ok - just wondered why you believed it. I'm going to propose that theoretically there can be only one 60 hz signal, therefore if you've seen anything more than that, its a product of your interference ( ie scope not correctly corrected, settings wrong, etc. )
It is a product of what signals we extract from the system and what the system can supply. If I extract only one signal then that is all we have supplied. If I extract three signals then that is what we have supplied.
Nothing magical happens. The signals are actually extracted and that is what the system can supply. The signals do indeed exist, physically and theoretically.
The discussion is about the signals we extract because that is what we are ultimately using.
To put it simply: there are two "flux events" that occur inside the transformer. These occur across two windings so we have four "event results". These are there waiting to be used however we want.
We can use that to either extract two waveforms with the same positive peak (netting two positive peaks and two negative peaks together) or two waveforms with positive peaks at a 180d displacement. Call these the 120v voltages.
We could also just take one larger waveform that combines the four "event results" to produce one larger waveform with two larger "event results" (a larger combined positive and negative peak). Call this the 240v voltage.
That is what Steinmetz was talking about. If you combine the two smaller phases in a 180d system by taking one to be the return of the other, you can get a single larger phase. But the two smaller phases do physically exist in the 180d system.
Anyway, for 180d, we extract one waveform starting at the first flux event and one waveform starting at the second flux event. This is the center-tap reference point.
There is nothing untoward happening. We are simply making use of electrical and physics fundamentals that say we get to define the voltage. It is a fundamental principle.
The reference is a choice and either way is correct. It is really that simple.
We'll have to agree to disagree on this point
OK