Imagine you're in a spacecraft travelling at a constant velocity. You'd be floating around pushing yourself off the walls, doing somersaults and playing games with globules of water. Now imagine that I magic up a planet beneath you, and you start falling towards it. You're still weightless, you don't feel the force of gravity, and you wouldn't notice any change in direction unless you looked out of the window. In a way you're not really accelerating - the Principle of Equivalence compares true acceleration with the force you feel when you're standing on the ground, not with the free-fall situation. You continue to fall in an arc towards the planet, then with a snap of my fingers I make the planet go away, and you continue travelling in a new direction. We can repeat this scenario with a smaller denser planet that provides a more intense gravitational field, so tightening the curve, but at no point will you be thrown around like in a swerving car. You don't feel a thing, because you're in free-fall all the time. When we replace the planet with an artificially-generated gravitational field, you end up making sharp turns without being mashed against the inside of your spaceship. Thus you defy inertia. If we employ an artificially-generated gravitational field in opposition to the Earth's, you defy gravity too.
It's important to appreciate here that when Einstein came up with General Relativity in 1916 he was talking about the equations of motion, not curved spacetime. Curved spacetime was popularised by Robert H. Dicke in the sixties, and it's the effect, not the cause. To understand this, think in terms of a boating lake, where I've dumped a truckload of gelatine powder all down the left hand side. You wind up a clockwork boat and send it beetling up the lake, and you notice it veers over to the left. That's because there's a viscosity gradient from left to right. The boat represents a photon, and the path of the boat represents curved spacetime. But the cause of that curved path, is a gradient in space. It's actually a gradient in vacuum impedance Z0 = √(μ0/ε0) wherein the speed of light is c = √(1/ε0μ0). The speed of light varies, and that's why light curves and why things fall down. If you've ever heard of pair production you'll know that a photon can be employed to make an electron and a positron. The electron exhibits spin and angular momentum, and you can think of it as a clockwork boat with the rudder jammed hard over. Wind it up and set it down on the boating lake, and it goes round and round in circles. But whenever it's heading up or down the lake, it's veering slightly over to the left because of the viscosity gradient. Hence it works its way over to the left hand side. It really is like this, and surprisingly, it goes all the way back to Newton. If you've got a copy of Opticks, check out queries 20, 21, and 30, and what you read is this:
"Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer? ... Are not gross bodies and light convertible into one another?"
Even more surprising is the fact that Einstein talked about the variable speed of light. See chapter 22 of Relativity: The Special and General Theory. What you read is this:
"In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)".
Einstein didn't actually use the word velocity. He spoke German, and the word he used was geschwindigkeit. It means both speed and velocity, and since the postulate of special relativity was the constant speed of light, this is Einstein telling us the speed of light varies, and that's why things fall down. UFOs don't fall down, and they aren't riding on reaction thrust like a rocket, or winging it on deflected airflow like an aircraft. Instead they're using antigravity. They can generate a gravitational field and use it to turn corners or to oppose the earth's gravitational field. It might sound like science fiction, but it's simple. It's like there's a little man in your clockwork boat throwing jello bombs into the water to make the boat veer to the right. You've even seen a form of antigravity already. It's called diamagnetic levitation. The pyrolytic carbon floating above the magnets isn't a magnet, and it doesn't fall down:
Images by Splarka, see http://en.wikipedia.org/wiki/Diamagnetism
Note however that this operates via the "helicopter" principle, which is a little clunky. There's a far more elegant "dirigible" principle which gets right down to the fundamentals of electrodynamics. It goes back to Maxwell and Faraday, but there's a nice example in Minkowski's wrench. Take a look at his Space and Time paper, and two pages from the end, there's this:
"Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis; the most perspicious way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete".
This analogy is saying an electric field is a "twist field", and if you move through it or it moves through you, you see a magnetic field, which is a "turn field". This is why we have generators and dynamos, and the right-hand rule:
Image by Rnkv2, see http://en.wikipedia.org/wiki/Right-hand-rule
To understand this, think of a single electron. It exhibits a spherical electric field. Now think of a string of electrons arranged in a vertical line. The electric field is cylindrical. Now move down the line of electrons, and you see this electric field as a magnetic field. It's the same when the electrons move past you as per the current going up the wire. For some real hands-on intuitive grasp, find a drill-bit or a reamer which exhibits a twist. Grip it in your right hand, put your left thumb on the bottom of it, and push upwards. It turns. The electric field doesn't create the magnetic field, it's the same thing. That's why it's the electromagnetic field. People say it's fundamental, but it isn't fundamental enough, because you create electrons with their electromagnetic field via pair production. You started with a photon, and to get right down to the true fundamentals we have to look at a photon more closely. It exhibits a sinusoidal electromagnetic field variation like this:
Image by Heron reproduced under the terms of the GNU FDL, see http://en.wikipedia.org/wiki/Light
Whilst the positive and negative field variation means there's no charge, it does tell us that there's current going first one way then the other. It's alternating current, which is why impedance Z0 = √(μ0/ε0) applies. Since the photon conveys energy, and since the dimensionality of energy is pressure x volume, the photon's sinusoidal field-variation is giving us the shape of a pressure pulse propagating through space at c.
