Abstract Despite almost a century’s worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as ‘quantizing gravity’, resulting in a theory of ‘quantum gravity’. The opposite approach is ‘gravitizing QT’ where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using a Bose–Einstein condensate (BEC) to search for clues. In particular, we study how a single BEC in a superposition of two locations could test a gravitizing QT proposal where wavefunction collapse emerges from a unified theory as an objective process, resolving the measurement problem of QT. Such a modification to QT due to general relativistic principles is testable near the Planck mass scale, which is much closer to experiments than the Planck length scale where quantum, general relativistic effects are traditionally anticipated in quantum gravity theories. Furthermore, experimental tests of this proposal should be simpler to perform than recently suggested experiments that would test the quantizing gravity approach in the Newtonian gravity limit by searching for entanglement between two massive systems that are both in a superposition of two locations.
Abstract Despite almost a century’s worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as ‘quantizing gravity’, resulting in a theory of ‘quantum gravity’. The opposite approach is ‘gravitizing QT’ where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using a Bose–Einstein condensate (BEC) to search for clues. In particular, we study how a single BEC in a superposition of two locations could test a gravitizing QT proposal where wavefunction collapse emerges from a unified theory as an objective process, resolving the measurement problem of QT. Such a modification to QT due to general relativistic principles is testable near the Planck mass scale, which is much closer to experiments than the Planck length scale where quantum, general relativistic effects are traditionally anticipated in quantum gravity theories. Furthermore, experimental tests of this proposal should be simpler to perform than recently suggested experiments that would test the quantizing gravity approach in the Newtonian gravity limit by searching for entanglement between two massive systems that are both in a superposition of two locations.
“Despite almost a century’s worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as ‘quantizing gravity’, resulting in a theory of ‘quantum gravity’. The opposite approach is ‘gravitizing QT’ where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using the Dirac–Pauli representation of free Dirac equation to search for the clues. In particular, we study how the double-slit diffraction experiment, when only one Dirac particle (‘say’ electron) at a time is in the apparatus, could test a gravitizing QT proposal in which the wavefunction collapse emerges on the detector screen from the Dirac–Pauli representation, as an objective process, resolving the measurement problem of QT.” [1] We found that the Dirac–Pauli representation is inherently a unified theory embodying a gravitizing QT proposal that Dirac–Pauli representation as wave nature is manifestation of inertial mass and the Foldy-Wouthuysen representation as particle nature is manifestation of gravitational mass such that the fact, that same physics is involved in these two representations, is simply the validity and exhibition of the principle of equivalence, of GR, in QT. [1] Richard Howl et al 2019 New J. Phys. 21 043047 DOI 10.1088/1367-2630/ab104a
Measuring effects of General Relativity and beyond in the gravitational field of the Earth is a main goal of current research and cutting-edge technology. These effects, predicted by Einstein’s theory, already play an important role in everyday life, for example in enabling for precise positioning and time keeping in global satellite navigation systems, such as GPS and GALILEO. The breakthrough experimental realisation of Bose-Einstein condensation in 1995, some 70 years after Einstein’s prediction, has since established matter-wave interferometers in laboratories worldwide, in which laser pulses are used to coherently split, reflect, and recombine a Bose-Einstein condensate. While already enabling highly accurate quantum sensors for technological applications as accelerometers, gyroscopes, and gravity gradiometers, matter-wave interferometers with their unprecedented potential sensitivity are highly anticipated to serve as formidable quantum probes of fundamental physics. For this reason, concentrated international efforts are currently under way to develop this promising technology into robust and sensitive instruments. The German QUANTUS collaboration is at the forefront of this development, having demonstrated the first Bose-Einstein condensates and matter-wave interferometers in free fall, and having recently achieved the very first BEC in space on the sounding-rocket mission MAIUS-1 in early 2017. As its long-time goal, QUANTUS is aiming at a quantum test of Einstein’s famous Equivalence Principle, which is at the heart of General Relativity