In my line of research I usually assume that light from two independent lasers will not produce an interference pattern when combined. This is because the light from one is not coherent with the other. For this reason I was surprised when a colleague of mine who works with frequency combs told me that light from two independent lasers will produce a beat note when combined
interfered. This means, for a short time, there will be an interference pattern, though it may change too rapidly for our eyes to see. One can understand this by assuming an ever-shrinking line width for each laser until each one is perfectly monochromatic. [It also helps that the center wavelengths be slightly different.]
Of course, in retrospect, I realize now the error in my thinking. Supposedly "general" rules when applied to the topic of coherence are almost always wrong because one must specify the relevant timescales involved to determine whether light is coherent or not. These time scales include the integration time of the detector, the width of a wave packet, the period of the carrier wave, etc. Because there are so many different parameters, optical coherence problems do not lend themselves to an easy generalization, at least when one is first learning the topic.
And even when one is experienced with it, he or she will likely continuously be surprised like I was this morning.
