What time-reversal symmetry can (and cannot) tell us about time?s structure

CRISTIAN LÓPEZ

Praga

Congreso; 16° Congress of Logic, Methodology and Philosophy of Science; 2019

The relevance of symmetries to know what the world?s structure is like has greatly grown in the last years (Baker 2010). We are said, for instance, that by knowing the space-time symmetries of a theory?s dynamics, we are allowed to draw metaphysical conclusions about space-time?s structure (North 2009). Shamik Dasgupta (2016) has called this sort of inferences ?the symmetry-to-reality inference?. Time symmetry is a special case of this: if a theory?s dynamics is invariant under time reversal, then the direction of time is superfluous. Therefore, the time?s structure of the world according to the theory is actually directionless.In analyzing the inference for time symmetry thoroughly, we find a mix of premises. Given an equation of motion L, we first find formal premises claiming that a symmetry holds, that is, that a variable in L may freely vary preserving L?s structure. In this case, by freely varying the sign of time (t by ?t), we also get physically equivalent solutions for L. The sign of t (standing for the direction of time) is hence said to be variant. Second, to the extent to which we adhere to the principle that symmetries in the laws must go hand-in-hand with the symmetries of the world?s structure (Earman 1989, North 2009), we interpret that a variant feature occurring in L is surplus structure. As we are advised to go with the least structure (by an Ockham?s razor), we infer that the direction of time does not belong to the world?s structure. Concluding, the direction of time is not part of the fundamental reality.In this presentation, I shall analyze the symmetry-to-reality inference for the case of time symmetry, focusing on the formal premises. In particular, I shall first argue that there are actually two divergent ways to conceive symmetries in physics: either as contingent properties of the dynamics or as principles guiding theory construction (Brading and Castellani 2007). Whereas the inference would work well when symmetries are considered in the first way, being thus a powerful tool for metaphysicians of science, it might rather be viciously circular when they are understood as guiding principle, and metaphysicians of science should be very careful in drawing metaphysical conclusions from them. In the second place, I shall show that time symmetry is typically understood as a principle guiding theory construction in fundamental theories (Arntzenius and Greaves 2009). Therefore, the inference wouldn?t work for drawing metaphysical conclusions about time?s structure.Baker, D. (2010). ?Symmetry and the metaphysics of physics?. Philosophy Compass, 5: 1157-1166Brading, K. and E. Castellani. (2007). ?Symmetries and Invariances in Classical Physics?. Handbook of the Philosophy of Science, Philosophy of Physics, Part B (Butterfield and Earman). Netherlands: Elsevier, 331?367.Dasgupta, S. (2016). ?Symmetry as an epistemic notion (twice over)?. British Journal for Philosophy of Science, 67: 837-878.Earman, J. (1989). World Enough and Space-Time. Cambridge, MA: MIT press.North, J. (2009). ?The ?structure? of Physics: A case study?. Journal of Philosophy, 106: 57-88.Arntzenius, F. and Greaves, H. (2009). ?Time reversal in classical electromagnetism?. The British Journal for the Philosophy of Science, 60: 557-584.