Entanglement Exists before Space and Time, Redefining Gravity’s Fundamental Role

Scientists are increasingly investigating how quantum entanglement might arise from gravity itself, a phenomenon known as quantum-gravity-induced entanglement of massive systems (QGEM). Hollis Williams from the University of Exeter, alongside colleagues, demonstrate that entanglement can exist even without pre-existing spacetime geometry. Their work reformulates the gravitational interaction within a twistor framework, revealing a well-defined entanglement phase independent of spatial distance. This finding is significant because it isolates the fundamental quantum aspects of QGEM, suggesting spacetime emerges as a consequence of, rather than a prerequisite for, this entanglement. The research clarifies that the familiar Newtonian interaction is a later approximation, appearing only when a specific spacetime representation is selected.

Scientists estimated in the nonrelativistic static limit by a Newtonian interaction between spatially separated masses. In this work, we reformulate the gravitationally mediated interaction phase in a conformally invariant twistor framework in which no notion of spacetime distance is assumed. We show that the bilocal phase responsible for entanglement generation remains well-defined and non-factorizable even in the absence of spacetime geometry. The familiar N.

Calculating entanglement phase from Newtonian gravitational interaction

Scientists have proposed quantum-gravity-induced entanglement of massive systems (QGEM) as a table-top probe of the quantum nature of gravity, based on the observation that purely classical channels cannot generate entanglement between spatially separated systems prepared in a quantum superposition. In the simplest implementations, two masses are placed in spatial superposition and interact gravitationally for a fixed duration.

The resulting entanglement is attributed to a relative phase generated by the gravitational interaction, usually by a Newtonian potential in the nonrelativistic static limit. The operational quantity governing entanglement generation is then the phase Φ ∼GmAmBT/ħr, and observation of entanglement is interpreted as evidence that gravity cannot be described by a purely classical mediator.

A substantial body of work has explored refinements and extensions of this basic idea, including schemes with improved robustness to decoherence, many-body generalizations, Casimir screening effects, and formulations in curved or higher-dimensional spacetimes. In nearly all such analyses, the gravitational interaction phase is computed from spacetime-dependent quantities, such as a Newtonian potential or a proper time difference, which are treated as the fundamental inputs into the protocol.

Although this approach is natural from the perspective of nonrelativistic gravity, it leaves implicit the extent to which spacetime itself is essential for the mechanism of entanglement generation. From an effective field theory viewpoint, the gravitational interaction between two localized masses arises when one integrates out a massless mediator, yielding a bilocal influence functional which couples their world-lines.

The resulting unitary evolution is characterized by a non-factorizable phase functional whose existence ensures the possibility of entanglement generation. Crucially, this bilocal structure is logically distinct from any particular geometric representation of the interaction, such as a distance-dependent spacetime metric.

Although QGEM protocols rule out purely classical channels, focusing exclusively on spacetime-based descriptions can obscure the more primitive role played by this non-factorizable bilocal phase. This motivates the search for a formulation in which the bilocal interaction can be defined independently of a spacetime metric, whilst still reproducing the familiar Newtonian limit when additional structure is introduced.

In this work, researchers make this distinction explicit by reformulating the bilocal gravitational interaction in a twistor framework, in which spacetime distance and metric structure are not assumed a priori. Twistor theory provides a natural language for describing conformal structure and propagation of massless particles, allowing the interaction phase to be defined directly in terms of invariant relations between worldlines rather than spacetime separations.

In this formulation, the bilocal phase responsible for entanglement generation remains well-defined and non-factorizable even in the absence of a metric. They show that the Newtonian 1/r interaction phase relevant for QGEM protocols emerges only after conformal invariance is broken via introduction of an infinity twistor, which selects a particular spacetime interpretation for the underlying bilocal quantum interaction.

Geometry therefore enters not as a prerequisite for entanglement generation, but as a representational structure imposed on a quantum channel which already exists prior to this choice. Their results clarify the operational content of QGEM-type experiments by isolating the genuinely quantum ingredient which they probe, the existence of a non-factorizable bilocal interaction, from the geometric assumptions used to describe it.

In this sense, gravitationally mediated entanglement occurs “before spacetime”: the interaction responsible for entanglement is defined prior to the introduction of a distance measure or a spacetime metric, with spacetime locality arising only as an emergent description of the underlying quantum structure. Before conformal symmetry is broken, the bilocal phase governing QGEM interactions is necessarily scale-free, implying that no metric notion of spatial separation can be defined.

At energies well below the Planck scale, the gravitational interaction between two localized massive systems A and B can be described within an effective field theory by integrating out the metric perturbations. This yields a bilocal interaction between their stress tensors Sint = 1 2 Z d4x d4x′ T μν A (x)DμνρσT ρσ B (x′), where Dμνρσ is the graviton propagator.

For a point particle following a worldline, the stress tensor may be written as T μν(x) = m Z dτ uμuν √−g δ(4)(x −x(τ)), where m and uμ are the mass and four-velocity of the particle, respectively. Substituting this back in, one obtains Sint = 1 2 Z dτdτ ′mAmBuμ Auν BDμνρσ(xA(τ), xB(τ ′))uρ Buσ B. This action is still fully relativistic.

To simplify, researchers will consider a scalar version of this interaction which is obtained by suppressing Lorentz indices and replacing the graviton propagator with the Green’s function of a massless mediator G(x, x′): Sint = 1 2 Z dτ dτ ′ mAmB G(xA(τ), xB(τ ′)) . The Green’s function corresponds schematically to the graviton propagator contracted with the conserved worldline currents, since the scalar structure is sufficient for present purposes.

