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Originally Posted by Tensor
Although most relativists will say spacetime is the actual physical component of the mathematical manifold.
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What do you mean?
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Originally Posted by Tensor
As soon as something changes, the manifold either contracts or expands. Within the math, it's the manifold that expands (as currently viewed).
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Since the manifold already contains time as a dimension, how could it expand over the course of time? Maybe it is "successive" three-dimensional cross-sections that "expand." I don't pretend to understand. I'm asking. Thank you.
edit: 1. Thank you, Tensor, for the article linked in your your last post.
2. I'm still not clear what it is that is expanding. The putative 3-dimensional cross-sections mentioned above wouldn't even be well-defined locally. Cancel that idea. But, maybe, as we proceed along wordlines, the metric tends to change so that, in general, things are further away. Am I babbling yet? OK, maybe you could talk about lightlike cross-sections that would be well-defined. Then it would make sense to say that one of them represents a later time than another. One representing a later time would, according to the metric, be larger.