This is a comment to the paper, Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics by C Cisneros et al 1998 Eur. J. Phys. 19 237. doi:10.1088/0143-0807/19/3/005. The proof that the authors construct for the limitation on the superposition of state vectors corresponding to different sectors of the Hilbert space, partitioned by a superoperator has a flaw as outlined below.
The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.
It is shown that for "ideal" macroscopic objects there are superselection rules forbidding superpositions of macroscopically distinguishable states of the objects. For real macroscopic bodies the notion of "weak" superselection rules is introduced. Some other aspects of the measurement problem are discussed.
In [N. Friis, New J. Phys. 18, 033014 (2016)] the non-relativistic description of fermions is considered and in particular the role of the parity superselection rule in relation to the characterization of entanglement. An argument based on the spin-statistics connection is presented as a physical motivation for the parity superselection rule. Since the spin statistics connection was derived in the context of relativistic quantum mechanics it is argued that the inclusion of the parity superselection rule is motivated by Lorentz invariance. Based on this it is further argued that fermionic Quant…
We consider a particle in a coherent superposition of states with different electric charge moving in the vicinity of a magnetic flux. Formally, it should acquire a (gauge-dependent) AB relative phase between the charge states, even for an incomplete loop. If measureable, such a geometric, rather than topological, AB-phase would seem to break gauge invariance. Wick, Wightman and Wigner argued that since (global) charge-dependent phase transformations are physically unobservable, charge state superpositions are unphysical (`charge superselection rule'). This would resolve the apparent paradox i…
We consider a huge quantum system that is subject to the charge superselection rule, which requires that any pure state must be an eigenstate of the total charge. We regard some parts of the system as "subsystems," and the rest as an environment E. We assume that one does not measure anything of E, i.e., one is only interested in observables of the subsystems. We show that there exist states with the following properties: (i) Its reduced density operator is completely equivalent to a vector state of the subsystems for any gauge-invariant observable of the subsystems. (ii) The vector state is a…
Mass-superselection rule (MSR) states that in the non-relativistic quantum theory superpositions of states with different masses are unphysical. While MSR features even in textbooks, its validity, physical content and consequences remain debated. Its original derivation is known to be inconsistent, while a consistent approach does not yield a superselection rule. Yet, superpositions of masses do not seem to be present in Newtonian physics. Here we offer a resolution of the MSR puzzle. Crucial for the result is the understanding of two issues: how the notion of a mass parameter arises from the …
Here a generalised argument showing the existence of the Bloch superselection rule is presented, in response to the recent comment by Sowinski. In light of the role played by the periodic boundary condition, locality and topology in the system, the claim made in the comment is found untenable.
We demonstrate that it is possible, in principle, to perform a Ramsey-type interference experiment to exhibit a coherent superposition of a single atom and a diatomic molecule. This gedanken experiment, based on the techniques of Aharonov and Susskind [Phys. Rev. 155, 1428 (1967)], explicitly violates the commonly-accepted superselection rule that forbids coherent superpositions of eigenstates of differing atom number. This interference experiment makes use of a Bose-Einstein condensate as a reference frame with which to perform the coherent operations analogous to Ramsey pulses. We also inves…
With the exception of superselection rules, there are no known explicit violations of the Principle of quantum Superposition. However, quantum measurement and the emergence of classicality seem to imply that the Principle of Superposition is not universal, so perhaps new superselection rules or something similar wait to be found. This invites us to search for explicit violations of superposition, even in places where we expect it to hold. Given that many quantum measurement devices rely on atoms absorbing photons, these processes are natural places for a first search for such violations. We pr…
The standard argument for the validity of Einstein's equivalence principle in a non-relativistic quantum context involves the application of a mass superselection rule. It is surprising that the consistency between such an important principle and quantum mechanics depends crucially on the imposition of a non-fundamental restriction. The objective of this work is show that, contrary to what the standard account holds, the compatibility between the principle of equivalence and quantum mechanics does not depend on the introduction of such a superselection rule. For this purpose, we consider the e…
We discuss the possibility of observing quantum nonlocality using the so-called mode entanglement, analyzing the differences between different types of particles in this context. We first discuss the role of coherent states in such experiments, and we comment on the existence of coherent states in nature. The discussion of coherent states naturally raises questions about the role of particle statistics in this problem. Although the Pauli exclusion principle precludes coherent states with a large number of fermionic particles, we find that a large number of fermionic coherent states, each conta…
