In 1993, in an essay about
Science and Religion, I described a project regarding the possibility to build an invisibility
machine. On describing the details. I realized that some problems were insolvable, not only
because of technological limitations but also for physical reasons imposing theoretical and
possibly insurmountable limits. The project starts from the central idea that in order to make
an object invisible, it is necessary for an external observer looking in its direction to visually
stop noticing its presence. This can be done in the following way: A sphere is constructed,
and its whole external surface is covered with minute, high-resolution TV cameras and
monitors. Millions or even billions of cameras and monitors are to cover the whole sphere in
such a way that each monitor transmits the image captured by a camera located in the point
diametrically opposite to that monitor. The result will be as shown in the figure
below.
The image of the object (blue square) is captured by a camera located in point A,
which transmits the image to a monitor in point M. As a result, an observer in point 0 will see
the blue square as if there were nothing in front of him. In that way everything inside the
sphere will be invisible to the external observer. But this scheme presents two problems. One
of them be solved in theory while the other one is insolvable. I indicate those two problems
and explain why one of them can be solved but the other one
cannot.
The problem seems to be like a pinhole
camera. However there is an important condition that must apply.
The cameras must
only have a very narrow field of view (like looking down a pipe or an optical camera or
telescope with a large focal ratio). This will mean that each camera can only accept a small
cone of rays and so will only see a small part of the blue square or its surroundings. If this is
not the case you will simply get lots of tiny images of blue squares.
If you look at the
diagrams of the "invisibility" sphere and that of the pinhole camera you should notice that
they are very similar.
The centre point of the sphere through which all the lines joining
camera to monitor run takes the place of the pinhole in the pinhole camera.
Therefore
what the observer sees will be just the same as they would see if they were looking at the
screen at the back of a pinhole camera.
However since the surface on which the image
is viewed is convex the view of the square will be distorted round the edges although if the
square is small or at a large distance from the "invisibility sphere" this will not be noticeable.
The main and insoluble problem is that the image that the observer sees will be inverted
in just the same way as it is in a pinhole camera.
When viewed from a distance all
objects behind the invisibility sphere will be seen as if the sphere was not there but the will
be inverted. The presence of the sphere can be detected although it cannot be seen because
the surroundings will not be inverted. Imagine looking at a set of trees in a park. Some will be
inverted, the presence of the invisibility sphere, while all the surroundings will be the right
way up.
It's interesting to imagine what a very large sphere of this type would do if it
passed in front of the Moon. The Moon would still be visible and the black sky around would
still be a black sky. However the Moon's image would be inverted just as it is in an
astronomical telescope.
