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1.
Recent works have independently suggested that quantum mechanics might permit procedures that fundamentally transcend the
power of Turing Machines as well as of ‘standard’ Quantum Computers. These approaches rely on and indicate that quantum mechanics
seems to support some infinite variant of classical parallel computing.
We compare this new one with other attempts towards hypercomputation by separating (1) its %principal computing capabilities
from (2) realizability issues. The first are shown to coincide with recursive enumerability; the second are considered in
analogy to ‘existence’ in mathematical logic.
PACS (2003): 03.67.
Supported by DFG project Zi1009/1-1. 相似文献
2.
A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation
of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic
if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This
definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in
terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the
dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically,
proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under
chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism
towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’ 相似文献
3.
We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering ‘mass’ as
a function of coordinates. Its usefulness in solving potential problems is discussed with specific examples. We also discuss
the ‘physical’ significance of the supersymmetric states in this formalism. 相似文献
4.
On the face of some recent experiments claiming the simultaneous presence of both ‘sharp interference’ and ‘highly reliable
which way information’ and some others casting light on the origin of complementarity in quantum interferometric experiments, the whole
issue is reviewed on the basis of our earlier precise formulation of Bohr’s complementarity principle. It is pointed out that
contradicting the principle (in this specific formulation) is impossible without contradicting quantum mechanics and a lack
of general consensus regarding the origin of the mutual exclusiveness is at the root of the controversy and confusions.
相似文献
5.
Henry P. Stapp 《Foundations of Physics》2012,42(5):647-655
Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ that he has developed, the
issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over
long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises
some essentially classical-physics-type assumptions that are not entailed by the precepts of quantum mechanics. Thus whatever
is proved is not a feature of quantum mechanics, but is a property of a theory that tries to combine quantum theory with quasi-classical
features that go beyond what is entailed by quantum theory itself. One cannot logically prove properties of a system by establishing,
instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths’ rejection of
hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that
does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had
examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But
he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by
his ‘consistent quantum theory’ shows that the cited proof is valid within that restrictive version of quantum theory. An
added section responds to Griffiths’ reply, which cites general possibilities of ambiguities that might make what is to be
proved ill-defined, and hence render the pertinent ‘consistent framework’ ill defined. But the vagaries that he cites do not
upset the proof in question, which, both by its physical formulation and by explicit identification, specify the framework
to be used. Griffiths confirms the validity of the proof insofar as that pertinent framework is used. The section also shows,
in response to Griffiths’ challenge, why a putative proof of locality that he has described is flawed. 相似文献
6.
Willem M. de Muynck 《Foundations of Physics》2004,34(5):717-770
The Copenhagen interpretation is critically considered. A number of ambiguities, inconsistencies and confusions are discussed. It is argued that it is possible to purge the interpretation so as to obtain a consistent and reasonable way to interpret the mathematical formalism of quantum mechanics, which is in agreement with the way this theory is dealt with in experimental practice. In particular, the essential role attributed by the Copenhagen interpretation to measurement is acknowledged. For this reason it is proposed to refer to it as a neo-Copenhagen interpretation. 相似文献
7.
We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ‘infinite’,
Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into
single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and
algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct
many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are: new
algebras for infinite statistics,q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen
order, ‘doubly-infinite’ statistics, many representations of orthostatistics, Hubbard statistics and its variations. 相似文献
8.
We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson’s quantum mechanics.
This generalization enables us to describe quantum system with channel couplings and optical potential in a real time stochastic
approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation 相似文献
9.
The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the
spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal
objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem,
as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity
and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the so-called “quantum liar paradox,”
an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s
implications for quantum gravity. 相似文献
10.
Ruth E. Kastner 《Foundations of Physics》2012,42(8):1094-1113
A recent ontological variant of Cramer’s Transactional Interpretation, called “Possibilist Transactional Interpretation” or
PTI, is extended to the relativistic domain. The present interpretation clarifies the concept of ‘absorption,’ which plays
a crucial role in TI (and in PTI). In particular, in the relativistic domain, coupling amplitudes between fields are interpreted
as amplitudes for the generation of confirmation waves (CW) by a potential absorber in response to offer waves (OW), whereas
in the nonrelativistic context CW are taken as generated with certainty. It is pointed out that solving the measurement problem
requires venturing into the relativistic domain in which emissions and absorptions take place; nonrelativistic quantum mechanics
only applies to quanta considered as ‘already in existence’ (i.e., ‘free quanta’), and therefore cannot fully account for
the phenomenon of measurement, in which quanta are tied to sources and sinks. 相似文献
11.
U. Mohrhoff 《Foundations of Physics》2009,39(2):137-155
This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves,
Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion
beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including
the claim that different pure states may legitimately be assigned to the same system at the same time, and the claim that
the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard
the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads
to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are
neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible
outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the
only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these
are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation
of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic.
This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory.
Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various
reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify
an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians
refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the
macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests
itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental
in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in
the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms
of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe
its manifestation. 相似文献
12.
A method for introducing relativistic quantum mechanics to energy students is described. The method complements existing modern
physics courses and relies on Feynman’s relativistic path integral approach to display a relationship between classical dynamics,
quantum theory, and relativistic quantum theory. 相似文献
13.
We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that
these correlations do not entail any form of “non-locality”, when viewed in the context of this interpretation. The abandonment
of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally
defined) separability, and locality. 相似文献
14.
We clarify Bohrs interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible. 相似文献
15.
The Geneva–Brussels approach to quantum mechanics (QM) and the semantic realism (SR) nonstandard interpretation of QM exhibit some common features and some deep conceptual differences. We discuss in this paper two elementary models provided in the two approaches as intuitive supports to general reasonings and as a proof of consistency of general assumptions, and show that Aerts’ quantum machine can be embodied into a macroscopic version of the microscopic SR model, overcoming the seeming incompatibility between the two models. This result provides some hints for the construction of a unified perspective in which the two approaches can be properly placed. 相似文献
16.
17.
Ulrich Mohrhoff 《Foundations of Physics》2002,32(2):217-254
Several errors in Stapp's interpretation of quantum mechanics and its application to mental causation (Henry P. Stapp, Quantum theory and the role of mind in nature, Foundations of Physics
31, 1465–1499 (2001)) are pointed out. An interpretation of (standard) quantum mechanics that avoids these errors is presented. 相似文献
18.
C. Wetterich 《Annals of Physics》2010,325(4):852-898
19.
Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing surrealistic trajectories proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian quantum mechanics in which only Bohmian positions supervene on our experience is discussed. 相似文献
20.
Fabio Scardigli 《Foundations of Physics》2007,37(8):1278-1295
The Titius–Bode law for planetary distances is reviewed. A model describing the basic features of this rule in the “quantum-like”
language of a wave equation is proposed. Some considerations about the ’t Hooft idea on the quantum behavior of deterministic
systems with dissipation are discussed. 相似文献