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Hrvoje Nikolić 《Foundations of Physics》2007,37(11):1563-1611
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”,
that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These
myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent
reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory
(QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy.
The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet
allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude
that QM is still a not-yet-completely-understood theory open to further fundamental research. 相似文献
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Jamie Vicary 《International Journal of Theoretical Physics》2008,47(12):3408-3447
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction
of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely
general one in which Hilbert spaces play no special role.
Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates
of the lowering operators. Generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent
states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of
these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures. 相似文献
4.
We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity. 相似文献
5.
Gerard ’t Hooft 《Foundations of Physics》2014,44(5):463-471
It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell’s powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions. 相似文献
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Bruno Galvan 《Journal of statistical physics》2008,131(6):1155-1167
An extension of the Born rule, the quantum typicality rule, has recently been proposed [B. Galvan in Found. Phys. 37:1540–1562 (2007)]. Roughly speaking, this rule states that if the
wave function of a particle is split into non-overlapping wave packets, the particle stays approximately inside the support
of one of the wave packets, without jumping to the others.
In this paper a formal definition of this rule is given in terms of imprecise probability. An imprecise probability space is a measurable space
endowed with a set of probability measures ℘. The quantum formalism and the quantum typicality rule allow us to define a set of probabilities
on (X
T
,ℱ), where X is the configuration space of a quantum system, T is a time interval and ℱ is the σ-algebra generated by the cylinder sets. Thus, it is proposed that a quantum system can be represented as the imprecise stochastic process
, which is a canonical stochastic process in which the single probability measure is replaced by a set of measures. It is
argued that this mathematical model, when used to represent macroscopic systems, has sufficient predictive power to explain
both the results of the statistical experiments and the quasi-classical structure of the macroscopic evolution. 相似文献
7.
Jochen Szangolies 《Foundations of Physics》2018,48(12):1669-1697
In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to Lawvere that illuminates and unifies the different perspectives on self-reference. 相似文献
8.
The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical
physics, as E. Schr?dinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that
quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the
theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order
language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum
non-individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic
variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also
given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined
for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities,
the quasicardinal needs not necessarily be a primitive concept.
Graciela Domenech — Fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). 相似文献
9.
Let Q be an idempotent and right-sided quantale. There is a one to one correspondence between quantifiers and non-commutative binary
operations making Q an idempotent and right-sided quantale. If Q is an atomic and irreducible orthomodular lattice there are only two such operations. Namely, the discrete quantifier and
the indiscrete quantifer.
PACS: 0210.Ab, 0210.De
This work is dedicated to Alberto Román. 相似文献
10.
Franklin E. Schroeck Jr. 《International Journal of Theoretical Physics》2008,47(1):175-184
On any quantum mechanical Hilbert space, the phase space localization operators form a set of operators that are both physically
motivated and form the groundwork for a C* algebra. This set is shown to be informationally complete in the original Hilbert
space. We also revisit the relation between having a complete set of eigenvectors, commutability and compatibility.
Dedicated to G.G. Emch. 相似文献
11.
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, super
partner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges,
super partner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with
the results of quantum mechanics. 相似文献
12.
Aalok 《International Journal of Theoretical Physics》2007,46(12):3216-3229
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the geometry in the background independent quantum mechanics. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kähler manifold. The metric of quantum states in the classical configuration space with the pseudo-Riemannian signature and its possible applications are explored. On contrary to the common perception that a metric for quantum state can yield a natural metric in the configuration space when the limit ?→0, we obtain the metric of quantum states in the configuration space without imposing the limiting condition ?→0. Here Planck’s constant ? is absorbed in the quantity like Bohr radii \(\frac{1}{2mZ\alpha}\sim a_{0}\). While exploring the metric structures associated with Hydrogen like atom, we witness another interesting finding that the invariant lengths appear in the multiple of Bohr’s radii as: ds 2=a 0 2 (? Ψ)2. 相似文献
13.
