No useful information can be transmitted FTL.
Nice change.
What change?
Earth's gravity, denoted by g, refers to the attractive force that the Earth exerts on objects on or near its surface (or, more generally, objects anywhere in the Earth's vicinity).
As useful as the equivalence between gravitational and inertial effect might be, it does not constitute a complete theory of gravity. Notably, it cannot answer the following simple question: what keeps the people on the other side of the world from falling off? We might be able to explain gravity near our location on the Earth's surface as a fictitious force – as due to the fact that we have chosen a reference frame that is not in free fall. But a freely falling reference frame on our side of the Earth cannot explain why the people on the opposite side of the Earth experience a gravitational pull in the opposite direction.
A more subtle manifestation of the same effect involves two bodies that are falling side by side towards the Earth. In a reference frame that is in free fall alongside these bodies, they appear to hover weightlessly – but not completely so: after all, if you look more closely, these bodies are not falling in the same direction, but towards the same point in space: the Earth's center of gravity. Because of this, there is a minute component of motion bringing the two bodies ever closer to each other (see the image at right).
Whenever bodies fall in different directions or at different rates due to differences in the strength and direction of gravitational forces, we are dealing with what are called tidal effects (since such differences in force are also responsible for the tides in the Earth's oceans). The equivalence between inertia and gravity cannot explain these tidal effects – it cannot explain the variation of the gravitational field from location to location.[9]
How to recognize fictitious forces / accelerated reference frames
So, suppose we observe things moving in a way which suggests that forces are acting on them. How can we tell whether we are in an inertial reference frame, and the forces we observe are real, or whether we are in an accelerated reference frame, and the forces we observe are "fictitious"? The answer lies in the Force Law, which specifies that the acceleration which an object receives depends not only on the force acting on it, but also on its own mass, or inertia, or resistance to a change in its motion. For real forces, there is no guarantee that the force acting on the object and the mass of the object will produce a particular acceleration. The acceleration could be large or small, for a given force, depending upon how much inertia the object has. For fictitious forces, all objects seem to be accelerated in the same way, which means that the force acting on the objects seems to be directly proportional to the inertia of the object. Things that have little inertia seem to have little force acting on them, and things that have a lot of inertia seem to have a lot of force acting on them.
In mathematical terms, real forces Freal acting on different masses m will produce varying accelerations a, according to the rule
Freal = m a
where a could have any value, while fictitious forces Ffictitious acting on different masses will all produce the same acceleration aconstant, according to the rule
Ffictitious = m aconstant
So if we see different objects moving with different accelerations, at least some of those accelerations, and the forces causing them, must be real; whereas if we see different objects moving with the same acceleration, the accelerations are probably not real, but a mirror-image of an acceleration of the reference frame, and forces required to explain them are "fictitious".
Is Gravity A Fictitious Force?
There is one situation in which we see accelerations which are the same, and presume that the forces causing those accelerations are real -- namely, when we see objects falling toward the Earth, under the influence of gravity. No matter what the objects are made of, or how big or small they are, all objects fall under the influence of gravity with exactly the same acceleration, the acceleration of gravity. Solids, liquids, gases, green cheese, moonbeams, fairy dust and horsefeathers would all fall the same under the influence of gravity, as would sand grains, pebbles, boulders, mountains, moons and planets. Because of this we write the Force Law in a special way for the force of gravity, replacing the force F with the object's weight W, and the acceleration a with the acceleration of gravity, g, thusly
W = m g
The fact that gravity, like fictitious forces, involves a constant acceleration, makes us wonder whether gravity could be a fictitious force. It's hard to imagine that anything so pervasive and seemingly real could be "fictitious", but the forces experienced by the person in the accelerated car feel real, and are presumably fictitious. Is there some way that we could create the phenomenon of gravity, without the force?
There is indeed such a way. Suppose that you were in a rocket ship, headed upwards at the acceleration of gravity, so that anything not attached to the ship seems to "fall" with a mirror image of that upward acceleration. Then every such object would fall toward the back of the ship, at the acceleration of gravity, and trying to stop such a fall would require a force, in the direction of the acceleration, proportional to the object's mass, which would be equal to, and appear to be, its real weight.
Of course, we can't explain gravity in that way, as that would require every part of the Earth to be accelerating upward and outward, which would make the Earth bigger and bigger, which is not observed. So the simplest explanation is to assume that, peculiar though it may be, gravity -- although a perfectly real force -- acts as though it is a fictitious force. No other real force is known to act in this way, but perhaps gravity is "special", and it is merely a coincidence that it looks like a fictitious force.
The strange and in some ways disturbing answer to this supposition is that the phenomenon of gravity (the fact that things fall, and have weight) is real, but the force of gravity, as described by Newton, is not a real force, but a fictitious force. According to Einstein's General Theory of Relativity, gravity is a curvature of space-time such that in the future, things are closer together than they are now, even if they are moving in straight, parallel lines, with no force between them. For in curved space-time, there is no such thing as a straight line, but instead, only curved lines, called geodesics, which are the straightest possible paths in curved space-time, but are always and inexorably curved. (for now, see the chapter on black holes and general relativity in the text for a more detailed discussion) And since curved paths, in our experience, require some centripetal force to create them, the motion of things along geodesics seems to require some force to explain the acceleration observed, as a result of that curvature.
So we see things falling, with an acceleration which we call the acceleration of gravity, and thinking that we live in a straight-line, uniformly moving or stationary inertial reference frame, we attribute that acceleration to a force, the force of gravity. Whereas in reality, objects falling toward the Earth are moving along geodesic paths, with no acceleration, and according to a modified version of the Law of Inertia (objects which are at rest tend to remain at rest, and objects which are moving tend to move along geodesic paths with uniform motion, unless some force acts on them), have no force acting on them. They fall simply because the curved space-time near the Earth makes it natural for them to be closer to us in the future, than they are now.
But if no force is required to make them fall, why do they seem to have weight, when we hold them? In Newton's physics, the weight we perceive is a direct measure of the force of gravity acting on them. How can they have weight, if there is no force acting on them?
The answer is, that if we are holding them, there is a force acting on them, namely the upward force we are exerting, which keeps them from doing what they are supposed to do, namely fall. And of course that upward force on the object we're holding creates a reaction force, which is downward and equal to the upward force we are exerting, and that is what we are observing, when we observe that something has weight. In fact, even when we perceive our own weight, that is what we are observing. Whatever is keeping us from falling is pushing us upward, with a force equal to our "weight", and what we think is our weight, pushing downward, is just a reaction to that upward push. If there weren't anything pushing us upward -- if, for example, we were to jump off the top of the D building -- we would feel no upward force, and would therefore feel "weightless". We would presume that we weren't really weightless, because the ground is rapidly rising to meet us, but that isn't because we have weight, but because it is natural, in the absence of a force preventing it, for us to fall toward the Earth, along a space-time geodesic. (splat conveying the distinct notion that there's some force around here, somewhere, Einstein's Theory or not)