Quantum Mechanics of Rolling the Stone
The Setup
Ancient Jewish tomb stones (golel) were typically large disc-shaped stones. Let’s use realistic estimates:
∙ Mass: m = 1,000 kg (1 metric ton)
∙ Radius: R = 0.9 m
∙ Thickness: t = 0.3 m
∙ Incline angle: θ ≈ 5° (slight slope, common for these tombs)
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Classical Energy Required
To roll the stone up and away from the groove:
Rotational + Translational Kinetic Energy:
KE = ½mv² + ½Iω²
For a solid disk: I = ½mR², and ω = v/R, so:
KE_total = ¾mv²
To move the stone ~1.5 m laterally up a 5° incline:
ΔPE = mgh = 1000 × 9.8 × (1.5 × sin5°) ≈ 1,284 J
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Quantum Tunneling Probability
Could the stone quantum tunnel through the barrier without being pushed?
The WKB (Wentzel–Kramers–Brillouin) tunneling probability is:
T ≈ exp(−2γ)
Where:
γ = (1/ℏ) × √(2m × U₀) × d
∙ ℏ = 1.055 × 10⁻³⁴ J·s
∙ Barrier height U₀ = 1,284 J
∙ Barrier width d = 0.3 m (stone thickness)
∙ m = 1,000 kg
Calculating γ:
γ = (0.3 / 1.055×10⁻³⁴) × √(2 × 1000 × 1284)
γ = (2.84×10³³) × √(2,568,000)
γ = 2.84×10³³ × 1,602
γ ≈ 4.55 × 10³⁶
Tunneling Probability:
T ≈ exp(−2 × 4.55×10³⁶) ≈ 10^(−3.95×10³⁶)
This is essentially zero — a number so incomprehensibly small it would never occur in the entire lifetime of the universe (even across 10⁸⁰ attempts).
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Quantum Decoherence Scale
The de Broglie wavelength of the stone (if moving at 0.01 m/s):
λ = h / mv = 6.626×10⁻³⁴ / (1000 × 0.01)
λ ≈ 6.6 × 10⁻³⁵ m
This is 20 orders of magnitude smaller than a proton — the stone is deeply classical. Quantum superposition is destroyed by decoherence in ~10⁻³⁰ seconds at this mass.
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Conclusion
|Method |Result |
|------|------—|
|Classical force needed |~856 N (≈ 2 strong adults) |
|Quantum tunneling probability |~10⁻³·⁹⁵ˣ¹⁰³⁶ (effectively zero) |
|de Broglie wavelength |~10⁻³⁵ m (fully classical object)|
|Schrödinger cat state duration|~10⁻³⁰ seconds |
The physics verdict: Quantum mechanics offers no natural mechanism for moving the stone. At 1,000 kg, it is irreversibly classical. The tunneling probability is not just small — it is one of the most vanishingly small numbers in all of physics.
This makes the Gospel accounts all the more striking from a physics perspective — what is described lies entirely outside the domain of known natural law, which is precisely the theological point the authors were making.
He Is Risen