Gödel's Incompleteness Theorems

Kennedy, Juliette

doi:10.1017/9781108981972

Cited by 21 publications

(15 citation statements)

References 60 publications

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“…Einstein's viewpoint was that QM is statistical, just as classical physics of Thermodynamics is and the Boltzmann's population density distribution with temperature is. We also now know Gödel's Incompleteness Theorem [45], which underscores that all theories are necessarily incomplete as they are constructed using unprovable axioms, or postulates, framed using incomplete knowledge of the universe. However, in our viewpoint, Schrodinger's commentary was dominantly in support of his well-established theory, but partly as a "tongue-in-cheek" sarcasm.…”

Section: Entanglement and Bell's Theoremmentioning

confidence: 99%

Resolving wave-particle duality could accelerate the mass production of quantum computers

Roychoudhuri,

Prasad

2024

Quantum Computing, Communication, and Simulation IV

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Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young's resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein's interpretation of photoelectric effect as due to "indivisible light quanta". However, Einstein disowned his "light quanta" postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton's and Maxwell's concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger's ψ represents atom's internal dipolar amplitude stimulations. This over-turns Born's interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical "internal amplitude stimulation" of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the "Local" cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be "Local", just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that "single photons" mysteriously generate the double slit pattern.

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Section: Entanglement and Bell's Theoremmentioning

confidence: 99%

Resolving wave-particle duality could accelerate the mass production of quantum computers

Roychoudhuri,

Prasad

2024

Quantum Computing, Communication, and Simulation IV

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“…But Turing machines are also positive integers. Conceptual constructions, such as numbers or logic, cannot prove properties about themselves [37]. A demonstration of this for Turing machines is a construction of a diagonal function on the numeral representation of Turing machines [10, p. 37].…”

Section: • the Set Of All Ordered Pairs Of Positive Integersmentioning

confidence: 99%

An analysis of how many undiscovered vulnerabilities remain in information systems

Spring¹

2023

Computers & Security

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“…Those who are acquainted with Gödel's incompleteness theorems [6] or with the axiomatic theories of truth [3] can ask: Aren't Peano Arithmetic or some of the theories of truth self-reflective? Not at all, because these formal theories are not interpreted theories: their descriptions say nothing about their interpretations.…”

Section: Introductionmentioning

confidence: 99%