: A second observer might decompose the same field using a different basis and operators Mixing : The new annihilation operator
To relate the perspectives of different observers or the state of fields at different times in an expanding universe, physicists use : Field Decomposition : A scalar field is expanded into a set of basis modes with creation and annihilation operators Quantum Field Theory in Curved Spacetime: Quant...
: An observer accelerating through a Minkowski vacuum will perceive it as a thermal bath of particles at a temperature proportional to their acceleration. : A second observer might decompose the same
: Strong gravitational fields near a black hole's event horizon polarize the vacuum, causing the black hole to emit thermal radiation and gradually lose mass. Robert Wald - Quantum Field Theory in Curved Spacetime
: In the early, rapidly expanding universe, time-varying gravitational fields can "excite" the vacuum, creating elementary particles that seed the large-scale structure of the universe. Robert Wald - Quantum Field Theory in Curved Spacetime
. This approach serves as a robust approximation for environments where gravity is strong but quantum gravitational effects—such as fluctuations of the metric itself—are not yet dominant. 1. The Fundamental Shift: From Particles to Fields