While the second half of your comment is correct:
>> The electrical outlets in your home have two power-carrying prongs.
>Only one of the prongs carries power. The other is attached to the earth, and is always at zero volts.
Voltages are about potential differentials, so "zero volts" is relatively meaningless without context.
The neutral line is required by the electric code to be connected to earth at the electric panel, but even if it were not, any ungrounded appliances would work correctly.
Both prongs absolutely carry power. Slap an ammeter on the neutral line; it should be identical to that on the hot line. Don't actually do this, but if you were to cut the neutral line with a live circuit, you would see sparks. This is particularly important when working on circuits with a shared neutral (two hot lines on alternate halves of the split phase with a single neutral line); despite the breaker being off for your hot line, you can get shocked when working on junction boxes for the neutral line. Yes this is up-to-code in all states (though a few places either recommend or require ganging the circuit breaker when doing so).
>> and then they will slowly switch places over the next 1/120 of a second so the right wire is at +170 volt
> No. The power prong (the smaller one) will switch from -170 to +170. The other one (the neutral) is always at zero (measured relative to you).
Here you use voltages as a relative measure, which is correct. As a nitpick you do assume that the person is grounded. Walking on carpet in the winter, I can be at a potential of thousands of volts away from that though.
[everything from here after in ars's comment is correct and I have no more nitpicks]