The theory of General Relativity, originally postulated by Albert Einstein (shown here in one of his gently pensive moments during his later years when overwhelmed with a desire to find a theory of unification), rests on two main hypotheses:
The theory of General Relativity, originally postulated by Albert Einstein (shown here in one of his gently pensive moments during his later years when overwhelmed with a desire to find a theory of unification), rests on two main hypotheses:
1) Gravitating matter distorts the space-time in its vicinity, causing it to become curved. The curvature depends on the distribution of mass.
2) The world lines of all freely falling bodies (including light rays) are geodesics in space-time.
WHOA!!!
Um, what's a geodesic? Moreover, what do you mean with this compound word, "spacetime??" Define "gravitating matter," please...
Let's start with gravitating matter:
The earth is an example of gravitating matter. Any object that has mass exerts a force of gravity upon its own mass and any mass nearby. This force expands out radially from the center of mass and is most easily pictured when we stand on the earth. Gravity holds us onto the earth because it is more massive than we are. Greater bodies of mass have stronger gravitational forces. Thus any massive body (massive as in "having mass" not as in gargantuan) is a gravitating mass. Lesser masses gravitate towards its center of mass.
How about spacetime?
Spacetime is the name given to a 4-dimensional universe, the fourth being time. More complex general relativity uses up to seven dimensions, but that is not necessary for our purposes. The idea of spacetime is that space is 3-dimensional and only exists over an interval of time. The force of gravity associated with a massive object actually distorts the spacetime around it. This causes spacetime to curve towards the mass! This image is a two-dimensional representation of the warped spacetime around a massive object. The more massive the object, the deeper the well of spacetime. When the object is so massive that it becomes a black hole (when the force of gravity is too strong to allow even light to escape), then the well ends in what is called a singularity. A singularity is the point where mass density and the length of a time interval reach infinity. Thus the well is infinitely deep because if time is stretching to infinity you can never reach the bottom! Creepy.
Geodesic sure is a cool word, but what does it mean?
A geodesic is a straight line in curved space. What?? Okay. A simple visualization involves merely the lines of longitude on the earth. Right at the equator, two lines will appear parallel. Following each line independently over small increments of distance, the lines both seem to stay completely straight. If you follow the lines all the way to one of the poles, however, they will actually meet. Thus in curved space parallel lines can cross!! What does this look like? If you drop two objects onto the earth from a certain distance apart (but the same height from the ground) the paths they follow lead to the very center of the earth. Thus apparently parallel paths to the ground are actually approaching each other along a curve. In curved spacetime, objects are drawn to a center of mass along the most direct curve possible--the geodesic.
There were three main tests that were used to prove The Theory of General Relativity:
1) Mercury's Perihelion Orbit
Mercury follows a highly elliptical orbital path around the sun. It is called "perihelion" because the nearest point to the sun shifts a tiny bit with each successive orbit. Newton's theories about gravitation couldn't quite account for the total amount of this discrepancy, he was off by about 43 arcseconds. Einstein, however, by using the idea that the spacetime around the sun is curved proportionally to its mass, predicted the additional shift of Mercury's orbit EXACTLY. Wow. That guy was brilliant.
2) Gravitational Lensing
If the spacetime around massive bodies is warped, then objects passing nearby said massive object and through the warped spacetime ought to experience some sort of effect due to this warping. One such object is light. As light passes by massive stars in the universe it should actually bend around these centers of mass, following the curve of spacetime. It is called "lensing" because as light curves around a mass it is actually focused into discrete points of light just as a glass lens focuses light. As you can see in the diagram to the right, the light from a single quasar is bent around a galaxy towards the earth so if we trace the light paths straight back they appear to come from two different sources.
This image to the left was taken with the Hubble Space Telescope. It shows what gravitational lensing actually looks like. Click on the image for more information.
3) Gravitational Redshift
The electromagnetic spectrum goes from high energy, high frequency, short wavelength gamma rays down to low energy, low frequency radio waves with long wavelengths. Redshift is a term used for one aspect of the Doppler Effect. The Doppler Effect describes what happens to waves as the source moves towards or away from the listener or viewer. As waves come towards you, imagine them becoming slightly compressed as they are pressed forward. This causes the wavelength to shrink and move slightly toward the gamma ray end of the spectrum.
This is called a blueshift because higher frequency light is on the blue end of the visible spectrum. Redshift is the opposite effect. As a wave source moves away from you the wavelength is slightly stretched and thus moves toward the red end of the spectrum. Graviatational Redshift is the idea that light leaving a massive body has to fight against a gravitaitonal field and thus loses energy. Lower energy means longer wavelengths which moves the light towards the redder end of the spectrum. This has actually been tested. The definitive experiment was conducted at Harvard in 1959 by Robert Pound and G. A. Rebka. They directed gamma rays down a 22.6 meter shaft and were able to detect a change in frequency of only 2.5 parts per 1000 trillion! This even miniscule amount was, however, in direct accord with the theoretical calculations they were trying to validate.
The most important prediction today is the concept of gravitational waves. The idea is that if the distribution of the mass of a highly massive object changes at a high rate, ripples will propagate outwards through spacetime. These waves are intrinsically different from electromagnetic waves. Electromagnetic waves move through the medium of space. Gravitational waves, however, move spacetime itself. Also, gravitational waves cannot be scattered or reflected by different objects the way electromagnetic waves can. Instead their paths are diverted if they encounter other massive objects whose warped spacetime interferes with their own.
There are a number of ongoing projects designed to test the implications of General Relativity. The majority of these experiments focus on detecting the still theoretical gravitational waves predicted by Einstein's theory. The other experiments take different angles and aim to verify gravitational redshift and the existence and effects of the curvature of spacetime around massive bodies.
A word to the wise: be careful with this topic. It is easy to convince yourself that general relativity is a magical, metaphysical topic with the promise of unlimited energy and the key to infinite survival of the human race. This is not the case. An excellent example of the misuse of general relativity is the story of the tachyon. It is easy to be misled because the topic demands the mind to visualize more dimensions that it is used to and essentially throw out ingrained assumptions about the world around us. Once we enter the realm of topics that are difficult to imagine it is easy to imagine ideas and solutions that are not real. Therefore I implore that when you are embarking upon the heavy task of understanding general relativity that you use accurate resources, like the ones i've compiled here, and go talk to your local physicist.