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Quantized Inertia under Covariant and Quantum-Field-Theoretic Audit: Proper Acceleration, Rindler Stress, Particle-Mass Claims, and Falsifiable Tests

Arellano-Peña, Henry
PhilArchive · Papers
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philosophy
Quantized inertia (QI), formerly described as modified inertia by a Hubble-scale Casimir effect, proposes that inertial response arises from acceleration-conditioned Unruh radiation restricted by Rindler and cosmological horizons. Its scalar law, \(m_{\mathrm I}=m(1-2c^{2}/|a|\Theta)\), has been applied to galaxy rotation, minimum accelerations, wide binaries, Proxima Centauri, Jupiter-mass binary objects, spacecraft anomalies, particle masses, and anomalous capacitor thrust. This framework-independent paper reconstructs and audits that programme. It distinguishes the KMS thermality of the Minkowski vacuum in a Rindler wedge from a local stress-energy distribution and shows that the standard Minkowski-vacuum expectation satisfies \(\langle T_{\mu\nu}\rangle_{\mathrm{ren}}=0\), so a Rindler decomposition alone supplies no pressure imbalance. The alternative Fulling--Rindler vacuum is a distinct, horizon-singular state whose comoving bulk energy density is negative and whose momentum flux vanishes; it is not the state generated merely by accelerating a body through the Minkowski vacuum. The paper identifies a covariant acceleration obstruction: the Unruh relation uses proper acceleration, while QI's galactic applications invoke acceleration relative to surrounding matter. Laboratory field-emission electrons and freely falling galactic stars therefore belong to different acceleration branches unless a new covariant bridge is derived; evidence from one branch cannot presently support the other. A second, previously unstated fork is identified within the scalar law itself. Because the law is implicit in \(a\), it admits an explicit kinematic reading and an implicit realized reading. Closing it on the realized acceleration yields \(a=F/m+a_{0}^{\mathrm{QI}}\) and \(m_{\mathrm I}/m=F/(F+ma_{0}^{\mathrm{QI}})\in[0,1]\), so positivity and the minimum acceleration are consequences of the dynamics rather than appended admissibility rules. That closure also converts QI into a universal additive acceleration floor, which is directly constrained by precision free-fall measurement and is evaded only through the same undefined relational acceleration. Reconstructing the primary galactic derivation shows that both the acceleration floor used for Jupiter-mass binaries and Proxima and the Tully--Fisher relation used for galaxy rotation follow from that one closure applied to a decomposed acceleration \(|A|=|a|+|a'|\), so the physical content lies in an undeclared decomposition rule rather than in the scalar law: the summation domain over surrounding matter is never specified, which is also what shields the floor from laboratory bounds, and the Tully--Fisher result follows only from an asserted assignment \(a'=a_{0}^{\mathrm{QI}}\) at a galaxy's edge. That assignment carries a sharp untested consequence, namely that internal small-scale accelerations must rise in the outer disc, which is checkable against resolved kinematics and is not shared with MOND. The audit also documents that the adopted value of \(\Theta\) changed between publications, moving the predicted floor by a factor of about \(3.3\). The audit also separates Hamiltonian expectation from variance, delimits the jurisdiction of \(\Delta E\,\Delta x\sim\hbar c\), confirms the circular use of \(G\) in the proposed gravity derivation, identifies the numerical factor \(2\pi b_{\mathrm W}=1.26546\ldots\) generated by the Wien wavelength coefficient \(b_{\mathrm W}=0.201405\ldots\), proves \(\hbar/(c\lambda_{\mathrm C})=m/(2\pi)\) for the ordinary Compton wavelength, distinguishes confinement-generated composite mass from an elementary-particle theory, reconstructs the dimensional capacitor coefficient and its factor-four transit-speed convention, and converts the claimed capacitor scaling into a free-exponent factorial test. The specific QI wide-binary peak prediction is rejected by the corresponding Gaia DR3 distributional test; the broader wide-binary gravity comparison remains actively
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