Is a ray of light, produced by an ordinary light bulb, filtered through a perfect monochromatic filter and 2 (in-line) pinholes, coherent?

Question

A physicist once told me it is not, because even if it is perfectly monochromatic and perfectly collimated (by the two in-line pinholes), each photon has a completely random phase. For a while I thought this answered my question of what the difference between in phase and coherent really is.

But then I realized that the definition of coherence, which states that the phase-relation needs to be stable (over space and/or time), is fulfilled here: Any two photons have a stable phase relation at any point along the beam (and also any point in time). So what is then the difference between such a (hypothetical perfectly monochromatic and perfectly collimated) beam consisting exclusively of random phase-photons - and a laser beam, if a laser beam is coherent, but not consisting exclusively of in phase photons? The latter is what physicists have explicitely told me on several occasions: Lasers produce coherent light but the photons are not all in phase. (I really hope there was a misunderstanding because otherwise I see no possibility of grasping the issue.)

Answer 1

If "coherent" means, "able to form interference patterns," then color filtering and spatial filtering are sufficient to create a "coherent" light source. That's how they used to provide the light for interferometry experiments before lasers* were invented.

It's a fact, established in the early twentieth century, that interferometry works even when you send one photon at a time through the apparatus. There's no requirement for individual photons to be in phase with each other. It's sufficient for each photon to be in phase with itself. https://en.wikipedia.org/wiki/Double-slit_experiment#Interference_from_individual_particles

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* The thing that makes lasers so special is that they don't waste any energy (or at least, don't waste much energy) making wavelengths or rays that aren't wanted. When you create coherent light by filtering, the filters throw away almost all of the incident wavelengths and rays. Lots of wasted power, not much coherent light.

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Ok, so the physicist, who told me the setup I laid out didn't produce a coherent beam of light, was wrong?

The coherence of a light source isn't just a yes/no quality. It can be quantified.

• https://en.wikipedia.org/wiki/Coherence_length
• https://en.wikipedia.org/wiki/Degree_of_coherence

In the apparatus you described, you can improve the coherence by making the bandpass filter more narrow, and by making the pinhole† smaller, but that means you're throwing away more of the light. A practical version of your apparatus can make light that approaches the coherence of a cheap, multi-mode laser, but the incoherent source lamp must be extremely bright in order to get a useful amount of coherent light out.

I'm guessing that it would be impractical to make such a device that would come anywhere near the coherence that a modern, high-tech, single-mode laser can achieve. So really, whether or not your professor is right or wrong depends somewhat on what you think is good enough to be called "coherent" light.

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† In your original question, you said, "two in-line pinholes." But, what you really want for spatial filtering is one pinhole, and one or two lenses. The input lens focuses rays of light that are parallel to the axis of the filter onto the pinhole, while all other rays are blocked. The optional output lens collimates the emerging, spatially coherent rays, into a parallel beam if that's what you need.

https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=10768

Answer 2

Let's examine the phenomenon of light diffraction and interference from the elementary to the complex.

As we know today, individually emitted photons are diffracted at slits and - statistically evaluated - produce an intensity distribution on a detector. The way out for science - which is always looking for explanations for phenomena, because that is exactly what science is - was to explain the individual photon as being in phase with itself.

Furthermore, it is known that light is also diffracted behind individual edges. Thus it can be assumed that individually emitted photons are also subject to diffraction and (statistical!) fringe pattern generation.

Coherent means that the superposition of two mutually coherent waves results either in their cancellation or in the increase of their amplitude while their frequency remains constant. Not so with light. Light rays that collide pass through each other unhindered. Photons (almost never) interact with each other.

Since every single photon is diffracted at edges and the image of the points of impact in sum results in a fringe pattern, coherence as a condition for the generation of fringe patterns is invalid. And indeed, coloured light also produces fringe patterns, as Newton already knew. It is the simple fact that monochromatic light produces the sharpest patterns.

TL;DR
Does the edge of the slit actually play a role in the deflection of the photon? It is time to think about this. Today we have studies that deal with phononic and other group excitations in solids. It is time to investigate the interaction between the surface electrons of the edge(s) and the photon and also the electron diffraction.
TL;DR