- #141

Dale

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If you didn’t understand it, then why have you waited this long to ask for clarification?student34 said:I do not understand the onion analogy. I understand that we can integrate many 2d onion bulbs to create a full onion. But I do not understand how that relates to this. What are we integrating in the example?

Each leaf of an onion is a sphere. So the metric of each leaf is ##ds^2=R^2 d\phi^2 + R^2 \sin^2(\phi) d\theta^2## which is curved. But when you add all of the leaves together the metric is the flat Euclidean ##ds^2=dx^2+dy^2+dz^2##.

The full space does not inherit the metric from the leaves. An onion has spherical leaves that foliate a Euclidean space. Spacetime has Euclidean leaves that foliate a Minkowski space.