Quantum Decoherence and Spacetime Noise

Quantum-gravity decoherence and spacetime noise are testable only after a coupling operator, correlation function, and spectrum are specified. Loss of visibility can arise from ordinary environmental entanglement, classical random phases, intrinsic nonunitary dynamics, or averaging over uncontrolled apparatus motion. Those mechanisms can produce the same one-number contrast while predicting different scaling and cross-correlations.

Required background. Equivalence Principles and Gravitational Measurement supplies the distinction between coordinate fluctuations, clock noise, and locally measurable tidal effects.

Helpful background. Flat-Spacetime Quantum Field Theory supplies open fields and spectra; Einstein Equations supplies metric response; Quantum Information supplies channels and complete positivity; Quantum Gravity supplies claim boundaries; and Gravitational Radiation and Waveforms supplies calibrated strain observables.

Open-system dynamics

A Markovian density operator obeys a Gorini–Kossakowski–Sudarshan–Lindblad equation,

$$\dot\rho=-i[H,\rho] +\sum_{ab}C_{ab} \left(L_a\rho L_b^\dagger -\frac12\{L_b^\dagger L_a,\rho\}\right).$$

The Kossakowski matrix $C_{ab}$ must be positive semidefinite for complete positivity. Choosing a damping rate by dimensional analysis without a positive matrix can yield negative probabilities, especially when the system is entangled with an ancilla. Energy conservation and translation covariance impose further restrictions on the $L_a$.

For pure position dephasing with one Hermitian operator $L=x$,

$$\dot\rho(x,x')= -i[H,\rho](x,x') -\frac{\Gamma}{2}(x-x')^2\rho(x,x').$$

A spatial superposition $\Delta x$ loses coherence as $\exp[-\Gamma(\Delta x)^2t/2]$. The prediction has units only after $\Gamma$ and its dependence on mass, temperature, cutoff, and gravitational scale are declared.

This simple model also heats a free particle. For $H=p^2/(2m)$ and $[x,p]=i$, the dissipator gives $d\langle H\rangle/dt=-\Gamma\langle[x,[x,H]]\rangle/2=\Gamma/(2m)$. Thus position dephasing by itself does not conserve the particle’s energy. A model claiming energy conservation must account for that energy in the environment or supply additional dynamics; positivity of $\Gamma$ alone is insufficient.

Thermal gravitons or weak gravitational environments can generate ordinary open-system decoherence without fundamental nonunitarity. Blencowe derives the Born master equation through its noise and dissipation kernels in Blencowe 2013, eqs. (9)–(10), pp. 2–3, before taking the weak-coupling, high-temperature limit. Calling every such rate “quantum spacetime” obscures whether the same effect follows from known quantum fields.

Metric fluctuations and spectra

Let an interferometric observable couple linearly to a real stationary stochastic perturbation $h(t)$ of zero mean. Use $\tilde h(f)=\int dt\,e^{2\pi ift}h(t)$, so that the inverse transform has the site’s negative time phase. Define the one-sided power spectral density for $f,f'\gt0$ by

$$\langle\tilde h(f)\tilde h^*(f')\rangle =\frac12\delta(f-f')S_h(f).$$

The measured phase-noise spectrum is

$$S_\phi(f)=|R(f)|^2S_h(f)+S_{\mathrm{instrument}}(f),$$

where $R(f)$ is the complete response, including geometry, optical storage, sampling, and filtering. A claim of “white Planck noise” must state whether whiteness refers to displacement, strain, phase, or another variable; the spectra have different units.

General covariance forbids interpreting arbitrary coordinate fluctuations as noise. A physical coupling can be written through proper time, geodesic deviation, curvature, or a relational clock comparison. Universal metric fluctuations should also respect the equivalence principle at wavelengths large compared with the apparatus unless a violation is part of the model.

Correlation and discrimination strategies

Two colocated or geometrically related instruments can search for the predicted one-sided cross-spectrum

$$S_{12}(f)=R_1(f)R_2^*(f)S_h(f)+N_{12}(f).$$

Cross-correlation rejects independent noise but not correlated magnetic, seismic, timing, or environmental backgrounds. The overlap geometry and propagation delay should predict a distinctive frequency dependence. Time slides estimate accidental backgrounds only if the hypothesized signal is removed by the slide.

Matter-wave experiments offer different scaling with mass and path separation. Atomic clocks test correlated proper-time fluctuations; optomechanical resonators test force or displacement noise. Agreement of one coupling across these platforms is stronger than a limit translated by dimensional analysis.

Non-Markovian and quantum-noise distinctions

A colored environment generally produces a memory kernel rather than a constant Lindblad rate,

$$\dot\rho(t)=\int_0^t ds\,\mathcal K(t-s)\rho(s).$$

Replacing it by a Markovian generator requires environmental correlation time much shorter than system evolution. If that separation fails, recoherence and frequency-dependent phase shifts can accompany visibility loss. Bounds on a constant $\Gamma$ then cannot be applied without folding the kernel through the pulse sequence.

