Leibniz´s and Newton´s understanding of time reversal

CRISTIAN LÓPEZ

Santiago de Chile y Valparaíso

Congreso; First Chilean Conference on The Philosophy of Physics; 2018

Sociedad Chilena de Filosofía de las Ciencias - Universidad Católica de Valparaíso

Symmetries are playing an increasingly paramount role in the philosophy of physics. In particular, many have taken symmetries to be both quite informative with respect to reality?s structure, and useful tools for addressing longstanding philosophical problems. Space-time symmetries have turned out to be crucial in this respect as long as they would not only shed some light on space-time?s properties, but they would also give a fresh view on the nature of space and time.Despite symmetries? world being quite flourished and varied, space-time symmetry transformations mostly intend to formally capture the idea of carrying out an action either upon space-time itself or upon how things are arranged with respect to the space-time background. How the space-time symmetry transformation is formally spelled out will determine what kind of symmetry transformation is being performed. In this sense, a space-time symmetry is defined by how the symmetry transformation operates on states, observables, operators, background parameters and so on. In turn, the symmetry transformation intends to formally capture a change in the physical situation (for instance, by rotating the space 180°). The point to be stressed here is that what is relevant to know is whether the physics remains unaltered under such a space-symmetry transformation.By this rationale, philosophers of time and of physics have drawn special attention to time-reversal invariance as the relevant symmetry to digging into time?s physical structure. If a physical theory fails to be time-reversal invariant, then time?s structure is intrinsically asymmetric according to that theory. Here, the relevant symmetry transformation is that of time reversal, which roughly consists in turning the direction of time around by changing t into -t. Even though it is broadly assumed that the notion of time reversal is theory-relative, featuring unalike formal properties in different theories, and much work has been done exploring its formal details, the metaphysical bases of the time-reversal transformation have been scarcely addressed in the literature, as if they didn?t play any role in determining time reversal?s features. As well known, there are roughly two metaphysical views on the nature of time in physical theories: relationalism and substantivalism. The former was famously supported by Leibniz, claiming that time is nothing but the temporal relations among things, being the notion of ?time? an abstract idealization. On the contrary, according to the latter, mainly promoted by Newton, time is something physically real and independent of things and of their temporal relations. In this presentation, I will claim that these metaphysical bases matter in something like other formal features are claimed to matter: they determine what one is supposed to transform when inverting the direction of time, and thereby how the transformation should be formally represented. To make my point clear, I will show in which way substantivalist and relationalists are metaphysically forced to formally represent time reversal differently. The point I want to make here is that when inverting the direction of time, relationalists a la Leibniz will aim at reversing the direction of motion and at representing the time-reversal transformation accordingly. Substantivalist like Newton will alternatively aim at reversing time itself, representing the time-reversal transformation simply as a reflection that inverts the time itself. Finally, I will mention that these two unalike representations of time reversal could lead to divergent results upon the determination of whether or not a theory is time-reversal invariant.In this presentation, I will argue that previously-assumed commitments with respect to the nature of time (to wit, relationalists or substantivalists) play a crucial role in implementing time reversal in physical theories. In particular, I will show that in some situations both philosophical stances could not only disagree on how time reversal should be formally represented, but also get to diverging conclusions as to whether a physical theory is time-reversal invariant or not. This would thereby have philosophically relevant consequences for the arrow of time debate in physics.