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Published equation contexts

η^=ηcl+η^diag+η^coh+η^sup+η^ent\hat\eta = \eta_{cl} + \hat\eta_{diag} + \hat\eta_{coh} + \hat\eta_{sup} + \hat\eta_{ent}

Why this formula appears here

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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η^diag\hat\eta_{diag}

Symbol hateta_diag

diagonal in the internal energy basis: it can make a clock in one internal state fall differently from the same species in another, which is what a clock-redshift test or a test comparing atoms prepared in different hyperfine states actually probes.

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η^coh\hat\eta_{coh}

Symbol hateta_coh

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

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η^sup\hat\eta_{sup}

Symbol hateta_sup

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

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η^ent\hat\eta_{ent}

Symbol hateta_ent

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

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Published contexts (1)

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η^=ηcl+η^diag+η^coh+η^sup+η^ent\hat\eta = \eta_{cl} + \hat\eta_{diag} + \hat\eta_{coh} + \hat\eta_{sup} + \hat\eta_{ent}

Equation 7 · 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…

Meanings in this article

  • ηcl\eta_{cl}: an ordinary number, the same for every state — MICROSCOPE’s slot.
  • η^diag\hat\eta_{diag}: diagonal in the internal energy basis: it can make a clock in one internal state fall differently from the same species in another, which is what a clock-redshift test or a test comparing atoms prepared in different hyperfine states actually probes.
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