Events

Although the debate about the epistemology of geometry has a long pedigree, the question of whether or not spacetime is orientable has been sorely missing from this literature. In the vast majority of discussions it is simply taken from granted. This is not surprising: time orientability is, for example, an underlying premise of such robust theories as causality and quantum gravity, and their utility makes it convenient simply to assume it. We feel reassured in this belief due to the apparent incongruence of such objects as hands, and therefore we are not interested in the experimental confirmation of spacetime orientability. However, it turns out that our empirical evidence do not definitely rule out the possibility that spacetime is, in fact, non-orientable. During my talk, I address these issues and suggest possible ways of testing spacetime orientability. 

I begin by pointing out an ambiguity in the notion of orientability. I distinguish between manifold orientability, defined for all differentiable manifolds, and time and space orientability, defined only for (3+1)-Lorentzian manifolds. These notions are, in general, independent. I then argue that current experimental data do not allow us to definitely determine whether spacetime is orientable in any of these senses. Standard arguments appeal to spinors in quantum field theory, causality in general relativity, parity violation in the Standard Model, and the arrow of time. However, I argue that each of these arguments can be challenged: in the case of quantum field theory – because spinors can be defined on non-parallelizable manifolds (see Pitts 2012); in the case of causality – because it can be violated in some circumstances; and in the case of parity violation and the arrow of time – because they are confined to some spacetime region (cf. Bielińska and Read 2022).

Finally, I discuss a proposed experiment to test spacetime orientability, building on Hadley (2002), and argue that it is physically impossible to confirm orientability empirically. We therefore cannot exclude the possibility that spacetime is non-orientable. I conclude with a discussion of orbifolds—generalisations of manifolds used, inter alia, in string theory—and show that in this context new and interesting issues arise concerning orientability and its epistemology (cf. Bielińska and Read 2026).

Zoom

Monday, March 30, 2026 9:30 AM

Inperson
BHI Conference Room and Zoom