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arxiv: 2604.18625 · v1 · submitted 2026-04-18 · 🌀 gr-qc · hep-th

Signatures of Quantum Gravity In Relativistic Quantum Systems

Soham Sen This is my paper

Pith reviewed 2026-05-10 07:25 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords quantum gravitygravitonsBose-Einstein condensatedecoherencedetector modelslinearized gravitymemory effectuncertainty relation
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The pith

Gravitons interacting with matter produce observable signatures that specific detector models can capture within a few years.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This thesis examines the interaction between gravitons and quantum matter systems under a linearized quantum gravity approximation. It begins with a two-particle detector obeying a generalized uncertainty principle and identifies a quantum gravity induced memory effect along with a modified uncertainty relation. The work then develops phenomenological models, including a trapped detector exhibiting stimulated absorption and spontaneous emission of gravitons, and proposes a detector based on graviton-mediated decoherence in an entangled relativistic scalar Bose-Einstein condensate. These constructions indicate that laboratory-scale experiments could register quantum gravity effects on accessible timescales.

Core claim

In linearized quantum gravity, the coupling of quantized gravitational fluctuations to matter degrees of freedom generates concrete effects including memory phenomena, altered uncertainty relations, graviton absorption and emission processes, and decoherence between entangled states, which can be exploited in two-particle and Bose-Einstein condensate detector designs to register these signatures.

What carries the argument

The graviton-matter interaction in linearized quantum gravity applied to two-particle systems and relativistic scalar Bose-Einstein condensates, which produces measurable quantum responses such as decoherence and memory effects.

If this is right

  • Gravitons induce a memory effect in simple two-particle matter systems.
  • Gravitational fluctuations modify the uncertainty relation obeyed by detector degrees of freedom.
  • Trapped detector systems exhibit stimulated absorption and spontaneous emission of gravitons.
  • Entangled relativistic Bose-Einstein condensates display graviton-mediated decoherence usable as a detection channel.
  • These interactions support detector constructions that operate on laboratory timescales of a few years.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same interaction framework could be applied to other quantum platforms such as trapped ions or superconducting qubits to widen the search for graviton signatures.
  • Detection of the predicted decoherence would supply a low-energy window into quantum gravity that complements high-energy approaches.
  • Absence of the effects in the proposed setups would indicate either stronger noise backgrounds or the breakdown of the linearization assumption at these scales.

Load-bearing premise

The linearized approximation remains accurate at the energy and length scales of the proposed detectors and graviton-induced signals can be isolated from ordinary environmental noise.

What would settle it

An experiment with the entangled Bose-Einstein condensate detector that records no excess decoherence traceable to gravitons, after subtracting all standard quantum and thermal contributions, would show the signatures are not observable as claimed.

Figures

Figures reproduced from arXiv: 2604.18625 by Soham Sen.

