This is how I understand the "elevator". It is_infinitely_ small. It encloses a single point in space rather than region of space so it is impossible to detect tidal variations from inside the elevator. If the elevator is allowed to have finite dimensions so that tidal variations are detectable then the equivalence principle ceases to have any theoretical significance and can be ignored or discarded.
Harry On Fri, Dec 9, 2016 at 5:02 PM, Stephen A. Lawrence <[email protected]> wrote: > > > On 12/09/2016 01:54 PM, H LV wrote: > > > > On Wed, Dec 7, 2016 at 4:04 PM, Stephen A. Lawrence <[email protected]> > wrote: > >> Well known result -- gravitational time dilation has to do with the >> gravitational potential, not the strength of the field. >> >> > GR's principle of equivalence depends on the concept of a force and not > on the concept of a potential. > A person in an elevator without windows can only detect either the > presence or an absence of a force. > > > A person in an elevator also can't detect redshift or blueshift of light > moving into or out of the elevator, because they are restricted to making > measurements *inside the elevator*. Gravitational time dilation is a > non-local effect, detectable only by comparing the results of measurements > at highly separated points. The elevator metaphor doesn't have anything to > do with it. In fact there is *no* time dilation of any sort associated > with either acceleration or a strong local G-field. > > On the other hand a person in an elevator *can* tell whether there's a > gravitational field present, by checking for tidal effects, which are IIRC > linear in the spatial dimension and hence detectable even at small scales. > That breaks the "elevator=gravity" correspondence, as real gravitational > fields *always* exhibit tidal effects. (Constructed fields which result > from funniness at a domain boundary don't show tidal effects but they're > also not real.) > > Don't confuse explanations using a metaphor with actual reasoning about > the results. The elevator is a metaphor, useful in looking for general > principles, but imperfect in detail. The drop-a-rock-down-a-well > experiment, on the other hand, can in principle be quantified, and in the > absence of gravitational redshift which depends on the potential, it > results in a violation of CoE. In fact it, or a simple variation on it, is > what led to the concept of gravitational redshift to begin with, or so I've > read. > > > > > >> Simple gedanken: Drop a rock through a slender shaft into a spherical >> hollow cut out of the center of a spherical planet. The rock has more >> kinetic energy when it gets to the center of the planet. >> >> Turn the rock (along with its kinetic energy) into photons, and beam them >> back up the shaft. At the top of the shaft, catch the beam and turn it >> back into a rock. >> >> The rock must have the same mass at the end as it had to start with (or >> something's very wrong), which is smaller than the mass it had at the >> bottom of the shaft (due its additional kinetic energy which shows up as a >> mass excess). This can only be true if the beam of light was *redder* >> at the top of the shaft than the bottom. So, there must have been a >> gravitational red-shift as the light climbed the shaft. >> >> So, the *frequency* of the light at the top of the shaft must be *lower* >> than the frequency at the bottom of the shaft. >> >> But the *total number of wave crests* in the beam of light can't >> change. (You can count them, using appropriate equipment; in that sense >> they behave like marbles.) A certain number of wave crests in the beam >> entered the shaft at the bottom; the same number of wave crests must have >> come out the top. >> >> So, if the *frequency* measured by an observer at the top of the shaft >> is *lower* than the frequency measured at the bottom of the shaft, the >> wave crests must have taken more time to exit the top of the shaft than >> they took to enter the bottom of the shaft, and so, >> >> *time must be passing faster for the observer at the top of the shaft. * >> > > The experiment is different in that it doesn't involve an exchange of > mass or energy between the surface and the interior. > > Harry > > > >> On 12/07/2016 12:53 AM, H LV wrote: >> >> According to the shell theorem the gravitational force on a test mass >> inside a hollow sphere is every where zero. This paper argues that this >> situation is not equivalent from the standpoint of General Relativity to >> the situation where gravity falls to zero far outside the sphere. They >> conclude that General Relativity predicts that a clock located inside a >> hollow sphere should run slower than a clock located outside the hollow >> sphere. (By contrast most people are familiar with the fact that General >> relativity predicts a clock should run faster as the force of gravity >> approaches zero far from a gravitational body) This could provide a >> laboratory test of Newtonian gravity which predicts that both clocks should >> run at the same rate. >> >> >> https://arxiv.org/pdf/1203.4428.pdf >> >> >> Harry >> >> >> > >
