The False Light of Day

Returning to the issue of urban population density (Hairbrain passim), it occurs to me that a major constraint on the nature of desirable habitation is the availability of light, and indeed a view, from outside. Unless one happens to be a troll, the absence of this link with the outdoors tends to make dwellings feel claustrophobic and unhealthy, with various adverse consequences. This constraint makes building underground - an otherwise appealing solution to the problems of overcrowding (consider the Earth's surface area to volume ratio), impractical.

Can we resolve this problem? ie, can we construct artifices capable of creating the illusion of depth, when such depth is in fact absent?

Artificial windows of sorts are commercially available ( http://www.theskyfactory.com/), but these tend to comprise merely a backlit photographic print; an improvement on unbroken concrete walls, but not convincing as real windows for more than a few moments.

Suitably framed and decorated mirrors have been used as artifical windows, but these are also a tad unconvincing when one sees one's own reflection in them. A suitably elaborate arrangement of mirrors can avoid this difficulty however, as well as creating a dramatic increase in the apparent depth of a space, using total internal reflection between suitably angled surfaces, see figure 1.


The arrangement demonstrated in figure 1 (a plan view of an arrangment of mirrors and foliage) effectively creates an 'infinity mirror' effect, but only, practically speaking, in a maximum of about 50% of the viewing area. Imaginative planting makes this limitation less obvious, but in practice, the real depth of a structure designed to create this depth illusion is at least 30 cm, and in any case, imaginative planting struggles to disguise the limited sky-line effect.


The most straightforward approach to simulating sky is probably to use an electroluminescently back-lit image lacking defined features on which the eye can focus and hence judge distance- a plain light-blue surface for example. An elaborate false window creating the illusion of a deep view of the outside can therefore be achieved in an actual depth of approximately 30 cm. A depth illusion incorporating both the 'infinity mirror' concept and electroluminescent back-lighting was constructed to test the principles thus far discussed, see figure 2:


Figure 2 (Electroluminescent back-lighting obscured by flash photography).

An alternative approach to this problem is the use of lenticular imaging to create the depth illusion in an actual depth measurable in millimetres. Lenticular images have been known for decades- essentially one uses a large array of parallel hemispherical cylinders to refract light reflecting from the image below them. Interlacing a multitude of images then creates a print which appears different depending on the angle from which it is viewed. Stereoscopic human vision then allows for an appearance of 3-dimensions. (http://en.wikipedia.org/wiki/Lenticular_printing). I have experimented with back-lit lenticular images, in conjunction with more traditional depth creating techniques to create a prototypical artifical window. However, the overall effect is not wholly convincing. (This may be in part due to the design of commercially available lenticular prints - apparent depth is limited, and the lenses only create the 3-D effect in one orientation). See figure 3.

Theoretically, it should be possible to project an entirely convincing image from a screen, simulating the view through an ordinary window. This is because vision is a passive detection system- the eyes receive light from a multitude of angles through the window, but does not contribute to the illumination in any way. An ordinary television screen emits light in a homogeneous fashion from each pixel- no depth information is conveyed. To duplicate the pattern of light emanating from a real window would require a screen possessed of hemispherical pixels, capable of emitting a different form of illumination depending on one's angle of observation. Unfortunately the resolution required to create a convincing visual effect from all angles may be beyond current technology.

Time is Pressing?

The black hole is a concept which fascinates- the density of a gravitational field becomes so great that it effectively forms a one-way membrane, an ‘event horizon’, from which, once engulfed, no information can ever escape, since the escape velocity of the singularity exceeds that of light. So the theory goes.

Consider, if you will, an astronaut piloting a spacecraft close to the speed of light. According to Einstein, (and repeated experimental verification), an object approaching the velocity of light increases in mass, from the perspective of an outside observer at a nominal ‘stationary point’ by a quantity M[1-(v^2/c^2)]^(-1/2), where M is the ‘rest mass’ of the spacecraft, v is the velocity of the spacecraft (relative to the ‘stationary’ observer) and c is the velocity of light. A moment’s consideration of this equation reveals that the mass of the spacecraft tends towards infinity as light speed is approached (relative to, and from the point of view of, the stationary observer).

Another peculiarity of General Relativity is that the spacecraft approaching light speed undergoes ‘Lorentz Contraction’, an apparent compression, as viewed from the point of view of the stationary observer, in the direction of motion. The length of the spacecraft as viewed by the stationary observer is then L[1-(v^2/c^2)]^(1/2), where L is the ‘rest length’ of the spacecraft. Length then, tends to zero, as velocity approaches that of light. The spacecraft’s dimensions perpendicular to the direction of relative motion are unaffected.

In summary then, as viewed by the ‘stationary’ observer, as the spacecraft approaches light-speed, it’s overall dimensions, and hence its volume, decreases, while its mass increases. A steady increase in mass and decline in volume necessarily equates to an increase in density- also tending to infinity. Inevitably then, the density of the spacecraft, as it accelerates, will reach the point that it finds itself inside its own event horizon, and is therefore a black hole, by definition. As such, no information from within the spacecraft can ever be communicated back to the wider Universe.

The ‘stationary observer’ whom we defined earlier however, is an arbitrary concept. One can just as easily define the pilot of the spacecraft as the stationary observer. In that case, from his perspective, he never moves, and the wider Universe appears to become contracted. The pilot may at any point decide to reverse thrust and reduce his velocity back to zero, relative to our previously defined ‘stationary observer’. In that case, he will apparently have gone from being a spacecraft, to being a black hole, back to being a spacecraft, conflicting with the notion that once formed, an event horizon can never communicate information back to the rest of us.

As long as one accepts that information lost to a black hole can never be retrieved, there appears to be a paradox.