Natural Science Forum / Physics / Research / August 2008

Interestingly, the effect on light is intuitively obvious; treating
light as a wave we can see that if there is 'more space' closer to the
gravitating mass (or, alternatively, light travels slower closer to the
mass in terms of flat space coordinates) light will bend towards the
mass.

Here's how I look at it:

Suppose we make a massless box with mirrors on the inside, and fill it
with light, then place it in a region of curved spacetime near a
gravitating mass.  We can see that light travelling from side to side
will get bent by the spatial curvature, and will cause a net downward
pressure on the mirrors (because it bends towards the mass).  

We can also see that the blue-shifted light reflecting from the bottom
of the box will apply more downward pressure than the red-shifted light
reflecting from the top applies pressure upward.

So our box of light will experience a net attraction towards the
gravitating mass.

In point of fact, our mirrored box is not such a bad model of matter -
it's reasonable to imagine that all matter can ultimately be described
in terms of massless[*] particles of some kind held in a bound state.  
The mirrored box is a very literal embodiment of this.

- Gerry Quinn

[*]Assuming mass is not fundamental, then it must ultimately derive from
the interactions of massless entities.

Thus spake J. B. Wood <wood@itd.nrl.navy.mil>

I think a better analogy is that of a map of the surface of the earth
(indeed this is the basis of the mathematical description of curved
spacetime). We understand that the surface is curved because the scale
factor of the map varies from point to point (as described by the metric
in the form of the line element).

Applying the above idea to space-time, in any given map (more precisely,
chart) the rate of time varies from point to point.

A fairly direct way to see that this affects energy (and hence force) is
to think of the effect on a wave function. (a little naughty, because we
don't actually have a consistent quantum gravity, but directly
measurable classically in the case of light). Changing rate of time
implies changing frequency, hence changing energy.

This was the argument Einstein originally found for curvature in the
equivalence principle in 1907. He initially showed, from sr, that a
constantly accelerating reference frame would require changes in clock
speed depending on position wrt the observers clock.

It took some while to put this into a mathematical theory, and it tends
to be a bit lost in modern mathematical treatments of gtr. I have made
it central in my treatment at

http://www.teleconnection.info/rqg/MainIndex

See, in particular, for the conceptual background, and for a graphical
demonstration of the equivalence between constant acceleration and
changing rate of clocks wrt position

http://www.teleconnection.info/rqg/BasicsOfCurvature
http://www.teleconnection.info/rqg/TheEquivalencePrinciple

Regards

Interestingly, the effect on light is intuitively obvious; treating
light as a wave we can see that if there is 'more space' closer to the
gravitating mass (or, alternatively, light travels slower closer to the
mass in terms of flat space coordinates) light will bend towards the
mass.

Here's how I look at it:

Suppose we make a massless box with mirrors on the inside, and fill it
with light, then place it in a region of curved spacetime near a
gravitating mass.  We can see that light travelling from side to side
will get bent by the spatial curvature, and will cause a net downward
pressure on the mirrors (because it bends towards the mass).

We can also see that the blue-shifted light reflecting from the bottom
of the box will apply more downward pressure than the red-shifted light
reflecting from the top applies pressure upward.

So our box of light will experience a net attraction towards the
gravitating mass.

In point of fact, our mirrored box is not such a bad model of matter -
it's reasonable to imagine that all matter can ultimately be described
in terms of massless[*] particles of some kind held in a bound state.
The mirrored box is a very literal embodiment of this.

- Gerry Quinn

[*]Assuming mass is not fundamental, then it must ultimately derive from
the interactions of massless entities.