Reference: RT104
Date: Nov-94
Author: Ray Tomes
Email: rtomes@kcbbs.gen.nz

The effect of gravity on photons has been dealt with by Einstein.
The normal terms such as acceleration are awkward when applied to
photons, and so I am defining a new variable, which I call PULL,
which has the same units as acceleration, and can be applied to
both photons and normal matter.  The advantage of this will then
be demonstrated for performing some calculations in areas not
previously explored.
                                                 1   dp
Definition:   PULL, symbol b, is defined as  b = - . --    (1)
                                                 m   dt
   where m = relativistic mass of object
         p = momentum of object
         t = time

The definition applies to any force, but in the following discussion
gravity in particular will be considered.

         g = acceleration of gravity

For NORMAL MATTER at NON-RELATIVISTIC speeds we may use p=mv
which, when substituted in (1) above simplifies as follows

       1   dp   1   d(mv)   m   dv
   b = - . -- = - . ----- = - . -- = a
       m   dt   m    dt     m   dt

For  normal matter at non-relativistic speeds in a gravitational
field,                        b = g       (2)

For PHOTONS there is a different result depending on the angle
between the photons path and the gravitational force.
For vertical photons, Einstein showed that

   d nu   nu g
   ---- = ----   and by applying  E = h nu and E = p c for photons
    dt      c

       1   dp   1    dE   h    d nu   h    nu g   Eg
   b = - . -- = -- . -- = -- . ---- = -- . ---- = -- = g
       m   dt   mc   dt   mc    dt    mc     c    E

That was a long winded way of showing that for vertical photons
the "pull" of gravity is      b = g       (3)

For horizontal photons however the effect is twice as much.
This was demonstrated by Einstein in the classic bending of
starlight by the sun during an eclipse, where the value he
predicted was twice the Newtonian prediction.  Experiment
proved Einstein right.

For horizontal photons therefore, the "pull" of gravity
is given by                   b = 2g      (4)

For angles between vertical and horizontal, the pull has values
between 1 and 2.  For photons with random directions, I believe
that the average value of the constant k in  b = kg  is k = 5/3.

For normal matter at relativistic speeds, the value of k also
changes from 1 at v=0 to 2 at v=c when v is horizontal.

I have never seen this expressed in any book, and yet it seems
a quite logical conclusion of relativity when expressed in terms
of the new definition of pull.  The fact that the effect of
gravity on random photons is different to the effect on normal
matter has, I believe, only escaped notice because we cannot
sensibly talk about the acceleration of photons.

The consequence of this constant k being 5/3 and not 1 will be
explored further, and found to explain several phenomena not
well understood previously.  I believe it can also explain
quite a few other seemingly unrelated things also.