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2. Photon absorption by electrical charges is the 4D equivalent to
mass particles falling into 5D black holes
Very close to the charge the 4D electromagnetic field dimensions will be curved in a
similar way as the 5D gravity dimensions are curved nearby a massive object,
causing the slowdown of any spatial coordinate speed of photons. Since the photon's speed
c in 3D is equivalent to the speed c of mass particles in 4D
(see Section 3 in [2] ) one
may assume that there will also be an equivalent mathematical expression for it.
If we bluntly replace mass by charge in the math this results in the following speed components expressed as a
function of the radial coordinate distance r to the charge
in a flat 4D coordinate system as used by an observer at infinity (note that
this is just an example formula; the exact formula must be
determined empirically):
One Coulomb of charge would thus slow down the photon's velocity
in space for about 1% at a distance of about 10-5m.
So far, no such effect was ever recorded through experiment but putting a net
charge of one Coulomb in such a tiny volume is a challenge on its own and may
very well prohibit an easy setup of such an experiment. The force involved would
be in the order of 2x1019 N!
The next section shows that the parallels between photon
absorption and mass particle absorption can be extended to the emission process
in black holes too.
In Euclidean relativity, the velocity
vector of any particle has constant magnitude c. When a mass particle approaches
the Schwarzschild radius of a black hole along a geodesic path, its velocity vector
is subject to a 3-dimensional rotation, eventually fully rotating to the axis of
x5, leading to a zero velocity in both space and proper time. In a way,
the particle "teams up" with the black hole's velocity c
in x5 (see Section 3 in [2]
). So we talk here about 5-velocity rather than 4-velocity.
The animation shows the three different speed components of a mass particle that falls radially to a black
hole from infinity with zero starting velocity in space. The speed components
are expressed as a function of the radial coordinate distance r in
a flat 5D coordinate system as used by an observer at infinity:
5D velocity vector and speed components of an object falling radially towards a black hole
The absorption of a photon by an electrical charge also involves a rotation of the photon's velocity vector.
This time it rotates into the
4th dimension, leading to a full stop in 3D at the moment it reaches the charge. A
trajectory close by the charge leads to a slowdown of its velocity in space.
So again, the photon's velocity "teams up" with the charge that, in
rest, has 4-velocity c in x4 (which is
the proper-time dimension in Euclidean relativity).
Although this may seem an explanation of why light slows down in a medium, this is not
the primary reason. The slowdown in a medium can be explained quite well in terms of the
electromagnetic interaction between the fields inside the medium and the
electromagnetic fields of the photon, leading to an only apparent slowing
down [1]. The description above should therefore seek a different physical
justification and the effect probably only takes place at distances that are extremely close to the
charge.
4D velocity vector and speed components of a photon being absorbed by an electrical charge
Next: 3. 5D Perspective Up:
Fractal Universe Previous:
1. Positive and negative charges
© Copyright 2004-2008 R.F.J. van Linden
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