We reinvestigate Bargmann's superselection rule for the overall mass of $n$ particles in ordinary quantum mechanics with Galilei invariant interaction potential. We point out that in order for mass to define a superselection rule it should be considered as a dynamical variable. We present a minimal extension of the original dynamics in which mass it treated as dynamical variable. Here the classical symmetry group turns out to be given by an $\reals$-extension of the Galilei group which formerly appeared only at the quantum level. There is now no obstruction to implement an action of the classi…
The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course, equivalent to the Schroedinger equation for the wavefunction, which is linear. However, quite simple constraints on the canonical fields P and S correspond to_nonlinear_ constraints on the wavefunction. Such constraints act to prevent certain superpositions of wavefunctions from being realised, leading to superselection-type rules. Examples leading to super…
Gong points out [quant-ph arXiv:1106.0062] a "direct connection" between our measure [PRL 106, 220401 (2011)] recently proposed to quantify macroscopic quantum superpositions and a previously studied quantity introduced to study classical and quantum chaos. We point out that the two measures are obviously different for some mixed states, and the previous one does not work as a sensible measure to quantify quantum superpositions.
We point out that argumentation presented in [Phys. Lett. A 417, 127699 (2021)], leading to the conclusion that in periodic systems there is a superselection principle forbidding two different Bloch states to form a coherent superposition of a fixed phase, is unjustified and false. As an example, we show that the operator projecting to the selected Wannier state can be experimentally utilized to determine relative phase between superposed Bloch states. In this way we argue that, in fact, the non-existence of the aforementioned superselection principle is manifested always when localized measur…
The phase space measure proposed by Lee and Jeong [PRL 106, 220401 (2011)] is shown to be closely related to a well-studied measure in the literature. For pure states, the newly proposed measure is equivalent to an old measure; for mixed states, some discussions are given.
Molecular matter-wave interferometry enables novel strategies for manipulating the internal mechanical motion of complex molecules. Here, we show how chiral molecules can be prepared in a quantum superposition of two enantiomers by far-field matter-wave diffraction and how the resulting tunnelling dynamics can be observed. We determine the impact of ro-vibrational phase averaging and propose a setup for sensing enantiomer-dependent forces, parity-violating weak interactions, and environment-induced superselection of handedness, as suggested to resolve Hund's paradox. Using ab-initio tunnelling…
Natural particle-number entanglement resides between spatial modes in coherent ultra-cold atomic gases. However, operations on the modes are restricted by a superselection rule that forbids coherent superpositions of different particle numbers. This seemingly prevents mode entanglement being used as a resource for quantum communication. In this paper, we demonstrate that mode entanglement of a single massive particle can be used for dense coding and quantum teleportation despite the superselection rule. In particular, we provide schemes where the dense coding linear photonic channel capacity i…
Here we show that two Bloch states, which are energy eigenstates of a quantum periodic potential problem, with different wavevectors can not be linearly superposed to display quantum interference of any kind that captures the relative phase between them. This is due to the existence of a superselection rule in these systems, whose origin lies in the discrete translation symmetry. A topological reason leading to such a superselection is found. A temporal analogue of this superselection rule in periodically driven quantum systems is also uncovered, which forbids the coherent superposition of any…
Bargmann's superselection rule, which forbids the existence of superpositions of states with different mass and, therefore, implies the impossibility of describing unstable particles in non-relativistic quantum mechanics, arises as a consequence of demanding Galilean covariance of Schrödinger's equation. However, the usual Galilean transformations inadequately describe the symmetries of non-relativistic quantum mechanics since they fail to take into account relativistic time contraction effects which can produce non-relativistic phases in the wavefunction. In this paper we describe the incompa…
We make a novel observation about the decoherence phenomenon of the fermion in the Witten's supersymmetric (SUSY) quantum mechanical model. It is shown that, when the bosonic partner in the SUNY model is unobservable in a certain energy scale, the quantum coherence meant by the superposition of fermion states can not be preserved for a long time due to the quantum decoherence induced by the overlooked boson. This refers to a supercharge superselection rule similar to the charge superselection. We numerically calculate the decoherence factor characterizing the extent of decoherence . The obtain…
Reply to Comment on "Neutrino oscillations originate from virtual excitation of Z bosons" and "Neutrinos produced from $β$ decays of neutrons cannot be in coherent superpositions of different mass eigenstates"
After a careful analysis of the feedback model recently proposed by Slosser and Milburn [Phys. Rev. Lett. 75, 418 (1995)], we are led to the conclusion that---under realistic conditions---their scheme is not significantly more effective in the production of linear superpositions of macroscopically distinguishable quantum states than the usual quantum-optical Kerr effect.
Einstein`s equivalence principle states the complete physical equivalence of a gravitational field and corresponding inertial field in an accelerated reference frame. However, to what extent the equivalence principle remains valid in non-relativistic quantum mechanics is a controversial issue. To avoid violation of the equivalence principle, Bargmann`s superselection rule forbids a coherent superposition of states with different masses. Here we suggest a quantum simulation of non-relativistic Schrödinger particle dynamics in non-inertial reference frames, which is based on propagation of polar…
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density matrix, coarse graining, and "events". 5. Conclusions.
Schlosshauer has advanced a theory of minimal no-collapse quantum mechanics for a decoherence-based subjective resolution of the measurement problem. The basic premise being that superposition states are maintained beyond the retinal apparatus, becoming correlated with neuronal arrays located in the occipital lobe of the brain. Decoherence for these neurons in a superposition of firing and resting, leads to an irreversible dynamical decoupling of the two branches, resulting in the emergence of a single subjective perception. Based upon prior retinal research, it is shown that his theory is unt…
The experimental observation of effects due to Berry's phase in quantum systems is certainly one of the most impressive demonstrations of the correctness of the superposition principle in quantum mechanics. Since Berry's original paper in 1984, the spin 1/2 coupled with rotating external magnetic field has been one of the most studied models where those phases appear. We also consider a special case of this soluble model. A detailed analysis of the coupled differential equations and comparison with exact results teach us why the usual procedure (of neglecting nondiagonal terms) is mathematical…
The covariance of the Schrödinger equation under Galilei boosts and the compatibility of nonrelativistic quantum mechanics with Einstein's equivalence principle have been constrained for so long to the existence of a superselection rule which would prevent a quantum particle from being found in superposition states of different masses. In an effort to avoid this expedient, and thus allow nonrelativistic quantum mechanics to account for unstable particles, recent works have suggested that the usual Galilean transformations are inconsistent with the nonrelativistic limit implied by the Lorentz t…
Space of states of PT symmetrical quantum mechanics is examined. Requirement that eigenstates with different eigenvalues must be orthogonal leads to the conclusion that eigenfunctions belong to the space with an indefinite metric. The self consistent expressions for the probability amplitude and average value of operator are suggested. Further specification of space of state vectors yield the superselection rule, redefining notion of the superposition principle. The expression for the probability current density, satisfying equation of continuity and vanishing for the bound state, is proposed.
A. Dragan and A. Ekert [New Journal of Physics, 22(3), p.033038.] have recently claimed that fundamental properties of quantum physics (e.g. fundamental indeterminism and the principle of superposition) can be derived solely from relativistic considerations, if one takes as physically meaningful superluminal reference frames. In this comment we show that their arguments are flawed and their claims therefore unwarranted.
