David Nebenzahl wrote:

A disagreement arose
thereafter about whether a center-tapped transformer actually delivers
two separate phases of electricity or not.

So, what do y'all say?

Formally, yes, there exist two phases set apart 180º. But formally also that
is never called a "two-phase system".

Reasons:
1.- In polyphase system there is an usual understanding that phases are
different when you can not get the other phase by simple means other than
using transformers (or transformer arrays). In a 3 Phase system, there is no
way to get a phase 120º away by adding, subtracting or switching cable ends
of one phase. In a true two phase system, be it a three wire part of a 3
phase system or the Niagara example, there is no way to get the other phase
(120º or 90º) by playing with the connections. In a "split phase" system,
the 180º phase is equal (in a balanced system) to the other one by just
exchanging the "hot" and "ground" wires.

2.- The phase supplying the power to the "split-phase" winding in the
secondary of home transformers is only ONE, there is no way to get more than
ONE phase out, even if formally the secondary winding could be measured
reversing the leads and appear as the negative value (hence the 180º figure)
Those two windings of the "split-phase system" are connected in such a way
as to provide a total voltage of 240V but could have been connected in
parallel to provide the double of current in one phase at 120V. Such
parallel connection would produce a "short" and high currents if in fact the
two windings were being driven by two distinct phases no matter what games
you play with the wire ends.

So, that's why any power engineer will raise an eyebrow if you address such
system with the clearly incorrect term of "two-phase system".

--
Mark Cross
If Linux doesn't have the solution, you have the wrong problem.