In 1675 the Danish astronomer Olaus Roemer noticed that eclipses of Jupiter's satellites are delayed by a few minutes when Jupiter is far from Earth, and occur a few minutes early when Jupiter is closer. This is due to the time it takes light to travel.
Modern measurements tell us that the Speed of light is c ~ 300,000 km/s
This is NOT the way material objects behave. Consider a gun firing a bullet with speed v. Now put the gun on a fast train, moving with speed u. What is the speed of the bullet to someone inside the train? Why, just the speed of the bullet relative to the gun, or v. What about to someone on the ground? Well, it is the SUM of the speed of the bullet with respect to the gun, and the speed of the gun with respect to the ground! The speed of the bullet as seen by someone on the ground is v + u (assuming the gun is fired towards the front of a forward-moving train). The two observers do NOT see the same bullet speed!
Light is different. No matter how fast you move relative to the source of the light, when it reaches you, it is always moving with the same speed (c).
c = constant has a basis in both theory and experimentation.
Uniform motion = observers moving with CONSTANT VELOCITY relative to one another. The observers are undergoing NO acceleration.
Equivalent means that the SAME laws of motion are valid for each observer.
A consequence of this is that there is no physical experiment by which an observer can detect his own state of uniform relative motion.
If two observers, moving at uniform but different velocities each perform the same set of experiments, they will get the same results. Neither can tell whether he is moving or how fast. Examples: drinking coffee on an airplane. Ping-pong on a ship. Is your BART train moving forward, or the next one moving backward?
As long as you don't accelerate, you can't tell whether you are moving or not! All reference frames in uniform motion are equivalent. There is NO absolute reference frame from which one can measure motion.
Assume the speed of light adds just like the bullet speed we discussed earlier. Consider a binary star system. Sometimes it is moving toward Earth with its orbital speed (v), and others it is moving away. If the speed of light were not constant, then when one star comes toward you, the speed of the light coming toward you would be faster (v + c) than the light you would see when the star is moving away ( v - c). At a great enough distance or great enough speed of the binary star you could see the light of the star moving toward you arrive at the same time as the light moving away from the other side of the orbit. You could see the star appear in multiple positions at once! This is never observed.
For a minute, keep assuming that the speed of light adds to the speed of the source. Consider two cars, one a black BMW travelling East and the other a red VW travelling North. Both cars are equally far from an intersection and headed toward it at 100 km/hr (about 60 mph). They will collide when they reach the intersection. However, if you are standing straight down the street in the direction that the BMW is heading (beyond the intersection), you would see its light moving faster than the light from the VW (because the VW is not moving towards you). Thus, you would see the BMW get to the intersection first, and there should be NO collision! What? This can't be! The collision happens, regardless of our location! In order for things to make sense, the speed of light must be the same for everyone.
Measurements in particle accelerators confirm that no matter how fast a particle is moving when it emits a photon, the speed of these photons is always c relative to the laboratory.
What does Jill see? To make this easier to understand, imagine that Jack is in another space craft, and they have a relative speed between them of v. Now, it doesn't matter who is moving. Bob thinks he is stationary and Jill is moving away at v, likewise Jill thinks that she is stationary and it is Jack that is moving away from her. Both viewpoints are valid. Jack has a clock just like hers. Therefore she will see his time to run slower than hers. Wow, that's weird!
This effect is called time dilation. From your point of view time runs slower for anyone moving relative to you. As their speed approaches the speed of light time seems to stop.
This effect has been experimentally verified. Very accurate atomic clocks have been taken aboard jet airplanes that flew in circles for hours. When the clocks aboard the plane were compared to clocks on the ground they had lost a few nanoseconds of time. Exactly the amount predicted by special relativity. The effect is obviously imperceptible at normal speeds. But as speeds approaching the speed of light it is much more noticeable.
In particle accelerators, physicists accelerate particles to near the speed of light and smash them into each other. In the collisions new particles are formed. One such particle is the muon. When at rest this particle live only 2.2 microseconds before decaying into other particles. But in experiments where it is created moving at 99% the speed of light it last for 15.6 microseconds, which is exactly the amount predicted by special relativity.
