L. J. Vinck

It has recently been claimed that algebraic methods can be used to give a background-independent description of semiclassical gravity. This paper aims to provide an entry point into recent algebraic approaches to quantum gravity and to analyse and critically assess the conception of background-independence here involved. We discuss an algebraic framework for formulating an algebra of observables along the worldline of an observer in a cosmological setting. By ‘gravitationally dressing’ the observables to the observer’s worldline, the reference to the spacetime background can be set aside at the level of the abstract *-algebra. Thus this *-algebra is taken to be independent of any particular spacetime realisation, with different states on the algebra corresponding to different backgrounds. We compare this algebraic framework to three influential notions of background-independence in the literature and argue that none of these fully captures the sense in which the *-algebra is taken to be background-independent. Building on this, we extract a novel notion of algebraic background-independence tied to the representation-independence of the *-algebra. This algebraic conception motivates two further concepts of background-independence tailored to semiclassical theories: semiclassical background-independence and perturbative background-independence. We suggest that these provide useful tools for evaluating the scope and limitations of semiclassical approaches to quantum gravity.

The Einstein-Bergson debate on the nature of time is historically regarded as a pivotal moment in the rift between the humanities and natural sciences. Bergson was generally conceived to have lost the debate, although opinions of philosophers remained divided. In contemporary discussions, the debate again appears relevant, as a renewed perspective on Bergson's critique of Einstein's interpretation of relativity provides cues into how to approach the ‘problem of time’ in the search for quantum gravity. In this paper I revisit the debate and provide a detailed philosophical analysis of Bergson's main arguments and his use of multiplicities. While Bergson made a mistake in his discussion of the twin paradox, I will argue that he was right in pointing out that time dilation is not a directly experienceable phenomenon. This will clarify how his thesis that the notion of a single ‘Time’ is compatible with the theory of relativity should be understood. In conclusion, I argue that Bergson's philosophy can be useful for making sense of contemporary approaches to the problem of time in physics, in which time is viewed as an observer-dependent or emergent phenomenon rather than a fundamental quantity.

The Einstein-Bergson debate on the nature of time is historically regarded as a pivotal moment in the rift between the humanities and natural sciences. Bergson was generally conceived to have lost the debate, although opinions of philosophers remained divided. In contemporary discussions, the debate again appears relevant, as a renewed perspective on Bergson’s critique of Einstein’s interpretation of relativity provides cues into how to approach the ‘problem of time’ in the search for quantum gravity. In this paper I revisit the debate and provide a detailed philosophical analysis of Bergson’s main arguments and his use of multiplicities. While Bergson made a mistake in his discussion of the twin paradox, I will argue that he was right in pointing out that time dilation is not a directly experienceable phenomenon. This will clarify how his thesis that the notion of a single Time is compatible with the theory of relativity should be understood. In conclusion I argue that the approach taken by some contemporary physicists, who argue that time should be viewed as an observer-dependent or emergent phenomenon rather than a fundamental quantity, are in agreement with the metaphysics of Bergson.