This situation is related to the one I asked in the previous post a few days back.(adsbygoogle = window.adsbygoogle || []).push({});

There is an apparatus which is made of partly mirror and partly lens. A particle P1 is passed through the apparatus. The wave function of the particle is such that there is a 75% probability of the particle hitting the mirror and 25% probability of the particle hitting the lens. Thus after the particle interacts with the apparatus, the wave function of the particle P1 transforms such that there is 75% probability of the particle landing on the same side of apparatus after reflection from the mirror and 25% probability of the particle landing on the opposite side of apparatus after refraction from the lens. Till this point, there is no confusion.

But suppose let us assume that the particle P1 is composed of constituent particles P2, just as a proton is composed of quarks. I think the wave function of particle P2 need not be the same as P1. Suppose the wave function of each P2 composing P1 is such that each P2 has a 60% chance of hitting the mirror and 40% chance of hitting the lens. Then after the interaction with the apparatus, the wave function of each P2 transforms such that it has a 60% chance of landing on the same side of apparatus having reflected from mirror and 40% chance of landing on the opposite side having refracted from the mirror.

But the confusion is that when we consider particle P1 as a whole without considering P2 individually as in the first case, the wave function of P1 splits on either sides of apparatus in the ratio 75%:25% which means each P2 composing P1 has a 75% - 25% chance of landing up on either sides of apparatus since the position of each P2 should be the same as the position of P1 since P2 is a constituent of P1.

But if we take the constituent P2 individually without considering P1 as a whole as in the second case, then the wave function of each P2 splits on either sides of the apparatus in the ratio 60%:40% thereby giving a 60-40 chance of each P2 landing on either sides of apapratus.

Thus when we approach our situation through two different angles i.e. one with respect to the whole particle and the other with respect to the constituents, we get two different probabilities of outcomes. I want to know what would happen in the real scenario, i.e. whether the wave function will transform in accordance to the first case or in accordance to the second case. Is there really some ambiguity here or is there is any flaw in the above reasoning and my understanding of quantum mechanics? Kindly clarify my doubt as soon as possible. Thanks in advance.

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# How can this possible tricky situation be explained?

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