Why can't two truly identical experiments on quantum scale give the same result?

When we refract light on air/water interface, some part of light is reflected while some of it gets refracted.

My question is when we consider light as a photon and send it (photons) one by one, what are those things which determine which photon will be reflected and which one will be refracted as reflection and refraction occur simultaneously?

• The photons are reflected/transmitted randomly, with some probabilities given by the squared amplitude of each component (reflected and transmitted). The whole incident light ray is made of billions of photons, so you see both reflection and refraction "simultaneously". – Cham Aug 23 at 17:32
• You seem to think that every outcome must have a cause. Why? – safesphere Aug 23 at 18:19
• @safesphere Quantum mechanics retains causality. It discards determinism. That's the whole point of the question. – puppetsock Aug 23 at 18:29
• @safesphere Causality means no information passes outside the light cone. Determinism means that exactly the same thing will happen given the same initial conditions. QM keeps causality and gives up determinism. – puppetsock Aug 23 at 20:38
• @ashi According to quantum theory, each photon is partly reflected and partly refracted. If we measure whether the photon was reflected or refracted, then the outcome of the measurement will be one of those two possibilities. Quantum theory only predicts the distribution (when the measurement is repeated many times), not the individual outcomes. Nobody knows how to predict which one will be obtained. Are you asking if somebody has an empirically-verified hidden variables theory? If that's the question, then the answer is no. We have no empirical clues about how to predict the outcome. – Chiral Anomaly Aug 23 at 23:14

It is called Quantum Mechanics. The photon is a quantum dynamical entity, it is not a small part of a beam of light. Classical light (electromagnetic wave) is made out of a quantum mechanical superposition of zillions of photons with energy $$hν$$, where $$ν$$ is the frequency of the emergent light.
Quantum mechanics obeys postulates, and the main one is that all particles obey wave equations , and the solutions of the boundary conditions for the given problem give different wave functions,$$Ψ$$, whose complex conjugate squared $$Ψ^*Ψ$$ gives the probability amplitude for the photon distribution after the interaction.