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And I said it is the shape of the world lines that exhibit the relative motion we associate with observers and objects. If you're asking why we don't atemporally perceive the entire world line of ourselves, that boils down to the question of how perception manifests from things, an open question.
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If it is indeed an open question, it is limited in its scope, and would require a fairly mystical explanation.
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They are the same theory: "The Wheeler-DeWitt equation embodies a stark form of presentism: it simply tells us which states the universe can find itself in, and says nothing about any evolution through time. " Is equivalent to Julian Barbour's:"The quantum universe is likely to be static. Motion and the apparent passage of time may be nothing but very well founded illusions." I.e. They are saying the universe is an unchanging configuration space, and change is an illusion generated by the Hamiltonian. The "present" in this case, is not a single 3D hypersurface, but rather all possible hypersurfaces, and all possible configurations.
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I'm not entirely sure about the idea of a 3D hypersurface, but, if I understand correctly, I don't have too much trouble with the idea that the universe is an unchanging configuration space and that change is an illusion.
Still, it would represent presentism though.
EDIT: it is probably worth clarifying the point about change being an illusion; change still manifests in the physical world we experience, but the physical world we experience is illusory.




