Our sense of reality is utterly dependent on an inherent trust in our eyes. “Seeing is believing”, as the old dictum goes. We must be cautious, however, because our eyes are not always perfect windows of truth. Their Achilles’ heel? Optical illusions.

Optical illusions are common to everyday life. If we look across the ocean, the horizon appears to be the edge of a flat Earth. If we look at the sky after a sun shower, a multicolored arc appears to hover in the distance. There are some illusions, however, that may not be so familiar. In particular, Space Contraction and Time Dilation, the two space-time distortions predicted by the great Albert Einstein in his Special Theory of Relativity, have often gone unrecognized as optical illusions. Many popular scientific articles have published erroneous claims that Space Contraction and Time Dilation are real, tangible phenomena that alter the mechanics of our universe (Field, 1998). These oversimplified articles assert that as a man moves faster, he will shrink in length (Space Contraction) and he will age more slowly (Time Dilation). These, however, are incomplete and inaccurate statements, and they can easily mislead anyone who harbors too much trust in their eyes.

In April of 1998, physicist J.H. Field of the University of Geneve in Switzerland published a paper that explains these phenomena quite nicely. He specifically emphasized their illusory nature, making it clear that Special Relativity does not predict real length-altering and time-altering effects. In his paper, Field derived two “new” consequences of Special Relativity from Einstein’s equations. He called these the “Space Dilation” and “Time Contraction” effects. Field first juxtaposed his new Space Dilation effect with the classical Space Contraction effect to show that any change in the length of an object due to Special Relativity is illusory rather than real. He then did the same with Time Contraction and Time Dilation to show that time distortion is also an optical illusion. Field’s logic is so straightforward that it can be used to clarify any confusion over the issue of reality versus illusion in Special Relativity.

The first half of Field’s paper deals with length distortion. To discuss this, Field introduces a “new” type of object, which he calls a “Transient Luminous Object” (TLO). Field defines a TLO as any object that is illuminated for only a short, limited time span (imagine a quick camera flash illuminating an object in the dark) (Field, 1998). He claims that a moving object viewed in this manner will appear to be elongated, while one viewed with a continuous stream of light illuminating it (by say a spotlight) will appear to be contracted in length (Field, 1998). The elongated object is said to undergo this “new” effect that Field dubbed Space Dilation, whereas the contracted one undergoes Einstein’s Space Contraction.
Field stresses, however, that these two effects are only apparent. His logic is that it wouldn’t make sense for the real, tangible length of an object to depend on the manner in which it is viewed (Field, 1998). If this were so, then every mechanical device known to man would simply fall apart due to its own internal motion, which is obviously not so. You may be wondering, “Why, then, would the apparent lengths of these objects change?” To understand this, you first have to have an understanding of how people “view” objects.

The human eye works like a snapshot camera. Objects in 3-dimensional space (i.e., the universe around us) are only “seen” because they reflect particles of light (“photons”). The human eye “captures” these reflected photons and translates them to a 2-dimensional image of the object. This image may appear to be 3-D because of shading caused by differences in angles of the incoming photons, but in reality it is only 2-D. If you find this absurd, think about a 3-dimensional cube sketched on a piece of paper. It appears to have 3-dimensions even though it is only drawn on a 2-dimensional surface.
When the reflected photons of a moving Transient Luminous Object (TLO) and a moving continuously illuminated object are translated to a 2-dimensional snapshot by the human eye, two totally different images are produced in each instance (Field, 2000). According to Field, these images differ in their “resolutions”. Field’s TLO is said to be viewed under “coarse time resolution” because its motion only allows it to reflect back a limited amount of light (Field, 2000, 368). A moving object viewed under continuous illumination, however, is said to produce a “sharp resolution” image because it reflects back a steady stream of light (Field, 1998, 1). This explains why two identically moving objects could appear to be different depending on the manner in which they are viewed. The human eye is tricked into seeing two differently distorted images in each instance. Length distortion is not real; it is simply an optical illusion!
In addition to length distortion, the other aspect of Einstein’s theory that Field’s paper deals with is “time distortion”. In the second half of his paper, Field claims that the distortion in time of a moving object is, like the distortion in length, merely an “optical illusion” (Field, 1998, 31). He showed this through a simultaneous examination of the classical Time Dilation effect and his newly derived Time Contraction effect.

