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Equation 5 · Part 4 · The Corner of the Equivalence Principle No Experiment Has Touched

=

mg=mi(1+η^)m_g = m_i(1 + \hat\eta)
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.