# The representation of spacetime through steep time functions

@article{Minguzzi2018TheRO, title={The representation of spacetime through steep time functions}, author={Ettore Minguzzi}, journal={Journal of Physics: Conference Series}, year={2018}, volume={968} }

In a recent work I showed that the family of smooth steep time functions can be used to recover the order, the topology and the (Lorentz-Finsler) distance of spacetime. In this work I present the main ideas entering the proof of the (smooth) distance formula, particularly the product trick which converts metric statements into causal ones. The paper ends with a second proof of the distance formula valid for globally hyperbolic Lorentzian spacetimes.

## 2 Citations

### The Lorentzian distance formula in noncommutative geometry

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- 2017

For almost twenty years, a search for a Lorentzian version of the well-known Connes’ distance formula has been undertaken. Several authors have contributed to this search, providing important…

### Space and time dimensions of algebras with application to Lorentzian noncommutative geometry and quantum electrodynamics

- MathematicsJournal of Mathematical Physics
- 2018

An analogy with real Clifford algebras on even-dimensional vector spaces suggests to assign a couple of space and time dimensions modulo 8 to any algebra (represented over a complex Hilbert space)…

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