Re: Double counting gravitational potential energy

On Feb 23, 1:56 am, Jonathan Scott <jonathan_sc...@xxxxxxxxxxxx>
wrote:
I still think that there seems to be a valid alternative relativistic
way of looking at this situation which is that the clock rate change
(in the central case caused by its own potential, or in the two-object
case caused by the potential due to the other mass) should essentially
multiply the rest energy of the relevant object by a factor (1-Gm/
rc^2). I cannot see how to explain the factor of 2 difference between
this view and the total potential energy of the system (except of
course by my "energy in the field" suggestion mentioned previously,
which however doesn't seem to have an equivalent in the GR
interpretation).

I have a possibly relevant (possibly not!) comment that a number of GR
effects rely on both local time dilation effects (clock rate) and
global curvature effects. The bending of starlight by the sun is a
classic example, where each effect contributes equally. So maybe your
approach is not taking spatial curvature effects into account ? (eg,
when bringing mass in from infinity).

For example, suppose one has a universe containing a single straight
cosmic string, with mass per unit length mu. The metric is then
locally flat everywhere outside the string, but with an angle deficit
proportional to mu (i.e., in cylindrical polar coordinates, with the
string lying along the z-axis, the metric is the usual
ds^2 = dt^2 - dz^2 - dr^2 - r^2 (sin^2 theta) d theta^2,
but where theta only runs from 0 to 2pi - k mu). One can equivalently
throw away the z-dimension, and instead consider a particle of mass
proportional to mu in 2+1 GR, instead of the string in the usual 3+1
GR.

Now, if one brings in mass from infinity, thus increasing mu, no
clock rates change at all. The only change is in the global angle
deficit.

I'm not sure what a 'semi-Newtonian' approach looks like for 2+1 GR,
but the above suggests that some of the 'energy' in your 3+1 case may
be involved in global curvature effects. In particular, bringing in
mass from infinity doesn't just add to the mass already there, it also
bends space.

.

Relevant Pages

  • Re: A research
    ... Einstein stated that the mass of a star distorts light's path near it. ... Does that mean that gravity attracts electromagnetic waves? ... Yes--spacetime curvature effects the path of everything including ... Also all mass and energy (including photons) effects the ...
    (sci.physics)
  • Re: A research
    ... Einstein stated that the mass of a star distorts light's path near it. ... Yes--spacetime curvature effects the path of everything including ... Also all mass and energy (including photons) effects the ...
    (sci.physics)