There's the old story of the carpenter who only had a hammer. When asked that there was something loose that needed tightening, what did he think it was, he responded by showing everybody his hammer. He passed it around, and described how it worked, how it had a heavy head on it with a flat face that was meant to drive a nail.
He then proclaimed that, since the hammer was meant to drive a nail, the problem must be a nail. If it were anything else, the hammer would not be designed that way.
When someone else said that he actually saw the problem, and that the problem was something called a wood screw that needed tightening down, and that it was tightened down by sliding a blade in a slot in it's head and turning it, the carpenter just scoffed and laughed at such an absurdity. "I've already showed you the hammer, and how it worked, and there's nothing there about a blade or a slot or turning anything. That's not how nails work. Nails are made to be hammered down."
"But how do you know it's a nail?", someone asked. To which the carpenter simply replied, "It has to be, because that's what hammers are designed to drive. I'm a carpenter, and have been for a long time. I know from where I speak."
This went back and forth, around and around in circles, with the carpenter stuck in the loop that because he had a hammer, the problem was always a nail, and as proof he kept saying, if it weren't a nail, then this wouldn't be a hammer. They argued for an hour.
In the meantime, the original guy who actually looked at the problem, and not at what tools anyone did or did not have, actually looked at the situation, saw it was a wood screw, went down to the hardware store and got a new tool called a Phillips screwdriver and got the problem solved himself.
Sonixx is, I'm sorry to say, presenting us with the perfect example of the carpenter and the hammer.
There is nothing wrong with those time-based equations he keeps regurgitating as his argument. they are perfectly valid equations, just as the carpenter's hammer is a perfectly good hammer. And as long as he sticks with those as his only tool, he'll be stuck in his beliefs.
See, the "w" in those formulas stands for radians per second. This means it stands for how fast in time that a wave is rotating through it's cycle. It's really just another version of "cycles per second" with approx. 6.28 radians per one cycle. This means those equations are specifically for calculating and manipulating the frequency of the sine wave, and yes because we are talking about how many things are happening per second, there is a definite time base and time dependency to those equations.
And sonixx keeps coming back with the argument that because time is crucial to those equations, that it must be crucial to phase as well. Because his hammer is flat, the problem must be a nail.
The problem with that is that phase is idependent if frequency. Take a look at any and every one of the charts presented in this entire thread - and there have been a lot of them
. Take a look at the waves in any one of them and tell us what their frequency is. We can't determine their frequency because nowhere is the time base defined. Those sines in the first diagram could have a frequency of 1Hz, 100Hz, once a day, or once a month (like the completely relevant phases of the moon.) The frequency is not defined in any of those charts exactly because it's frequency is not important. In fact, look at that last one; the x axis is measured in radians (position on a circle), not in any unit of time. Phase can be talked about, diagrammed and manipulated without any need to define the time.
As I argued from the very start, shifting in time can indeed bring things in phase or out of phase, and can cause things to resemble a phase change. Move a 1Hz sine wave one second down the timeline and it will resemble a phase inverted version of another sine of the same frequency that has not moved. I never said that was not true, and that is what his equations support. That is phase
relation, just as sonixx said. But it's NOT a phase
change.
The problem is, the only thing that has changed in the moved wave there is it's position on the timeline. Other than it being
delayed, nothing has changed about it's description. It's frequency, amplitude, in fact it's complete physical and mathematical description has not changed one bit. It's frequency, it's amplitude, and yes, it's phase, have not changed. It just starts one second later, that's all.
But that can't be possible, comes the reply. The equations show time, therefore time has to be there. There is no such thing as intrinsic phase. And since time has to be there, phase has to take place as a relation in time.
It's a circular argument. That has to be a nail, because this is a hammer; therefore, since that is a nail, this hammer is the right tool.
The Phillips screwdriver in this case is the concept of phase space and the diagramming of phase as a third property in the third dimension, and just how simple it can be to rotate - change - the phase of a single waveform without having to slide it down a timeline and compare it to another wave. This is a valid concept and mathematical tool that is used every day in physics, chemestry, medicine and, yes, even electronics engineering. The fact that sonixx is unfamiliar with it is something I cannot account for other than maybe they just did not cover it in his classes. I mean, this thread contains someone else who graduated from audio engineering school and he doesn't know and doesn't care what polarity is.
But even then, the idea of phase as a property even simpler to see, and doen't need the z axis. That "experiment" I gave you guys, which I'm sorry that nobody has taken me up on yet is almost painfully simple in it's execution. All you have to to is take a sine wave, use that graph I gave you, and for every point on that x line in radians, add some number of radians to each value to represent a rotation in the phase value, and then take the sin of each sum. Plot each result in the graph. What you'll wind up with is a phase shifted representation of the original wave, without any movement in time whatsoever, and without any fancier frequency-based equations.
Don't take my word for it. Try it for yourself.
G.
Right now I can't even wrap my head around what they're saying. 
