Notice that the same thing happens with two batteries in series, which is an appeal to logic, a broad, true, and useful description. The usefulness of the description makes it science. If the description does not convey understanding, it fails the test of usefulness.
Well sir, the battery comparison fails because there is no direction reversal in a series battery array. You will not get a different phase like you do with an AC waveform. I have posted a graphic on this before but don't feel like looking for it at the moment. But you are knowledgeable enough to graph it out for yourself.
Look at the battery waveform vs the AC waveform and you will note that the battery voltages are always in the same relative position while the AC waveforms alternate position. That physical property is what makes the opposing phase available, not that you have to use it like that.
At most universities. After they finish laughing at you for getting your leads backwards. Then they'll have you adjust your gains until you can see the waveforms are identical.
Not true at all. The voltages can be used either way. Both are valid and depend on the circuit.
I'm more focused on how the voltages are used, not how they are derived as they can be derived in a miriad of ways. What becomes important is that the waveforms are what they are. All the talk about the "windings in phase" with each other and name-dropping polarity-marking standards is just dragging in a different topic to try to enhance a viewpoint. The problem is, the polarity is not the same as the voltage direction and is a separate, but related, issue.
There is nothing wrong with using polarity marking or terminal labels as a reference, but they are related to instantaneous relationships and that is a separate issue from positive voltage direction.
Phase of a circuit is independent of how YOU decide to look at it.
The label may be set by convention, but what is actually there is not independent of how the voltages are used. Keep in mind that the meter/scope is just a load. Using the voltages in one way shows in-phase voltages while using them another way shows two phase-opposed voltages. The meter is not lying to you because it simply shows what is really there.
Both options are available but they are produced by a single device. You would get the same results if the voltages were produced by two phase-opposed sources. That is why I say the configuration of the source does not always define what you take from the cource. Many times the source is capable of delivering more than one output option.
Sure. My dryer has both 120V and 240V circuits. Their only common point is A not N. Using N as the reference doesn't make any sense whatsoever. But you keep telling me it's absolutely, positively the only common point and absolutely, positively the only point that makes sense. Yet in my dryer A make sense where N does not.
It is not the only point that makes sense, but it is probably the most common in the world. The grounded conductor is tied to what is essentially the world's most common reference: Earth. Power quality meters also use this as the reference instead of trying to use two difference reference points (not that there is anything "wrong" with two reference points).
No one is saying there are two phases. We are discussing phase angles, namely he phase angles of V1n and V2n.
I guess that would depend on your definition of phase. While we might not all be able to agree on a definiton, we should be able to agree that there are indeed two equal-magnitude real voltages available as in-phase sources or phase-opposed sources. In fact, that is simply a physical reality.
The labeling and naming conventions really should be the only ambiguity.