Gerd Niestegge 《Foundations of Physics》2008,38(3):241-256
The well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization
is further developed. The major results include some new concepts like the different grades of compatibility, the objective
conditional probabilities which are independent of the underlying state and stem from a certain purely algebraic relation
between the events, and an axiomatic approach to quantum mechanics. The main axioms are certain postulates concerning the
conditional probabilities and own intrinsic probabilistic interpretations from the very beginning. A Jordan product is derived
for the observables, and the consideration of composite systems leads to operator algebras on the Hilbert space over the complex
numbers, which is the standard model of quantum mechanics. The paper gives an expository overview of the results presented
in a series of recent papers by the author. For the first time, the complete approach is presented as a whole in a single
paper. Moreover, since the mathematical proofs are already available in the original papers, the present paper can dispense
with the mathematical details and maximum generality, thus addressing a wider audience of physicists, philosophers or quantum
computer scientists. 相似文献
14.
John Harding 《International Journal of Theoretical Physics》2009,48(3):769-802
Abramsky and Coecke (Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, pp. 415–425, IEEE Comput.
Soc., New York, 2004) have recently introduced an approach to finite dimensional quantum mechanics based on strongly compact closed categories
with biproducts. In this note it is shown that the projections of any object A in such a category form an orthoalgebra Proj
A. Sufficient conditions are given to ensure this orthoalgebra is an orthomodular poset. A notion of a preparation for such
an object is given by Abramsky and Coecke, and it is shown that each preparation induces a finitely additive map from Proj
A to the unit interval of the semiring of scalars for this category. The tensor product for the category is shown to induce
an orthoalgebra bimorphism Proj
A×Proj
B→Proj (A
⊗
B) that shares some of the properties required of a tensor product of orthoalgebras.
These results are established in a setting more general than that of strongly compact closed categories. Many are valid in
dagger biproduct categories, others require also a symmetric monoidal tensor compatible with the dagger and biproducts. Examples
are considered for several familiar strongly compact closed categories. 相似文献
15.
The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum
Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent non-unitary
and decoherence. Here we show that a close approximation to standard Quantum Mechanics can be recovered from conditional Quantum
Mechanics for semi-classical clocks, and we use these clocks to compute the minimum decoherence predicted by the Conditional
Probability Interpretation. 相似文献
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Graciela Domenech Hector Freytes Christian de Ronde 《International Journal of Theoretical Physics》2008,47(1):168-174
Kochen–Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual
orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer consistently
to actual and possible properties of the system. By means of a topological argument, more precisely in terms of the existence
of sections of sheaves, we give an extended version of Kochen–Specker theorem over this new structure. This allows us to prove
that contextuality remains a central feature even in the enriched propositional system.
Graciela Domenech is a fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Hector Freytes
is a fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). 相似文献
18.
This is a basically expository article, with some new observations, tracing connections of the quantum potential to Fisher information, to Kähler geometry of the projective Hilbert space of a quantum system, and to the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter.Á Denise 相似文献
19.
It is shown that the hallmark quantum phenomenon of contextuality is present in classical statistical mechanics (CSM). It is first shown that the occurrence of contextuality is equivalent to there being observables that can differentiate between pure and mixed states. CSM is formulated in the formalism of quantum mechanics (FQM), a formulation commonly known as the Koopman–von Neumann formulation (KvN). In KvN, one can then show that such a differentiation between mixed and pure states is possible. As contextuality is a probabilistic phenomenon and as it is exhibited in both classical physics and ordinary quantum mechanics (OQM), it is concluded that the foundational issues regarding quantum mechanics are really issues regarding the foundations of probability. 相似文献
20.
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=εijk
θk and a momentum noncommutativity matrix parameter
β=εijk
βk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints
on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a
lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the
physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant
characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among
the obtained results, we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β,
representing the same particle in presence of a magnetic field
$\vec{B}=q^{-1}\vec{\beta}$. For the other examples, additional
correction terms depending on β appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign. 相似文献