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Even if there were as many positrons as electrons in the universe, I don't get the time-reversed character at a macro level. When leaving antimatter out of the picture, I dimly understand that the arrow of the arises from entropy. If time reversed particles are antiparticles, shouldn't we sometimes see a diffuse cloud of antiparticles in a lab spontaneously condense into a very low entropy concentrated configuration?

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The answer is that they don’t literally go backwards in time showing reverse causality. They are representable in QFT by reversing the time component of their counterpart, which doesn’t impact how they interact with broader causality, just their internal configuration. Further - this does not play out in the lab as reversed causality even between anti particles. You can collide two positrons then detect them later at their destinations just fine in normal causality. It’s a shame because it would be really sweet to find some reversal of entropy and causality somewhere or somehow!

May I introduce you to Maxwell’s Demon?

https://en.wikipedia.org/wiki/Maxwell%27s_demon

I'm too low energy to click on that link.

You may, but if you read the link, you’ll find it consistent with the second law of thermodynamics despite being clever about it. The demonstration of consistency requires a modern understanding of information theory, but it’s been long realized it’s likely not a real “out.”

_We_ are still traveling forwards in time. If you followed a cloud of antiparticles backwards in time along its direction of travel, then you would see entropy decrease yes, though regular particles would do the same if we followed them back in time.

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