The information-Einstein equation states that the information dissipation tensor is a source of spacetime curvature. As the order parameter field approaches a quantum critical point (M→0), two effects occur synergistically—the information dissipation coefficient Υ diverges with power-law scaling 1/x̃^ν, and the geometric back-reaction coefficients diverge as (Λ_op/M)². Together, these constitute the "critical geometric back-reaction enhancement" effect. This paper designs two independent platforms to test this prediction. Platform 1 (superconducting quantum chip) measures the decoherence rate and dissipation noise spectrum near a quantum phase transition critical point. Platform 2 (cold-atom BEC acoustic horizon) measures collective excitation damping near a Feshbach resonance critical point. The two platforms correspond to different universality classes and cross-validate each other. This paper also points out that the high-T_c pseudogap, strange metal linear resistivity, heavy fermion non-Fermi liquid behavior, and 1/f noise universality may be projections of this enhancement in different systems. If both platforms observe divergent signals with scaling exponents consistent with respective universality classes, the information-Einstein equation receives experimental confirmation in the critical region, and the information–geometry closed loop is detected at the laboratory scale for the first time. If the signal is absent, the back-reaction coefficient expansion or the information-Einstein equation needs revision.
The information-Einstein equation states that the information dissipation tensor is a source of spacetime curvature. As the order parameter field approaches a quantum critical point (M→0), two effects occur synergistically—the information dissipation coefficient Υ diverges with power-law scaling 1/x̃^ν, and the geometric back-reaction coefficients diverge as (Λ_op/M)². Together, these constitute the "critical geometric back-reaction enhancement" effect. This paper designs two independent platforms to test this prediction. Platform 1 (superconducting quantum chip) measures the decoherence rate and dissipation noise spectrum near a quantum phase transition critical point. Platform 2 (cold-atom BEC acoustic horizon) measures collective excitation damping near a Feshbach resonance critical point. The two platforms correspond to different universality classes and cross-validate each other. This paper also points out that the high-T_c pseudogap, strange metal linear resistivity, heavy fermion non-Fermi liquid behavior, and 1/f noise universality may be projections of this enhancement in different systems. If both platforms observe divergent signals with scaling exponents consistent with respective universality classes, the information-Einstein equation receives experimental confirmation in the critical region, and the information–geometry closed loop is detected at the laboratory scale for the first time. If the signal is absent, the back-reaction coefficient expansion or the information-Einstein equation needs revision.
The quantum–classical boundary is one of the deepest unsolved problems in physics. The Information Bottleneck Theorem of the Order Parameter Spacetime Theory provides a precise criterion: when the total information dissipation coefficient Υ=0, the system resides in the quantum sector (unitary evolution, entanglement conservation); when Υ>0, irreversible classicality emerges. How can this binary criterion be tested experimentally? This paper reveals that the binary nature of the Information Bottleneck Theorem—the transition of entanglement from "strict conservation" to "onset of decay"—does not manifest as a discontinuous jump of entanglement, but rather as a nonlinear signature in the decoherence rate. This nonlinearity originates from complex metric back-reaction: information dissipation alters the spacetime geometry, and the geometry in turn modifies the dissipation rate, forming an information–geometry closed loop. Specifically, for a two-qubit entangled state evolving under a pure dephasing channel, the standard Lindblad theory predicts that log C(t) is a straight line; the complex metric back-reaction predicts that log C(t) bends upward—the decay rate slows down as entanglement decreases, i.e., entanglement is protected. At the critical coupling α=1/r₀², the theory predicts exact protection of entanglement (C(t)=constant); in the strong-coupling regime α>1/r₀², the theory predicts that in the initial stage entanglement exceeds its maximum value (C>1). This paper provides a complete theoretical prediction and data analysis scheme to test these predictions using existing experimental data. The decision logic is binary: either log C(t) is a straight line (α=0, complex metric back-reaction falsified), or it is not (α>0, information–geometry closed loop verified).
The Irreversible Equivalence Principle of the Order Parameter Spacetime Theory proposes a central assertion: dissipation can be geometrized as the imaginary part of a complex metric. But is this geometrization a physical reality or merely a mathematical trick? This paper answers this question by designing an experimental scheme on a cold-atom interferometer platform to simultaneously measure the geometric offset of interference fringes and the visibility decay, testing whether the real and imaginary parts of the complex metric exist as two components of the same complex number. Furthermore, we predict that when the external driving frequency equals the local relaxation rate, the system enters an irreversible geometric resonance state, and the energy absorption rate exhibits an anomalously enhanced resonance peak. If these two predictions are experimentally confirmed, they will constitute irrefutable evidence that dissipation is not just "geometric bending in appearance", but is physically complex geometric bending. We also systematically comb through traces in existing cold-atom experiments that narrowly missed these signals. If both predictions are verified, it directly proves that the Irreversible Equivalence Principle possesses physical reality. If falsified, the principle must be weakened from "dissipation = complex geometric bending" to "dissipation can be described by complex geometry".
