• Quantum gravity, minimum length and holography

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/095/0040

• # Keywords

Quantum gravity; trace dynamics; pre-quantum theory; pre-space–time theory; length uncertainty.

• # Abstract

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

• # Author Affiliations

1. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

• # Pramana – Journal of Physics

Volume 95, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019