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Equation 1 · Part 6 · How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

Interaction time

φij=GmAmBt/(ℏdij)\varphi_{ij} = G m_A m_B t / (\hbar d_{ij})
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What this part means

How long the two branches maintain the gravitational interaction. Doubling this duration doubles the angle in this idealized constant-separation model.

Its job in the formula

The phase accumulates while the masses interact. With no interaction time, the phase in this approximation is zero.

The passage around this formula

…quantities — distances between mass A’s branches and mass B’s branches — and relational quantities do not change when you change which system you have designated the reference frame. Write φij\varphi_{ij} = G mAm_A mBm_B t / (ℏ\hbar dijd_{ij}) for the phase a pair of branches i,j ∈\in \{L,R\} accumulates over interaction time t at separation dijd_{ij} , with G Newton’s constant and ℏ\hbar the reduced Planck constant. Three of the four possible combinations of these branch-pair phases can always be removed by a purely local…

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