It's essentially a spacewarp, akin to a lemon, in that the twist rises to a maximum a quarter-way along its length, and then goes to zero at the midpoint, then to a maximum the other way, and finally back to zero. The pressure "conditions" the surrounding space, the electromagnetic field is where the squares are twisted out of true, and the gravitational field is the surrounding pressure gradient. The pressure alters permittivity ε0 which is "twistability", and also the permeability μ0, the reciprocal of which is "turnability". In essence it makes space stronger. At the fundamental level, gravity is the result of a gradient in vacuum impedance wherein the speed of light c = √(1/ε0μ0) is subject to a similar gradient. Gravity doesn't cause the gravitational time dilation that reduces the non-local speed of light. That's back to front. We use the motion of light to calibrate our clocks. It's the gradient in the speed of light that causes gravity. And it's energy that causes the gradient in the speed of light. It's a little like the rubber-sheet analogy. Get rid of the bowling ball and tie a knot in the rubber sheet instead. The knot represents the matter/energy of a planet, and surrounding it is a tension gradient. Now turn the rubber sheet into a rubber block, and flip things around so it's under pressure rather than tension. The planet is creating a pressure gradient in the surrounding space. As an aside, there's also a gradient in the relative strength of electromagnetic force versus the strong force, as demonstrated by the fact that the fine structure constant is a "running" constant. This means that gravity itself is an exhibition of the unification of the forces. The irony is delicious.
So how do we actually make a pressure gradient? It's actually very simple, we do it every day. Radio engineers know all about it. It's the "near field", the region close to a transmitter. It's what's called an evanescent wave. It's a standing wave, like a bow wave on a boat or a bridge pier. There's even one in your kitchen, in your microwave cooker. But that's too small, and is merely a by-product. Instead of throwing out a signal and dissipating most of the power in an outgoing pressure pulse, we need to keep it there and pump it up. Whilst the magnetron in your microwave is like blowing a whistle, what we want to do is blow up a balloon. That's why it's akin to a dirigible. We need to pump up the pressure and let the gradient counteract the earth's gravitational field. We need radio wavelengths for this, because the near-field region is typically half a wavelength in extent. And we need some power. We're probably talking big current and big voltage, so I don't feel like messing around in my garage. To get the ball rolling we lean a short-wave HRS antenna on its side, we set a hosepipe flowing and watch the arc of water. Once we've got something basic going, we then figure out how to handle it so we can do a fast inflation then swing round the gradient to turn on a sixpence. There's doubtless lessons already learned from radar here. Magnetrons are used in radar, along with considerable computing power. We need to turn that computing power around to set the pulse location duration and intensity instead of decoding a signal. Then we ramp things up a little. Think medium wave. Think long wave.
Of course, there is no free lunch. Think back to that circling clockwork boat working its way over to the left-hand-side of the lake. Only half the cycle is ever heading up or down the lake, which is why matter is affected only half as much as light. But more to the point, once it's over on the left hand side, the boat is circling more slowly. Some of the circling motion was converted into lateral motion, and in similar vein the kinetic energy of a falling body comes from the falling body itself. Forgetting about air resistance, a falling body will hit the earth at 11 km/s. That's a lot of kinetic energy, and it's been bled out of the body itself by virtue of the reducing c. Assuming you've caught the body and cooled it down, its total energy is now less than that of the original body in free space. And if we use antigravity to lift that body, we aren't putting any energy back. Lift it too far, too fast, and every atom of that body is going to go cold. We're talking deep cold here, limb-shattering cold. So we'll have to take care. But it won't get in our way, not now we know how simple it all is. Not now we can see what pair production was telling us all along. Not now we can see what was always there in special relativity: electrons are made of light, along with protons, and our rods and clocks. We are made of light. That's why we always measure the local speed of light to be the same.
A cold wind's been blowing, but now the future is bright. Does anybody know anybody with a few radio and radar engineers on the staff? And who's up for a trip to Mars? After that we won't be reaching for Mars any more. I look up to the night sky and feel another shiver. Because we'll be reaching for the stars.