Time does exist though, at least directionally, because of entropy, no?
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So we might have time's flow emerging from quantum correlations while time's direction remains real due to thermodynamic entropy. It's like asking if "up" exists, gravity creates real directional asymmetry even though "up" emerges from mass distributions.
Maybe time's arrow is real even if time's existence is emergent? Though honestly this is where my physics knowledge hits its limits!