The development of special relativity gave rise to another problem in physics. According to Isaac Newton, and the accepted theory at the time, gravity was a force that was felt instantaneously. This means that the presence of mass sent the information of its presence across universal distances at a speed faster than light. According to special relativity, this was simply not allowed.

Newton’s theory of gravity fell short on one other point as well. Though it defined the effects of gravity superbly, it did not actually describe what gravity was. In his book, he left his readers to figure that out.

Again, Albert Einstein stepped in to solve this problem. He realized that an object in the presence of a gravitational force is no different than an object experiencing accelerated motion. In other words, if you were trapped in a box you would have no way of knowing whether you were on earth, or accelerating through a vacuum at 9.8 m/s2. This realization eventually lead him to the conclusion that matter warps the fabric of spacetime. I will explain what this means a bit later, however for now it is important to know that Einstein’s conclusion solved the problem of the instantaneous gravitational effect, and also described exactly what gravity is. Let’s try and examine some of the logic Einstein used to come to his conclusion based on what we know about special relativity.

For the following set up, it is important to know that any object in circular motion is constantly accelerating. Though its angular speed may be the same, its linear velocity is constantly changing due to a change in the direction of its motion. If you have ever been inside a twister ride, it may be easier for you to follow this example. For those that haven’t, the twister ride basically has many people inside it. Once the ride starts, it picks up angular speed. The people inside feel an outward push, and are eventually pinned to the wall. If the ride were suspended in a vacuum, this would basically act as gravity. The wall could be considered the floor.

To see the curving of space we must examine the circumference and radius of the ride while in motion. From above, we know that the length of an object in motion will contract in the direction of its motion. Therefore, the circumference will contract while the ride is on. However, since the radius of the ride does not move in the direction of the motion, it does not contract. How is it possible for one radius to produce a circle with two different circumferences? Well, in Euclidean geometry, it’s not. However, if we assume that space curves during acceleration, and assume that it is not flat during the ride as Euclidean geometry would have us believe, then this is possible. For instance, a circle with radius r on a sheet of paper will not have the same circumference as a circle with radius r drawn on a sphere.

We know that an object in the presence of a massive body and a body in accelerated motion are practically the same thing. Knowing this, Einstein postulated that mass, which causes gravity, warps space around it. Imagine stretching a bed sheet out by its four corners. Now, imagine placing a bowling ball in the center. Just as the bowling ball warps the fabric of the bed sheet around it, a massive body warps the fabric of the cosmos around it. From this example, we can see that many of the conclusions derived from general relativity match Newton’s observations. The further out you get from a massive body, the less space is warped. Also, the more massive a body, the more space is warped. This agrees with Newton’s findings. Einstein’s theory takes Newton’s theory one step further. It defines exactly what gravity is: the bending of spacetime. Also, Einstein’s theory conforms to the rules of special relativity. Gravity’s effect is no longer instantaneous.

How exactly does a satellite stay in orbit? Imagine the same setup as before except this time add a ping pong ball. Assuming that the bed sheet is frictionless, if you give the ball a sufficient speed inside the depression created by the bowling ball, the ping pong ball will continue to endlessly orbit the bowling ball. If the ball had no initial velocity, it would fall into the bowling ball just as expected.

There are a couple of pitfalls to this example, however. In the case of the bowling ball, it is due to the force of gravity that the bed sheet is bent. This is not the case when considering the effects of mass on space. The mass itself warps the space around it. It does not require the presence of an outside force for assistance. Secondly, when considering the ping pong ball, it is again the force of gravity which is keeping the ping pong ball in orbit rather than having it fly away on a tangent. This is not the case for a satellite orbiting a star or a planet. Rather, the satellite takes the path of least resistance. Warped space causes these paths to be curved. Keeping these facts in mind, the bowling ball analogy is perfectly acceptable to help visualize the concept of the curving of space.

The above example gives a concept of the warping of space. I can’t think of an acceptable analogy that will convey the warping of time. However, know that acceleration, and gravity, do cause time to warp. The greater the magnitude of one’s acceleration, the slower time passes. In other words, time moves slower in Houston than in Denver, albeit the difference being far too small to measure. However, in the presence of a sufficiently massive body the warping of time could be easily observed. Near the event horizon [2] of a black hole, time could conceivably be 10,000 times slower than here on Earth.