# On the tensor product structure of general covariant systems

### APA

Vidotto, F. (2020). On the tensor product structure of general covariant systems. Perimeter Institute. https://pirsa.org/20030072

### MLA

Vidotto, Francesca. On the tensor product structure of general covariant systems. Perimeter Institute, Mar. 03, 2020, https://pirsa.org/20030072

### BibTex

@misc{ pirsa_PIRSA:20030072, doi = {10.48660/20030072}, url = {https://pirsa.org/20030072}, author = {Vidotto, Francesca}, keywords = {Quantum Foundations}, language = {en}, title = {On the tensor product structure of general covariant systems}, publisher = {Perimeter Institute}, year = {2020}, month = {mar}, note = {PIRSA:20030072 see, \url{https://pirsa.org}} }

Francesca Vidotto Western University

## Abstract

Defining a generic quantum system requires, together with a Hilbert space and a Hamiltonian, the introduction of an algebra of observables, or equivalently a tensor product structure. Assuming a background time variable, Cotler, Penington and Ranard showed that the Hamiltonian selects an almost-unique tensor product structure. This result has been advocated by Carrol and collaborators as supporting the Everettian interpretation of quantum mechanics and providing a pivotal tool for quantum gravity. In this talk I argue against this, on the basis of the fact that the Cotler-Penington-Ranard result does not hold in the generic background-independent case where the Hamiltonian is replaced by a Hamiltonian constrain. This reinforces the understanding that entropy and entanglement, that in the quantum theory depend on the tensor product structure, are quantities that are observable dependent. To conclude, I would like to pose the question of whether clocks can be thought as a resource, and how thinking of time in terms of physical clocks can inform our interpretation of quantum mechanics