A double slit thought experiment leading to a paradox

In summary: 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
  • #1
Gezstarski
15
6
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)
 
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  • #2
I'm not sure I follow what you are saying or understand your question.
 
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Likes hutchphd and vanhees71
  • #3
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 )
 
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  • #4
Are you assuming that a photon is a pulse?
 
  • #5
jartsa said:
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.
 

Related to A double slit thought experiment leading to a paradox

1. What is a double slit thought experiment?

A double slit thought experiment is a theoretical experiment used to demonstrate the principles of wave-particle duality in quantum mechanics. It involves shining a beam of particles, such as photons or electrons, through two parallel slits and observing the resulting interference pattern on a screen behind the slits.

2. What is the paradox in the double slit thought experiment?

The paradox in the double slit thought experiment arises when the particles are observed or measured at the slits, causing the interference pattern to disappear and the particles to behave like individual particles rather than waves. This challenges the idea that particles can also behave as waves, as demonstrated by the interference pattern.

3. How does the double slit thought experiment relate to quantum mechanics?

The double slit thought experiment is often used to illustrate the principles of quantum mechanics, specifically the concept of wave-particle duality. It shows that particles can exhibit both wave-like and particle-like behavior, depending on how they are observed or measured.

4. What is the significance of the double slit thought experiment?

The double slit thought experiment is significant because it challenges our understanding of the behavior of particles at a fundamental level. It also has implications for the nature of reality and the role of observation in shaping it, as well as the limitations of our current understanding of quantum mechanics.

5. How is the double slit thought experiment relevant to everyday life?

The double slit thought experiment may seem abstract and unrelated to everyday life, but it has practical applications in fields such as electronics, optics, and computing. It also has philosophical implications and can help us better understand the nature of reality and our place in the universe.

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