Well, how does one hope to create a true picture of a tree from a shadow? Adding these supposed hidden dimensions is an exercise in guessing.
Interestingly, the idea that what we observe might be a shadow of a higher dimensional reality provides an instructive way of looking at the physical shortening of material objects with increasing speed. We are told that measuring rods, and all other objects are, in the frame of reference of an outside observer, shortened in the direction of motion, and that this shortening becomes significant as the speed of travel approaches “c”. If we assume that these measuring rods are on a spacecraft, the occupants of the craft would not observe the shortening; only observers in a F of R that was stationary relative to the craft would see it.
A fairly straightforward way to visualise how this apparently contradictory situation can arise is to try a simple experiment. Shine a light on a plain wall. Hold a twelve inch ruler (any length will do, but we will stick to twelve inches for this example) between the light source and the wall in such a way that the wall and ruler are parallel. The shadow of the ruler, which is a two-dimensional representation of a three-dimensional object, is the same length as the ruler. Now, if you alter the angle of the ruler with respect to the wall, the ruler remains twelve inches long, but the shadow becomes shorter as you rotate the ruler. As the person holding the ruler, you will always be able to measure it as being twelve inches long. This puts you in the place of the on-board observer. Someone who could see only the shadow would measure it as being shorter, and her measurement would be accurate too, she would be in the position of the outside observer.
If you were a flatlander, the shadow would be all that you would ever be able to see, the shortening would be a reality in your frame of reference. All that your world would contain would be a line that was, somehow, able to vary its length. Only by reference to a higher dimensional world, one which was out of your reach, would you be able to find an explanation for the behaviour of this line.
This must, surely, point towards the possibility that relativistic effects could be explained with reference to higher dimensions.
