Wormholes May Remain Stable Thanks to Quantum Effects from Vacuum Fluctuations

Calculations reveal how vacuum fluctuations impact the geometry of a timelike topological wormhole supported by an anisotropic fluid. Haris Mehulic and Tomislav Prokopec at Utrecht University used techniques of dimensional regularisation and semiclassical gravity to show that these quantum backreactions can either destabilise or stabilise the wormhole, depending on the chosen gravitational counterterms. The results keyly demonstrate that classical traversability persists even when quantum effects are considered. This provides insight into the interplay between quantum field theory and general relativity and represents a sharp step towards understanding the viability of wormholes as potential structures within the universe.

Quantum renormalisation reveals angular pressure shifts on traversable wormholes

Calculations reveal that quantum backreaction alters angular pressure on a timelike topological wormhole by up to ±1/8πGaL0, a significant shift from the classical prediction of zero pressure. This precise quantification of quantum influence was previously unattainable due to the challenges of renormalizing divergent quantum fluctuations in curved spacetime. The standard approach to calculating quantum fields in curved spacetime inevitably leads to infinities, necessitating a procedure called renormalisation to extract physically meaningful results. Dimensional regularisation, a specific technique within renormalisation, involves analytically continuing the spacetime dimension to a noninteger value to tame these divergences. This allows for a well-defined calculation of quantum corrections to classical quantities. The introduction of gravitational counterterms, terms added to the classical action to cancel the divergent contributions arising from the quantum field, was key to overcoming these hurdles, allowing for a more thorough picture of the wormhole’s potential longevity. These counterterms are necessary because the standard Hilbert-Einstein action is not sufficient to absorb all quantum divergences when considering matter fields coupled to gravity.

Quantum effects modify the angular pressure exerted on a wormhole, inducing either negative or positive values dependent on the choice of finite counterterms, and consequently affecting stability. The specific choice of counterterms reflects ambiguities in the definition of the quantum stress-energy tensor in curved spacetime. Further analysis of the energy-momentum tensor, achieved through renormalisation using dimensional regularisation and gravitational counterterms, demonstrates that the geometry is supported by an anisotropic fluid. Anisotropic fluids possess different pressures in different directions, a crucial requirement for maintaining the exotic geometry of a traversable wormhole. Singular shells exist at the boundary between the wormhole and surrounding Minkowski space, a feature of its unique structure. These shells represent a discontinuity in the spacetime metric and require careful treatment within the semiclassical framework. Calculations indicate a classically traversable wormhole remains traversable when quantum backreaction is considered, provided the length, L0, is much larger than its radius, a. This condition, L0 ≫ a suggests that macroscopic wormholes are more likely to withstand quantum destabilization than microscopic ones. These calculations assume a simplified geometry, specifically a product spacetime M2 × S2, and do not yet address how these effects would manifest in a fully self-consistent solution of the semiclassical gravity equations, leaving an open area for further investigation. The M2 × S2 geometry represents a two-dimensional Minkowski space cross a two-dimensional sphere, simplifying the calculations while still capturing the essential features of a wormhole throat.

Quantum fluctuations’ dual role in theoretical wormhole maintenance

The semiclassical equations of gravity, which combine general relativity with quantum field theory, are notoriously difficult to solve exactly. This work represents a linear perturbation around a classical background, meaning that the quantum effects are treated as small corrections to the classical solution. A full solution would require solving the equations to all orders in the quantum corrections, a computationally challenging task. Despite being limited to a first-order approximation, this work offers valuable insight into a profoundly difficult problem. Quantum fluctuations, arising from the very fabric of space, demonstrably influence wormhole stability, either reinforcing or undermining these theoretical tunnels.

Understanding this interaction is vital, as it clarifies the conditions needed, however improbable, for maintaining a traversable shortcut through spacetime, and provides a foundation for more thorough modelling. The existence of traversable wormholes, even in principle, has profound implications for our understanding of spacetime and the possibility of faster-than-light travel. Temporary energy appearing from seemingly empty space, known as quantum fluctuations, can both support and undermine the stability of these hypothetical shortcuts. Classically traversable wormholes, previously confined to theoretical discussions, may indeed remain open even with these quantum effects accounted for. This resilience suggests that the quantum properties of spacetime may not be as hostile to wormhole existence as previously thought.

Quantum vacuum fluctuations exert both stabilising and destabilizing forces on theoretical wormholes; these tunnels through spacetime are not necessarily disrupted by quantum effects. Calculations utilising dimensional regularisation, a technique to manage infinities arising in quantum calculations, reveal that quantum backreaction can alter angular pressure on a wormhole, influencing its structure. The magnitude of this alteration is quantified as ±1/8πGaL0, providing a precise measure of the quantum influence on the wormhole’s geometry, where G is the gravitational constant and a is the wormhole radius. Above all, a wormhole initially permitting travel remains open even when these quantum influences are accounted for, suggesting a degree of inherent durability.