Spacetime is Curved

“General relativity can be summed up in two statements:

  1. Spacetime is a curved pseudo-Riemannian manifold with a metric of signature (− + + + ).
  2. The relationship between matter and the curvature of spacetime is contained in the equation
    R_{mu nu} - {1 over 2} , R ; g_{mu nu} = 8 pi ; G , T_{mu nu}.”

Sean Carroll

There you have it, ladies and gentlemen! The universe summed up in two sentences.

Regarding the first statement: a metric of signature (− + + + ) just means that time goes the opposite direction as space. (Think light cones.)

No matter how fast you go — or if you stand still — time is flowing through you at the speed of light.

Another way to think about going somewhere, say Bermuda, is that you will meet up with Bermuda’s future. To hurry to Bermuda is to meet an earlier future — but no matter how fast you go, the Bermuda that is now will be gone by the time you get there.

And so we beat on, boats against the tide, borne back ceaselessly into the past.


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