The Fundamental Holographic Uncertainty Principle and its Primary Applications

Vitaly Kuyukov

Otto Charles Anthony Gadea, Gardo Blado

We examine quantum gravity effects by applying the generalized uncertainty principle (GUP) to entropic uncertainty relation conditions on quantum entanglement. In particular, we study the GUP corrections to the Shannon entropic uncertainty condition for entanglement. As in an earlier paper [Blado, Herrera, Erwin arXiv:1706.10013 [quant-ph]] which dealt with variance relations, there is an increase in the upper bound for the entanglement condition upon the application of the generalized uncertainty principle. Fundamental concepts of the generalized uncertainty principle, entanglement and the entropic uncertainty relations are also discussed.

Lee Smolin

We propose an approach to quantum theory based on the energetic causal sets, introduced in [1]. Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Fundamentally there are amplitudes for such causal processes, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no ~. All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality, nor non locality, are primary concepts, only causality exists at the fundamental level.

P Kuyukov Vitaly

Maria Chiara Braidotti, Ziad H. Musslimani, Claudio Conti

Marina Cortês, Lee Smolin

We propose an approach to quantum theory based on the energetic causal sets, introduced in [M. Cort\^es and L. Smolin, arXiv:1307.6167]. Fundamental processes are causal sets for which the events carry momentum and energy, which are transmitted along causal links and conserved at each event. Fundamentally there are amplitudes for such causal processes, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no $\ensuremath{\hbar}$. All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality nor nonlocality is a primary concept; only causality exists at the fundamental level.