Figure 3.1
Figure 3.1. Figure 3.1: A time-like geodesic ζτ is perpendicular to a space-like geodesic ζs at the point P(τ ) where the space-like geodesic is parametrized by the proper distance s and the time-like geodesic is parametrized by the proper time τ . Here, ∂ ∂τ is the tangent vector to ζτ at P(τ ) and ∂ ∂s gives the tangent normal vector at the crossing point. functional [89]. This Feynman-Vernon influence functional captures the… view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: The dimensionless standard deviation is plotted against time where the standard deviation without any β correction is considered to be the reference line. The maximum frequency of the incoming gravitational wave is set to ω max ∼ 1 Hz. The small inset image indicates the long-term behaviour of the GUP modified standard deviation where one observe a residual standard deviation which asymptotes towards σ s… view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: A box of volume L 3 is compared with a sphere of radius √ L 2 such that the surface area of both the sphere and the box are closest to each other signifying almost a similar amount of transfer of energy through the surface of both of the geometrical objects. sides of the box lies on the surface of the sphere. The surface area of the box is 6L 2 whereas for the sphere, it is 2πL2 . It is very straightforw… view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: A pictorial representation of the formation of a Bose-Einstein condensate. in a gas of Rubidium atoms in 1995 [129], and later that year in a gas of Sodium atoms [130]. In [111], a quasi (1+1)-dimensional Bose-Einstein condensate at zero temperature has 95 [PITH_FULL_IMAGE:figures/full_fig_p105_6_1.png] view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Two nearby density matrices are placed on the perimeter of an unit circle, where dφB denotes the Bures angle and dsB denotes the geometric distance also known as the Bures distance between the two nearby quantum states ρˆϑ and ρˆϑ+dϑ. This Fidelity is indeed symmetric in its input is considered to be a good measure of distance between two quantum states [137]. Fidelity is a measure of overlap between the… view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Plot of |Ih(t)| against t when the upper limit of integration in Ih(t) is finite versus the case when the upper limit of integration is infinite. where αˆ B(t) and βˆB(t) denotes the graviton-noise induced Bogoliubov operators. If the mea￾surement time is corresponding to a single mode of the Bose-Einstein condensate is t = τM 11 then without loss of any generality, one can set t = τM in the Bogoliubov c… view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: We plot the function B(t, rk, φk) against t when rk = 10 and ΩM = 108 Hz for the values of the squeezing angle φk = π 4 , π 2 , π . We have plotted B(t → ∞, 10, φk) as a reference line to have a proper understanding of the fluctuations. It is now quite logical to replace τM by τ in the above expression. Restoring the dimen￾sions carefully and substituting the analytical form of κG = 8πℏG c 3 and using t… view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: p ⟨(∆ε) 2⟩Min vs τ plot for different values of the graviton squeezing parameter rk = {41.5, 42}. Other parameter values are set to rB = 0.8, φk = ζB = π 2 , ωB = 10 Hz, and Ω0 = 20 Hz. Ω0 = 20 Hz. From Fig.(6.5), we observe that for very high graviton squeezing the uncertainty in ε is quite low and for a lower value of the squeezing parameter the uncertainty in the measurement of ε increases. In the sta… view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: We plot the quantum Fisher information as well as the quantum gravitational Fisher information and compare it against the quantum gravitational correction term of the quantum gravitational Fisher information where the parameter values are set to rB = 12, rk = 20, ζB = φk = π 2 , with the frequencies set at ωB = 10 Hz and Ω0 = 20 Hz. primordial gravitational wave from the inflationary time. This is a very… view at source ↗
Figure 6.7
Figure 6.7. Figure 6.7: p ⟨(∆ε) 2⟩Min vs τ plot for rk = 42, rB = 0.83, φk = ζB = π 2 , ωB = 10 Hz, and Ω0 = 20 Hz. p ⟨(∆ε) 2⟩Min ∼ 10−4 initially (τ → 0) for a graviton squeezing as low as rk = 20 when the phonon squeezing is high enough. This implies that even for relatively lower squeezing from the gravitons, at the starting of the experiment, the BEC will still respond provided the phonons are squeezed as well. If the squee… view at source ↗
Figure 6.8
Figure 6.8. Figure 6.8: p ⟨(∆ε) 2⟩Min vs τ plot for rB = 0.83, φk = ζB = π 2 , ωB = 10 Hz, and Ω0 = 20 Hz. The graviton squeezing is set to different values of the parameter. We shall restrict ourselves up to the two-point noise-noise correlator and as a result, one can obtain the standard deviation in the quantum gravitational Fisher information as (∆H(ε))2 ≃ 1 2048ε 2 ⟨⟨{δNˆ(τ, 0), δNˆ(τ, 0)}⟩⟩(H(1)(ε))2 = l 2 PlΩ 2 M 960πε2c… view at source ↗
Figure 6.9
Figure 6.9. Figure 6.9: Plot of ∆H(ε) against the phonon mode frequency when a gravitational wave comes with a frequency of Ω0 = 20 Hz. τ 0.1 sec τ 0.08 sec τ 0.06 sec 0 10 20 30 40 50 0 2.×10-7 4.×10-7 6.×10-7 8.×10-7 1.×10-6 B (in Hz) Δℋ ( ε ) [PITH_FULL_IMAGE:figures/full_fig_p152_6_9.png] view at source ↗
Figure 6.10
