Equation 1 · Part 7 · How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

Distance for this branch pair

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

d_{ij}

What this part means

The separation between mass A on branch i and mass B on branch j. A smaller separation gives a larger gravitational interaction energy and therefore a larger accumulated phase.

Its job in the formula

This is the branch-dependent input. Different pair distances produce different phase angles; equal distances would give no relative gravitational phase.

Full expressionDistance for this branch pairArticle meaning

The passage around this formula

…— 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 $\varphi_{ij}$ = 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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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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.