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Equation 3 · Part 2 · The Corner of the Equivalence Principle No Experiment Has Touched

Symbol m

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

What this part means

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

Its job in the formula

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

The passage around this formula

…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 internal, and for two-body tests the joint, Hilbert space. Expand that operator and, the…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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