Maybe a bad analogy?

Do you really not see any relevance of the two clocks example with electromagnetism?

It exemplifies the convention used to define positive oriented areas in vector integral calculus.

The orientation of the path defines the orientation of the area.

Now, that is instrumental in computing the flux of a vector field. And the flux of a function of said field, like its time derivative.

Even the flux of the rotor of a vector field.

And what is the definition of rotor? Basically, it's the circulation around a tiny closed path around a point. So the flux of the rotor can be computed by summing, integrating, all those tiny contributions.

And what happens to the contours? Well, thanks to that 'bad' clock analogy they all cancel out except for those on the external border (look at figure 3.9 here

http://www.feynmanlectures.caltech.edu/II_03.html). That's what Stokes theorem tells you: the surface integral of the rotor of a field on an oriented area is the circulation of that field along the closed contour encircling it, with the convention of the right hand rule. Like the hand of a clock.

Add in Faraday-Maxwell equation that tells you that the rotor of E is the time derivative of B (ok, there's a sign but that does not change anything since it's always the same) and you should now see the relevance of that analogy.

In fact, if you split a finite area in two parts with a common side, just like those two clocks, you will find that despite the orientation of the areas be the same, the orientation of the common path will come out reversed. Namely, if we assume the same flux configuration, you will get opposite contributes to the circulation along that path depending on which loop it is considered to be part of.

This 'reversal' of the integral of E dot dl (which in an electrostatic situation we would call "the" potential) is not because of bad probing or a measurement error, it is just a consequence of that inversion you see along the common side of two adjacent clocks.

I doubt anyone would find it surprising, just as they would find perfectly normal that the hand of the right clock is seen going up along the common side, while the hand of the left clock is seen as going down.

And there is no escape from this, no matter how small you choose the adjacent contours.

And when you consider finite contours, you can still divide them in two with a common side: the result is the same: if the same flux is intercepted by both partial areas (

**edit**: actually this is not even required, what it counts is that the E field is the same along the common side and well, it has to be since it's the same set of points), the contribute to the emf on the common path will be reversed.

Would you call that measurement error, or probing error?

I would call that "that's just the way it is", Kronkite style.

This is the same inversion that comes out with Lewin's experiment when both resistor are the same.

Would you call that probing error?

To me, that's just how EM works. And the roots of this behavior go down to both that orientation behavior and the fact the circulation of one quantity is related to (a function of) the flux of another one.

No, I would not call that a bad analogy. But that's just me.

(of course, if you remove the link with the flux because the function of B is always zero you get a very special situation where this weird shit does not happen)

EDIT: changed "convention" with "behavior", because its the correlation between area orientation and path orientation that makes all this happen (clockwise-countclockwise vs up and down in this case)

EDIT: changed "infinitesimal" with "tiny" for not riling up mathematicians. Added link to picture. Corrected some minor typos.

EDIT: changed path with contour where relevant to avoid ambiguities.