Let us now perform another level-set. So far, we recognize and accept the obvious existence of matter within the Universe. Furthermore, as E=mc2 tells us, whether any unit of matter happens to take the form of energy or mass does not subtract from its overall qualification (or quantification) as matter. In other words, mass and energy are interchangeable; they are only different forms of matter. Of course, this is not to suggest that switching between these two states is a trivial thing - far from it, but that is a topic for another day.
Next, we know that empty space isn't exactly empty. Meaning, in a very real sense, there is a spacetime fabric that can be coerced into forming gravity wells, or producing other observable effects such as gravitational lensing. Gravity wells then, are constructed of spacetime itself; they do not fall within the realms of matter, but have identifiable characteristics nonetheless.
Given that gravity is the curvature of spacetime caused by the presence of mass, it will be useful for us to understand how much force is required to bend it. How rigid is the spacetime fabric?
This calls for another analogy.
At the Lakeview Museum of Arts and Science in Peoria Illinois, there is a partial model of the sun, which is 36 feet in diameter. Scale models of all the planets of our Solar System are then distributed across the region at distances relative to where they would appear if the sun were actually that size. Together, this model of the sun and planets form an enormous scale-model of the Solar System.
In this model, the earth is roughly the size of a small grapefruit (4 inches in diameter), and 3/4 of a mile away from the sun. Pluto, on the other hand, is only the size of a golf ball, and 40 miles away. Of course, we know that there are many Kuiper Belt objects that are much farther away from the sun than Pluto, but they are not depicted in the model (as far as I know).
This model does a great job of bringing the true size of the Solar System into perspective. Even so, it is amazing for reasons far beyond the simple sizes and distances involved. To see how, we must quickly dispense with a commonly held misconception about gravity.
When we observe videos of astronauts in space, it is easy to get the impression that there is no gravity in space at all; that somehow, once astronauts pass above the atmosphere of the earth, gravity is no longer present. But, that is not true at all. Any satellite in orbit (even living ones like astronauts) stay aloft only by striking a correct balance of orbital velocity and distance from the earth. This relationship between velocity, distance and mass is spelled out in Kepler's Third Law of Planetary Motion.
For example, if we could somehow reach into space and slow the velocity of the International Space Station to zero (relative to the surface of the earth), leaving it hanging momentarily in space with no forward momentum, it would fall like a rock. Interestingly, it wouldn't even burn up in the atmosphere on its way to earth, it would simply fall (although it may pick up enough speed before encountering the atmosphere to heat up quite a bit once it did).
Amazingly, this same principle applies even to the earth's orbit around the sun. If the earth's velocity around the sun could somehow be stopped, the earth would plunge into the sun like a meteor. The same goes for any other planet in our Solar System - even one as far away from the sun as Pluto.
Returning to the earlier illustration of rolling a marble around the inner surface of a bowl, this would be like simply setting the marble on the edge of the bowl and letting it roll directly towards the center.
Next, we know that empty space isn't exactly empty. Meaning, in a very real sense, there is a spacetime fabric that can be coerced into forming gravity wells, or producing other observable effects such as gravitational lensing. Gravity wells then, are constructed of spacetime itself; they do not fall within the realms of matter, but have identifiable characteristics nonetheless.
General Relativity actually predicts Embedding Diagrams rather than Gravity Wells, but intimates that gravity is an effect of the curvature of spacetime nonetheless. This distinction is actually quite important, but will not become entirely relevant to this discussion until we reach much finer details later in the series.If we entertain the notion that galactic Gravity Wells may predate the matter within them, it does not necessarily mean that the two cannot be connected in some way. In fact, it seems likely that the two will prove to be closely related (more on this later), given that they usually seem to occur together (galactic gravity wells are usually filled with stars and other matter). To understand this connection, we must take a moment to consider the rigidity of space.
Given that gravity is the curvature of spacetime caused by the presence of mass, it will be useful for us to understand how much force is required to bend it. How rigid is the spacetime fabric?
This calls for another analogy.
At the Lakeview Museum of Arts and Science in Peoria Illinois, there is a partial model of the sun, which is 36 feet in diameter. Scale models of all the planets of our Solar System are then distributed across the region at distances relative to where they would appear if the sun were actually that size. Together, this model of the sun and planets form an enormous scale-model of the Solar System.
In this model, the earth is roughly the size of a small grapefruit (4 inches in diameter), and 3/4 of a mile away from the sun. Pluto, on the other hand, is only the size of a golf ball, and 40 miles away. Of course, we know that there are many Kuiper Belt objects that are much farther away from the sun than Pluto, but they are not depicted in the model (as far as I know).
This model does a great job of bringing the true size of the Solar System into perspective. Even so, it is amazing for reasons far beyond the simple sizes and distances involved. To see how, we must quickly dispense with a commonly held misconception about gravity.
When we observe videos of astronauts in space, it is easy to get the impression that there is no gravity in space at all; that somehow, once astronauts pass above the atmosphere of the earth, gravity is no longer present. But, that is not true at all. Any satellite in orbit (even living ones like astronauts) stay aloft only by striking a correct balance of orbital velocity and distance from the earth. This relationship between velocity, distance and mass is spelled out in Kepler's Third Law of Planetary Motion.
For example, if we could somehow reach into space and slow the velocity of the International Space Station to zero (relative to the surface of the earth), leaving it hanging momentarily in space with no forward momentum, it would fall like a rock. Interestingly, it wouldn't even burn up in the atmosphere on its way to earth, it would simply fall (although it may pick up enough speed before encountering the atmosphere to heat up quite a bit once it did).
Amazingly, this same principle applies even to the earth's orbit around the sun. If the earth's velocity around the sun could somehow be stopped, the earth would plunge into the sun like a meteor. The same goes for any other planet in our Solar System - even one as far away from the sun as Pluto.
Returning to the earlier illustration of rolling a marble around the inner surface of a bowl, this would be like simply setting the marble on the edge of the bowl and letting it roll directly towards the center.