Whether or not hairs are being split is a matter of opinion. That you are incorrect is a fact. As I stated earlier, a phase shift is a difference in time whereas inverted polarity means a change from positive to negative or vice versa.
I don't have any illusion that any of this discussion will change the terminology, but I do think we should understand that phase and polarity are not the EXACT same thing just because audiophiles use the terms interchangeably.
If you take a pure sine wave and shift it 180 degrees then it will look EXACTLY the same on an oscilloscope and will sound EXACTLY the same. However, if you take a "signal" containing many different frequencies like music you get a much different result. Since each frequency has a different period, if you shift each frequency by the same number of degrees it will sound different because each frequency is shifted by a different amount of time which results in a waveform that is not the EXACT same thing. That is a reason why speaker crossovers distort the signal. Here is a discussion of it.
https://www.passlabs.com/press/phase-coherent-crossover-networks
I don't have any illusion that any of this discussion will change the terminology, but I do think we should understand that phase and polarity are not the EXACT same thing just because audiophiles use the terms interchangeably.
If you take a pure sine wave and shift it 180 degrees then it will look EXACTLY the same on an oscilloscope and will sound EXACTLY the same. However, if you take a "signal" containing many different frequencies like music you get a much different result. Since each frequency has a different period, if you shift each frequency by the same number of degrees it will sound different because each frequency is shifted by a different amount of time which results in a waveform that is not the EXACT same thing. That is a reason why speaker crossovers distort the signal. Here is a discussion of it.
https://www.passlabs.com/press/phase-coherent-crossover-networks
