| Diósi–Penrose criterion | |
|---|---|
| Name | Diósi–Penrose criterion |
| Caption | Schematic depiction of mass distributions in superposition leading to gravitationally induced collapse |
| Field | Quantum physics |
| Introduced | 1987–1996 |
| Proponents | Lajos Diósi; Roger Penrose |
| Related | Objective-collapse theory; Quantum gravity; Decoherence |
Diósi–Penrose criterion
The Diósi–Penrose criterion is a proposed quantitative estimate for the lifetime of quantum superpositions of mass distributions, arguing that gravity induces objective collapse of the wavefunction. It matters because it offers a conceptually economical bridge between Quantum mechanics and General relativity by predicting when microscopically coherent states become effectively classical, thereby addressing the measurement problem and the quantum–classical boundary.
The criterion emerged from independent proposals by Hungarian physicist Lajos Diósi and British mathematical physicist Roger Penrose in the late 20th century. Both authors sought a physically motivated mechanism for state-vector reduction that depends on the difference in spacetime geometry between branches of a superposition. The idea responds to longstanding puzzles in foundations of quantum mechanics such as the measurement problem and the role of gravity in quantum theory, engaging communities at institutions like Imperial College London (Penrose) and the Budapest University of Technology and Economics (Diósi). It also interfaces with programmatic efforts in quantum foundations and with experimental groups at laboratories including Institut Laue-Langevin and Max Planck Institute for Gravitational Physics seeking macroscopic quantum coherence.
The Diósi–Penrose estimate assigns a collapse timescale τ ≈ ℏ/E_G, where ℏ is the reduced Planck constant and E_G is a gravitational self-energy characterizing the difference between mass distributions in the superposed states. E_G is computed from the Newtonian potential energy of the mass-density difference Δρ(x): E_G = −(G/2) ∫∫ [Δρ(x) Δρ(y)] / |x − y| d^3x d^3y, with G the Newton's gravitational constant. The formulation assumes nonrelativistic mass densities and uses concepts from Newtonian gravity and potential theory; it connects to objective-collapse models such as the GRW theory and the Continuous Spontaneous Localization (CSL) model by providing a physically motivated collapse rate dependent on mass distribution rather than ad hoc parameters. Diósi provided a master equation form analogous to the Lindblad equation used in open quantum systems, while Penrose emphasized conceptual links to gravitationally distinct spacetime geometries and the notion of incompatible time translations for different branches.
The criterion is positioned as a minimal phenomenological link to quantum gravity: it implies that a full theory combining General relativity and Quantum mechanics must account for the instability of macroscopically distinct superpositions. Penrose has argued for a connection to gravitational degrees of freedom and to the nonlinearity of state reduction, invoking thought experiments involving Schrödinger's cat-like mass configurations and the concept of gravitationally induced superselection. Diósi's approach can be seen as a specific collapse kernel within the objective-collapse family and has inspired hybrid proposals combining collapse dynamics with semiclassical gravity equations (e.g., the Semi-classical gravity approximation). The criterion thus informs research programs at theoretical centers such as CERN and university groups working on phenomenological signatures of quantum-gravity-inspired collapse.
Experimental tests target systems where predicted collapse times are short enough to be measurable yet coherence is attainable: matter-wave interferometry with large molecules, optomechanical oscillators, nanomechanical resonators, and levitated microspheres. Notable experimental platforms include experiments by groups at University of Vienna (quantum optomechanics), Harvard University and Vienna collaborations on macromolecule interferometry, and efforts at NIST and University of Chicago on electromechanical systems. Constraints on collapse parameters arise from observed coherence times, heating rates, and spontaneous emission bounds; current experiments have set limits that challenge some numerical instantiations of the Diósi–Penrose estimate but have not decisively falsified a broad class of gravitational collapse hypotheses. Astrophysical and cosmological observations, such as limits from cosmic microwave background anisotropies and stellar cooling, also provide complementary bounds.
Critiques center on ambiguities in defining mass density for quantum fields, the nonrelativistic nature of the original estimates, and potential conflicts with energy conservation and Lorentz invariance. Alternative approaches include decoherence via environmental interactions (studied in Wojciech Zurek's program), stochastic collapse models like GRW and CSL, and attempts to quantize gravity in canonical or covariant frameworks such as loop quantum gravity and string theory. The Diósi–Penrose proposal faces the theoretical challenge of embedding a precise, relativistically covariant collapse mechanism in a complete theory; debates continue about whether the effect is fundamental or an effective consequence of entanglement with gravitational degrees of freedom. Prominent critics and authors discussing these issues include Stephen Adler, Eugene Wigner (historically), and Colin P. (C. P.)] ] scholars in quantum foundations.
If a gravitationally induced collapse mechanism of Diósi–Penrose type operates at observable scales, it would provide a principled explanation for classicality of macroscopic bodies and the emergence of definite outcomes without recourse to observer-dependent postulates. The criterion complements environmental decoherence by offering an intrinsic, system-dependent timescale for loss of coherence based on mass distribution, thereby informing models of macroscopic superpositions such as matter-wave interferometry and macroscopic quantum coherence experiments. Its adoption would influence interpretations of quantum mechanics, favoring objective-collapse or realist stances over strict instrumentalist readings, and would guide experimental roadmaps at institutions such as Caltech, MIT, and national metrology labs toward tests that could cement a conservative, law-like account of the quantum-to-classical transition.
Category:Quantum mechanics Category:Foundations of quantum mechanics Category:Quantum gravity