[rubyrescue]

"If you’re in a car, you see watches outside the car go slower. They only go a little slower, so you wouldn’t notice it in your normal life; it takes the best watches in the world to even tell that it’s happening. But it really does happen."

He said it backwards...

[Steuard]

The crazy thing about special relativity is that from the perspective of the observer in the car, they're sitting still and everyone else is moving. That means that the observer in the car will see the watches of people on the sidewalk ticking slowly, at the same time that the people on the sidewalk will see the car's clock ticking slowly.

Everyone sees everybody else's watch ticking slowly (unless they appear to be at rest). And yet it all hangs together in a beautifully consistent way. The catch is that moving observers don't just disagree on whose watch is running slow, they also tend to disagree on whether distant clocks are correctly synchronized or not. The disagreements about which clock is ticking too slow always perfectly balance out the disagreements about which clock chimed noon earlier.

[btilly]

In the path from special to general you have to give this point of view up.

More exactly, special relativity starts with the assumption that there are special inertial frames of reference, here is what they look like, and here is what they look like relative to each other.

General relativity starts with arbitrary coordinate systems, and ways of expressing physics such that whatever was measured in one coordinate system can be translated into what should have been measured in another. These coordinate systems can have any mixture of weird effects.

The physics involves something called a metric. General relativity is what falls out if you insist on the following statements:

1. "Locally" things behave like special relativity.

2. Given only low velocity and low mass, things behave like Newtonian gravity.

3. The terms of the metric satisfy a first order differential equation whose definition is independent of the chosen coordinate system.

This gives you general relativity up to an arbitrary constant of integration (the cosmological constant). And in the presence of mass it gives you the prediction that no truly inertial frame of reference exists over any region with matter in it. (The effects of gravity are all due to stuff being non-inertial.)

From that prediction we find that the point of view and understanding from special relativity is only a local approximation. You can't really describe any interesting system that way.