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Jim-
A final clarification, though I am concerned you still won't understand.
You write: "Otherwise, when you step on the gas at a green light, the rest of the universe could just as well be said to be accelerating in the opposite direction."
That is precisely what can be said of what you observe when you are in an accelerated (therefore non-inertial) frame of reference.
You are always at rest in your own frame of reference, inertial or otherwise. As anon says, that is the definition of the term. In this example, you can tell it is a non-inertial frame by putting a spring between you and your seat-back.
Leaving out the knowledge of the gas pedal, that observation can be interpreted in either of two equivalent ways. You are in a gravitational field pointing the backwards direction, or you and your frame of reference are accelerating forward.
Either interpretation explains why the rest of the Universe is accelerating backwards with respect to you.
And now I am taking anon's advice and getting back to my book writing. If you don't "get it" now, then I have to consider the situation hopeless.
Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)