Equation 7 · Part 5 · How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

A on R, B on L

\varphi_{\text{ent}} = \varphi_{LL} + \varphi_{RR} - \varphi_{LR} - \varphi_{RL}

\varphi_{RL}

What this part means

The phase of the other crossed branch pair. It is also subtracted in the local-phase-invariant combination.

Its job in the formula

This crossed-path phase is also subtracted, completing cancellation of A-R and B-L local phase choices.

Full expressionA on R, B on LArticle meaning

The passage around this formula

None of this makes the experiment ambiguous, and this is the paper’s second and sharper result. The branch separations that enter the gravitational phase each mass’s superposition 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 removed…

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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.

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.