Quantum Mechanics and the Nature of Spacetime

Hans-Thomas Elze

The canonical answer to the question posed is "Yes." – tacitly assuming that quantum theory and the concept of spacetime are to be unified by 'quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? – We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which are free or subject to spatially constant but possibly time dependent, or harmonic forces, if represented appropriately. This result suggests a way to incorporate anharmonic interactions, including fluctuations which are tentatively related to the underlying discreteness of spacetime. Being linear and local at the quantum mechanical level, the model offers a decoherence and natural localization mechanism. However, the relation to primordial deterministic degrees of freedom is nonlocal.

Vesselin Petkov

Carl Friedrich von Weizsäcker, Thomas Görnitz, Holger Lyre

Ed Seidewitz

Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincaré invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, “off-shell” theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to nonrelativistic quantum mechanics.

Changlong Wen

This paper explores the fundamental nature of spacetime from the perspective of emergent causal structures, rooted in quantum mechanical principles. We propose a theoretical framework that treats spacetime not as a pre-existing background, but as a collective phenomenon arising from the interaction of quantum causal relations. By analyzing the constraints of causality and quantum coherence, we derive key implications for the emergence of classical spacetime geometry and the limits of local realism. Our results suggest a new way to bridge quantum mechanics and gravitational theory, providing a foundation for future studies in quantum gravity and spacetime physics.

G. Papini