On Wed, Dec 7, 2016 at 4:04 PM, Stephen A. Lawrence <sa...@pobox.com> 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. > 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 > > >
