Three-Space as a Quantum Hyperlayer in 1+3 Dimensions: A Case Study in Quantum Space and Time

Area of Science:

• Quantum physics
• Cosmology
• Theoretical physics

Background:

• Classical cosmology assumes universes are spacelike sections of spacetime.
• Existing models often treat curvature as a parameter.

Purpose of the Study:

• To introduce a novel formalism for quantum universes.
• To investigate the dynamics and properties of such universes.
• To generalize the Cariñena-Rañada-Santander (CRS) model.

Main Methods:

• Modeling the universe as the support of a spacetime-propagating wave function.
• Employing a squeezing-type dynamics (shrinking in time, expanding in space).
• Testing the formalism with a universe containing a harmonic oscillator.

Main Results:

• The universe is a hyperlayer of finite timelike width, not a 3D submanifold.
• Curvature becomes a quantum observable, not a fixed parameter.
• Asymptotic reconstruction of standard quantum mechanics with decreasing effective mass for oscillators over time.

Conclusions:

• The proposed formalism offers a new perspective on quantum universes.
• The decreasing effective mass suggests a potential dependence of elementary particle masses on cosmological evolution or distance.
• Further research may explore implications for fundamental physics and cosmology.