Recently, Elio Conte has commented a paper by the present author devoted to analyze the possibility of checking experimentally whether the perceptual process can lead to the collapse of the wavefunction. Here we answer to the comments by Conte and we show that he has missed to grasp the crucial elements of our proposal. Morever, we discuss some ideas put forward by Conte concerning the occurrence of quantum superpositions of different states of consciousness and we show that they are rather vague and not cogent.
A recent paper by Souza, Oliveira and Sarthour (SOS) reports the experimental violation of a Leggett-Garg inequality (sometimes referred to as a temporal Bell inequality). The inequality tests for quantum mechanical superposition: if the inequality is violated, the dynamics cannot be explained by a large class of classical theories under the heading of macrorealism. Experimental tests of the LG inequality are beset by the difficulty of performing the necessary so-called 'non-invasive' measurements (which for the macrorealist will extract information from a system of interest without disturbing…
While agreeing with our exact expression for the time dependence of the motion of a free particle in an initial superposition state, corresponding to two identical Gaussians separated by a distance $d$, at temperature $T$, Gobert et al., in the preceding Comment [Phys. Rev. A xxx], dispute our conclusions on decoherence time scales. However, the parameters they used to generate their figures are outside the regime of validity of our interpretation of the results and, moreover, are not of physical interest in that they correspond to $T\approx 0$. The point is that in their figures they have cho…
A recent discussion of quantum limitations to the fidelity with which superpositions of internal atomic energy levels can be generated by an applied, quantized, laser pulse is shown to be based on unrealistic physical assumptions. This discussion assumed the validity of Jaynes-Cummings dynamics for an atom interacting with a laser field in free space, that is, when the atom is not surrounded by a resonant cavity. If the laser field is a multimode quantum coherent state, and the Rabi frequency is much greater than the spontaneous decay rate, then the total atomic decoherence rate is on the orde…
The Schroedinger equation is up-to-a-phase invariant under the Galilei group. This phase leads to the Bargmann's superselection rule, which forbids the existence of the superposition of states with different masses and implies that unstable particles cannot be described consistently in non-relativistic quantum mechanics. In this paper we claim that Bargmann's rule neglects physical effects and that a proper description of non-relativistic quantum mechanics requires to take into account this phase through the Extended Galilei group and the definition of its action on spacetime coordinates.
It has been suggested by Sorkin that a three-slit Young experiment could reveal the validity a fundamental ingredient in the foundations of one of the cornerstones in modern physics namely quantum mechanics. In terms of a certain parameter $κ_S$, it was argued that a non-zero value could imply a breakdown of the fundamental Born's rule as well as the superposition principle. Here we argue that a physical realization of such arguments could lead to an erroneous conclusion and contradict the basic rules of quantum mechanics. In fact, we argue that a proper interpretation of the procedures involv…
In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of spacetime can be associated with a manifold-like structure in which particular patches of spacetime are associated with states or density matrices in specific quantum systems. We argue that quantum entanglement between microscopic degrees of freedom plays an essential role in the emergence of a dual spacetime from the nonperturbative degrees of freedom. In par…
The quantum superposition principle has been extensively utilized in the quantum mechanical description of the bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of near-exact electronic wavefunctions. On the other hand, its existence in composite systems may give rise to nonclassical correlations that are regarded now as a resource in quantum technologies. Here, we approach the electronic ground states of three prototypical molecules from the point of view of fermionic information theory. For the first time in the literat…
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are associated with Fibonacci numbers, this paper shows that the mathematical formalism of quantum mechanics is non-constructive since it permits an undecidable (or effectively impossible) subset of Hilbert space. On the other hand, as it is argued in the paper, if one believes that testability of predictions is the most fundamental property of any physical theory, …
This paper investigates the relationship between subsystems and time in a closed nonrelativistic system of interacting bosons and fermions. It is possible to write any state vector in such a system as an unentangled tensor product of subsystem vectors, and to do so in infinitely many ways. This requires the superposition of different numbers of particles, but the theory can describe in full the equivalence relation that leads to a particle-number superselection rule in conventionally defined subsystems. Time is defined as a functional of subsystem changes, thus eliminating the need for any ref…
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square …
