Equation 1 · Part 8 · How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

Reduced Planck constant

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

\hbar

What this part means

The quantum constant that converts energy multiplied by time (action) into a phase angle. Dividing the gravitational energy-time product by ħ leaves a dimensionless number of radians.

Its job in the formula

This turns gravitational energy multiplied by time into a dimensionless quantum angle, measured in radians.

Full expressionReduced Planck constantArticle meaning

The passage around this formula

…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 — a relabeling with no physical content. Exactly one combination survives that removal:

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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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.