If you now put a detector in path A , it will find a photon with probability ((1√2)2=12 ), and same for path B. This means that there is a 50% chance of the configuration |photon in path A only>, and 50% chance of the configuration |photon in path B only>. The arrow direction still has no effect on the probability.
This 50⁄50 split is extra surprising and perhaps misleading? What’s the cause? why not 100 on path A and 0 on path B (or the reverse)?
As a layman it seems like either:
The world is not deterministic, so when we repeat the experiment sometimes the detector goes off on path A and sometimes it goes off on path B. That’s very surprising.
We are in a deterministic world, that means that if we can repeat the same experiment we get the same result each time. But actually we don’t get the same result, which means we failed to repeat the experiment, or rather the initial conditions were significantly different. The probabilities tell us something about the experimental setup, not about quantum mechanics: as an analogy if I roll a fair plastic dice N times, and observe it falls on 6 with probability half, this tells me a lot about my dice rolling skills, but not so much about plastic. In a similar way when we send N photons in an interferometer setup, the setup actually varies with time: maybe the photon does not land quite on the same spot on the mirror each time, or some atoms have decayed, whatever, so the 50⁄50 probabilities we observe actually tell us about the setup and our inability to repeat the same experiment to the degree that it matters, not about quantum mechanics. This is misleading because if the probabilities have nothing to do with QM why mention them at all?
This 50⁄50 split is extra surprising and perhaps misleading? What’s the cause? why not 100 on path A and 0 on path B (or the reverse)?
As a layman it seems like either:
The world is not deterministic, so when we repeat the experiment sometimes the detector goes off on path A and sometimes it goes off on path B. That’s very surprising.
We are in a deterministic world, that means that if we can repeat the same experiment we get the same result each time. But actually we don’t get the same result, which means we failed to repeat the experiment, or rather the initial conditions were significantly different. The probabilities tell us something about the experimental setup, not about quantum mechanics: as an analogy if I roll a fair plastic dice N times, and observe it falls on 6 with probability half, this tells me a lot about my dice rolling skills, but not so much about plastic. In a similar way when we send N photons in an interferometer setup, the setup actually varies with time: maybe the photon does not land quite on the same spot on the mirror each time, or some atoms have decayed, whatever, so the 50⁄50 probabilities we observe actually tell us about the setup and our inability to repeat the same experiment to the degree that it matters, not about quantum mechanics. This is misleading because if the probabilities have nothing to do with QM why mention them at all?