In flat (Minkowski) spacetime, Poincaré invariance provides a unique vacuum state and a global definition of "particles". In curved spacetime, these "crutches" disappear:
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
: A second observer might decompose the same field using a different basis and operators Mixing : The new annihilation operator
: An observer accelerating through a Minkowski vacuum will perceive it as a thermal bath of particles at a temperature proportional to their acceleration.
This framework predicts several landmark effects that bridge the gap between thermodynamics, gravity, and quantum mechanics: