Philosophy of Physics Discussion Club: Mini-Workshop next Thursday
Guy Hetzroni
Avi Levy (with Meir Hemmo; University of Haifa): Quantum Field Theory and the Measurement Problem in Quantum Mechanics
Joab Rosenberg (Weizmann institute): Epistemic Physics: Putting information into the Hamiltonian
The measurement problem in Quantum Mechanics (QM) arises from the discrepancy between the unitary temporal evolution of quantum states dictated by the Schrödinger equation (in the non-relativistic case) and the non-unitary evolution (“collapse”) of the quantum state in a measurement process. In Quantum Field Theory (QFT), the standard interpretation of the S-matrix scattering formalism assumes that the in-state of an interacting system evolves unitarily to a superposition of all possible out-states and it collapses to a unique out-state only when a measurement is performed. Hence, QFT too is subject to the measurement problem.
In this paper we propose a novel physical solution to the measurement problem based on QFT. According to our proposal, there exists a “collapse” trigger in the S-matrix formalism of QFT. This trigger occurs in certain types of elementary interactions, in which the “particles content” of the system is changed and the evolution is indeed non-unitary. We argue that these interactions, which are almost instantaneous, lead to a genuine stochastic selection of an outcome subspace that has a distinct particles content, but can be a superposition of states with different individual particles’ momentum, spin etc.
Our proposal is supported by Haag’s theorem form which it follows that the existence of a unitary evolution from every free in-state to every free out-state of a non-trivial interaction is mathematically unsound. A version of Haag’s theorem implies that a non-unitary evolution occurs in those processes where new types of particles are created and / or destroyed leading to a “particles content” change. Since in QM such processes are excluded (because the particles’ content of a physical system is fixed), the appearance of a “collapse” of the wavefunction in QM seems mysterious. Not so, we argue, in QFT.
We address and explain in detail the key concept of particles content change in QFT (which requires clarification) as well as the locality properties of non-unitary processes. Finally, we show that in typical measurement processes, there is a well-defined non-unitary stage. Our proposal de-mystifies the projection postulate for measurement in the standard formulation of QM in that it identifies the physical conditions under which the “collapse” occurs. We argue that non-unitary processes are not specific to “measurement” since they occur in other naturally originated processes in which there is a particles content change. We further argue that our proposal is consistent with all known experimental results in QM and QFT.