Riddle me this....

The question is what is "absolute phase" in reproduced music where the music itself has been recorded using several different microphones, set up usually without regard to their relative phases, and is then played back through speakers with crossovers and drivers which are a further source of phase error even including sometimes 180 degree differences in phase, and then into a room with reflections that further alter phase relationships. It is one thing to say absolute phase makes a difference but quite another to apply that principle to the reproduction of music in a typical home environment using typical source material and multi-way loudspeakers. And anyway even after all that, the question is only whether a particular individual can hear a difference. It is not necessary for me to deny there is a difference in order for me to report I cannot hear a difference. I attribute my failure in that regard in part to the fact that I use full-range, crossover-less dipolar speakers. (In a dipolar speaker there is rearward radiation of the same magnitude as the forward radition that is 180 degrees out of phase.) And to test my own acuity, I have asked others to sit in my room while I switched phase by 180 degrees under conditions where the tested persons were blinded. No one I have asked to perform this test can hear a difference in my room through my system. And finally, I think we all can agree that the actual question posed by the OP, whether a point source is perceived to relocate precisely in space with respect to a 180 degree alteration of phase. The answer is for a particular listener it is possible a difference in soundstage is perceived but not a difference that can be described so precisely as described in the OP.  At least that is my answer.

@jeffseight 

I suggest you try it and listen for yourself.

Here is some reading material for you:

https://forum.audiogon.com/discussions/preamp-inverts-phase-question

https://forum.audiogon.com/discussions/amp-inverted-or-non-inverted-phase

http://www.6moons.com/industryfeatures/polarity/polarity.html

https://www.enjoythemusic.com/magazine/rickerinterview/ricker9.htm

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This would only help on a interconnect to a preamp That is known  have reverse  polarity , older CJ preamps used to, not speaker terminals. That’s was the only time to reverse one end of ale Ad on a interconnect.

....in short:

Reversing your phase may pervert your stage...something like that...;)

There was onceuponatime a means of crosswiring the L & R channels that didn't seem to indicate 180ing one or the other, but was purported to 'nifty things' to the stage....and wouldn't cook ones' amp...

If anyone has a better SSD between ears in regard to this, chime in... 

(I already sift enough leisure into this digital sandbox....*L*)

@mahgister i just want to say that you gave an exquisite explanation of the phenomenon. Even though I am not a physicist, the terms and relationships of the effect were clear. More importantly, you were able to draw a parallel with wider debates in the audio sphere.