Figure 6.10. Figure 6.10: Plot of ∆H(ε) against the phonon mode frequency for a gravitational wave with a frequency of Ω0 = 20 Hz where the measurement time τ is fixed at different values. where all other parameter values are kept fixed as has been used for the plot in Fig.(6.9). We observe from Fig.(6.10), that with an increase in the measurement time, the maxima of the standard deviation tends more and more towards the resonan… view at source ↗
Figure 6.11
Figure 6.11. Figure 6.11: The BEC sensitivity formula is plotted against the LISA sensitivity curve against different values of the incoming gravitational wave frequency. presented in SciRD reads [159] Sh,SciRD(ν) = 10 3  SI (ν) (2πν) 4 + SII (ν)  R(ν) Hz−1 (6.246) SI (ν) = 5.76−48  1 + ν 2 1 ν 2  sec−4 . Hz−1 (6.247) SII (ν) = 3.6 × 10−41Hz−1 (6.248) R(ν) = 1 + ν 2 ν 2 2 (6.249) with the value of ν1 and ν2 being ν1 = 0.4 mH… view at source ↗
Figure 6.12
Figure 6.12. Figure 6.12: Sensitivity versus frequency plot for the standard BEC-classical gravitational wave interaction case along with the BEC-graviton case with high graviton squeezing and then it is compared against the LISA-SciRD projected sensitivity curve. see from Fig.(6.11), for a significantly higher squeezing of the gravitons, the BEC becomes very sensitive towards incoming gravitational wave signals. Consider a futu… view at source ↗
Figure 6.13
Figure 6.13. Figure 6.13: Sensitivity is plotted against frequency and observed for the case when there is a balance between graviton and phonon mode squeezing. Hz range. The important observation lies in the fact that for a relatively lower squeezing of the phonon modes (rB = 10.0) for a graviton squeezing as low as rk = 32.5 the BEC based graviton detector becomes sensitive in the 0.001 − 10 Hz range. Hence, the requirement of… view at source ↗
Figure 6.14
Figure 6.14. Figure 6.14: Plot of p ⟨(∆ε) 2⟩Min versus τ (in sec) when the phonon modes are interacting against the standard non-interacting case. of sound to be cS = 1.2 × 10−2 m · sec−1 . For the number density being nB = 7 × 1020 m−3 , the Beliaev damping factor has the value γ = 9.034×10−19 sec−1 which is significantly small. For such a small value of the damping coefficient, there is barely any change while measuring the un… view at source ↗
Figure 7.1
Figure 7.1. Figure 7.1: The state and the evolution of the two coherent BEC sources has been depicted, where just after the formation of the BEC at t = 0, the state goes into a superposition state in the time-interval t ∈ [ti , tf ]. which has a structure identical to the reduced density matrix in eq.(7.60). Eq.(7.71) is very important in our analysis. We see that after a finite time interval tf − ti = tf (ti = 0), the final de… view at source ↗
Figure 7.2
Figure 7.2. Figure 7.2: The decoherence term exp(−Γ(t)) is plotted against time t for different values of the graviton squeezing. We observe that for higher values of rk, the loss of coherence is faster compared to the case where the squeezing parameter has a lower value. As a result the resonance frequency of the BEC shall lie at ωB = Ω0 2 = 0.5 Hz. It is also quite important to properly choose the value of the coupling consta… view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: We plot the decoherence term against the time t when the difference term in eq.(7.74) has time dependence and both the Bogoliubov coefficients are non-vanishing. loss of coherence in the time interval tf − ti ≃ 2 µs. For rk = 41, however, a 10% loss of coherence occurs for a time interval as large as 4 × 107 sec. This observation is indicative of the fact that graviton induced decoherence is very difficu… view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: We plot the decoherence rate Γ(t) against the measurement time t for a strongly coupled BEC with λB = 10 and compare the case with varying graviton-squeezing parameter. being calculated using the expression Tµν = √ 1 −g δS δgµν . The action S corresponds to the total action for the relativistic BEC and the classical gravitational wave. For a quantum gravitational set-up the change in the energy momentum … view at source ↗
Figure 7.5
Figure 7.5. Figure 7.5: The time dependence of the decoherence term e −Γ Sq. = e − cosh2 (2rB)Γ(tf ) is plotted for different values of the graviton and phonon squeezing parameters with rk ∈ {19.8, 20.0} and rB ∈ {11.0, 11.2}. where Γ(tf ) is given in eq.(7.75). In recent experimental scenarios, a phonon squeezing of rB = 0.83 has already been achieved which is equal to 7.2 dB of phonon squeezing [169]. Using the semiclassical … view at source ↗
Figure 7.6
Figure 7.6. Figure 7.6: The logarithmic negativity is plotted against total measurement time for differ￾ent values of the graviton squeezing parameter. We observe a jiggly decay pattern of the entanglement negativity over time. In order to plot the negativity with respect to measurement time, we use the analytical form of the decoherence rate from eq.(7.75), and plot N(t) against t in Fig.(7.6) for different values of the gravi… view at source ↗
Figure 7.7
Figure 7.7. Figure 7.7: A schematic diagram is presented for a Bose-Einstein condensate based graviton detector where a freely falling atom laser set-up is placed inside a cavity under the effect of Earh’s gravitational field. After the generation of maximal entanglement between two split coherent atom laser beams from a single source, they are recombined and further split into four coherent atom laser beams. They are then furt… view at source ↗
read the original abstract

