Ask Ethan: Why Can't Time Be Reversed For Three-Body Systems?

It’s a very clever result to learn that, for the realistically large-mass objects we have in our Universe, the precision required to calculate a truly time-reversible solution is greater than the precision the physical Universe actually allows. If the laws of quantum physics and General Relativity are both correct, as we have every reason to believe that they are, then even purely gravitational systems with as few as three masses are fundamentally irreversible.

Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical consequence is that integrations of the N-body problem unavoidably magnify truncation and rounding errors to macroscopic scales. Hitherto, a quantitative relation between chaos in stellar dynamical systems and the level of irreversibility remained undetermined. In this work we study chaotic three-body systems in free fall initially using the accurate and precise N-body code Brutus, which goes beyond standard double-precision arithmetic. We demonstrate that the fraction of irreversible solutions decreases as a power law with numerical accuracy. This can be derived from the distribution of amplification factors of small initial perturbations. Applying this result to systems consisting of three massive black holes with zero total angular momentum, we conclude that up to five percent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable.

Amazing result. What do the @Physcists think?

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This is an interesting paper. I have a few thoughts:

  1. It is unclear if the Planck length represents any sort of boundary whatsoever. This is still a conjecture.
  2. At the Planck scale, the equations used to evolve the systems in the paper is no longer valid. The true equation of motion might not even be reversible in the first place.
  3. Time irreversibility for gravitating bodies in pure classical mechanics has been demonstrated before, usually as artifacts of the bodies’ mathematical models. The novelty of the irreversibility in this paper is that it is not pure classical mechanics, but requires arguments involving the Planck length.
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