RE: No perfect circles in space...
July 23, 2018 at 12:28 pm
(This post was last modified: July 23, 2018 at 12:30 pm by polymath257.)
(July 23, 2018 at 10:22 am)Jehanne Wrote:(July 23, 2018 at 8:46 am)polymath257 Wrote: My bad. I had misremembered the Schwartzchild solution (the inverse is on the radial piece, not the time piece). Yes, the circumference would be shorter than 2*pi*r.
It is hard to imagine in one's head those type of circles with respect to a planetary orbit in 3 dimensions with zero eccentricity.
The way I do it is by thinking of distance as a number. As we go out from the origin, that number runs slower than might be 'expected' for the radius. So, we get a radius that is lower than would be expected for the given circumference.
(July 23, 2018 at 11:51 am)Jehanne Wrote: Those who would imagine the Universe just "popping into existence" need to stop doing that and perhaps start focusing on this problem instead.
I'm not sure I see a problem here at all. The math is well-defined and accurately predicts observations. Curvature is defined *internal* to the spacetime manifold, not from any embedding.
The only issue seems to be the difficulty in 'imagining' that distance doens't work in the way Euclid expected. That is overcome through practice.
