Special vs. General Relativity Special relativity deals with inertial/non-accelerating reference frames General relativity deals with accelerating reference frames.

A Thought Experiment 2 observers are standing inside closed elevators Elevator 1 is at rest on the surface of the Earth. If Observer 1 throws a ball it will fall toward the floor of the elevator, accelerated by gravity

Elevator 2 is at rest or moving at a constant velocity in deep space Elevator 2 is at rest or moving at a constant velocity in deep space. Everything in the elevator experiences weightlessness. Observer 2 drops a ball and it remains in place.

Now elevator 2 is given an acceleration equal to 9.8m/s2 (g). The ball stays at rest compared to the background stars. But the elevator floor rushes up toward the ball. If the ball is given a slight horizontal velocity, it will make a parabolic path as the floor rushes to meet it. Once it hits, the floor exerts a force of mg on not just the ball, but on Observer 2 as well.

In conclusion The results of experiments conducted by Observer 2 in his accelerated elevator will have the same results as experiments conducted by Observer 1 back on Earth. Einstein generalized this result into the Principle of Equivalence

Principle of Equivalence All physical experiments conducted in a uniform gravitational field and in an accelerated frame of reference give identical results. Thus our observers could not tell (while in the closed elevator) if they are accelerating in space or sitting in a uniform gravitational field.

Does this effect light? If Observer 2 at rest has a flashlight, the beam would go straight across the room. But if the elevator were being accelerated, the beam would hit lower on the wall just like the ball would (because the wall will have moved up). In fact, the beam would even follow a parabolic path.

If this works in an accelerated frame, then it should work in a gravitational field too. And it does. Light will bend in a large gravitational field.

The proof: Gravitational Lensing Apparent position of star as star’s light is bent around the sun Proved during a solar eclipse in 1919 Actual path of light Sun Earth Real position of star Moon during solar eclipse

Time and Gravity Time is also effected by gravitational fields. We saw before that moving clocks run slow. Clocks in a strong gravitational field run slow as well. This has also been tested.

Atomic Clocks Atomic clocks are extremely accurate. An error for 1 second in 3 million years is typical. This error can be described as about 1 part in 1014. There are atomic clocks in Boulder, CO and Washington DC. Boulder is about 1 mile higher in altitude then DC. Which clock runs slow?

The closer to the center of the Earth one is, the more the gravitational field is. Therefore, DC’s clock must run slow. And it does! The Washington DC clock is often 15 nanoseconds (15 x 10-9 seconds) behind the one in Boulder! Yes, this isn’t a huge difference, but it is about 17 times larger then the typical error from an atomic clock.