as a geometric theory of gravity. In this context, it is relevant to develop a precise description of free fall in Earth’s gravity beyond the usual Newtonian approximation, and thus to take into account the full reality of curved space-time in terms Einstein’s theory of General Relativity. In this thesis, we take a grand tour of the relevant concepts of Special and General Relativity and eventually apply these to the modelling of free falling quantum gases. We base our description on the experimentally relevant local inertial and non-inertial frames which we can think of as moving along with experiments in free fall, for example in a drop tower, or in satellites orbiting the Earth, such as the International Space Station ISS. Our main tool are Fermi normal coordinates attached to these frames, which provide a local curvature expansion around flat space-time that exhibits local tidal effects, and can thus be seen as an expansion around the Equivalence Principle. Being fairly under-represented in the literature, we extensively discuss these Fermi coordinates, as well as the so-called Riemann normal coordinates on which they are built. In particular, we provide a new combinatorial interpretation for the complicated polynomials in the Riemann tensor and its derivatives, which arise in the expansion for the tetrads and the metric in these coordinates. We finally apply these methods to the mean-field description of free falling Bose-Einstein condensates in the gravitational field of the Earth. Modelling the space-time curvature around our planet in terms of the Schwarzschild metric, we explicitly calculate the metric in Fermi coordinates for local inertial frames in free fall along purely radial geodesics, which approximates the experimental situation in a drop tower, as well as along circular equatorial geodesics which can be used to model the situation on satellites, such as the ISS. We then use these metrics in the non-linear Klein-Gordon equation which can be seen to generalise the usual Gross-Pitaevskii equation to curved space-time. Performing the non-relativistic limit, we obtain the different local tidal-type Newtonian and relativistic corrections and discuss their orders of magnitude.
Why Quantum–Gravity Experiments Signal Ordering Failure, Not Ontological Crisis Recent experimental proposals at the quantum–gravity interface investigate the behavior of massive systems placed in spatial superposition, raising questions about the stability and meaning of gravitational sourcing under quantum delocalization. These efforts—most notably those involving Bose–Einstein condensates (BECs) and mesoscopic mass superpositions—are often framed as challenges to physical realism or as motivations for modifying quantum mechanics itself. In this paper, we argue that such experiments instead expose a regime boundary arising from incorrect theoretical ordering. When mass and force are treated as fundamental, superposition produces internal inconsistency. When structure is treated as primary and force as a restorative, regime-limited description, the apparent paradox resolves. We reinterpret contemporary quantum-gravity experiments as probes of structural admissibility rather than tests of metaphysical primacy, situating them as empirical support for a structure-first framework.
Quantum Physics
Quantum mechanics and the general theory of relativity represent two pillars of modern physics, but unification of the two theories remains an open problem. Theories of quantum gravity abound, but they tend to lack an experimental foundation. One such proposed theory, event formalism, predicts that a pair of entangled particles decorrelate as they pass through different regions of the gravitational well of a planetary object. Xu et al. present results of a quantum optical test of this proposal using the quantum satellite Micius. Using entangled photon pairs, one sent to the satellite and the other retained on Earth, they find no evidence for the predicted decorrelation effects. The results may help shed light on the interplay between quantum theory and gravity.
Science , this issue p. [132][1]
[1]: /lookup/doi/10.1126/science.aay5820
FINDING: Quantum gravity remains experimentally untested; proposed tabletop tests (matter-wave interferometry, optomechanics) probe Planck-scale effects via superposition of massive objects, with no confirmed mathematical discovery yet. MATH: No new equations or constants extracted. Relevant framework: Planck mass mP=ℏc/G≈2.176×10−8kg, Planck length ℓP=ℏG/c3≈1.616×10−35m. Proposed test scales: superposition separation Δx∼ℓP2/3λC1/3 (where λC is Compton wavelength) — from Bose–Marletto–Vedral entanglement criterion. No golden-ratio or base-60 structure appears in the cited abstracts. CONNECTION: None explicit. However, the Bose–Marletto–Vedral test relies on gravitational entanglement of two masses — a bipartite quantum correlation. If gravity is quantum, the interaction Hamiltonian H∝Gm1m2/r yields entanglement e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com