On Thu, Feb 13, 2014 at 7:41 PM, Edgar L. Owen <[email protected]> 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 <[email protected]> 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 [email protected]. > To post to this group, send email to [email protected]. > 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
