> This is another way of saying that T-symmetry implies that all possible histories must have occured.
Actually, it's the opposite. Consider:
• A→{B,C}
• B←(A,D}
• C←{A,E}
That doesn't mean that A, D and E are all possible histories; when you consider B and C separately, D and E appear to be possible histories, but considering both B and C, you find that D and E cancel out,¹ leaving only A. So you can't actually make a claim about how many histories there are.
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¹: This is horribly misleading. D and E aren't the same thing-I've-been-calling-a-state-but-that's-the-wrong-word-sorry, so their amplitude doesn't get summed, so they can't cancel each other out. My analogy wouldn't work as well if I'd used the same letter, though. (Consider also that I didn't use bra-ket notation. This is an analogy, not rigorous.)
Actually, it's the opposite. Consider:
• A→{B,C}
• B←(A,D}
• C←{A,E}
That doesn't mean that A, D and E are all possible histories; when you consider B and C separately, D and E appear to be possible histories, but considering both B and C, you find that D and E cancel out,¹ leaving only A. So you can't actually make a claim about how many histories there are.
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¹: This is horribly misleading. D and E aren't the same thing-I've-been-calling-a-state-but-that's-the-wrong-word-sorry, so their amplitude doesn't get summed, so they can't cancel each other out. My analogy wouldn't work as well if I'd used the same letter, though. (Consider also that I didn't use bra-ket notation. This is an analogy, not rigorous.)