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1.
Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic
interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually
taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free”
interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least
equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically
intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something
to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make
sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett
interpretation. 相似文献
2.
Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics
and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics. Of course,
at the nuclear level, because of some complications, it is not clear that we can claim the same confidence. One way of taking
these complications and corrections into account seems to be a modification of the standard quantum theory. In this paper
and its follow ups we consider a straightforward way of extending quantum theory. Our method is based on a Bohmian approach.
We show that this approach has the essential ability for extending quantum theory, and we do this by introducing “non-Bohmian”
forms for the quantum potential. 相似文献
3.
We have considered the possibility of formation of a massless particles with spin 1 in the region of negative energies, within the framework of the Weyl-type equation for neutrinos. It is proved that the represented approach allows to get a stable structural formation in the ground state, which can be interpreted as a fundamental massless particle. The structure and properties of this vector boson are studied in detail. The problem of entangling two vector bosons with projections of spins +1 and −1 and, accordingly, the formation of a zero-spin boson is studied within the framework of a complex stochastic matrix equations of the Langevin type. The paper discusses the structure of the Bose particle of a scalar field and the space–time properties of an empty space (quantum vacuum). 相似文献
4.
In 1960–1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons. The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his calculus by developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent. A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms. 相似文献
5.
We argue that it is fundamentally impossible to recover information about quantum superpositions when a quantum system has
interacted with a sufficiently large number of degrees of freedom of the environment. This is due to the fact that gravity
imposes fundamental limitations on how accurate measurements can be. This leads to the notion of undecidability: there is
no way to tell, due to fundamental limitations, if a quantum system evolved unitarily or suffered wavefunction collapse. This
in turn provides a solution to the problem of outcomes in quantum measurement by providing a sharp criterion for defining
when an event has taken place. We analyze in detail in examples two situations in which in principle one could recover information
about quantum coherence: (a) “revivals” of coherence in the interaction of a system with the measurement apparatus and the
environment and (b) the measurement of global observables of the system plus apparatus plus environment. We show in the examples
that the fundamental limitations due to gravity and quantum mechanics in measurement prevent both revivals from occurring
and the measurement of global observables. It can therefore be argued that the emerging picture provides a complete resolution
to the measurement problem in quantum mechanics. 相似文献
6.
A powerful approach to solve the Coulombic quantium three-body problem is proposed.The approach is expeonentially convergent and more efficient than the hyperspherical coordinate method and the correlaion-function hyperspherical harmonic method.This approach is numerically competitive with the variational methods.Such as that using the Hylleraas-type basis functions,Numerical comparisons are made to demonstrate the efficiency of this approach,by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom.The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in thuis paper and the true wavefunction.This full matching was not reached by most other methods.For example,the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock.Two important approaches are proposed in this work to reach this full matching:the coordinate transfomation method and the asymptotic series method.Besides these,this work makes use of the least square method to substitute complicated numerical integrations in solving the Schroedinger equation without much loss of accuracy,which is routinely used by people to fit a theoretical curve with discrete experimental data,but here is used to simplify the computation. 相似文献
7.
The state variables in the novel model introduced in this paper are the fields playing this role in the classical Landau-Tisza
model and additional fields of mass, entropy (or temperature), superfluid velocity, and gradient of the superfluid velocity,
all depending on the position vector and another tree dimensional vector labeling the scale, describing the small-scale structure
developed in 4He superfluid experiencing turbulent motion. The fluxes of mass, momentum, energy, and entropy in the position space as well
as the fluxes of energy and entropy in scales, appear in the time evolution equations as explicit functions of the state variables
and of their conjugates. The fundamental thermodynamic relation relating the fields to their conjugates is left in this paper
undetermined. The GENERIC structure of the equations serves two purposes: (i) it guarantees that solutions to the governing
equations, independently of the choice of the fundamental thermodynamic relation, agree with the observed compatibility with
thermodynamics, and (ii) it is used as a guide in the construction of the novel model. 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.
Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied
with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior of the
cosmic string space-time and that they loose this property at the singular boundary except for the cosmic string space-times
with the following deficit angles: Δ=2 π(1−1/ n), n=1,2,… .
A connection between smoothness of fields at the conical singularity and the scalar and electromagnetic conical bremsstrahlung
is discussed. It is also argued that the smoothness assumption of fields at the singularity is equivalent to the Aliev and
Gal’tsov “quantization” condition leading to the above mentioned discrete spectrum of the deficit angle. 相似文献
12.
The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium
statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that
relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics
of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics,
but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we
do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics
of the full system 相似文献
13.
I argue that quantum theory can, and in fact must, be applied to the Universe as a whole. After a general introduction, I discuss two concepts that are essential for my chain of arguments: the universality of quantum theory and the emergence of classical behaviors by decoherence. A further motivation is given by the open problem of quantum gravity. I then present the main ingredients of quantum cosmology and discuss their relevance for the interpretation of quantum theory. I end with some brief epistemological remarks. 相似文献
15.
I argue that algebraic quantum field theory (AQFT) permits an undisturbed view of the right ontology for fundamental physics, whereas standard (or Lagrangian) QFT offers different mutually incompatible ontologies. My claim does not depend on the mathematical inconsistency of standard QFT but on the fact that AQFT has the same concerns as ontology, namely categorical parsimony and a clearly structured hierarchy of entities. 相似文献
16.
It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the
same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is
further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent
rays that prove the theorem. 相似文献
17.
An appropriate kind of curved Hilbert space is developed in such a manner that it admits operators of
- and
-differentiation, which are the analogues of the familiar covariant and D-differentiation available in a manifold. These tools are then employed to shed light on the space-time structure of Quantum
Mechanics, from the points of view of the Feynman ‘path integral’ and of canonical quantisation. (The latter contains, as
a special case, quantisation in arbitrary curvilinear coordinates when space is flat.) The influence of curvature is emphasised
throughout, with an illustration provided by the Aharonov-Bohm effect. 相似文献
18.
Recently, Gudder proved that the set of all generalized quantum gates coincides the set of all contractions in a finite-dimensional
Hilbert space (S. Gudder, Int. J. Theor. Phys. 47:268–279, 2008). In this note, we proved that the set of all generalized
quantum gates is a proper subset of the set of all contractions on an infinite dimensional separable Hilbert space ℋ. Meanwhile,
we proved that the quantum operation deduced by an isometry is an extreme point of the set of all quantum operations on ℋ.
This subject is supported by NSF of China (10571113). 相似文献
19.
Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein’s preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein’s attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927. 相似文献
20.
Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments have been explained by some theoretical works. We study electronic double-slit diffraction with a quantum mechanical approach and obtain the following results: (1) When the ratio of d + a /a=n (n = 1,2, 3,...), orders n, 2n, 3n,... are missing in diffraction pattern. (2) When the ratio of d+a/a≠ n (n =1,2, 3,...), there is a not missing order in diffraction pattern. (3) The slit thickness c has a large affect on the electronic diffraction pattern, which is a new quantum effect. We believe that all the predictions in our work can be tested by the electronic double slit diffraction experiment. 相似文献
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