Refuting Observer-Independence in Quantum Theory

Decoherence framework for Wigner's-friend experiments

“…The Hilbert spaces of the simplified versions of the laboratories discussed in these papers are spanned by {|A h |h , |A v |v , |A h |v , |A v |h }. Notwithstanding, the last two states are never occupied, and hence such two-state interference experiments are feasible [4]. The situation arising from the decoherence framework is far more complex.…”

“…2, we conjecture that all the 2 N states of the environment are populated, and therefore 2 N +1 states of the whole laboratory become relevant for further interference experiments. Hence, the first consequence of the results discussed in this section is that experiments like the ones in [1][2][3][4] become extremely difficult. However, as | ε 1 (t)|ε 2 (t) | 2 ∼ 0, it is true that only two states, |h |A h |ε 1 (t) and |v |A v |ε 2 (t) , are populated at each time t; the rest of the Hilbert space is irrelevant at that particular value of the time t. Unfortunately, these states change very fast with time, and in a very complex way.…”

“…where |→ S = 1 2 (|↓ S + |↑ S ). To simplify the notation and make it compatible with [3,4], the following changes are made: (i) instead of the quantum coin and the spin in Eq. (30), two polarised photons are used; (ii) the first photon is denoted by the subindex a, and the second one, by the subindex b; (iii) the superpositions of vertical and horizontal polarisation are denoted |+ = 1 2 (|h + |v ) and |− = 1 2 (|h − |v ), respectively.…”

“…All the measurements are performed on a pair of entangled quantum systems, each one being measured in a different laboratory. An experiment to prove the second no-go theorem has recently be done [4].…”

“…Hence, the laboratory in which Wigner's friend lives must include three different objects: the measured system, the measuring apparatus, and the uncontrolled environment. The last one, not present in standard Wigner's friend setups [1][2][3][4], determines to which states the part of the laboratory observed by Wigner's friend collapses. And, at the same time, it guarantees the unitary evolution of the whole laboratory, and therefore makes it possible for Wigner to observe the system as an entangled superposition of his friend, the measuring apparatus, and the environment.…”