Black Hole Zero-Knowledge Proofs by Melanie Swan

Melanie Swan

Essay Abstract

This essay argues that the AdS/CFT correspondence, as a limits-based model of undecidability and non-computability, highlights quantum reality as being not only information-theoretic, but rigorously computational as a mathematically-sound domain with built-in cryptographic security features such that black holes provide their own zero-knowledge proofs. The AdS/CFT correspondence (anti-de Sitter space/conformal field theory) is a hypothesis asserting that any physical system with a bulk volume (such as a black hole) can be described by a boundary theory in one fewer dimensions. The result is that a seemingly complex incomputable system in a chaotic bulk volume is rendered solvable as a boundary theory in one fewer dimensions. Nature's quantum security features provide an even more robust computational domain than was appreciated. These include the no-cloning theorem, the no-measurement principle, error correctability, provably-random statistical signatures per the SEI properties of quantum objects (superposition, entanglement, and interference), and zero-knowledge proofs (proofs revealing no information except whether a proposition is True or False). The zero-knowledge property is implicated in quantum computational systems in that a traditional prover-verifier relationship (an external prover) is not necessary because the quantum computer performs its own truth verification as part of the proof. The implication is that quantum computing has zero-knowledge proof technology built into it as a feature. BQP (the class of problems solvable with a quantum computer) computes quickly and soundly enough to provide its own computationally-verifiable proof. The consequence is that any quantum computational domain, including black holes, performs its own truth verification through zero-knowledge proofs. The result of this work is that the AdS/CFT correspondence is demonstrated as a juggernaut formulation that ties together not only physics and information theory in a limits-based computational method as a feature for analyzing problems in contemporary physics, but also incorporates a new level of soundness with cryptographic mathematical properties.

Author Bio

Melanie Swan, PhD, is a Technology Theorist in the Philosophy Department at Purdue University, a Research Associate at the UCL Centre for Blockchain Technologies, and a Singularity University faculty member. Her educational background includes an MBA in Finance from the Wharton School of the University of Pennsylvania, a PhD in Philosophy from Purdue University, and a BA in French and Economics from Georgetown University. She is the author of the best-selling book Blockchain: Blueprint for a New Economy and has a third book coming out in 2020, Quantum Computing: Physics, Blockchains, and Deep Learning Smart Networks.

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David Brown

"Theoretical experiments applying information theory to problems such as the black hole information paradox have led to a refinement of expectations of what is thought to be possible in a potential era of quantum computing. ... Susskind (1995, extending the ideas of 't Hooft) proposed the holographic principle to consider black holes, suggesting a holographic correspondence between the 3D interior bulk and the 2D surface of the event horizon. Black holes are a domain in which the incompatibilities between general relativity and quantum mechanics become more prominent. " Where is the empirical evidence that black holes have event horizons? Is Milgrom the Kepler of contemporary cosmology? Do the empirical successes of Milgrom's MOND suggest that something is seriously wrong with Newtonian-Einsteinian gravitational theory? Please google "kroupa milgrom", "mcgaugh milgrom", "scarpa milgrom", and "sanders milgrom". Is it possible that the Gravity Probe B science team misinterpreted their own data? Does string theory with the finite nature hypothesis imply MOND and no supersymmetry? Consider 3 conjectures: (1) Milgrom is the Kepler of contemporary cosmology, and the empirical validity of Milgrom's MOdified Newtonian Dynamics (MOND) requires a modification of Einstein's field equations. (2) The Koide formula might suggest a modification of Einstein's field equations. (3) Lestone's theory of virtual cross sections might suggest a modification of Einstein's field equations. I suggest that there might be 3 possible modifications of Einstein's field equations. Consider Einstein's field equations:

R(mu,nu) + (-1/2) * g(mu,nu) * R = - κ * T(mu,nu) - Λ * g(mu,nu) -- what might be wrong? Consider the possible correction R(mu,nu) + (-1/2 + dark-matter-compensation-constant) * g(mu,nu) * R * (1 - (R(min) / R)^2)^(1/2) = - κ * (T(mu,nu) / equivalence-principle-failure-factor) - Λ * g(mu,nu),

where equivalence-principle-failure-factor = (1 - (T(mu,nu)/T(max))^2)^(1/2) -- if dark-matter-compensation-constant = 0, R(min) = 0, and T(max) = +∞ then Einstein's field equations are recovered.

Pavel Poluian

Dear Melanie!

We understood a little in your essay. But what we understood - we really liked it. We believe that everything else is also good. We set your essay to a maximum rating of 10 points.

We wish you all the best!

Truly yours,

Pavel Poluian and Dmitry Lichargin,

Siberian Federal University.