The contribution of the interaction to the unitary evolution of the joint system is given by the phase ΦAB = 1 ħSint. Whenever the kernel G(x, x′) is nontrivial, the resulting unitary operator UAB = exp(iΦAB) is non-factorizable and can therefore generate entanglement between the two massive systems when they are prepared in a spatial superposition.

As noted above, one can connect with QGEM-type protocols by considering the nonrelativistic static limit in which the two masses remain approximately at rest at a fixed spatial separation r = |xA −xB|. In this limit, the dominant contribution to the Green’s function is instantaneous and one finds G(xA(τ), xB(τ ′)) −→−G δ(t −t′) r.

Substituting this into Eq. (4) yields ΦAB −→−GmAmB ħ Z dt 1 r. For an interaction time T, this gives a total phase ΦAB ∼GmAmBT ħr, in agreement with the expressions appearing in previous publications. Researchers emphasize that although equation (9) is usually assumed in QGEM analysis, it actually arises from two distinct steps.

To summarize, they describe the interaction between the two worldlines in twistor space by a bilocal kernel K(X, X′), which is an Abstract scalar function defined on bitwistor space. Its functional form is initially unspecified, but it is constrained by conformal invariance, projective rescalings, and GL(2, C) transformations on each bitwistor.

They next look to classify all the scalars which may appear in the interaction phase after imposing these symmetries. The two bitwistors may be contracted over to form an independent conformal invariant IAB:= Xαβ A XB αβ. This quantity is dimensionless and invariant under all symmetries listed above.

It characterizes the relative incidence of the two worldlines but does not encode any notion of spatial separation. Another possibility for obtaining invariants is to evaluate the scalar kernel on the twistor components of the two bitwistors, producing quantities such as K(ZA, ZB) and K(ZA, WB). However, none of these are invariant under GL(2, C).

The unique invariant combination is the determinant KAB = det K(ZA, ZB) K(ZA, WB) K(WA, ZB) K(WA, WB). This object is invariant under independent GL(2, C) transformations on each bitwistor, under projective rescalings, and under the action of the conformal group SL(4, C). It follows that, prior to any breaking of conformal invariance, the interaction phase can depend on the bitwistor worldlines only through scalar invariants constructed from the corresponding bitwistors.

Once the appropriate symmetries are enforced, the most general bilocal phase must take the form ΦAB = Z dτ dτ ′ F(IAB, KAB), where IAB and KAB are the scalar invariants defined above. Notably, no notion of spatial distance or temporal separation appears at this stage, and no dimensionful invariant can be constructed. Since the Newtonian interaction phase scales as 1/r, the resulting amplitude is short-range at high energies.

Emergence of Newtonian gravitational phase from conformally invariant quantum entanglement

Researchers reformulated the gravitationally mediated interaction phase within a conformally invariant twistor framework, dispensing with the assumption of spacetime distance. The bilocal phase responsible for entanglement generation remained well-defined and non-factorizable even without spacetime geometry.

This work demonstrates that the familiar Newtonian 1/r phase, crucial for quantum-gravity-induced entanglement (QGEM) protocols, emerges only after breaking conformal invariance by introducing the infinity twistor. This twistor specifically selects a spacetime representation of the underlying bilocal quantum interaction.

The study establishes a distinction between the genuinely quantum content of QGEM protocols and the contingent role of spacetime geometry in mediating entanglement. The operational quantity governing entanglement generation is a phase, Φ, approximately proportional to GmAmBT/ħr, where G is the gravitational constant, m represents mass, A and B denote the interacting systems, T is the interaction duration, and r is the spatial separation.

The bilocal interaction, derived from integrating out a massless mediator, yields a non-factorizable phase functional essential for entanglement generation. This bilocal structure is logically separate from any geometric representation, such as a distance-dependent spacetime metric. Before conformal symmetry is broken, the bilocal phase governing QGEM interactions is necessarily scale-free, indicating that no metric notion of spatial separation can be defined at this level.

The effective field theory describes the gravitational interaction between two localized massive systems using a bilocal interaction between their stress tensors, represented by Sint. For a point particle, the stress tensor is defined in terms of its mass and four-velocity, with the interaction ultimately expressed as a phase ΦAB = 1/ħ Sint. The scalar version of this interaction simplifies the analysis by suppressing Lorentz indices and utilizing the Green’s function of a massless mediator.

Twistor analysis reveals entanglement’s independence from spacetime geometry

Entanglement between massive systems, frequently studied through the lens of quantum gravity experiments, does not fundamentally require spacetime locality. This work reformulates the gravitationally mediated interaction using a twistor framework, a mathematical approach that avoids assuming a pre-existing spacetime distance.

Results demonstrate that a bilocal phase, responsible for generating entanglement, remains well-defined even without a conventional spacetime geometry. The familiar Newtonian interaction, commonly used in analyses of quantum gravity experiments, emerges only after breaking the conformal invariance of the system by introducing a specific mathematical construct called the infinity twistor.

This suggests that spacetime geometry does not create the underlying quantum interaction, but rather provides a particular interpretation of it. Entanglement arises from the existence of this non-factorizable bilocal interaction, effectively a quantum channel between massive systems, and is not dependent on a Newtonian distance-based description.

The authors acknowledge that their analysis relies on a specific mathematical framework and does not directly address experimental limitations. Future research could explore the implications of this framework for designing and interpreting quantum gravity experiments, potentially refining the search for measurable entanglement mediated by gravitational interactions. This work clarifies that experiments probing gravitationally induced entanglement investigate the existence of a fundamental bilocal quantum interaction, with the Newtonian 1/r dependence representing an additional geometric assumption rather than a core requirement.