Phase information of a signal when creating a spectrogram
Yes, you are correct. If you take a DFT of square wave and only look at the amplitudes, doing an inverse DFT but using different or random phases for the sine components, it does not look like square wave in time domain any more. But it will have a matching spectra. Kind of like two racecars on a circular track, they might always have same velocity, but without knowing the initial position, or even the direction they are going, it will be impossible to know if they side by side or on the opposite side of track.