In this thesis, we have used a linearized quantum gravity setting to investigate the effects of gravitons on matter systems. Based on the graviton-matter interaction, we have then proposed detector models that may be able to pick up graviton-induced signatures in a matter of a few years. We start with the simple model of a two-particle model detector system interacting with quantized gravitational fluctuations while the detector degrees of freedom obey the generalized uncertainty principle (GUP). For the first part we have hinted at the existence of quantum gravity induced memory effect as well as obtained a quantum gravity modified uncertainty relation. For the next part of the thesis, we have mainly focused on the phenomenological aspects of a linearized quantum gravity theory. For the initial phenomenological model, we have considered the same two-particle model detector system interacting with gravitational fluctuations where the entire set-up is placed inside a harmonic trap potential and looked at the stimulated absorption and spontaneous emission scenario for gravitons. In order to inspect a more involved phenomenological aspect, instead of the standard matter-detector system, we make use of a relativistic scalar Bose-Einstein condensate (BEC) and investigated the response of the BEC based model towards incoming gravitons and proposed a graviton detector based on graviton mediated decoherence from entangled BECs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript explores signatures of quantum gravity in relativistic quantum systems using a linearized quantum gravity approach. It examines a two-particle detector model with generalized uncertainty principle (GUP) to identify memory effects and modified uncertainty relations, then analyzes a trapped two-particle system for graviton absorption and emission, and finally proposes a detector based on decoherence in an entangled relativistic scalar Bose-Einstein condensate (BEC). The key claim is that these setups could detect graviton-induced effects within a few years.

