A double slit thought experiment leading to a paradox

[Gezstarski]

Consider a Double Slits experiment in which the light source is monochromatic and each slit very narrow. There will be many fringes visible on either side of the axis.

1) If the light source is pulsed with very short, randomly spaced, pulses it will produce spectrally broadened radiation and so the number of fringes will be reduced. Effectively each component wavelength will produce fringes with a different pitch so at large off-axis distances they will blur together. Equivalently one can say that for large offsets the path difference for radiation passing through the two slits exceeds the coherence length of the radiation. Or that the difference in light travel time for radiation passing through one slit or the other exceeds the pulse duration so photons taking the two routes cannot interfere,

2) The same effect would arise with a continuous monochromatic source if a hypothetical ultra-fast (electro-optic?) shutter were used to modulate a monochromatic light source. If the shutter is only opened for very brief intervals, again the spectrum would be broadened and the number of visible fringes reduced.

3) Suppose the shutter were placed not before the slits but immediately in front of the detector – would the effect still be the same?

4) Now suppose that instead of the shutter, the detector is one that records images at a very high frame-rate. Taking a widely spaced subset of the frames would appear to be like using the shutter and so you might expect to see just a few fringes and beyond that a uniform mean level. But stacking all the frames would be expected to be equivalent to an unmodulated source and so fringes should be apparent, even far off-axis. So in the subset there will be photons in positions where nulls are seen in the full set !

(This sequence captures the same basic physics as another thread which was closed because of an unfortunately chosen header, but it is the physics behind the problem that interests me)

 

[PeroK]

I'm not sure I follow what you are saying or understand your question.

 

[jartsa]

So in case 4 we have basically a very fast film camera on which a laser beam is shined, through a double slit screen.

I would say that all frames will show a picture that is not a picture out of which we can read the wave-length of the light source very accurately. Because each frame is a measurement of wave-length measured during a very short time. There is this uncertainty relation between time and frequency, which says it a long time to do a exact measurement of frequency.

(Maybe thic could be changed to be about recording sound. Then it would be 100% classical physics )

 

[tech99]

Are you assuming that a photon is a pulse?

 

[Gezstarski]

So in case 4 we have basically a very fast film camera on which a laser beam is shined, through a double slit screen.

I would say that all frames will show a picture that is not a picture out of which we can read the wave-length of the light source very accurately. Because each frame is a measurement of wave-length measured during a very short time. There is this uncertainty relation between time and frequency, which says it a long time to do a exact measurement of frequency.

(Maybe thic could be changed to be about recording sound. Then it would be 100% classical physics )

You are considering looking at the fringe pattern as a way of measuring wavelength, which is fine because the fringe pitch is proportional to wavelength. If you see only a few fringes then you have only an approximate measure of wavelength.

This is getting to the crux of it.

If you believe that a single frame will not show an extended set of fringes, what about a large number of frames added together? Why should that be different from a single long frame, which would show lots of fringes ?

Remember we are not concerned about signal-to-noise ratio - we can imagine that the source is strong enough that a large number of photons are recorded even in a single frame.