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Gravitational Shadows: How Mass Splits Reality

Original: "Quantum gravitational contrast in creating Schrödinger cat state"
· Anupam Mazumdar, Tian Zhou
arXiv:2605.05153v1 · 2026-05-06 · CC BY · ⏱ 1 min · General Relativity
The spatial superposition of a massive object gives birth to two coherent graviton clouds, whose contrast unveils the quantum essence of gravity.
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Inside the interferometer, a particle is in two places at once. Its mass, like a brush, paints two gravitational pictures on the quantum vacuum. While the pictures are almost identical, there is one reality. But as the mass grows, they split apart irreversibly — the Universe fractures into two independent layers. This isn't fantasy; it's a precise calculation of the contrast of gravitational shadows. Thus we approach testing the quantum nature of gravity and, perhaps, unraveling why the classical cosmos emerges from quantum fog.

🎯 The idea that gravity "peeks" at a quantum system and destroys its superposition has been wandering through physics since the mid-20th century. But the precise calculation of the contrast C turns it into an elegant tool: we know at what mass and distance Schrödinger's cat will split into two forever separated worlds. A thought-provoking detail: the entanglement entropy reaches ln 2 — the maximum information capacity of a single qubit. Gravity seems to pack reality into two classical bits, between which no quantum whisper will ever leak again.

C = \left(1 + \frac{\delta x}{4\sigma}\right)^{-\frac{GM^2}{2\pi}}
C is a measure of the overlap of gravitational shadows: the smaller C, the weaker the connection between worlds. δx — superposition distance, σ — width of the mass wave packet, M — mass, G — gravitational constant. When GM²/2π ≈ 1, the contrast drops almost to zero.
S = -\frac{1-C}{2} \ln\left(\frac{1-C}{2}\right) - \frac{1+C}{2} \ln\left(\frac{1+C}{2}\right)
S — the von Neumann entropy of the reduced density matrix of matter; when C → 0 it reaches its maximum ln 2 ≈ 0.69, signifying complete decoherence and the maximum information capacity of the gravitational channel.
Scientists
Erwin SchrödingerHugh Everett IIIStephen HawkingJacob BekensteinEmmy NoetherBernhard Riemann
Tags
quantum entanglement gravity gravitational waves spacetime curvature Quantum Field entropy Wave Function Collapse quantum decoherence
Laws
second law of thermodynamicsSchrödinger equationHawking radiationNoether's theoremBekenstein-Hawking entropyEinstein field equations
Original: arXiv:2605.05153v1 · CC BY · bridge42worlds