Intertheoretic Implications of Non-Relativistic Quantum Field Theories
I consider what non-relativistic quantum field theories (NQFTs) suggest about the intertheoretic relations between classical and quantum theories of particles and fields, both in the presence and in the absence of gravitational effects. In the absence of gravity, interacting NQFTs exist for which Haag's theorem, the CPT theorem, and the Spin Statistics theorem all do not apply; and while the Reeh-Schlieder theorem is valid, it does not have the same implications that it does in the relativistic context. Moreover, a consistent NQFT exists that includes gravitational effects. This "Newtonian" quantum theory of gravity is an example of an NQFT in a classical curved spacetime, and is not afflicted by the conceptual problems surrounding relativistic QFTs in curved spacetimes. These examples provide clues to how the fundamental theories in physics relate to each other and to the quest of formulating a fully relativistic quantum theory of gravity.