What 1V jump is there? Its simply voltages measured across the wires inside the magnetic field by taking a different path with the voltmeter. The voltages are there in Dr. Lewins experimental circuit if you probe it just the right way.

And that's what he did. There is 0.9V across one resistor, and 0.1 across the other. Those are the only voltages present in the circuit. If you're measuring anything else, it's because you are choosing a different path than that of the circuit.

Simple as that.

The lumped model simply has a different way of expressing the effects of magnetic fields, that's it.

This is impossible since the lumped model is derived from Maxwell. That's explained by Feynman in his chapter 22.

The whole circuit still acts identical and that's what matters. Cirucit mesh models are supposed to model the high level behavior of circuits, not model physical electrons moving trough wires and the fields they make around them.

When Maxwell published his equations, they didn't know about the existence of electrons. Maxwell is about fields and geometry. Every time your circuit is affected by fields or geometry, you'll have to use them.

As long as the circuit behaves the same its considered a accurate model.

Unfortunately your "model" doesn't behave the same as Lewin's circuit nor is accurate. In fact it is aberrant. And, if you pardon me, asinine. It proposes the existence of 250mV across a wire that has a resistance of about zero ohms carrying a current of 1mA.

250mV = 0Ω · 1mA !!!!!!!!!!!!!

Besides, your model contradicts Faraday's law that states that any circuit under varying magnetic will have its voltages adding up to a value different from zero.

To help you avoid those gross errors, I prepared a quick guide to lumpiness. I hope that it will be useful for you.