As an illustration, imagine that there is a physics student (we’ll call him “Ben”) standing on a railway platform. Then on the tracks, picture a linked train filled with synchronized clocks, one resting in each of the train’s carts. As the train chugs by the platform, Ben will observe that each individual clock that passes by him will appear to be ticking slowly (Field, 1998). This is Time Dilation, meaning that each second of train-time appears to be expanded (or “dilated”) over a long interval (perhaps 2 or 3 seconds). However, if Ben then tries to compare simultaneously the time in one of the carts that has already passed to that of a cart that is just about to pass, he will notice that time will appear to be ticking away faster for the latter (Field, 1998). Eventually (after enough carts have gone by), the train-time will appear to be running faster than that of the stationary platform (Field, 1998). This is Time Contraction, meaning that each second of train-time appears to be shortened (or “contracted”) into a smaller interval (perhaps a small fraction of a second).
Through similar logic used in examining the length distortions, Field deduced that because two opposite effects could be observed of identical clocks in motion, time distortion must also be illusionary. It just wouldn’t make sense for the real “speed of time” to depend on the viewing scenario (Field, 1998). Otherwise, Einstein’s theory would have unearthed a so-called “fountain of youth”. People would effectively be able to fight the aging process by altering their own bodily motions so as to generate a Time Dilation effect. As appealing as this may sound, Field concluded that this is not possible because time distortion is simply an optical illusion.

Again, you may be wondering “Why does this illusion occur?” Staying with the train-station analogy, what is actually happening is that the clocks at the front end of the train are being seen at an earlier time than those at the rear end (Field 1998). This may sound absurd because I originally said that Ben tries to observe them simultaneously. Although it appears to him that he is observing them simultaneously, in reality he is viewing them at different moments in time (Einstein 1961). According to Field, here is what is happening. The photons of light from each clock that Ben observes reach his eye at the same instant, so he believes that he is viewing each clock simultaneously. However, what Ben does not know is that the photons of light from the clock at the front end of the train must have departed at an earlier time than those from the clock at the rear end. This is a direct result of Einstein’s postulate that the speed of light is always constant (Einstein 1961). Since the photons departing from each of the clocks travel at the same constant speed, and because one clock is moving away from Ben while the other one is approaching him, the photons of light from each clock must have departed at different times for them to reach his eye at the same instant. So what Ben is really seeing simultaneously is each clock at a different moment in their past. His eyes, however, trick him into believing that the clocks are really ticking out of synch; it is yet another optical illusion!

Although optical illusions deceive the human eye on a daily basis, they do not obfuscate our picture of the world so long as we are aware of their existence. However, when popular science literature publishes falsified claims about what is real and what is illusion, then the general public’s outlook on reality is greatly distorted. This is particularly a problem when these claims seem to agree perfectly with what our eyes tell us. If we were to believe the countless assertions that Space Contraction and Time Dilation are the real effects that our eyes make them out to be, then we would remained puzzled as to why mechanical devices operate effectively or why people don’t take advantage of Einstein’s “fountain of youth”. Field’s logic has helped to shed light on this paradox, as he has implied that even when the oversimplified claims of an article agree with the world as our eyes perceive it, we still should not harbor too much trust in our vision. Seeing is not always believing.

References

Einstein, Albert.  1961.  Relativity.  Three Rivers Press, New York. 

Field, J.H.  1998. Space Time Measurements in Special Relativity.  University of Geneva preprint UGVA-DPNC 1998/04-176.  http://arxiv.org/abs/physics/9902048

Field, J.H. 2000.  Two novel special relativistic effects: Space dilation and time contraction.  American Journal of Physics Online 68.367.  http://ojps.aip.org/ajp/