Now suppose we have a photon in transit in region 3. The photon has already passed the slits.
We can yet choose to leave the screen in place, in which case we do not know which slit the photon went through.
Or we can choose to remove the screen. If we remove the screen, we will expect to see a flash at one telescope or the other (or both, except that never happens) for every photon sent through. Why? Because the photon has to go through either one slit, the other slit, or both slits. Those are all the possibilities. By watching both slits, we must see one of the following:
- a flash at the left telescope and no flash at the right telescope, indicating that the photon went through the left slit; or
- a flash at the right telescope and no flash at the left telescope, indicating that the photon went through the right slit; or
- a weak half-flash at both telescopes indicating that the photon went through both slits.
Those are all the possibilities.
Upon observation at the screen QM tells us what we will get: Pattern 4r, which is exactly reminiscent of wave interference caused by two symmetrical waves, one emanating from each of the slits.
Upon observation at the telescopes QM tells us what we will get: Pattern 5r, which is exactly reminiscent of particle-like behavior traveling from the source, through one slit or the other, and being detected at the telescopes.
Consider the difference in the experimental set up depending on our choice of detection. If we choose to leave the screen in place, we get a particle distribution consistent with the interference pattern that would be produced by two hypothetical symmetrical waves, each emanating from one of the slits. We might say (although we are extremely reluctant to say this) that the photon traveled as a wave from the point of origin, through both slits, and on to the screen.
On the other hand, if we choose to remove the screen, we get a particle distribution consistent with the clumping pattern that would be produced by particle motion from the point of origin through one slit or the other and to the left telescope or to the right telescope. After all, the particle "appeared" (we saw a flash) at one telescope or the other, rather than "appearing" at some other point along the length of the screen.
In summary, we have chosen whether to know which slit the particle went through, by choosing to use the telescopes or not, which are the instruments that would give us the information about which slit the particle went through. We have delayed this choice until a time after the particles "have gone through one slit or the other slit or both slits," so to speak. Yet, it seems paradoxically that our later choice of whether to obtain this information determines whether the particle passed through one slit or the other slit or both slits, so to speak. If you want to think of it this way (I don't recommend it), the particle exhibited after-the-fact wave-like behavior at the slits if you chose the screen; and it exhibited after-the-fact particle-like behavior at the slits if you chose the telescopes. Therefore, our delayed choice of how to measure the particle determines how the particle actually behaved at an earlier time.
Does our choice "change the past"?
How long can we delay the choice? In Wheeler's original thought experiment, he imagined the phenomenon on a cosmic scale, as follows:
1. A distant star emits a photon many billions of years ago.
2. The photon must pass a dense galaxy (or black hole) directly in its path toward earth.
"Gravitational lensing" predicted by general relativity (and well verified) will make the light bend around the galaxy or black hole. The same photon can, therefore, take either of two paths around the galaxy and still reach earth – it can take the left path and bend back toward earth; or it can take the right path and bend back toward earth. Bending around the left side is the experimental equivalent of going through the left slit of a barrier; bending around the right side is the equivalent of going through the right slit.
3. The photon continues for a very long time (perhaps a few more billion years) on its way toward earth.
4. On earth (many billions of years later), an astronomer chooses to use a screen type of light projector, encompassing both sides of the intervening and the surrounding space without focusing or distinguishing among regions. The photon will land somewhere along the field of focus without our astronomer being able to tell which side of the galaxy/black hole the photon passed, left or right. So the distribution pattern of the photon (even of a single photon, but easily recognizable after a lot of photons are collected) will be an interference pattern.
5. Alternatively, based on what she had for breakfast, our astronomer might choose to use a binocular apparatus, with one side of the binoculars (one telescope) focused exclusively on the left side of the intervening galaxy, and the other side focussed exclusively on the right side of the intervening galaxy. In that case the "pattern" will be a clump of photons at one side, and a clump of photons at the other side.
Now, for many billions of years the photon is in transit in region 3. Yet we can choose (many billions of years later) which experimental set up to employ – the single wide-focus, or the two narrowly focused instruments.
We have chosen whether to know which side of the galaxy the photon passed by (by choosing whether to use the two-telescope set up or not, which are the instruments that would give us the information about which side of the galaxy the photon passed). We have delayed this choice until a time long after the particles "have passed by one side of the galaxy, or the other side of the galaxy, or both sides of the galaxy," so to speak. Yet, it seems paradoxically that our later choice of whether to obtain this information determines which side of the galaxy the light passed, so to speak, billions of years ago.
So it seems that time has nothing to do with effects of quantum mechanics. And, indeed, the original thought experiment was not based on any analysis of how particles evolve and behave over time – it was based on the mathematics.
This is what the mathematics predicted for a result, and this is exactly the result obtained in the laboratory.
If you are serious about the idea that the result is determined only upon observation ...
Can we delay the choice even longer? Can we delay the choice until after the photons have "hit" the
telescopes or the screen? It turns out we can. We do so with a handy quantum eraser. But that's a whole
'nuther experiment. See the Delayed Choice Quantum Eraser Commentary.
This is great stuff, isn't it?