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 General Relativity
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Basis:
Acceleration
Einstein continued working in all three fields explored in his 1905 papers and made important contributions to other fields, but he increasingly sought to expand special relativity to include the effects of acceleration. He found the key to this problem in principle of equivalence, by which gravitational mass (mass related to having a gravitational field) is indistinguishable from inertial mass (mass of accelerating in empty space). This means that there is no difference between the effects of standing on Earth and accelerating at approximately 9.8 meters per second squared.

His theory, now known as the General Theory of Relativity, was published in late 1915. He later said of the labor behind devising this remarkable theory

The years of anxious searching in the dark, with their intense longing, their alternations of confidence and exhaustion, and the final emergence into light--only those who have experienced it can understand that.

Spacetime
In the universe of relativity, space and time were no longer separate entities but rather different aspects of a four-dimensional continuum called space-time. Although space and time as separate entities are relative, space-time is absolute. It's a little difficult to picture a four-dimensional continuum considering we live in a three-dimensional universe, but don't worry. You don't need to know what it looks like to know how it works. Just imagine an ordinary coordinate system with the three normal space coordinates (x-, y-, and z-) with an extra coordinate for time.

While special relativity was primarily concerned with submicroscopic physics, general relativity was concerned with the macroscopic effects of gravitation, the realm of astrophysics and cosmology. The gravitational field equations were similar to Maxwell's equations in that they remained in the same form in all equivalent frames of reference. This property of the field equations effectively predicted the observed perihelion motion of Mercury. Einstein's original form of General Relativity has been verified many times since it's conception. In 1916 Einstein expanded his Special Theory to include the effect of gravitation on the shape of space and the flow of time. This theory proposed that matter causes space to curve.

Hyperspace
Here we go with the extra dimensions again. "How can space curve?," you might ask. Well, imagine the surface of a sphere (a ball-shaped object). The surface itself is two-dimensional (flat and thin like a piece of paper with two possible directions to go, horizontal and vertical), right? But it's curved around a three-dimensional space, the shape of the sphere. The same thing happens with three-dimensional space, only it curves into a higher-dimensional hyperspace. This hyperspace contains extra dimensions of space (specifically, six), not to be confused with the time dimension of space-time. Of course, we can't see the extra dimensions. Imagine two dimensional creatures living on the surface of the sphere. They go about, doing their daily business, totally unaware that their world is bent into the third dimension, but even if they knew, they couldn't see it. All they see are flat shapes and lines, just like all we see are flat images. Of course, the different images from our two eyes give our brains a sense of depth, but our field of vision is two-dimensional, like a movie screen.

Curvature
Now that we've established the concept of hyperspace, lets find out how this curvature works. The two dimensional beings could discover that their world was warped into the third dimension by moving continuously around the sphere. Eventually, they'll be back where they started. Knowing that they could never end up back where they started by going in one direction along a perfectly flat two-dimensional surface (like the top of a table that extends forever), they conclude that their world is imbedded in a three-dimensional space.

In our three-dimensional world, Newton's first law of motion says that objects that are moving in a straight line tend to stay moving in a straight line, without outside influence, that is. But as we know, a massive objects possesses a mysterious force called "gravity" that draws other objects towards it. Einstein had a different way of looking at this so-called "gravity." Instead having a force, large objects warp the space around them, thus drawing smaller objects towards them.

An easy way to illustrate this effect is by using embedding diagrams. Let's picture a large, stretched rubber sheet. Now, let's put a very massive object, let's say, a large iron ball, on it. The weight warps the rubber sheet, so a smaller object, like a ball bearing, will roll towards the weight when placed on the sheet. We have to remember, though, that this embedding diagram does not represent our ordinary space. It is just a model that shows the curvature of our space in comprehendible terms. In Einstein's universe, a very massive object, like a star, warps the space around it, making smaller objects, like planets, move towards it. This explains why the planets move in ellipses around the Sun instead of just going straight.

Gravity and Time
The equations of General Relativity also predict another interesting effect: gravitational time dilation . Einstein first dwelled upon this idea that gravity affects time (or at least the measurement of time) in 1908, before General Relativity was completed. This may sound daunting, but it simply means the slowing down or "dilation" of time by gravity. Because of space and time's fundamental connection, the distortions caused by very massive objects change both space and time. Thus, at the same time that the warped spacetime alters the paths of objects in its vicinity, it also changes the time.

