Much larger masses will push the structure of Ψ(x, t) towards the Planck scales, such role of the mass is what our work aims to emphasize

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- Quantum-gravitational limitations of our very notion of space-time were conjectured by Bronstein in 1936, the same issue was famously characterized by Wheeler’s foamy structure of space-time In the back-ground of quantized matter, the classical notion of space-time continuum can not be maintained at short distances
- Direct observation of distances like 10−33 cm would require incredible high precision — beyond imaginations. Their indirect test would be possible around the extreme high Planck energy EPl = 1.2 × 1019 GeV per particle, which existed right after the Big Bang only
- Much larger masses will push the structure of Ψ(x, t) towards the Planck scales, such role of the mass is what our work aims to emphasize
- We argued how quantum-gravity, relativistic by its definition, should influence nonrelativistic quantum mechanics
- Summary We wished relaxing the belief, based mainly on quantum-field-theory considerations, that the significance of quantum-gravity is restricted for the regime of extreme high energies
- We argue that the Planck length lPl invokes a mandatory —gravity-related, yet to be specified— modification of non-relativistic quantum mechanics of massive degrees of freedom because their de Broglie wave lengths can descend into the vicinity of lPl non-relativistically
- No matter whether space-time is classical or quantized, some ultimate statistical or quantum uncertainties are attributed to the background space-time, to result in some particular decoherence of massive degrees of freedom

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