Classical Gaussian noise is characterized by a symmetrized spectrum, whereas a quantum environment also has an antisymmetric correlator tied to response and dissipation. Measuring only dephasing may not distinguish them. Varying temperature, pulse ordering, and probe frequency can test the fluctuation–dissipation relation and reveal whether the same spectrum predicts heating. A “decoherence without dissipation” claim must show how complete positivity and energy balance are maintained.

Results and open questions through 2026-08-20

This discussion reflects results available through 2026-08-20. Experiments constrain many declared collapse, decoherence, and stochastic-noise models, but no excess is accepted as quantum-gravity noise. Competing positions expect Planck-suppressed local noise, nonlocal correlations amplified by macroscopic separation, or no intrinsic decoherence because fundamental evolution is unitary. The result remains unresolved and depends on the operator, spectrum, state, bandwidth, and environment.

Model or evidence channel	Result at the cutoff	Scope and limitation
Thermal-graviton open system	The primary Born equation exposes both noise and dissipation kernels Blencowe 2013, eqs. (9)–(10), pp. 2–3	Weak coupling, thermal state, high-temperature/Markov reduction; it is environmental decoherence, not evidence for fundamental nonunitarity
Collapse and intrinsic-decoherence noise	LIGO, LISA Pathfinder, and AURIGA noise curves bound a declared CSL model, and the same analysis excludes one older wormhole-induced coefficient Carlesso et al. 2016, §IV and eq. (18), p. 6	Force calibration, rigid-body approximation, white spectrum, and the named mass-density coupling are essential; it is not a universal bound on gravity-induced decoherence
Correlated spacetime-position noise	The 704-hour, two-interferometer Holometer cross-spectrum was consistent with zero for the tested two-parameter shear spectrum Chou et al. 2017, eqs. (2)–(4), fig. 3, pp. 4–5	The optical geometry was insensitive to other correlation symmetries, explicitly including the rotational model discussed in §5
Matter-wave and clock coherence	Proposed phase, proper-time, and decoherence observables are compared in Addazi et al. 2022, §5.4	Thermal, electromagnetic, vibration, timing, and control noise dominate, and one-platform visibility does not identify the microscopic channel

The phenomenology review catalogs proposed spectra and their experimental reach Addazi et al. 2022, §§ 5–6. Bounds must not be extrapolated outside their frequency band or correlation length.

The conclusions could change if a reproducible cross-platform excess follows one predicted spectrum and geometric response, or if a complete-positivity or covariance test excludes a model; the interpretation could also change with a calibration revision, a newly identified correlated background, or a non-Markovian derivation replacing a quoted Lindblad rate.

Failure tests

Propagate an entangled system and ancilla to check complete positivity. Verify that the noise kernel is positive and obeys any fluctuation–dissipation relation claimed. Inject synthetic signals before selection cuts, vary bandwidth and coarse graining, and report the transfer function. Monitor magnetic, acoustic, thermal, seismic, laser, and clock channels. A residual with the wrong geometry or mass scaling is adverse evidence.

Exercise

For the position-dephasing model above, an interferometer holds a superposition with separation $\Delta x$ for time $t$. If visibility is no smaller than $V/V_0=0.99$, derive an upper bound on $\Gamma$.

Solution

The model predicts

$$\frac{V}{V_0}= \exp\!\left[-\frac12\Gamma(\Delta x)^2t\right].$$

Taking logarithms and using the observed lower bound,

$$\Gamma\le \frac{-2\ln(0.99)}{(\Delta x)^2t} \approx\frac{0.0201}{(\Delta x)^2t}.$$

This constrains only the declared Markovian position-dephasing coefficient. Converting it into a quantum-gravity scale requires a sourced relation between $\Gamma$ and that scale, plus marginalization over ordinary visibility loss.

References

• Addazi, Andrea, et al. (2022), “Quantum Gravity Phenomenology at the Dawn of the Multi-Messenger Era—A Review,” Progress in Particle and Nuclear Physics 125, 103948, arXiv:2111.05659.
• Blencowe, Miles P. (2013), “Effective Field Theory Approach to Gravitationally Induced Decoherence,” Physical Review Letters 111, 021302, arXiv:1211.4751.
• Carlesso, Matteo, Angelo Bassi, Paolo Falferi, and Andrea Vinante (2016), “Experimental Bounds on Collapse Models from Gravitational Wave Detectors,” Physical Review D 94, 124036, doi:10.1103/PhysRevD.94.124036.
• Chou, Aaron, et al. (2017), “Interferometric Constraints on Quantum Geometrical Shear Noise Correlations,” Classical and Quantum Gravity 34, 165005, doi:10.1088/1361-6382/aa7bd3.