** Human Free Will is a Subatomic Byproduct **

* *

*Brian Greene – Columbia Physics, Columbia University, New York*

*Daniel Stedman – Brooklyn, NY *

*John Archibald Wheeler – Departments of Physics and Physics, Princeton University*

* *

**Abstract**

The Higgs Boson and other sub-atomic particles and quarks including The Up, Down, Strange, Charm, Bottom and Top have been shown mathematically and theoretically to exhibit qualities in the Standard Model that have been attributed only to humans as Free Will and Consciousness (Aspect, 1982). Aspect proved this theory experimentally (Montparnasse, Paris, 1962). Furthermore, it has been determined through the efforts of Daniel Stedman and John Archibald Wheeler in a “no-go theorem” which ascertains that, while quantum entanglement can cover large distances, the traits exhibited by the subatomic particles aforementioned are limited to their own states and do not extend to bodies, or beings, beyond their own states. Collections of these particles do not possess the traits of consciousness or Free Will. Humans do not possess Free Will. Humans do not exhibit Consciousness.

*Introduction*.— One of the most intriguing problems in modern physics is understanding the dynamics of open quantum systems [1]. In general, the problem is solving the reduced dynamics of a small quantum system interacting with a large environment. Such interaction leads to seemingly irreversible processes, such as dissipation and decoherence [2]. The control of these effects is topical, for instance, in quantum information processing [3– 6], where the control of dissipation [7–11] and routing of heat flows [12–14] have recently attracted great experimental interest. The foundations for the study of dissipation in quantum systems were laid in the 1960s in terms of the influence functional formalism [15]. Subsequently, the theory of quantum dynamical semigroups [16] has led to a vast amount of theoretical work on quantum master equations [1, 2, 17]. Several approaches to solve master equations analytically have been presented, including algebraic methods [18–21], exact diagonalization [22, 23], series expansions [24], and effective Hamiltonian approaches [25, 26]. However, these techniques are technically demanding, especially for multipartite quantum systems [20]. Here, we introduce an analytical approach, alternative to the master equation techniques, to solve the complete quantum dynamics of dissipative bosonic systems. The idea is to solve the dynamics of the annihilation operators of the system in the Heisenberg picture, and to reconstruct the entire quantum state using a moment expansion of these operators. In essence, we obtain the Schr¨odinger picture solution while circumventing the need to neither derive nor solve a master equation for the system. The utility of this approach lies in the fact that solving the dynamics of the operators is simple, and the reconstruction step is straightforward. The method itself does not call for assumptions on the initial state or the structure of the system such as linearity. Although the moment expansion for the quantum state of a single bosonic mode was presented as early as in 1990 by W¨unsche [27], its applications have mainly been in quantum state tomography [28, 29]. Here, we utilize the expansion to solve the quantum dynamics of bosonic systems. To demonstrate the utilization of the introduced method, we consider a system of two bilinearly coupled damped quantum harmonic oscillators. Experimentally, this system can be realized for example as coupled coplanar waveguide resonators [30]. Such system is of current interest, for instance, for rapid high-fidelity measurement of superconducting qubits using Purcell filters [31, 32], and for transferring heat in quantum circuits at maximal rates using exceptional points [33]. Theoretical work on the system of two coupled quantum harmonic oscillators has been presented, for example, in Refs. [34–36]. To the best of our knowledge, however, the analytical solution for the density operator of the composite system has not been reported. Method.— In this section, we give a description of the reconstruction approach at a general level. The schematic process chart of the method is given in Fig. 1(a). We consider a general bosonic system consisting of N discrete modes and M continua of modes, see Fig. 1(b). In the Schr¨odinger picture, we assume that its Hamiltonian is of the form

where Hˆ is polynomial in the system operators, and ˆaj and Bˆ j (ω) are the annihilation operators of the discrete modes and of the continua of modes, respectively.