18 pages. v2: Some text and two references added. v3: Minor changes, one reference added. v4: 21 pages. Submitted to AmJP (not accepted). v5: Minor changes (mainly formulations). v6: Accepted by Found.Phys. Final version is available at http://www.springerlink.com
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave functions) can be interpreted as occupation numbers for objects with a formal mass (defined by the field equation) and spatial wave number ("momentum") characterizing classical field modes. A superposition of different oscillator eigenstates, all consisting of n modes having one node, while all others have none, defines a nondegenerate "n-particle wave function". Other discrete properties and phenomena (such as particle positions and "events") can be understood by means of the fast but smooth process of decoherence: the irreversible dislocalization of superpositions. Any wave-particle dualism thus becomes obsolete. The observation of individual outcomes of this decoherence process in measurements requires either a subsequent collapse of the wave function or a "branching observer" in accordance with the Schrödinger equation - both possibilities applying clearly after the decoherence process. Any probability interpretation of the wave function in terms of local elements of reality, such as particles or other classical concepts, would open a Pandora's box of paradoxes, as is illustrated by various misnomers that have become popular in quantum theory.
Quantum computers are believed to surpass the classical ones. Moreover, it is claimed that this belief reaches the level of a mathematically proven fact within the oracle model of computation. Here we impair the whole class of the so-called rigorist proofs of quantum speed-up obtained within this model.
Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of …
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a counting argument. This also demonstrates that a computational model based …
An unknown quantum state of a single system cannot be discovered, as a measured system is reprepare: it jumps into an eigenstate of the measured observable. This impossibility of finding the quantum state and other symptoms usually blamed on wave-packet collapse follow (as was recently demonstrated for pure states of measured systems) from unitarity (which does not, however, allow for a literal collapse) and from the repeatability of measurements: Continuous unitary evolution and repeatability suffice to establish the discreteness that underlies quantum jumps. Here we consider mixed states of …
Elementary particles in quantum mechanics (QM) are indistinguishable when sharing the same intrinsic properties and the same quantum state. So, we can consider quantum particles as non-individuals, although non-individuality is usually considered as a consequence of the formalism of QM, since the entanglement of states forbids any labelling process. We show how to consider non-individuality as one of the basic principles of QM, instead of a logical consequence. The advantages of our framework are discussed as well. We also show that even in classical particle mechanics it is possible to consid…
Founding our analysis on the Geneva-Brussels approach to quantum mechanics, we use conventional macroscopic objects as guiding examples to clarify the content of two important results of the beginning of twentieth century: Einstein-Podolsky-Rosen's reality criterion and Heisenberg's uncertainty principle. We then use them in combination to show that our widespread belief in the existence of microscopic particles is only the result of a cognitive illusion, as microscopic particles are not particles, but are instead the ephemeral spatial and local manifestations of non-spatial and non-local enti…
Another Bell test "loophole" - imperfect rotational invariance - is explored, and novel realist ideas on parametric down-conversion as used in recent "quantum entanglement" experiments are presented. The usual quantum theory of entangled systems assumes we have rotational invariance (RI), so that coincidence rates depend on the difference only between detector settings, not on the absolute values. Bell tests, as such, do not necessarily require RI, but where it fails the presentation of results in the form of coincidence curves can be grossly misleading. Even if the well-known detection loopho…
Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that…
While looking for evidence of quantum coherent states within the brain, many quantum mind advocates proposed experiments based on the assumption that the coherent state of a photon entering the visual system could somehow be preserved through the neural processing, or in other words they suppose that photons collapse not in the retina, but in the brain cortex. In this paper we show that photons do collapse within the retina and subsequent processing of information at the level of neural membranes proceeds. Moreover, we explicitly stress on the fact that due to existent amplification of the sig…
By proposing a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions, we predict that when a change happens to the conditions that determining the status of a quantum system, the system will show no response to this change at all, until after a certain time interval. Otherwise either special relativity or quantum mechanics will be violated. As a consequence, no physical process can actually happen within Planck time. Therefore time is discrete, with Planck time being the smallest unit. More intriguingly, systems with a larger size an…
We explore some implications of the hypothesis that quantum mechanics (QM) is universal, i.e., that QM does not merely describe information accessible to observers, but that it also describes the observers themselves. From that point of view, "free will" (FW) - the ability of experimentalists to make free choices of initial conditions - is merely an illusion. As a consequence, by entangling a part of brain (responsible for the illusion of FW) with a distant particle, one may create nonlocal correlations that can be interpreted as superluminal signals. In addition, if FW is an illusion, then QM…
Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to corrections to the Schrodinger equation, which in turn affect all quantum mechanical Hamiltonians. In particular, by applying it to a particle in a one dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself. …
Various approaches to Quantum Gravity suggest an existence of a minimal measurable length. The cost to have such minimal length could be modified uncertainty principle, modified dispersion relation, non-commutative geometry or breaking of continuous Lorentz symmetry. In this paper, we propose that minimal length can be obtained naturally through spin-orbit interaction. We consider Dresselhaus anisotropic spin-orbit interaction as the perturbative Hamiltonian. When applied to a particle, it implies that the space, which seizes this particle, should be quantized in terms of units that depend on …
It is shown that the Diósi-Penrose criterion of gravity-induced quantum collapse may be inconsistent with the discreteness of space-time, which is generally considered as an indispensable element in a complete theory of quantum gravity. Moreover, the analysis also suggests that the discreteness of space-time may result in rapider collapse of the superposition of energy eigenstates than required by the Diósi-Penrose criterion.
