The double slit experiment for electron beam demonstrated the so call “particle-wave” duality. ( It does not mean particle can be wave, wave can be particle, but the position probability of a particle behave like a wave, everything is particle, matter is particle, light is particle.) Since the position probability behave like a wave, that means the world line of a particle is mot well defined, in the order of the de Broglie wave length. Although the de Broglie wave length is extremely small, so that the world line is almost well define, this fuzzy world line in the quantum scale, some how, not compactable with special relativity. For example, the fuzzy position also means fuzzy time, that allow particle moving backward in time or do crazy things, for example, go back in time and interact with itself.
The most mysterious thing for the double slit experiment is that, the particle seems to be passing though both slits at the same time, in fact, quantum mechanic treat it so and regard it as a matter of fact, no reason, no why, no how.
Suppose we have a scattering experiment, say, proton-proton elastic scattering experiment. After the scattering, the kinematics of the two protons are correlated. And now, send these correlated protons into two double slits.
Suppose the distance between the slit is as small as the de Broglie wave length. And also, suppose the detector position resolution is like 10th of the de Broglie wave length. Let the detected proton position be x1 and x2. The DAQ will record data when both detectors are trigger.
We can imagine, without the double slits, there is a strong correlation between x1 and x2. And if we plot x1 vs x2, it should be a line with 10th of the de Broglie wave length thickness.
Now, lets insert the double slit for the upper proton. According to the double slits experiment, x1 would be a diffraction pattern. What will be the pattern in detector 2?
If the double slit do nothing on the proton 1, because of the position correlation, Should the x2 shows 2 slits with distance of a de Broglie wave length? Or, x2 also shows the same diffraction pattern as x1, and x1 vs x2 still a line, as if not slit there.
Or, because of the detection of proton 2, that constrained the position of proton 1 that it can only go either of the slit but not both, so, no interference pattern on both detectors, simply 2 slits. However, the detection of proton 2 is later then the proton-1 passing through the slit, how is proton 1 being constrained?
Or, the slit interact with proton 1 and destroy the proton-proton position correlation? In that case, can we say something on the proton world line?
Now, what if we put both double slits in? What is the patterns of x1 and x2?
I bet that some people already did similar experiment using laser beam and a beam splitter. But the difference between beam splitter and scattering experiment is that, the proton has angular distribution, that it may point to the slit, the middle of the slit, or totally blocked. And the two protons positions are correlated. How is correlation under the effect of the slit? Does the slit do interact with the proton? If the slit do interact with the proton, that could destroy the proton-proton correlation.
Lets calculate the de Broglie wave length of proton.
For slit of nano-meters, we need less than 200 eV/c proton. 200 eV/c proton has almost zero kinetic energy, and it will be stopped for everything. Unless using 2 proton beams for the experiment, and ultra high vacuum.
How about electron-electron scattering? Although the electron mass is ~2000 times smaller, the maximum KE of the electron for ~ nm de Broglie wave length is 0.01 eV. Still almost impossible.
Update: I found an article Quantum double-double-slit experiment with momentum entangled photons.
It is interesting that the result shows that, “Since the photos are quantum entangled, their individual quantum state are phase incoherent, and the formation of a single photon interference is suppressed.”
In my opinion, people can try :
- only 1 double-slit and see the pattern in the screen without the double-slit.
- place 1 double-slit at far far away than the other, and try to block the path for the far-far away slit. That can investigate the causality.
- Using larger detectors, such as position sensitive scintillator, so that can plot the correlation.
- The article still using the Copenhagen interpretation, in my opinion, should try the quantum bayesian, or quantum trajectory theory.
- using a real double-slit, instead of Fresnel Biprism. In the article, a single scan on a single photon shown no interference pattern.
- confine the source size to be smaller than