Entropy is an important indicator in physics of the passage of time. Briefly, time increase is usually matched by entropy increase. Is it possible that the Universe contains regions in which time runs in a direction opposite to ours? This exciting, but unlikely, possibility has been investigated by Schulman, L.S. (Phys. Rev. Lett. 83, 5419–5422; 1999), who has studied the entropy of two interacting gases of particles with opposing arrows of time.
If such regions exist, can each see the radiation emitted by the other? The laws of electrodynamics have also been proposed as indicators of the passage of time, because radiation, once emitted, must be subsequently absorbed elsewhere. But electrodynamics, unlike entropy, can be shown to be time symmetric. Indeed, according to the simple cosmological equations for a model universe, such a universe may contract just as easily as it may expand. We know which solution applies to our Universe by comparison with observation.
This problem can be solved using Wheeler–Feynman absorber theory (Wheeler, J.A. & Feynman, R.P. Rev. Mod. Phys. 17, 157; 1945 & 21, 425; 1949). Suppose that electromagnetic radiation is emitted by a system, S, in both directions of time and as equal parcels of energy. The normal radiation, R, is later absorbed by matter at S′ and the remainder, r, goes backwards in time. The particles in the absorber S′ are stimulated to emit radiation themselves, which also proceeds with equal energy: half (R′) into the future and half (r′) into the past. In due course r′ reaches S, where it cancels the original wave r emitted by S into the past, leaving only the wave going forward in time, in agreement with observation.
Schulman extends this theory to his two gases with opposing arrows of time, assuming a purely theoretical interaction. He then finds that the entropy histories of the two systems are affected by their interaction, but not as strongly as might be expected; and the results are “still consistent with electrodynamics”. On this basis, systems with opposing arrows of time may be able to coexist and see each other. Bizarre as it seems, he proposes that such objects could exist in our own Galaxy, and might have properties expected of dark matter.
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Landsberg, P., Vickers, J. Conflicting arrows of time. Nature 403, 609 (2000). https://doi.org/10.1038/35001182
Revue de Synthèse (2009)