Resource: Einstein's Special Theory of Relativity

Einstein's special theory of relativity is one of the greatest intellectual achievements in mathematical physics ever made. While difficult to grasp, with a basic knowledge of algebra and some careful thought, it is possible to attain a certain level of understanding of the subject and why it has had such a profound impact on our view of the physical world.

The first tenet of relativity is that the rules governing the way things move and interact are the same for two observers moving at constant velocity with respect to one another. An object can be in motion for one observer and at rest for another. But physical laws -- for instance, the ones that govern how things are put into motion -- must be the same.

At the time Einstein began work on relativity, mathematical theory, backed by experimental results, had already established that the speed of light was not dependent on the speed of its source. As a light-giving object -- say, a bicycle headlight -- moves toward you, the energy that collects on its surface lifts off the surface in the form of tiny interactive electric and magnetic fields. (This light can be conceived of as photons or as a localized bundle of electrical and magnetic fields carrying energy.) Once light breaks free from the material thing that gave birth to it, it flies off at a speed completely determined by its own internal electromagnetic processes -- that is, at a speed that does not depend at all on how (or whether) its source is moving.

Now, this property of light is a bit peculiar, especially considering our experience with normal, everyday projectiles. When an object is launched from a moving platform, it picks up the speed of its platform. Imagine pitching a baseball from a mound that is moving toward home plate at 50 miles per hour. That's one way to speed up your fastball! But if you were pitching light instead of a baseball, the moving mound wouldn't change the speed of your pitch. That is because the speed of light is constant.

Einstein took this peculiar phenomenon to the absolute limit of seriousness. He realized that time and space must be quite different from the way we normally think of them if the speeds of projectiles and their launch pads do not always add up the way we assumed they did. So Einstein conceived a new theory of time and space that showed, among many other things, that if speeds don't add up when one of the objects is moving at the speed of light, then they don't actually add up so simply even for slower-moving objects.

The steps Einstein took to develop his special theory of relativity are as follows: First, Einstein tried to understand what must be implied by the fact that light travels at a speed independent of its source. From this, he realized that time and space are not simply two unrelated concepts; rather, they must be linked in a space-time system whose properties appear most dramatically when objects move very fast and are observed by two different observers moving with respect to one another. His final and greatest step led him to discover and clarify mathematically many new things about the world that are important in each and every frame of reference.

In each and every frame of reference, there are relationships that hold because of the nature of space and time. If space and time were to be reconceived in a new interactive way, then other things, like momentum and energy, had to be reconceived, too. In fact, momentum and energy are linked like space and time. The famous equation E=mc² first emerged due to the newly understood properties of space and time. As you give a projectile more motional energy, its inertia, or resistance to acceleration, also increases. In other words, mass increases with energy. This equation also relates to all chemical and nuclear reactions that release radiation or thermal energy. It establishes that in a reaction that produces energy, the mass of the products will be less than the mass of the reactants, and the difference is related to the amount of energy produced.

Both jugglers see the clubs moving at the same speed. Why is this possible if one of them is moving and the other is standing still?

Why can't the two observers agree on when the lightning bolts hit the poles? (Consider the relationship between distance, time, and speed.)

Consider the implication that to an observer, the car would shrink to 44 percent of its length. How does this relate to both jugglers seeing the clubs moving at the same time?