- #1
Sonderval
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In the Feynman Lectures on Physics, Feynman explains the curvature of spacetime by drawing a rectangle in spacetime, see
http://www.feynmanlectures.caltech.edu/II_42.html Fig. 42.18
First waiting 100 sec and then moving 100 feet in height on Earth's surface results in a different situation than first moving 100 feet and then waiting 100 sec due to the time dilation that depends on height.
The time dilation effect is (h as height, g as gravitational acceleration, c=1, t(0) the time waiting at the lower height)
[tex]t(h) = (1+ gh) t(0)[/tex]
So the difference between the end points in the diagram is given by [tex]g h t(0)[/tex]. It is thus proportional to the area of the rectangle.
However, in Road To Realty, Fig 14.9 b and c, Penrose says that in a torsion-free space, a small rectangle with sidelength ε is closed up to an order ε³.
To me this seems like a contradiction - so obviously I'm making a mistake somewhere.
Can anybody tell me where I'm going off?
http://www.feynmanlectures.caltech.edu/II_42.html Fig. 42.18
First waiting 100 sec and then moving 100 feet in height on Earth's surface results in a different situation than first moving 100 feet and then waiting 100 sec due to the time dilation that depends on height.
The time dilation effect is (h as height, g as gravitational acceleration, c=1, t(0) the time waiting at the lower height)
[tex]t(h) = (1+ gh) t(0)[/tex]
So the difference between the end points in the diagram is given by [tex]g h t(0)[/tex]. It is thus proportional to the area of the rectangle.
However, in Road To Realty, Fig 14.9 b and c, Penrose says that in a torsion-free space, a small rectangle with sidelength ε is closed up to an order ε³.
To me this seems like a contradiction - so obviously I'm making a mistake somewhere.
Can anybody tell me where I'm going off?