We demonstrate that quantum information geometry—specifically the fidelity susceptibility metric on parameter manifolds—exhibits finite-size scaling and curvature singularities at quantum critical points that are structurally identical to geometric response equations, and we propose that Floquet discrete time crystals (DTCs) extend this framework to include temporal metric components whose divergence at DTC melting transitions can be experimentally tested as a probe of emergent spacetime structure in driven quantum matter.
We propose that quantum critical systems, when collective dynamics dominate over particle-like behavior, can be described by an effective curved geometry. Working within this geometric framework, we derive three testable predictions for quantum chaos near criticality: (1) the Lyapunov exponent saturates to a constant at criti- cality rather than diverging or vanishing; (2) out-of-time-ordered correlators exhibit geometric scrambling with saturation at strong coupling; and (3) the level spacing distribution transitions from Poisson to Wigner-Dyson with a universal crossover function. These predictions are independent of microscopic details and can be tested in cold atom systems, trapped ion chains, and superconducting qubit arrays. Com- plete computational validation is provided in two accompanying SageMath notebooks (DOIs: 10.5281/zenodo.18440342 and 10.5281/zenodo.18720405).
Abstract We take physical distinguishability as the sole primitive of physics: two states are distinct if and only if some measurement can tell them apart. From this single principle, a geometry emerges on the space of all physical states. Its universal threshold — the point where the rate of change of distinguishability saturates — is simultaneously the quantum speed limit, the event horizon of a black hole, and the critical point of a thermodynamic phase transition. Quantum mechanics, general relativity, and thermodynamics are three expressions of the same geometric threshold on different state spaces; the constants ℏ, c , and k B are conversion factors between them. Within this structure, we identify a parameter-free geometric mechanism that yields the Schrödinger equation; the Einstein field equations both on the horizon (exactly) and in the bulk (to corrections smaller than 10⁻³² at all accessible energies); the Lorentzian signature of spacetime; and a structural resolution of the cosmological constant problem, reducing the standard discrepancy of 10¹²³ to order unity. Consequently, the framework evaluates a vacuum length scale of 88 μm and energy 2.25 meV from the observed dark-energy density, placing the dominant source in the lightest neutrino sector. The framework further suggests that macroscopic quantum coherence suppresses geodesic distinguishability — the Bose–Einstein condensate (BEC) analogue of the Meissner effect — with a predicted breathing-mode shift of ~1.5 mHz in ⁸⁷Rb. IBM Quantum experiments on three independent 156-qubit Heron processors show excitation probabilities differing by a factor of 3.8 across protocols with identical control parameters but different geometric paths, consistent with the prediction that endpoint distinguishability governs the outcome. Cross-backend transfer errors remain below 1%. Physical reality is what is distinguishable. The laws of nature are the geometry of distinguishability.
Abstract We take physical distinguishability as the sole primitive of physics: two states are distinct if and only if some measurement can tell them apart. From this single principle, a geometry emerges on the space of all physical states. Its universal threshold — the point where the rate of change of distinguishability saturates — is simultaneously the quantum speed limit, the event horizon of a black hole, and the critical point of a thermodynamic phase transition. Quantum mechanics, general relativity, and thermodynamics are three expressions of the same geometric threshold on different state spaces; the constants ℏ, c , and k B are conversion factors between them. Within this structure, we identify a parameter-free geometric mechanism that yields the Schrödinger equation; the Einstein field equations, exactly on the horizon and in the bulk to corrections below 10⁻³² for stationary configurations (the fully dynamical case is not established here); the Lorentzian signature of spacetime; and a structural mechanism that reduces the standard 10¹²³ discrepancy of the cosmological constant problem to order unity, conditional on two framework-internal postulates (Section 13.8). Applying this, the framework evaluates a vacuum length scale of ~88 μm and energy ~2.25 meV from the observed dark-energy density, placing the dominant source in the lightest neutrino sector. The framework further suggests that macroscopic quantum coherence suppresses geodesic distinguishability — the Bose–Einstein condensate (BEC) analogue of the Meissner effect — with a predicted breathing-mode shift of ~1.5 mHz in ⁸⁷Rb. IBM Quantum experiments on three independent 156-qubit Heron processors show excitation probabilities differing by a factor of ≈3.7 across protocols with identical control parameters but different geometric paths, consistent with the prediction that endpoint distinguishability governs the outcome. Cross-backend transfer errors remain below 1%. Physical reality is what is distinguishable. The laws of nature are the geometry of distinguishability.