Quantum gravity, minimum length and holography

The Karolyhazy uncertainty relation states that if a device is used to measure length l, there will be minimum $$\delta l$$ in the measurement, given by $$(\delta l)^3 \sim L_{\mathrm {P}}^2 . This consequence of combining principles quantum mechanics and general relativity. In this letter we show how arises our approach gravity, bottom-up fashion, from matrix dynamics atoms space–time–matter. We use define space–time–matter (STM) foam at Planck scale, argue theory holographic. By coarse graining over time-scales larger than time, one obtains laws gravity. Quantum gravity not scale phenomenon; rather it comes into play whenever classical space–time background available describe system. Space–time relativity arise spontaneous localisation highly entangled gravitational continues hold emergent theory. An experimental confirmation constitute definitive test nature