On Thu, Feb 13, 2014 at 7:41 PM, Edgar L. Owen <edgaro...@att.net> wrote:
> Jesse, Brent, Liz, et al, > > Free fall in a gravitational field is NOT acceleration. Standing on the > surface of the earth IS acceleration because only then is the acceleration > of gravity felt as such. > Yes, that's why I equated inertial motion in flat spacetime with freefall in a gravitational field--"Bob" could be either one in my example. I also equated accelerated motion in flat spacetime with non-freefall in a gravitational field--"Alice" could be either one in my example, note where I said she'd observe the same thing "regardless of whether she's accelerating through Bob's region in flat spacetime, or passing through his region because he's in free-fall while she is not (say, she's standing on a platform resting on a pole embedded in the Earth below, while Bob falls past her)." > Now imagine that elevator is enormous, the size of a planet (but assume > also in this thought experiment that it has no mass and thus has no > gravitational effect). > The equivalence principle simply doesn't apply to large regions of space where tidal forces can be observed, mathematically it only applies in the infinitesimal neighborhood of a point in spacetime, though in practice if your measuring instruments aren't too precise a reasonably small space like an elevator should be OK (at least in the Earth's gravitational field--in the gravitational field of a black hole even an elevator would be too large because there'd be a significant tidal force between the top and bottom). See the discussion about how tidal forces spoil any attempt to make the equivalence principle work in a non-infinitesimal region at http://www.einstein-online.info/spotlights/equivalence_principle Jesse > On Thursday, February 13, 2014 2:02:15 PM UTC-5, jessem wrote: >> >> >> >> On Thu, Feb 13, 2014 at 12:22 PM, Edgar L. Owen <edga...@att.net> wrote: >> >>> All, >>> >>> By the Principle of Equivalence acceleration is equivalent to >>> gravitation. >>> >> >> Too vague. A more precise statement is that in an observer in free-fall >> in a gravitational field can define a "local inertial frame" in an >> infinitesimally small neighborhood of spacetime around them, and that if >> the laws of physics are expressed in the coordinates of this frame, they >> will look just like the corresponding equations in flat SR spacetime, >> though only in the first-order approximation to the equations (i.e. >> eliminating all derivatives beyond the first derivatives). See for example: >> http://books.google.com/books?id=ZfMWbQB2dLIC&lpg=PP1&pg=PA52 and >> http://books.google.com/books?id=95Frgz-grhgC&lpg=PP1&pg=PA481 and >> http://books.google.com/books?id=jjBMw0KFtZgC&lpg=PP1&pg=PA5 >> >> Even though the curvature disappears in the first order terms, it remains >> in the higher order terms, whereas curvature is really zero in all terms >> for an accelerating observer in flat spacetime. So, the answer to your >> question is that acceleration does not in itself cause spacetime curvature, >> SR can handle acceleration just fine as discussed at >> http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html , >> but this isn't a violation of the equivalence principle since the >> mathematical formulation of the principle deals only with first-order terms. >> >> Jesse >> >> >> -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
