Because the influence of special relativity is seen mostly at speeds near to that of light, its predictions seem to fly in the face of common sense. However, all of the predictions that have been able to be tested so far are reliable.

1) Length contraction: An object has a length l when measured by an inertial observer that sees the object as not moving. Another inertial observer, seeing that same object moving with speed v in a direction parallel to its length, reports that its length is l' = [1 - v²/c²]^1/2 l.

2) Time dilation: An inertial observer keeps track of the time between two events with his wristwatch and reports the time interval as T. Another inertial observer, moving with constant speed v relative to the first one, tracks the time between the same two events and reports it as T'. Further, he also looks at the first observer's watch through a telescope and says it is running slow. He finds that his T' = T/[1 - v²/c²]^1/2. (Even stranger, if the first observer looks through his telescope at the second observer's watch, he says that the second observer's watch is running slow in the same way!)

If length and time are not constant in special relativity, what is?

While Galilean relativity did away with the Aristotelian notion of absolute distance, it did retain absolute time. The loss of absolute time measure is a very troubling concept to us. But, Einstein's spacetime closely links measures of time and space together, so that it no longer is reasonable to consider them independently. In their place, Einstein offers a new measure called interval.

Interval, t = [t² - x²/c²]^1/2, is now the quantity that all inertial observers can agree on. The interval measured between a pair of events will have the same value according to all inertial observers in Einstein's spacetime. It is referred to as a Lorentz invariant.

3) Relative velocities (along the direction of relative motion): The idea of relative velocity we are accustomed to comes from Galilean relativity: If you are driving along in your car at 60 mph and a second car passes you moving 20 mph faster than you, their speed along the road is 80 mph. But, the same idea taken to relativistic speeds won't give an acceptable answer: If you are standing at the front of a spaceship moving at 0.5c and shine a flashlight out the front window (so that the light beam is moving at c away from you), then the light beam is moving at 1.5c in space.

But, all inertial observers see the light cone the same way in special relativity - which means that all light beams travel at c in empty space. The Galilean result of 1.5c cannot happen.

Instead, if one inertial observer sees an object moving with speed u, special relativity says that another inertial observer moving with speed v relative to the first (and in the same direction as the moving object) will say the object is moving with speed u' = (u - v)/[1-uv/c²]. In this way, the highest speed any object can have is c.

4) Equivalence of mass and energy: E = mc². Einstein's equation about the equivalence (and interchangeability) of mass and energy is actually a "by-product" when Newton's concepts of momentum and energy are altered to agree with the principles of special relativity.

In Newton's mechanics, the momentum of a system (or group) of objects is a conserved quantity. But, just as interval rather than distance is a conserved quantity in special relativity, so must Newton's idea of momentum conservation be altered.

The new form of Lorentz invariant energy is E² = p²c² + m₀²c⁴, where m₀ is the mass in the rest frame of the object (where it is not moving). This can also be written in the form E = mc² = gm₀c², where the object's mass m now changes from its rest value m₀ depending on its speed as viewed in the inertial frame where its energy and momentum are being evaluated. [Recall from the Lorentz transformation that g = 1/[1 - v²/c²]^1/2.]

Or, since mass and energy are equivalent, different inertial observers won't agree about an object's mass, any more than they agree on its size or the rate of its "clock." But with the relationships of special relativity in hand, all inertial observers will know how to "translate" their observations to compare with others.

This list of predictions is not nearly complete, but may tell you about some of the unique and non-intuitive results that come from logically following the one fundamental change that Einstein made - replacing the assumption of "absolute time" with universal agreement on the speed of light.