Hoy subieron un paper interesante a Arxiv/gr-qc titulado Spacetime from Quantum Physics donde el autor propone un sistema de osciladores desacoplados del cual “emergería” el espacio de Minkowski (el espacio de toda la vida… al menos desde 1905). Afirma:

The aim of this Letter is to prove that the flat 4D Minkowski space-time of special relativity can indeed be seen as a local approximation of a real manifold which arises naturally from the algebra obeyed by the ladder operators of two independent ‘abstract’ quantum harmonic oscillators. This Letter does not claim that the proposed construction is the only possible one, nor that it is the physically correct one, though it may be. The sole aim of this work is to show that Minkowski spacetime can be derived from a purely quantum framework

El autor se las arregla para incorporar las transformaciones de Lorentz y mostrar que esto acopla los dos osciladores. Y en medio de toda la complicación de cuentas que hay a lo largo del trabajo se usa otra cosa que aparece bastante en la materia… la exponencial de matrices de Pauli.

Ajeno a los detalles técnicos de cómo surge una variedad (el espaciotiempo) de un espacio de Hilbert (el de los dos osciladores); es interesante es ver cómo, aunque parezca un modelo de juguete, uno puede encarar una pregunta tan fundamental como la naturaleza cuántica de la gravedad usando osciladores armónicos como los vimos en clase.

El paper termina diciendo:

From the classical point of view, the most natural question is about general relativity. Can the above procedure be extended to deliver curved Lorentzian manifolds? Could this be done by allowing for example the oscillators to interact with each other? And could this pave the way to a possible laboratory quantum simulations of general relativistic space-times i.e. of relativistic gravitation, for example in the contexts of quantum optics or condensed matter physics?

Finally, one can only wonder if and how matter fits into the picture developed here. The link between spacetime and quantum harmonic oscillators presented in this article seems to suggest that matter and space-time may be two sides of the same coin. If so, what is exactly that coin, and how does what we call dynamics emerge from a unified quantum pictures?