Cohere - rant

It was just a passing thought but it turned into a big discussion on Facebook. We all know that two lamps won't interfere with each other, the reason is that they are not coherent. Each lamp is made of a large number of atomic wave sources that have random phase, the wavefront produced from each lamp changes with time so any interference effect will not be stable. To achieve interference the light from one lamp can be passed first through one slit then two slits. The single slit selects part of the wavefront and makes that the source, this source is then passed through the double slits to form two sources, each source originates from a single source so are coherent and form a stable interference pattern.

My question was; If the lamps are identical as stated in the question then won't they form a stable interference pattern. Each lamp would be made of a large number of identical atoms giving out EM radiation with the same phase changing phase. To answer the question we need to consider two atomic sources with changing phase. If the phase of each changes by the same amount will the phase difference between each stay the same? Quite clearly it will so a stable interference pattern will be formed. The answer to the exam question is that there is no interference, that's because the lamps are not identical down to an atomic level, but how do we know when identical is identical and when it is just macroscopically identical.

I think most people thought I didn't understand the reason why the lamps don't interfere (I do). Others thought I was being unnecessarily pedantic and (I was). Actually I was asking a question, what if they were identical, would there be interference? Interestingly yht PhET sim on interference shows two sources interfering. I don't think that it is at all obvious that two lights don't interfere like two sounds.

I tried making an animation using Paul Falstad's ripple tank showing the interference between two sources. Each source is two atomic sources, when nothing changes the pattern is stable but if the phase of one of the atomic sources randomly changes the pattern changes. However if the phase of one of the atomic sources in each "lamp" changes randomly at the same time, the pattern is stable. Well that's what I tried to show but all the waves just made me dizzy.

One atomic source changing in 1 lamp:

One atomic source changing in both lamps at the same time:

Hmm, not very convincing, they both look like the peaks change, however in the second one it's more the brightness of the peaks that changes than their position.