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

Phase of branch pair i,j

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

\varphi_{ij}

What this part means

The dimensionless phase angle, in radians, acquired by the joint path in which mass A uses branch i and mass B uses branch j. Its individual value depends on phase convention; differences between branch-pair phases can affect interference and entanglement.

Its job in the formula

This is the calculated phase for one chosen pair of paths. Comparing it with the other three pair phases is what reveals a possible entangling effect.

Full expressionPhase of branch pair i,jArticle meaning

The passage around this formula

…picks up are relational 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 $\varphi_{ij}$ = 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…

Read this part in the article →

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.

Open the illustrated quantum phase and two-path entanglement guide →

See this notation across published equations →

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.