Exploring the unification of quantum theory and general relativity with a Bose-Einstein condensate (1812.04630v3)

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 ofquantum 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.

Analyzing the Unification of Quantum Theory and General Relativity Using a Bose-Einstein Condensate

The pursuit of a unified theory that successfully amalgamates quantum theory (QT) and general relativity (GR) remains one of the enduring challenges in theoretical physics. This paper contributes to this ongoing discourse by exploring the potential role of Bose-Einstein condensates (BECs) in elucidating aspects of a unified theory. The focus of the paper is on the "gravitizing quantum theory" approach, which proposes modifying QT principles to reflect GR concepts, such as the equivalence principle, rather than the more traditional approach of "quantizing gravity."

Mathematical Framework and Theoretical Foundation

The authors propose that the intersection of GR and QT necessitates modifications to the superposition principle inherent in QT. Such modifications could yield an objective mechanism for wavefunction collapse, hence addressing the measurement problem in QT. The paper leverages the gravitational self-energy difference between superposed states, denoted as $E_G$, as a metric to anticipate the collapse time of a superposition due to gravitational effects. The relationship $\tau \sim \hbar /E_G$ suggests that the lifetime of such a superposition is inversely proportional to this energy difference.

Examination of Mass Distributions

The paper investigates various mass configurations, particularly focusing on the gravitational self-energy differences for uniform spherical and spheroidal mass distributions. The results demonstrate that manipulating the geometry of the mass distribution, such as utilizing non-spherical (spheroidal) configurations, can alter the value of $E_G$, consequently affecting the rate of wavefunction collapse. The analysis reveals that certain spheroidal configurations yield higher $E_G$ values than spheres, presenting a compelling case for experimental pursuits utilizing geometrically complex mass distributions within BECs.

BEC Experiments and Implications

The application of BECs in testing these theoretical constructs is notably advantageous due to their highly controllable nature and the possibility of achieving macroscopic quantum superpositions. The paper details the construction of macroscopic superposition states in BECs confined within double-well potentials. Through numerical exploration, the authors contend that with appropriate manipulation—such as modifying the atom-atom interaction strength—BECs can serve as viable systems to experimentally test and validate the theories concerning wavefunction collapse from gravitational effects.

Addressing Environmental Decoherence

A significant consideration in examining gravitational-induced state reduction via BECs is the challenge posed by environmental decoherence. The authors methodically outline potential decoherence sources, including three-body recombination, interactions with a thermal cloud, and ambient foreign atom collisions, assessing how these might influence coherence times relative to the hypothesized collapse mechanisms. The analysis specifies conditions and experimental parameters—such as atom number, scattering length, and environmental temperature—necessary to discern gravitationally-induced collapse from these decoherence effects.

Conclusion and Future Prospects

The research emphasizes that the implications of observing gravitationally-induced state reduction are profound, offering potential insights into a unified theory that coherently incorporates QT and GR. Positive experimental confirmation would redefine our understanding of quantum mechanics, suggesting that classical limits may emerge from quantum phenomena modified by gravitational influences. Conversely, the absence of such evidence within achievable experimental parameters could impose stringent constraints on this and similar models, guiding future theoretical refinements.

The paper concludes by acknowledging the need for further exploration of other geometric configurations and improved analytical techniques to better understand approximate macroscopic superposition states. These explorations underscore the dynamic interplay between theoretical predictions and experimental realizations in the quest to unify the fundamental forces governing the mechanics of the universe.