Gravity Is Not Like the Other Forces
I put in the work to study GR from Susskind&#x27; theoretical minimum (fantastic lecture series: <a href="https:&#x2F;&#x2F;theoreticalminimum.com&#x2F;courses&#x2F;general-relativity&#x2F;2012&#x2F;fall" rel="nofollow">https:&#x2F;&#x2F;theoreticalminimum.com&#x2F;courses&#x2F;general-relativity&#x2F;20...</a> ). I still don&#x27;t understand GR.<p>Yes I can now say &quot;oh gravity is &#x27;&#x27;&#x27;just&#x27;&#x27;&#x27; curvature on a lorentizian manifold&quot;, but what in the world does it _mean_? My current picture is something like this:<p>A Lorentizian manifold looks locally hyperbolic, so we need to imagine a light cone. Now the curvature of this manifold tells us how we need to <i></i>distort light cones<i></i> at different points to build up the full space.<p>How the fuck do I visualize this? Is there some way to embed this in low dimension to play with it? For example, to understand regular curvature, you can play around with a sphere and a cone to get a feel for curvature ~= angle deficit ~= loopy deficit ~= holonomy.<p>I don&#x27;t know how to visualize the curvature of space-time, and I&#x27;m completely unconvinced I actually understand it beyond squiggles on paper. I&#x27;d love a way to embed and visualize this. Please tell me if you know how!<p>As an aside: It is definitely possible to get a feel for _hyperbolic geometry_ by playing HyperRogue: (<a href="https:&#x2F;&#x2F;roguetemple.com&#x2F;z&#x2F;hyper&#x2F;" rel="nofollow">https:&#x2F;&#x2F;roguetemple.com&#x2F;z&#x2F;hyper&#x2F;</a>) --- A free roguelike set in hyperbolic space.<p>What I don&#x27;t grok at all is the _curvature_ across hyperbolic spaces, analogous to how a sphere has _curvature_ across flat spaces. I&#x27;d love to know how to get a feel for this.