4 ms·
When I'm talking about the Planck scale being "blown up" to observable size during the Big Bang, I'm not talking about any need to look past the CMB, I'm talkin
by Steuard 12y ago
When I'm talking about the Planck scale being "blown up" to observable size during the Big Bang, I'm not talking about any need to look past the CMB, I'm talking about right here, where we're sitting. If there's some issue in which significant "stretching" of spacetime (as via a coordinate transformation) can make Planck scale effects important even in regions of finite curvature, then we ought to be sitting in such a region right now, here on Earth.
Based just on what you've said here, you seem to be conflating the notion of a true curvature singularity (where "physics breaks down") with a mere coordinate singularity (like the event horizon of a Schwarzchild black hole in asymptotically flat spherical coordinates, or the north/south poles of the earth in latitude/longitude coordinates: there's an "infinitely stretched coordinate transformation" required to resolve the latter, too). Specifically, it sounds like you're worried about the coordinate transformation that's necessary to eliminate the infinity that shows up at the event horizon in "normal" spherical coordinates. But why should I think that those coordinates (which are optimized to describe the flat space infinitely far from the black hole) reflect any special physical "truth"? Just for instance, if you set up a local coordinate system based on the proper time and length as measured by a freely-falling infalling observer, there's no trace of any infinity in the coordinates or metric at the event horizon. And there's no coordinate-independent quantity in classical GR that diverges at the event horizon. This is why most physicists aren't worried about the event horizon being a meaningful singularity in classical GR.
Now, bringing in a semiclassical analysis (or presumably a full quantum analysis, if you've got one; also, call Stockholm) does lead to interesting effects related to the event horizon. But that has nothing to do with coordinate singularities in classical GR and everything to do with the causal structure of spacetime. (Personally, I do harbor some significant doubts about whether we should trust the classical description of the black hole interior once we have a full quantum theory, so I've been quite interested to see the recent firewall questions come up. But the arguments casting doubt on those conclusions are pretty strong, too.) But regardless of my hunches about what will be true in a "final" theory, semiclassical theory is really quite clearly in agreement with classical GR that a local observer won't see anything special as they cross the event horizon.