating clocks, their quadratures, and their comparison channels as physically real rather than abstract mathematical decorations, the entire relativistic structure reorganizes itself. Proper time emerges from ticking, the light cone from null comparison, geometry from transport, and spacetime itself becomes a bookkeeping device rather than a substance. What follows is not a reinterpretation of old equations, but a reversal of what we take as fundamental—and once the foundations shift, the physics becomes startlingly clear.