Wouldn't the noise introduce both positive and negative jitter, so it nets out to zero in the long run?

Yes, both negative and positive, and zero in average, yet it accumulates as larger and larger time jitter. In fact, I re-"discovered" that myself, by accident, while trying to measure something else. At first I was intrigued by the same question, until it was kindly explained in another forum by somebody named "cirip", whom I want to thank for.

The explanation had some math in it, but I'll try an intuitive one (as in rough and no math):

- phase noise can be seen as a frequency modulation (an ideal oscillator is FM modulate by some noise)

- frequency modulation can be seen as a "lenght" modulation (the length between two consecutive zero crossings)

- the noise has both + and - variations, averaging on zero

- let's make an analogy with a (foot) walking down an alley, where each wavelenght of the oscillator is a step made in the same direction, and the phase will be a small error, let's say randomly distributed in the range of +/- 0.1 steps

- we make one step, we arrive at the distance 1 +/- 0.1 steps

- if we walk 100 steps, we arrive in average at a distance of 100 steps, correct, but what will be the

*range* of the final error?

The real question here is what is

*the worst possible* error? That would be if by chance all the errors (at each step) will be +0.1 (or -0.1). In conclusion:

- walk 1 step and arrive at the distance 1 step +/- 0.1, so the end point is at [1 step +/-0.1] steps

- walk 10 steps and arrive at the distance 10 steps +/-0.1*10, so the end point is at [10 steps +/-1] steps

- ...

- walk 999 steps and arrive at the distance 999 steps +/-0.1*999, so the end point is at [999 steps +/-99.9] steps

- the more we walk, the bigger the

*range* of the final error.

The +/- n steps is the error after walking n steps (caused by the noise), and this length error is what we perceive as time jitter on the oscilloscope.