Einstein's Relativity has opened up whole new worlds of knowledge for the human race. However, the general consensus, that it is the end-all, be-all of physical theory is far from accurate. Einstein himself knew that the theories were incomplete, and even riddled with paradox, if one but knew where to look.
To illustrate, let us emulate the Master and conduct a thought experiment:
In the theory of Special Relativity, Einstein pictured himself riding on a train, moving at incredibly high speeds. He envisioned himself staring at a mirror when the train reached the speed of light threshold. He considered that, should his image suddenly vanish from the mirror, he would be able to deduce his speed from this change, without any other outside information. He found this result to be unacceptable - but the only way to fix it was to presume that the speed of light is constant for all observers.
Now, Einstein had a strong basis for this presumption. The Lorentz transformation was already a well-known effect, and translating it into Relativity Theory seemed perfectly reasonable. In fact, with out it, Relativity would look quite different. Despite that, it is that effect, the concept of spatial and temporal dilation, that leads us to our own thought experiment.
Imagine yourself on Einstein's train, traveling, let's say, at 80% of the speed of light. Looking at a mirror in front of you - in the direction of travel - you can't tell whether you are standing still or in motion. Certainly, from an outside perspective, the light is traveling to the mirror at a meager 20% of the speed of light (cumulatively), but its return trip is accelerated to 180% of the speed of light, causing it to average out.
For the moment, let's forget about the fact that mirrors don't reflect radio waves well, which is what the light waves would be to the mirror, from that outside perspective, when they made contact. If we did consider it, we'd have the light reflecting back for the person inside, and passing right through the mirror for the observing person outside. Obviously, this would lead to an inevitable paradox.
Add into the equation another mirror positioned to your side, so that it faces perpendicular to the direction of travel. Because you should not be able to determine your velocity based on your own reflection, these two images should remain in perfect sync. However, using Einstein's own inferences, we can see that they do not.
Ironically, this sort of setup uses exactly the same principle that was meant to prove the existence of the Aether at the turn of the 20th Century, but ended up proving the opposite. A beam of light was forked into two, sent to perpendicular mirrors, and then rejoined so that the interference might be measured, thus proving a sum velocity in one direction through the Aether. Of course, no interference was measured, but the experimenters did not have Einstein's spatial dilation in their arsenal at the time.
Now, since, for you, the mirrors retain their original positions (the train car is seemingly at rest), spatial dilation does not alter your perceptions of the dimension of the car, as it does for the outside observer. To you, the mirrors are equidistant. From outside, the forward mirror is much closer to you.
Now, looking in the side mirror, you see your reflection as always. For you, the light reflecting off your face speeds to the mirror, bounces off, and is reflected back all as perfectly normal. For the outside observer, the light must travel at an angle, to account for the shift in your position. This is the basis for Einstein's time dilation.
However, focusing entirely on your perspective for a moment, as Relativity requires that you be unable to determine your own velocity, suppose you were to focus your gaze on a point between the two mirrors, so as to watch both of your reflections at once. The light returning from the forward mirror has a simple back-and-forth travel against the velocity of the train. The light from the side mirror must travel at an angle to return to you, even though you cannot tell that it is also a simple back-and-forth reflection.
This is an exactly analogous situation to the famed 'two swimmers' experiment, which was also the basis of the Aether experiment. Suppose each of your reflections represents a swimmer, and the train's velocity is the velocity of a river's flow. One swimmer travels 100 meters upstream and back, while the other swims 100 meters across the river, to the far shore, then back again.
If both swimmers swim at 4 m/s (your constant view of the speed of light), and the river flows at 2 m/s, then the first swimmer, the one moving in line with the current will travel at 6 m/s to the point where he turns around, then 2 m/s on the way back, for an average velocity of 4 m/s. The second swimmer will, in order to maintain his line of travel, have to swim against the current, in part, both ways (this represents the light moving in a straight line from your view, but at an angle from outside). Because of that, this swimmer will average only 3 m/s both ways.
And therein lies the conundrum. The light from the first mirror, even without the added benefit of spatial dilation, will always arrive before the light from the second. This is not in spite of the constancy of the speed of light, but because of it. Careful examination will reveal that were any other behavior were to take place, your constant view of light's speed would be compromised.
Because the light from the forward mirror will always arrive first, you'd see a slightly different image on either mirror. More precisely, there would be a slight time delay between the two reflected images. Dilation cannot account for this, as space is altered only in the direction of travel. Obviously, one cannot envision a facing-based time dilation, as that would result in you, the person in the car, measuring two different times at once, depending on which way you were facing, which is also illogical, and far less realistic.
No matter what happens, or how the theory is modified to compensate, there will be some sort of inescapable discrepancy between the forward and side directions. Because of that, you will be able to determine that you are in motion, and, with careful timing, even be able to calculate your own velocity.
Relativity's premise of your being unable to determine that you are in motion unfailingly leads to conditions that allow you to determine that you are in motion. It seems old Albert was quite the paradoxalog after all.
A simpler situation involves two space travelers. One at rest, the other moving away at the speed of light. If a single photon passes them by, moving in the direction of the speeding astronaut's line of travel, and they both must measure the speed of the photon as the speed of light, relative to each of them, then it quickly becomes apparent that the single photon will have to be in two places at once, depending on who is looking at it. For the one at speed, it will shoot ahead, because it is moving at the speed of light, relative to him. For the one at rest, it will keep pace with the speeding astronaut, because it is moving at the speed of light relative to him.
Now, there are all manner of complications dealing with this idea, such as the concept of simultaneity, which Einstein addressed, but, to keep it simple, the basic fact is that the photon must become bi-locational. Technically, Quantum Physics allows this, but where does one draw the line at absurdity? Suppose there are ten astronauts, all moving at increasing intervals of 10% of the speed of light. Now, the photon is in ten places at once!
It quickly becomes apparent that if we pursue this reasoning to its inevitable conclusion, that single photon must occupy the whole of the universe at the same time. To make the problem even more obvious, replace the photon with Jupiter.
Clearly, Relativity still has a few kinks to be worked out. Or, from another perspective, whole new worlds, as yet untouched by human minds, to be explored.