Significance. If the missing quantitative validations were supplied, the work could offer novel phenomenological models for graviton detection, extending quantum gravity effects to matter systems in a way that might inform experimental efforts. The use of GUP, trapped systems, and BEC provides a range of approaches, but without error analyses, the significance remains potential rather than demonstrated.

major comments (3)
  1. Abstract and concluding sections: The claim that proposed detector models 'may be able to pick up graviton-induced signatures in a matter of a few years' is central to the paper's phenomenological contribution but is not supported by any signal-to-noise calculations, decoherence rate comparisons to environmental noise, or integration time estimates.
  2. Two-particle GUP model and trapped system sections: The derivations of the quantum gravity induced memory effect and modified uncertainty relation, as well as the stimulated absorption/emission scenarios, rely on the linearized gravity approximation; however, there is no analysis of the validity regime for detector scales or energies where this approximation holds.
  3. BEC-based detector section: The proposal for a graviton detector using graviton-mediated decoherence from entangled BECs lacks quantitative error budgets or background subtraction protocols, which are necessary to assess whether the effects can be isolated from thermal, electromagnetic, or other noise sources.
minor comments (1)
  1. Notation and presentation: Ensure consistent use of symbols across sections for the interaction Hamiltonian and detector parameters to improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The comments identify key areas where additional analysis would strengthen the phenomenological claims. We respond to each major comment below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: Abstract and concluding sections: The claim that proposed detector models 'may be able to pick up graviton-induced signatures in a matter of a few years' is central to the paper's phenomenological contribution but is not supported by any signal-to-noise calculations, decoherence rate comparisons to environmental noise, or integration time estimates.

    Authors: We agree that the statement lacks supporting quantitative calculations such as signal-to-noise ratios or integration times. The phrasing was meant to indicate the order-of-magnitude scale suggested by the derived interaction rates, but it is not rigorously justified in the text. In the revised manuscript we will either remove the specific claim or replace it with a more qualified statement that reflects the absence of detailed noise and timing analyses. revision: yes

  2. Referee: Two-particle GUP model and trapped system sections: The derivations of the quantum gravity induced memory effect and modified uncertainty relation, as well as the stimulated absorption/emission scenarios, rely on the linearized gravity approximation; however, there is no analysis of the validity regime for detector scales or energies where this approximation holds.

    Authors: The linearized gravity framework is the standard starting point for weak-field, low-energy graviton-matter interactions in laboratory settings. We acknowledge that an explicit discussion of its regime of validity (e.g., conditions on the metric perturbation amplitude and detector energy scales relative to the Planck scale) is missing. We will add a dedicated paragraph or subsection outlining these validity conditions and confirming that the parameters chosen in the two-particle and trapped-system models lie within the regime where higher-order corrections remain negligible. revision: yes

  3. Referee: BEC-based detector section: The proposal for a graviton detector using graviton-mediated decoherence from entangled BECs lacks quantitative error budgets or background subtraction protocols, which are necessary to assess whether the effects can be isolated from thermal, electromagnetic, or other noise sources.

    Authors: The BEC section develops the theoretical mechanism of graviton-induced decoherence but does not include a full error budget or detailed background-subtraction protocol. We will expand the discussion to identify the leading environmental noise channels (thermal, electromagnetic, and vibrational) and outline possible subtraction strategies at a qualitative level. A complete quantitative error analysis would require experimental design details that lie beyond the scope of the present theoretical work; we will therefore note this limitation explicitly. revision: partial

Circularity Check

0 steps flagged

No circularity: abstract and model sequence contain no equations or self-referential reductions.

full rationale

The provided abstract outlines a progression from a two-particle GUP detector under linearized quantum gravity (memory effect, modified uncertainty) to a trapped variant (absorption/emission) and then a BEC-based decoherence detector. No equations appear in the abstract, precluding any inspection for self-definitional mappings, fitted inputs renamed as predictions, or ansatz smuggling. Repeated use of the two-particle model across sections is a consistent modeling choice rather than a reduction of later outputs to earlier fitted quantities. No self-citations are quoted that load-bear uniqueness theorems or central premises. The derivation chain is therefore self-contained against external benchmarks with no exhibited circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated. The linearized gravity approximation and GUP are invoked without derivation.

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