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arXiv · 2405.10574

Partial Derivatives on Causal Sets

Samuel Shuman
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Abstract

We will discuss two approaches to estimating partial derivatives and the metric components; one utilizing past work describing a causal set $\Box$ operator, and one using a construction from linear algebra called the Moore-Penrose inverse. After running numerical tests on a causal diamond in $\mathbb{M}^2$, we find that the approach using the Moore-Penrose inverse is significantly more accurate. Despite the large variances in the method using the $\Box$ operator, there is reason to believe both approaches should become more accurate at higher densities.

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Samuel Shuman. 2024-05-17. Partial Derivatives on Causal Sets. https://arxiv.org/abs/2405.10574

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