Why don't two identical monochromatic lamps form interference patterns?

Question

Monochromatic light of intensity I from two identical lamps is incident on a screen. How will the intensity vary with distance, x, from the center of the screen.

From my knowledge of Physics, I would instantly point this out to be an example of double slit interference where the slit width is negligible, i.e. there is not single slit diffraction effects. Strangely, I found the answer to this question to be a horizontal line, with the intensity 2I.

First of all, how is the graph horizontal, and second of all how is the intensity just double the original intensity? I would have thought that as a result of interference, the amplitude at the center would be twice the amplitude of light from one lamp, and so the intensity from two lamps if four times the intensity from one? One of the answers I came across is that the phase difference is not constant, but how is this the case if the two lamps are identical?

Answer 1

When two lamps are placed side by side so that light from both lamps combine, no interference effects are observed because the light waves from one lamp are emitted independently of those of the other lamp.

Light waves from such sources of light (also called incoherent sources) undergo random phase changes in time intervals less than a nanosecond, and the conditions for any kind of interference are maintained only for such small time intervals, which the ordinary eye cannot perceive.

To understand why intensities add linearly, see this answer written by @Farcher:

Net intensity for interference from incoherent sources

Hope this helps.