17 problems

Low's conjecture. Events $x,y\in X$ are causally related if and only if their skies $S_x,S_y$ are linked in $\mathcal N_X$.

Hawking's chronology protection conjecture. The laws of physics prevent the formation of time machines or spacetime regions containing closed timelike curves.

Let the spacetime be $(3+1)$-dimensional and globally hyperbolic, with a Cauchy surface homeomorphic to $\mathbb{R}^3$. The skies of events are viewed as Legendrian links in the re…

Modified Low conjecture. Two events are causally unrelated if and only if the lifts of their fronts are unlinked in the appropriate sense.

Links–Gould polynomial conjecture. The invariant $\mathrm{LG}$ completely captures causality in such spacetimes.

Allen–Swenberg's conjecture. The Jones polynomial should be sufficient to detect whether the skies $S_x$ and $S_y$ are linked, and hence to detect causality.

Conjugation quandle detection conjecture. The collection of all conjugation quandles over all dihedral groups is able to detect causality across $(2+1)$ globally hyperbolic spaceti…

Legendrian Low conjecture. If the skies of two events are Legendrian linked, then the events are causally related.

Smeared-field causality conjecture. An ideal measurement of a smeared field should respect relativistic causality.

Sormani–Vega conjecture. The null distance encodes causality:

Let $(X,g)$ be a causally simple spacetime that can be conformally embedded as an open subset into some globally hyperbolic spacetime $(\widetilde X,\widetilde g)$. Let the space o…

Let $(X^{m+1},g)$, $m>1$, be a causally simple spacetime that does not admit a metric $g'$ such that $(X,g')$ is refocussing and causally simple. A Legendrian link is a link formed…

Let $H(g)$ denote the full Hamiltonian at coupling parameter $g$, and let $H_{C}^{I}(g)$ denote the corresponding interaction Hamiltonian contribution in the model. Central-role co…

The measures under discussion include transfer entropy, causation entropy, directed information, Granger causality, and intervention-based measures of information flow. They are in…

Strict V-causality hierarchy conjecture. For every $k$, there exists a $V^kBox$ which is $V^k$-causal but not $V^{k+1}$-causal.

Consider the normal-ordered square $\mathcal O(x)=:\phi\star_M\phi:(x)$ of a free scalar field in four-dimensional spacetime, defined using the Moyal star product, with space-space…

Let a space-time be a solution of the Einstein equations, and call a singularity naked when it is observable. The conjecture concerns generic space-time solutions and whether such…