Equation 1 · Part 2 · How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

Branch labels

\varphi_{ij} = G m_A m_B t / (\hbar d_{ij})

i,j

What this part means

Each label is L or R. The first chooses mass A’s path and the second chooses mass B’s path, giving LL, LR, RL, and RR.

Its job in the formula

These labels select one of four path pairs, and therefore select the distance that must be inserted into this calculation.

Full expressionBranch labelsArticle meaning

The passage around this formula

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

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Learn the underlying idea

A quantum phase is an angle attached to a complex amplitude. One path’s phase can be changed by convention; phase differences between alternative paths can change interference and entanglement.

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Sources cited in the article section

[6] On the possibility of laboratory evidence for quantum superposition of geometries ↗

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