The gravitational field of Earth creates a very small dilation (time goes slower near the Earth's surface than far up above the atmosphere), but it is too small to be perceived. However, time is monstrously dilated near an extremely massive object...like a black hole .

Now, lets try a little theoretical experiment to show the effects of a black hole's enormous gravity on the flow of time. A small spaceship decelerates near the vicinity of a black hole...an astronaut, whose name happens to be Jimmy, disembarks from the ship on a suicide mission into the ominous, yawning black portal to the end of the universe...and beyond. While our courageous friend takes that one-way flight to oblivion, he's going to help us with our experiment. On his way to the edge of the black hole, Jimmy sends out a signal, which happens to be a white light, at a defined rate, once a second, as defined by an atomic clock that he carries with him. As Jimmy nears the black hole, the astronauts back in the spaceship notice two things: more and more time elapses between the signal pulses, and the light will be shifted increasingly towards the red end of the spectrum.

In his paper on the photoelectric effect, Einstein used the description of light as particles, stating that the energy of each photon is proportional to the frequency. Since the redshifting of the signal given off by Jimmy means that the frequency of the light is decreasing from the other astronaut's point of view, it follows that the photons are losing energy. But where did the energy go? The gravity of the black hole pulls photons--and all other particles--down just like weights pull you down, so the particles need energy to escape it. But since light cannot slow down from the strain of gravity, it must lose energy by decreasing its frequency.

Although it is the weakest, gravity is the only fundamental force that acts at a distance. In fact, it can act at any distance. This means that every body in the universe feels the force of every other body. So, the black hole has really been slowing down Jimmy's atomic clock since before he even left Earth, but not by any measurable amount. The time that the clock measures moves smoothly and increasingly slowly as he nears the black hole, slowing down more and more as he gets closer and closer.

After the publication of Einstein's Theory of General Relativity, many experiments were carried out to test its predictions. These predictions were derived from the mathematical representation of Einstein's theory, which is a set of formulas known as the Einstein Field Equations.

Because General Relativity was meant to accommodate all possible situations, describing all the ways space and time are changing at a given point, the mathematics behind it are extremely tedious and difficult. The theory is based upon ten "coupled hyperbolic-elliptic nonlinear partial differential equations." And yes, it is as complicated as it sounds. This problem of calculation was so serious that all but the most brilliant of theoretical physicists did not dare attempt to understand, and it was impossible for even them to solve for all but the simplest scenarios. Alas, the General Theory had to wait for technology (in the form of powerful supercomputers) to catch up with it.

Luckily, we can use General Theory of Relativity without solving all the complicated math. General Relativity was tested in many ways, one of the most significant of which was finding real-world examples.

An important prediction of General Relativity was that like matter, light is also bent by the warped spacetime by a massive body, an effect now know as gravitational lensing. And what better body to test it on, thought scientists, than our own sun? Of course, that wasn't as simple as it sounds. In order to observe this effect, one would have to see the bent starlight behind the sun, but the sun's glare usually obscures it. This does not happen, however, during a solar eclipse. So, scientists finally got to witness General Relativity in action during the solar eclipse of 1919. An eminent English physicist, Sir Arthur Eddington, and a group of British scientists observed the eclipse carefully. They found that light from the Hyades star cluster, whose position is very well documented, was indeed bent by the exact amount Einstein's equations predicted.

Of course, the sun's comparatively feeble gravitational field only produced a small gravitational lensing effect. Close to a gravitational giant like a black hole, the stars behind it would look like concentric rings (circles with the same center) of light!

This confirmation of General Relativity brought Einstein instant fame.

Gravitons
Over the years, many tests of General Relativity have been carried out, and the theory has held out very well, but there is one prediction that has never been confirmed: gravity waves. The theory predicts gravitational disturbances, such as a stellar collision or supernova, should produce ripples in spacetime in the form of gravitational waves, or gravitons, using the particle model of radiation. We have many sensors that detect electromagnetic waves, but gravity waves? That would be a difficult task indeed, but a great challenge for the next generation of scientists.