Second-Order Moment Quantum Fluctuations and Quantum Equivalence Principle
arXiv:2408.09630 · doi:10.1016/j.physleta.2025.130273
Abstract
The second-order moment quantum fluctuations or uncertainties are mass-dependent, and the incompatibility between the quantum uncertainty principle and the equivalence principle is at the second-order moment (variation) level, but not the first-order moment (mean) level. To reconcile the two fundamental principles, we find that the second-order moment quantum fluctuations are actually distinguished into two parts: a dynamic part and a geometric part. The dynamic part is indeed mass-dependent and governed by a non-zero Hamiltonian in a non-general-covariant inertial frame, and the geometric part is mass-independent and comes from coarse-graining and/or geometric effects. The dynamic part is coordinate dependent, it can be canceled away by a coordinate transformation, and hence it plays no role in general covariant theories whose Hamiltonian automatically vanishes. However, the geometric part is valid for general coordinate, and it can not be eliminated by a coordinate transformation. On the contrary, the geometric part of second-order moment fluctuation of quantum spacetime leads to coordinate transformation anomaly, which induces an effective Einstein's gravity theory. The geometric part is mass-independent and universal, so it is only this part measures the universal second-order moment quantum fluctuation of the spacetime, while the dynamic part plays no role in the general covariant description. The observation generalizes the classical equivalence principle to the quantum level. And according to the principle, a general covariant theory with only geometric part quantum fluctuation, i.e. a non-linear sigma model, is proposed as a theory of a material quantum reference frame system. The effects of the universal second-order moment quantum fluctuations in the material quantum reference system and its implications to an effective gravity theory are also discussed.
14 pages. v2: Final version published in Phys. Lett. A
References in corpus (20)
- Quantum mechanics and the covariance of physical laws in quantum reference frames
- Quantum superposition of spacetimes obeys Einstein's Equivalence Principle
- Quantum mechanics and the equivalence principle
- Equivalence Principle for Quantum Systems: Dephasing and Phase Shift of Free-Falling Particles
- Does Quantum Mechanics Clash with the Equivalence Principle - and Does it Matter?
- Quantum test of the Universality of Free Fall using rubidium and potassium
- Testing the Universality of Free Fall using correlated K -- Rb interferometers
- Is Einstein's equivalence principle valid for a quantum particle?
- On the quantum analogue of Galileo's leaning tower experiment
- The Cosmological Constant Problem and Re-interpretation of Time
- On free fall of quantum matter
- The Cosmological Constant Problem and Quantum Spacetime Reference Frame
- Ricci Flow Approach to The Cosmological Constant Problem
- Local Conformal Instability and Local Non-Collapsing in the Ricci flow of Quantum Spacetime
- Free Fall of a Quantum Many-Body System
- A Statistical Fields Theory underlying the Thermodynamics of Ricci Flow and Gravity
- Trace Anomaly, Perelman's Functionals and the Cosmological Constant
- Quantum Modified Gravity at Low Energy in the Ricci Flow of Quantum Spacetime
- Weak Equivalence Principle and Propagation of the Wave Function in Quantum Mechanics
- The Ricci Flow and the Early Universe