We Proved Physics in Zero Knowledge -- Here's What That Means
A 1,088-byte proof that a bubble reached 12,348 K -- without revealing a single simulation parameter. ZK meets physics.
We proved a physics simulation is correct — without revealing a single parameter.
Not with a trusted server. Not with an NDA. With a zero-knowledge proof: 1,088 bytes that anyone can verify in a millisecond.
What We Built
We constructed a ZK proof system for sonoluminescence — one of the most dramatic phenomena in physics. Drive sound waves through water, and tiny bubbles collapse so violently they reach temperatures exceeding 12,000 Kelvin. Hot enough to emit light. A bubble, producing photons from sound.
The governing physics is the Rayleigh-Plesset equation, a nonlinear ODE that describes bubble dynamics under pressure, viscosity, and surface tension. We encoded this equation — step by step, 3,000 integration steps — inside a zero-knowledge circuit built on halo2 PLONK with KZG commitments.
What the Proof Reveals
The proof exposes exactly three values:
- Initial bubble radius — what physical setup is being claimed
- Final temperature — the simulation reached 12,348 K
- Cumulative emission count — how many steps exceeded the sonoluminescence threshold
Everything else stays private. The driving pressure. The gas properties. The viscosity. The surface tension. Every intermediate state of the simulation. The verifier learns that the claimed result follows from some valid set of parameters — and nothing else.
The Numbers
- 3,000 simulation timesteps, fully constrained
- 1,088 bytes — constant proof size (same for 10 steps or 10,000)
- 2.4 seconds to generate the proof
- 1–3 milliseconds to verify
Why This Matters
Until now, ZK proofs have lived in the world of discrete mathematics — hashes, signatures, blockchain transactions. Nobody had applied them to continuous physics simulations.
The applications are immediate: pharmaceutical companies proving drug simulations pass safety thresholds without revealing proprietary parameters. Defense contractors verifying weapon physics without disclosure. Climate modelers demonstrating compliance without exposing calibration data. A new category of verifiable science where the proof is the deliverable and the parameters stay secret.
Go Deeper
The full technical breakdown — halo2 architecture, fixed-point arithmetic at 1030 scale, why Störmer-Verlet integration instead of Euler (Euler diverges at collapse and produces false proofs), code walkthroughs of the constraint system, and detailed performance benchmarks — is available exclusively to Pro members.
New here? Grab the free ZK Privacy Patterns guide — zero-knowledge fundamentals, protocol comparisons, and implementation patterns in one reference.