Abstract
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new type of nonminimal coupling of the fields and is shown to admit a canonical quantization procedure. For the resulting quantum theory we demonstrate the emergence of a particle interpretation, fully consistent with general relativistic geometry. The path dependency of parallel transport forces each observer to carry their own quantum state; we find that the communication of the corresponding quantum information may generate extra particles on curved spacetimes. A speculative link between quantum information and spacetime curvature is discussed which might lead to novel explanations for quantum decoherence and vanishing interference in double-slit or interaction-free measurement scenarios, in the mere presence of additional observers.
Highlights
Quantum field theory on Minkowski spacetime admits a clear particle interpretation
That the free scalar field equation (6) takes in observer coordinates ðxAÞ on TM. Since this has the same form as it would have on flat spacetime in the usual geometric framework, we may proceed by canonical quantization; see, e.g., [2]
Since parallel transport in general relativity physically identifies the same momenta at different spacetime points, the particle observation theorem implies that each observer of a noninteracting quantum field measures an initial vacuum state or momentum state completely unchanged along their worldline at later times
Summary
Quantum field theory on Minkowski spacetime admits a clear particle interpretation. On the level of classical field theory, every field satisfies a suitable wave equation that may be solved in terms of a Fourier expansion. A later measurement of the quantum particle state by the same observer should register as unchanged, where vectors at different spacetime points are identified by parallel transport This could be expected since the quantum field is spread over the spacetime region where the observer moves, and the particle momentum state is a nonlocal concept. There, as another key result of this paper, we will discuss how each observer is enabled to identify the vacuum state and particle momentum states along their worldline, and arrive at a quantum particle picture consistent with general relativistic geometry. V with a summary of our results and an outlook on further possible consequences arising from our new construction
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