# Quantum jumps, superpositions, and the continuous evolution of quantum states

## TL;DR

This paper explores how the development of photon quantization and the scattering matrix formalism reconcile the apparent dichotomy between quantum jumps and continuous evolution, impacting interpretations of quantum mechanics and quantum computing.

## Contribution

It demonstrates that quantum jumps correspond to transitions in Fock space sectors and that continuous evolution is a sum over jump amplitudes, linking field quantization with quantum state dynamics.

## Key findings

- Quantum jumps are transitions between Fock space sectors.
- Continuous evolution is a sum over jump amplitudes.
- Implications for quantum interpretations and qubit superpositions.

## Abstract

The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schroedinger's time-dependent equation also seemed to require a modification of the explanation for the origin of line spectra due to the apparent possibility of superpositions of energy eigenstates for different energy levels. Indeed, Schroedinger himself proposed a quantum beat mechanism for the generation of discrete line spectra from superpositions of eigenstates with different energies. However, these issues between old quantum theory and Schroedinger's wave mechanics were correctly resolved only after the development and full implementation of photon quantization. The second quantized scattering matrix formalism reconciles quantum jumps with continuous time evolution through the identification of quantum jumps with transitions between different sectors of Fock space. The continuous evolution of quantum states is then recognized as a sum over continually evolving jump amplitudes between different sectors in Fock space. In today's terminology, this suggests that linear combinations of scattering matrix elements are epistemic sums over ontic states. Insights from the resolution of the dichotomy between quantum jumps and continuous time evolution therefore hold important lessons for modern research both on interpretations of quantum mechanics and on the foundations of quantum computing. They demonstrate that discussions of interpretations of quantum theory necessarily need to take into account field quantization. They also demonstrate the limitations of the role of wave equations in quantum theory, and caution us that superpositions of quantum states for the formation of qubits may be more limited than usually expected.