QUANTUM THEORY: Reconsideration of Foundations—5

On the “principle of the quantumness,” the quantumness of Relativity, and the computational grand‐unification
View Description Hide DescriptionI will argue that the proposal of establishing operational foundations of Quantum Theory should have top‐priority, and that the Lucien Hardy’s program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational “principles of the quantumness,” I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm “the universe is a huge quantum computer,” reformulating QFT as a Quantum‐Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space‐time. In this way Quantum Theory remains the only theory operating the huge computer of the universe.
Is the computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam’s razor, depending on the mathematical simplicity of QCFT. Here I will just start scratching the surface of QCFT, analyzing simple field theories, including Dirac’s. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake the QCFT project, since QCFT makes all such problems manifest, and forces a re‐foundation of QFT.

Towards Quantum Experiments with Human Eye Detectors Based on Cloning via Stimulated Emission ?
View Description Hide DescriptionIn a recent theoretical paper published in Physical Review Letters, Sekatsky, Brunner, Branciard, Gisin, Simon report an extended investigation on some properties of the human eye that affect its behavior as a quantum detector. We believe that the content of this work, albeit appealing at fist sight, is highly questionable simply because the human eye cannot be adopted as a sensing device within any quantum measurement apparatus. Furthermore, the criticism raised by these Authors against a real experiment on Micro—Macro entanglement recently published in Physical Review Letters (100, 253601, 2008) is found misleading and misses its target.

Quantum interference with macroscopic objects
View Description Hide DescriptionWe demonstrate that an interference pattern is not only characteristic for a wave (packet) but that it can also be build up by many particles arriving one by one at a detector without direct information exchange between the particles. We also demonstrate that full which‐path information does not necessarily rule out interference effects. We illustrate this by an interference circuit for people. Our results prove that it is possible to give a particle‐only description of single‐particle interference experiments without first solving a wave equation.

The SCOP‐formalism: an Operational Approach to Quantum Mechanics
View Description Hide DescriptionWe present the SCOP‐formalism, an operational approach to quantum mechanics. If a State—COntext—Property—System (SCOP) satisfies a specific set of ‘quantum axioms,] it fits in a quantum mechanical representation in Hilbert space. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter N. In the case the system reduces to a model for the spin measurements on a quantum spin‐1/2 particle. In the limit N→∞ the system is classical. For the intermediate cases it is impossible to define an orthocomplementation on the set of properties. Another interesting feature is that the probability of a state transition also depends on the context which induces it. This contrasts sharply with standard quantum mechanics for which Gleason’s theorem states the uniqueness of the state transition probability and independent of measurement context. We show that if a SCOP satisfies a Gleason‐like condition, namely that all state transition probabilities are independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented.

A Brief Discussion of Convergences in Interpretations of Quantum Mechanics
View Description Hide DescriptionBohr’s approach to the measurement process implies a shifty split between the classical and quantum descriptions of the world. The current work presents arguments purporting to show that this split has not been satisfactorily removed from subsequent interpretations of the quantum theory. However, in their attempts to do so, rather obscure notions needed to be invoked, which were anticipated, explicitly or implicitly, and carefully circumvented by Bohr. We discuss von Neumann’s description of the measurement process, the decoherence approach, the de Broglie‐Bohm interpretation, and dynamical collapse models.

Black Holes as Dark Matter
View Description Hide DescriptionWhile the energy of the universe has been established to be about 0.04 baryons, 0.24 dark matter and 0.72 dark energy, the cosmological entropy is almost entirely, about from black holes and only from everything else. This identification of all dark matter as black holes is natural in statistical mechanics. Cosmological history of dark matter is discussed.

The Representation of Mixtures in the ESR Model for QM
View Description Hide DescriptionThe extended semantic realism ( ESR ) model proposes a new theoretical perspective which embodies the mathematical formalism of Hilbert space quantum mechanics (QM) into a broader noncontextual, hence local, framework, reinterpreting quantum probabilities as conditional (in a nonstandard sense). We have proven in a previous paper that each generalized observable introduced by the ESR model is represented by a family of positive operator valued measures (POVM) parametrized by the pure states of the physical system Ω that is considered. We show here that each mixture is represented in the ESR model by a family of density operators parametrized by the physical properties characterizing Ω. This representation implies predictions that may differ from those of QM and avoids some deep problems that arise in the interpretation of mixtures provided by QM. We also show that the state transformations induced by idealized nondestructive measurements can be obtained by means of a nontrivial generalization of the Lüders postulate, and discuss our results in the special case of discrete generalized observables.

A Trigonometry of Quantum States
View Description Hide DescriptionI introduce a trigonometry to accompany the geometry of quantum states. This trigonometry is based upon my noncommutative operator trigonometry in which central entities are antieigen‐values, antieigenvectors, and operator turning angles. The outcome of this paper is new understandings from this trigonometric viewpoint of important quantum state properties of entanglement, entropy, Bloch spheres, disentanglement, decoherence, Schmidt angles, quantum channels, and orbit stratification.

Positive Curvature Can Mimic a Quantum
View Description Hide DescriptionWe elaborate on the existing idea that quantum mechanics is an emergent phenomenon, in the form of a coarse—grained description of some underlying deterministic theory. We apply the Ricci flow as a technical tool to implement dissipation, or information loss, in the passage from an underlying deterministic theory to its emergent quantum counterpart. A key ingedient in this construction is the fact that the space of physically inequivalent quantum states (either pure or mixed) has positive Ricci curvature. This leads us to an interesting thermodynamical analogy of emergent quantum mechanics.

