Published equation contexts

$\hbar$

Why this formula appears here

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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Research cited beside this formula

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

Published contexts (1)

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\hbar

Equation 6 · Quantum Relativity

How Much of Gravitationally Induced Entanglement Is in the Eye of the Frame

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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…