English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the nature of quantum properties in non-relativistic quantummechanics (QM) and relativistic QFTs, and examine the connection between formalquantization schemes and intuitive notions of wave-particle duality. Based onthe map between classical Poisson brackets and their associated commutators,such schemes give rise to quantum states obeying canonical dispersionrelations, obtained by substituting the de Broglie relations into the relevant(classical) energy-momentum relation. In canonical QM, this yields a dispersionrelation involving $\hbar$ but not $c$, whereas the canonical relativisticdispersion relation involves both. Extending this logic to the canonicalquantization of the gravitational field gives rise to loop quantum gravity, anda map between classical variables containing $G$ and $c$, and associatedcommutators involving $\hbar$. This naturally defines a "wave-gravity duality",suggesting that a quantum wave packet describing {\it self-gravitating matter}obeys a dispersion relation involving $G$, $c$ and $\hbar$. We propose anansatz for this relation, which is valid in the semi-Newtonian regime of bothQM and general relativity. In this limit, space and time are absolute, butimposing $v_{\rm max} = c$ allows us to recover the standard expressions forthe Compton wavelength $\lambda_C$ and the Schwarzschild radius $r_S$ withinthe same ontological framework. The new dispersion relation is based on"extended" de Broglie relations, which remain valid for slow-moving bodies of{\it any} mass $m$. These reduce to canonical form for $m \ll m_P$, yielding$\lambda_C$ from the standard uncertainty principle, whereas, for $m \gg m_P$,we obtain $r_S$ as the natural radius of a self-gravitating quantum object.Thus, the extended de Broglie theory naturally gives rise to a unifieddescription of black holes and fundamental particles in the semi-Newtonianregime.

Which quantum theory must be reconciled with gravity? (And what does it mean for black holes?)