Particle‐based simulation approach for single‐particle interference experiments: Application to double‐slit experiments
View Description Hide DescriptionWe review recent progress in the development of event‐by‐event simulation algorithms that do not rely on concepts of quantum theory or probability theory but are nevertheless capable of reproducing the averages computed from quantum theory. The simulation approach is illustrated by applications to single‐photon double‐slit experiments. We demonstrate that it is possible to give a particle‐only description of single‐photon interference experiments without first solving a wave equation.

Correlations of Entangled Systems from Fluctuations of the Prequantum Field: the Case of an Arbitrary Density Operator
View Description Hide DescriptionPrequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie’s “double solution” approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson’s stochastic QM and its generalization by Davidson, ‘t Hooft’s models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrödinger. There is no quantum particles at all, only waves. In particular, photons are simply wave‐pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special “prequantum fields”: the electron field, the neutron field and so on. PCSFT claims that (soon or later) people will be able to measure components of these fields: components of the “photonic field” (the classical electromagnetic field of low intensity), electronic field, neutronic field and so on. However, at the moment (in this paper) we restrict our efforts to reproduce “simply” predictions of QM in the classical field framework. We will show that correlations of entangled systems can be obtained from fluctuations of the prequantum field. We consider the most general case: in QM the state is given by the density operator.

Energy‐time entanglement, Elements of Reality, and Local Realism
View Description Hide DescriptionThis paper discusses energy‐time entanglement experiments and their relation to Einstein‐Podolsky‐Rosen (EPR) elements of reality. The interferometric experiment proposed by J. D. Franson in 1989 provides the background, and the main issue here is a detailed discussion on whether a Local Realist model can give the Quantum‐Mechanical predictions for this setup. The Franson interferometer gives the same interference pattern as the usual Bell experiment (modulo postselection). Even so, depending on the precise requirements made on the Local Realist model, this can imply a) no violation, b) smaller violation than usual, or c) full violation of the appropriate statistical bound. This paper discusses what requirements are necessary on the model to reach a violation, and the motivation for making these requirements. The alternatives include using a) only the measurement outcomes as EPR elements of reality, b) the emission time as EPR element of reality, and c) path realism. The subtleties of this discussion needs to be taken into account when designing and setting up future experiments of this kind, intended to test Local Realism.

The Art and Science of Experimentation in Quantum Physics
View Description Hide DescriptionTaking its historical point of departure in Heisenberg’s work, this article offers a view of quantum mechanics as, arguably, the first truly experimental and truly mathematical physical theory, that is, a theory concerned with experimenting with nature and mathematics alike. It is truly experimental because it is not, as in classical physics, merely the independent behavior of the system considered, in other words, what happens in any event, that we track, but what kind of experiments we perform that defines what happens. By the same token, the theory is also truly mathematical because, at least in the interpretation adopted here, its mathematical formalism does not stand in the service of a mathematical description of (quantum) physical processes in space and time in the way the formalism of classical physics does, but is only used to predict the outcomes of relevant experiments. It also follows that quantum theories experiment more freely with mathematics itself, since we invent predictive mathematical schemes, rather than proceed by refining mathematically our phenomenal representations of nature, which process constrains us in classical mechanics.

Measurement Epistemology and Time‐Frequency Conjugate Spaces
View Description Hide DescriptionWe present the critical steps involved in any measurement process, which tell us that force‐free and intervention‐free measurements are not possible. We add to this the NIW‐principle, Non‐Interference of Waves, which has been neglected by us for centuries even though it is obvious from careful observations of crossing of all material based waves and light beams. Then we underscore that the foundational assumption behind the time‐frequency Fourier theorem does not represent any physical reality even though mathematical computation does give the desired results. It assumes that simple superposition of monochromatic Fourier waves, by themselves, can generate time finite pulses due to interference. Unfortunately, the NIW‐principle forbids it. Founders of quantum physics, oblivious of the existence of the NIW‐principle, assumed that superposition of light beams produce the observed fringes. In reality, the superposition effects become observable because the quantized detectors carry out the summation of the joint stimulations. Thus, quantum physicists mistakenly assigned the quantum behavior of detectors on to light (photons). Based on these observations, we underscore that the ultimate purpose of physical theories is to facilitate the visualization of the invisible interaction processes, rather than simply model the measured data, as is customary now.

Multipartite entanglement and hypermatrices
View Description Hide DescriptionWe discuss how the entanglement properties of a multipartite pure state can be described by extending conventional matrix theory to the hypermatrix formed by the coefficients of the state with respect to a product basis. In particular, we show that the geometric measure of entanglement is given by an analogue of the largest singular value of a matrix.

On Quantum Entropies of Quantum Dynamical Systems
View Description Hide DescriptionWe review some techniques and notions for quantum information theory. It is shown that the C*‐ dynamical entropies are discussed and some numerical computations of these entropies are carried for several modulated states.

Quantum entanglement and interference from classical statistics
View Description Hide DescriptionQuantum mechanics for a four‐state‐system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical statistical ensemble. Quantum systems are subsystems of larger classical statistical systems, which include the environment or the vacuum. They are characterized by incomplete statistics in the sense that the classical correlation function cannot be used for sequences of measurements in the subsystem.

Nelson‐type Limit for a Particular Class of Lévy Processes
View Description Hide DescriptionBrownian motion has been constructed in different ways. Einstein was the most outstanding physicists involved in its construction. From a physical point of view a dynamical theory of Brownian motion was favorable. The Ornstein‐Uhlenbeck process models such a dynamical theory and E. Nelson amongst others derived Brownian motion from Ornstein‐Uhlenbeck theory via a scaling limit. In this paper we extend the scaling result to α‐stable Lévy processes.

Complementary observables in low dimensions
View Description Hide DescriptionWe review sets of complementary observables in low dimensions. The qualitatively different structure found in dimension six gives rise to some fundamental questions about the kinematics of quantum systems in composite dimensions.