On Wed, Feb 19, 2014 at 12:42 PM, John Clark <johnkcl...@gmail.com> wrote:
> > > > > There is no sense in which an observer in an accelerating elevator in >> the flat spacetime of special relativity could correctly conclude that >> spacetime has any "curvature" >> > > What you say is true but only according to Einstein's 1905 Special > Relativity because that theory says nothing about gravity and only deals > with special cases, objects in uniform motion; that's why it's called > "special". > It's true that SR says nothing about gravity, but incorrect that it deals only with "objects in uniform motion". Special relativity can handle acceleration just fine too, either by analyzing it in the context of an inertial frame, or by using a non-inertial coordinate system like Rindler coordinates. See for example this section of the Usenet Physics FAQ, hosted on the site of physicist John Baez: http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html "It is a common misconception that Special Relativity cannot handle accelerating objects or accelerating reference frames. It is claimed that general relativity is required because special relativity only applies to inertial frames. This is not true. Special relativity treats accelerating frames differently from inertial frames but can still deal with them. Accelerating objects can be dealt with without even calling upon accelerating frames." Are you claiming the above is incorrect? > > > If you could never tell experimentally if spacetime was curved or not then > the very idea of curved spacetime would become an idea as as useless as the > concept of the luminiferous aether. > I didn't say in the post you're responding to that "you could never tell experimentally if spacetime was curved or not", I said you couldn't tell *if* you were only measuring the laws of physics to the first order, and *if* were only measuring in an infinitesimally small region, both of which are conditions for the equivalence principle to apply (as mentioned in the references I provided at https://groups.google.com/d/msg/everything-list/xOpw-X9J2MY/wTDTy1Dr7s4J ). I said specifically that the guy in the elevator *could* measure curvature if he wasn't restricted in such ways: "In fact the observer inside the elevator should have ways of measuring curvature if he can measure second-order effects, or if the size of the elevator is taken as non-infinitesimal, and in either case he could definitely conclude that spacetime was *not* curved within an elevator accelerating in flat SR spacetime". > But you can tell. Pick any 3 points inside that sealed elevator. Place a > Laser pointer at each of the 3 points and form a triangle with the light > beams. Measure the 3 angles of the triangle in degrees. Add up the 3 > measurements. If the sum comes out to be exactly 180 then you know that the > spacetime within your sealed elevator is flat. > Do you have any reference for the idea that this is a valid way to measure spacetime curvature in general relativity? According to a poster at http://www.physicsforums.com/showthread.php?t=454705 who I've found to be quite knowledgeable on the subject of GR, "To measure actual curvature, rather than 'non inertial motion through spacetime', J.L. Synge has a proof in his book on GR that you need a minimum of 5 points. He then defines an idealized 5 point curvature detector. I don't know how easy it is to get this book, but I don't really want to type in the whole discussion. It is fun though - he even carries it out to producing ideal rods, trying to arrange them in a certain way, and the last one minutely fails to fit if there is actual curvature." Presumably this is referring to the section on p. 408 of "Relativity: The General Theory" which you can see a brief excerpt of here: http://books.google.com/books?id=CqoNAQAAIAAJ&focus=searchwithinvolume&q=detector I would also guess that one of the conditions needed for building a valid curvature detector would be that all the components are in free-fall, though without having that section of the book available I can't verify that this is true for the one suggested by Synge. 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.