The effects of gravity are exactly equivalent to the effects of acceleration.
Imagine that you are sitting in a closed room with the shades drawn. If your room was magically moved to outer space and was accelerated at a rate of 9.8 m/s/s you would not notice anything different. If you did physics experiments by dropping balls and so forth, you would get the same results as you did when the room was on Earth.
If you are in a spaceship with an acceleration of 9.8 m/s/s, you would feel "weight". Once you switch off the engine, you will coast along at constant velocity, and float relative to the ship.
In a freely falling elevator, you would be weightless! The force of gravity is pulling on both you and the elevator, so you are both moving at the same speed. You will be weightless, even though you are still under the influence of the Earth's gravity.
Consider the space shuttle in orbit about the Earth. One of the astronauts has a flashlight. Remember that there is no experiment that the astronaut can perform to distinguish whether he is weightless in remote interstellar space or in free fall in a gravitational field about the Earth. His flashlight beam had better travel along with the space shuttle! But the shuttle is falling around the Earth! The light beam MUST fall with the ship in orbit about a gravitating body!
Is light actually bent from its straight line path by the force of gravity? Einstein says no. Light always follows the shortest path, but that path may not always be straight!
On Earth, the shortest distance between two points is not a straight line, but follows a great circle, or "geodesic". The shortest distance is not straight because the surface is curved. In general relativity, the presence of massive objects causes space-time to curve around them, so the shortest path for light in space-time may not be straight!
In this view, there are no gravitational forces, just curved "geodesics" in space-time.
Here's another way of thinking of this. Light loses energy as it escapes a gravitational field, due to the conservation of total energy (it requires energy to escape). Because the energy of light is inversely proportional to the wavelength, the wavelength of the light must increase, or shift to the red.
Here's thought experiment to provide one more way of looking at the gravitational redshift. Imagine you're in a falling elevator. Remember that this is equivalent to being weightless in space far from any massive bodies. Suppose you shine a flashlight upwards. The top of the elevator is accelerating downwards towards the flashlight. So by the time the light reaches the ceiling, the ceiling is moving towards the location from which the light was emitted. Wouldn't we then expect the light at the ceiling to be Doppler shifted to the blue? But this violates the principle of equivalence, because that would imply that we can tell that we are in a falling elevator, and not weightless in space! Einstein concluded that there must be a gravitational redshift that exactly compensated for the Doppler blue-shift that is otherwise expected.
This gravitational redshift has been confirmed, using experiments in which light emitted with a particular wavelength at one altitude was detected at a higher altitude, and observed to have a longer wavelength (1960s/1970s).
Gravitational lensing occurs when the light of a distant source passes through or close to a massive foreground object, and is bent by curved space-time. Depending on the detailed geometry of the two objects with respect to the Earth, several images of the background object may be seen. This has been observed in many clusters of galaxies.
Light from a distant source passing very near the edge of the Sun takes longer to reach the Earth than one would expect if space-time were not curved. The Viking signal from Mars was delayed in just this way (1976).
GR predicts that the orbit of the planet Mercury should not be a closed ellipse, but should "precess" by 43 arcseconds per century. This is due to the fact that Mercury's orbit is an ellipse, and the effects of GR are more pronounced when it is close to the Sun than when it is further away. This effect was observed in the 19th century, but was not understood until Einstein's theory.
This precession effect has also been observed in a binary pulsar system. The pulsar (B1913+16) is in orbit with another neutron star, and (due to the curvature in space-time created by these massive compact objects) the orbit precesses by 4 degrees per year. In addition, the pulsar is a "clock", which appears to run slower when it is closer to the second neutron star, just as is predicted by General Relativity.
If two massive objects are orbiting one another, GR predicts that they will emit "gravity waves" (ripples in the curvature of space-time). The system is therefore losing energy, and so the two stars will get closer together and the orbital period will decrease. The orbit of the binary pulsar system (orbital period ~ 8 hours) is observed to change in exactly the way predicted by Einstein's theory. Joe Taylor and Russell Hulse won the Nobel Prize for Physics in 1993 for the confirmations of General Relativity associated with this system.