We propose a new thought experiment, based on present-day Quantum Information Technologies, to measure quantum gravitational effects through the Bose-Marletto-Vedral (BMV) effect by revealing the gravitational $t^3$ phase term, its expected relationships with low-energy quantum gravity phenomena and test the equivalence principle of general relativity. The technique here proposed promise to reveal gravitational field fluctuations from the analysis of the stochastic noise associated to an ideal output of a measurement process of a quantum system. To improve the sensitivity we propose to cumulat…
This article compares treatments of the Stern-Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector (uniqueness) but we cannot explain why there are only two locations where the electron is ever found (discreteness). Using non-relativistic or relativistic quantum mechanics, we can explain both uniqueness and discreteness. Moving …
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic appro…
A relativistic Wigner function for free Discrete Time Quantum Walks (DTQWs) on the square $2D$ space-time lattice is defined. Useful concepts such as discrete derivatives and discrete distributions are also introduced. The transport equation obeyed by the relativistic Wigner function is obtained and degenerates at the continuous limit into the transport equation obeyed by the Wigner function of $2D$ Dirac fermions. The first corrections to the continuous equation induced by the discreteness of the lattice are also computed.
The idea about a quantum nature of Planck's blackbody radiation law is deeply rooted in minds of most physicists. Einstein's work, in which the coefficients of spontaneous and induced emission were introduced, has always been regarded as a proof that quantum energy discreteness of an atom plays a crucial role in the derivation of this law. In our paper we avoid this standpoint. It may be shown that the de Broglie wave assigned to every material particle is a result of interaction of the particle with zero-point vibrations of electromagnetic ground field. The energetic spectrum of a harmonic os…
In a series of recent papers it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems to include quantum field theory. The inherent discrete nature …
The decoherence of quantum fluctuations into classical perturbations during inflation is discussed. A simple quantum mechanical argument, using a spatial particle wavefunction rather than a field description, shows that observable correlations from inflation must have a discrete spectrum, since they originate and freeze into the metric within a compact region. The number of discrete modes is estimated using a holographic bound on the number of degrees of freedom. The discreteness may be detectable in some models; for example, if there is a fundamental universal frequency spectrum, the inflatio…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the theory). This is possible provided we adopt Feynman's suggestion of dropping the assumption that the probability for an event must always be a positive number. This approach has the advantage of allowing a reformulation of quantum theory in phase space without introducing the unphysical concept of probability amplitudes, together with all the problems concerning …
We propose the consistent statistical approach to consider a wide class of classical open systems whose states are specified by a set of positive integers(occupation numbers).Such systems are often encountered in physics, chemistry, ecology, economics and other sciences.Our statistical method based on ideas of quantum theory of open systems takes into account both discreteness of the system variables and their time fluctuations - two effects which are ignored in usual mean field dynamical approach.The method let one to calculate the distribution function and (or)all moments of the system of in…
Bohmian mechanics allows us to understand quantum systems in the light of other quantum traits than the well-known ones (coherence, diffraction, interference, tunneling, discreteness, entanglement, etc.). Here the discussion focusses precisely on two of these interesting aspects, which arise when quantum mechanics is though within this theoretical framework: the non-crossing property, which allows for distinguishability without erasing interference patterns, and the possibility to define quantum probability tubes, along which the probability remains constant all the way. Furthermore, taking in…
To avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not have a uniform step-size, implying complications in their analysis and solutions. We propose a numerical method based on Taylor expansions, which can give us the necessary information to calculate the wave-function at any given lattice point. The method we propose can be applied in any lattice-refined model, while in addition the accuracy of the method can be…
