The Core Assumption of Every Known Single-Photon Experiment Is Wrong,
Freeing The Schrödinger's Cat I (has an additional discussion of the general methodology of science);
Freeing The Schrödinger's Cat II;
The Uncertainty Principle;
The Origins of Quantum Mechanics, and
Part II of this book review.
The authors should have written -"According to one of the interpretations ..." (more on this in Appendix II and other publications).
“Schrödinger imagined putting a cat in a box along with the sealed glass vial of cyanide, with a small hammer hanging or the vile. The hammer, in turn, would be connected to a Geiger counter, which detects radioactivity, and that counter will be pointed at a tiny lump of slightly radioactive metal.” (page 3).
BTW: Schrödinger did not apply quantum mechanics to a macroscopic object (it was a radioactive material), he was much more accurate than many contemporary physicists who invent thought experiments implying a direct application of quantum mechanics to a large system, and then point at a paradox. Of course! When you apply a theory beyond its limits you get "paradoxes" - because you are making a trivial mistake!
I am, as we all are, an external observer who can open the box and look at the cat and make a conclusion if the cat is dead, or if the cat is alive. First let's make sure that the cat can live as long as we need it, so, the box also has installed inside it all the facilities required to keep the cat alive. The only reason for the cat to be dead is if the hammer breaks the vial with poison, and the only reason for that to happen is if a Geiger counter registers a particle, and the only reason for that to happen is if radioactive metal emits that particle. For a regular person, this whole setup looks pretty much ludicrous already, so we can make it as ludicrous as we want to, if it helps to achieve our goal, which is to understand what is happening inside the box. So, let’s imagine that we have not just one but many, thousands, millions, maybe even billions of identical boxes with identical cats waiting for their fate. We created all those boxes at exactly same time, we waited exactly same time period, and we opened all the boxes at exactly same instant. Since, when we open all the boxes and look at all the cats, in every single box every single cat can be only dead or alive, all we can see is:
The whole idea of a path integral is based on the assumption is that an electron is always located somewhere, i.e. it is always localized, because it is always traveling through this point and then this, and then this, etc. A path does not split, there are no forks (even when a particle circles back making a loop the time keeps running ahead and on each path a particle is always located at one place at a time), hence, there are no instances when an electron is located at to places at the same time (a path integral was a brilliant idea of a genius: just assign an amplitude to each possible path and add them up! So obvious! After you learn it. That is why many physicists feel - it's natural, and do not think about implications to the fundamentals of quantum mechanics, including the interpretation of wave-particle duality).
Many physicists analyzed the original Feynman’s experiment; for example, J. D. Cresser writes (2009; http://physics.mq.edu.au/~jcresser/Phys301/Chapters/Chapter4.pdf)
“If electrons are particles, like bullets, then it seems clear that the electrons go either through slit 1orthrough slit 2, because that is what particles would do. The behavior of the electrons going through slit 1 should then not be affected by whether slit 2 is opened or closed as those electrons would go nowhere near slit 2. In other words, we have to expect that P12(x)=P1(x)+P2(x), but this not what is observed. It appears that we must abandon the idea that the particles go through one slit or the other. But if we want to retain the mental picture of electrons as particles, we must conclude that the electrons pass through both slits in some way because it is only by ‘going through both slits’ that there is any chance of an interference pattern forming. After all, the interference term depends on d, the separation between the slits, so we must expect that the particles must ‘know’ how far apart the slits are in order for the positions that they strike the screen to depend on d, and they cannot ‘know’ this if each electron goes through only one slit. We could imagine that the electrons determine the separation between slits by supposing that they split up in some way, but then they will have to subsequently recombine before striking the screen since all that is observed is single flashes of light. So, what comes to mind is the idea of the electrons executing complicated paths that, perhaps, involve them looping back through each slit, which is scarcely believable. The question would have to be asked as to why the electrons execute such strange behavior when there are a pair of slits present, but do not seem to when they are moving in free space. There is no way of understanding the double slit behavior in terms of a particle picture only.”
And then one goes to building an elaborated picture of a wave packet that is a particle and a wave at the same time, etc., etc..
And then, following Feynman, he discusses another mystery, that is when we know through each hole an electron travelled (e.g. using light) we destroy the interference. Only when we do not know how exactly electrons travel through the holes, interference exist. Why? No one knows.
The answer, however, lies in the very statement used to prove that electrons cannot ravel through one hole or another one.
Let’s read it one more time.
“If electrons are particles, like bullets, then it seems clear that the electrons go either through slit 1orthrough slit 2, because that is what particles would do. The behavior of the electrons going through slit 1 should then not be affected by whether slit 2 is opened or closed as those electrons would go nowhere near slit 2. In other words, we have to expect that P12(x)=P1(x)+P2(x), but this not what is observed. It appears that we must abandon the idea that the particles go through one slit or the other.”
But abandoning “the idea that the particles go through one slit or the other” is not only one logical solution.
Another one is to abandon a previous statement, that said: “The behavior of the electrons going through slit 1 should then not be affected by whether slit 2 is opened or closed as those electrons would go nowhere near slit 2.”
If particles do travel through one hole or another, and if the interference pattern does exist, it means that this statement is wrong. And that means that the behavior of the electrons going through slit 1 is affected by whether slit 2 is opened or closed even though those electrons would go nowhere near slit 2. Or, in general, when two slits are open an electron (and a photon!) behaves differently than it does when one slit is open; when it travels to the screen with holes it "knows" already how many holes are open there. How? That is a different discussion (closely related to the discussion of the nature of quantum entanglement; for example, here).
But if we assume that an electron “knows” or “feels” if the hole 2 is open or closed, we solve the contradiction.
And when we shine a light on it, an electron actually “forgets” about the existence of another hole and travels like the only one hole exists – hence, the destruction of interference.
So, there is a way of understanding the double slit behavior in terms of a particle picture only-ish. The question now is how does electron “knows” about the state of another slit? The answer is - in the same way to entangled particles "know" about the state of each other.