Thread: The Copenhagen Interpretation: Double slit experiment

Originally Posted by mediumharris

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Also, I don't see how a Fourier transform of geometry even makes sense. Fourier transforms have to do with frequencies. They are used to describe any single, complicated wave as an infinite sum of sine and/or cosine functions with certain amplitudes and frequencies (something much easier to deal with in a lot of cases). We usually model the two slit experiment as a sum of a few simple waves, so I don't see why the Fourier transform would be necessary.

This is a great thread, just wanted to throw in my two cents.

A fourier transform is a mathematical operation. There is no restriction on what can be fourier transformed. True, a frequency spectrum is the fourier transform of time-based data. However, the fourier transform of geometric data results in a wave-vector object. All diffraction patterns are fourier transforms of the diffracting medium. Crystallography is the science of crystal structure. Xray diffraction patterns are taken of the crystal. Inverse fourier transforms of the diffraction pattern give the crystal structure.

Interesting. I do remember working with reciprocal space, etc. now in a solid state physics class. Didn't realize how connected these concepts were.

EDIT (added links and descriptions of two interesting articles):
Here is an interesting article related to this discussion. Wheeler's Delayed Choice Experiment. The idea is that after the electron/light/etc. has passed through the slits but before the outcome is measured, a decision is made as to whether information about which slit it went through will be included in the final measurement. The outcome changes when this information is included, defying common sense (according to common sense, the wave/particle should have already passed through the slit, fixing the outcome).

Other experiments have been done using quantum erasure, where information about which slit something went through can be effectively erased, changing the outcome from particle-like to wave-like and back, when the information is reintroduced. This wave-particle stuff runs very deep in physics and cannot be simply attributed to the slit detector messing with the particle (although this is the case when detectors are not cleverly designed like in the experiments above). Looks more like particle/waves obeying pure probability laws than anything.

My take on the Copenhagen interpretation starts with this little fellow. It's a single-slit, 4-\lambda diffraction pattern. Rather than a random, yet uniform dispersion of photons, however, we clearly see faint, but recognizable rays of reinforcement and cancellation caused by edge diffraction associated with the two edges of the one slit.

For smaller lambda, the number of those rays increases as the edge effects become more noticeable compared to the overall pattern of waves.

If you take a 2-\lambda photo, set transparency to 50%, and superimpose it on itself, but offset so that there are "two" slits rather than one, you find yourself staring at the classical interference pattern exhibited by a traditional 2-\lambda slit experiment, along with the corresponding banding along the far wall.

Thus, intuitively, it doesn't matter whether one slit is covered for a time while photons are passed through the other, afterwards the processed is reversed, or whether both slits are open as in the conventional experiment. What's intuitive is that the far edge banding is the result of edge diffraction effects on each slit interfering with the same type of effects on the other slit.

In summary, my take on the Copenhagen approach is that focusing one's attention at the subatomic level to the exclusion of all else also excludes what appears to me to be quite obvious.