LOL. Have to repeat that you are "arguing against the nonexistent strawman who is apparently suggesting that Farady's law is incorrect, and Kirchoffs is always correct", like broken record.
I have to agree with Ogden. Who are you actually arguing with?
To make things easier i will summarize most of my claims in a list:
1) There are indeed two voltages present at the measured points in Dr. Lewins experiment when using the formal textbook definition of voltage.
2) The formal definition of voltage is path dependant
3) Faradays law is correct, however the E field in that equation refers only to the non conservative E field generated by the magnetic field on the other side of the equation. No other E fields are included on the left side (Tho you can include the conservative E field too since it integrates to zero anyway).
4) Voltmeters can only measure charge density across the terminals and can't detect the non conservative component of voltage around the whole loop, only observe the effects of this non conservative field in the form of charge separation.
5) If voltmeters ware capable of measuring voltage as formally defined then measuring the voltage across a transformer secondary would always result in 0V with the secondary terminals open, or when the transformer is powering a load the voltage would be the restive drop in the wingdings.
6) In Dr. Lewins circuit charge density is always defined as a single number for all points at any given moment, giving every point of the circuit a defined "effective voltage"
7) Closed loops of wire with a defined area are not a requirement for having induction happen. Open loops of wire can experience induction and even act like LC tank circuits.
8 ) Open lengths of wire in a changing magnetic field indeed have zero textbook voltage along them, but in most cases do have a different charge density at the ends giving them "effective voltage" that is capable of being detected with voltmeters or in extreme cases make electrons arc across gaps.
9) Lengths of wire connecting the voltmeter to the probing points are part of the circuit and need to be analyzed along with the rest of the circuit. These wires transfer the voltage from the probing points to the voltmeter terminals where it is actually measured. If it is found that these wires generate a voltage that affects the voltmeters reading then this voltage must be subtracted out to get the voltage at the probe points. Failure to realize this, correct it, or compensate for it is considered as "bad probing".
10) Changing the path of the probe wires in Dr. Lewins circuit does change the voltmeter reading due to changing the charge density present on the voltmeter terminals. However when doing correct probing as mentioned above the result of the voltage at the probing points it always the same, regardless of wire path or voltmeter location (The effect is always substracted out).
11) Kirchhoffs circuit laws always work in circuit mesh models where all voltages use the "effective voltage" definition
12) Kirchhoffs cirucit laws can not be directly applied to just any real life circuit with the assumption of ideal wires, especially when high frequency AC signals are involved or significant magnetic effects are present
13) Kirchoffs voltage law does not contain an intergal of E as Dr. Lewin shows. Its actually a algebraic sum of all voltages on components and as such can only be used on a lumped model.
14) Kirchoffs cirucit laws do not go against Faradays law or Maxwells equations. All three can exist without conflict. Faradays law and KVL describe two different things and as such are not mutually exclusive.
15) Kirchoffs citucit laws have nothing to do with Maxwells equations, but they are used together whenever circuit analysis is used on reactive components such as inductors or capacitors.
16) The circuit from Dr. Lewins experiment can easily be lump modeled using multiple coupled inductors to represent wires. As such all common methods of circuit analysis can be applied to it including KVL to get results matching the real physical experiment
17) The inductor lump models can be split any number of times and distributed around the loop to expose any point of interest in the circuit.
18) Circuit mesh models assume there is no flux outside of individual components, however coupled inductors models can be used to get this flux sharing behavior when desired.
19) The "effective voltage" is just as real as the formal textbook voltage, yet more useful due to being always defined and shown by real life voltmeters.
I might have missed a few but these are the ones i remember right now. Any disagreement on these?