Why Won't Observation in a 2 Slit Experiment Cause 1 Slit Diffraction?

[vanhees71]

I don't understand that question. In what scenario are we increasing momentum uncertainty and reducing diffraction?

If the beam is not "monochromatic" enough the contrast of your interference pattern goes down of course.

 

[kent davidge]

If the beam is not "monochromatic" enough the contrast of your interference pattern goes down of course.

because then the beam is no longer coherent?

 

[vanhees71]

Yes. It's because the position of the maxima and minima of intensity behind the double slit depend on the momenta (de Broglie wavelenths) of the particles. So if you have a spread in momentum the minima and maxima get "washed out" and you get "less contrast" of your interference pattern.

 

[Dr_Nate]

Yes, I understand that there are probability amplitudes that constructively and destructively interfere. I think what is confusing is how momentum uncertainty apparently also plays a role in the formation of interference patterns.

Momentum uncertainty is related to spatial uncertainty. That's really all the Heisenberg Uncertainty principle says. It isn't about interference patterns. You really should go to the math at this point. $\Delta x$ and $\Delta p$ represent equations. They are standard deviations of the wave function in position space or momentum space. Those two spaces are related by Fourier transforms; another set of equations.

 

[vanhees71]

Sure, it is also about interference patterns.

First of all look at the incoming wave: If you want double-slit interference the wave packet has to be spatially broad enough to cover (more or less with equal intensity) both slits. This implies that the momentum uncertainty must be small enough to get a sufficient width in position space. Note that the usual textbook treatment uses the limit of plane waves, i.e., as generalized momentum eigenstates (which are strictly speaking not represent true states, because they are no square-integrable functions though; so you have to take their interpretation with a grain of salt), i.e., your two slits are "illuminated" with strictly equal intensity since the spatial width goes to infinity.

The same holds behind the slits: If you put your observation screen (nowadays, e.g., a CCD cam or some other "pixel detector") too close the "partial waves" originating from each slit (in the sense of Huygen's principle) have no significant overlap, i.e., there's no interference and thus no refraction pattern though here you get some which-way information. Only if the partial waves overlap at a far enough put onservation screen you get interference and a double-slit interference pattern at the cost of loosing which-way information.

In some sense the uncertainty principle particularly manifests in this paradigmatic example of wave-function interference phenomena at slits and gratings!