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M^=m(1+H^int/mc2)\hat M = m(1 + \hat H_{int}/mc^2)

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Magdalena Zych and Časlav Brukner’s 2018 paper supplies the anchor the new work builds directly on top of: a classical body’s equivalence principle, they argue, says nothing at all about whether the quantum version holds, because a quantum system’s mass is not one number but an operator, and equivalence has to be stated as equivalence between its rest, inertial, and gravitational internal-energy operators rather than between their average values [ 1 ] . Model that operator, call it M^\hat M , as M^\hat M = m(1 + H^int\hat H_{int}/mc2c^2) , where H^int\hat H_{int} is the system’s internal Hamiltonian, and let the gravitational mass be mgm_g = mi(1+η^)m_i(1 + \hat\eta) for some violation operator η^\hat\eta acting on the…

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H^int\hat H_{int}

Symbol hat H_int

hat HiH_int is one of the signed contributions combined to compute the quantity on the left.

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M^=m(1+H^int/mc2)\hat M = m(1 + \hat H_{int}/mc^2)

Equation 3 · Quantum Relativity

The Corner of the Equivalence Principle No Experiment Has Touched

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Magdalena Zych and Časlav Brukner’s 2018 paper supplies the anchor the new work builds directly on top of: a classical body’s equivalence principle, they argue, says nothing at all about whether the quantum version holds, because a quantum system’s mass is not one number but an operator, and equivalence has to be stated as equivalence between its rest, inertial, and gravitational internal-energy operators rather than between their average values [ 1 ] . Model that operator, call it M^\hat M , as M^\hat M = m(1 + H^int\hat H_{int}/mc2c^2) , where H^int\hat H_{int} is the system’s internal Hamiltonian, and let the gravitational mass be mgm_g = mi(1+η^)m_i(1 + \hat\eta) for some violation operator η^\hat\eta acting on the…

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