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25
Quantum Equilibrium and the Origin of Absolute Uncertainty
, 1992
"... The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when ..."
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Cited by 111 (47 self)
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The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when we merely insist that "particles " means particles. While distinctly nonNewtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by "p = IV [ 2.,, A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.
NPcomplete problems and physical reality
 ACM SIGACT News Complexity Theory Column, March. ECCC
, 2005
"... Can NPcomplete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Mal ..."
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Cited by 33 (5 self)
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Can NPcomplete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, MalamentHogarth spacetimes, quantum gravity, closed timelike curves, and “anthropic computing. ” The section on soap bubbles even includes some “experimental ” results. While I do not believe that any of the proposals will let us solve NPcomplete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics. 1
Scattering Theory From Microscopic First Principles
 Physica A
, 2000
"... We sketch a derivation of abstract scattering theory from the microscopic first principles defined by Bohmian mechanics. We emphasize the importance of the fluxacross surfaces theorem for the derivation, and of randomness in the impact parameter of the initial wave functioneven for an, inevitabl ..."
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Cited by 15 (11 self)
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We sketch a derivation of abstract scattering theory from the microscopic first principles defined by Bohmian mechanics. We emphasize the importance of the fluxacross surfaces theorem for the derivation, and of randomness in the impact parameter of the initial wave functioneven for an, inevitably inadequate, orthodox derivation. 1 Dedicated to Joel Lebowitz, with love and admiration, for his 70th birthday. Supported in part by the DFG, by NSF Grant No. DMS9504556, and by the INFN. Preprint submitted to Elsevier Preprint 8 November 1999 1
Is quantum mechanics an island in theoryspace
 Proceedings of the Växjö Conference “Quantum Theory: Reconsideration of Foundations
, 2004
"... This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2norm by some other pnorm, then there are no nontrivial normpreserving linear maps. Second, if we relax the demand that norm be preserved, we ..."
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Cited by 8 (6 self)
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This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2norm by some other pnorm, then there are no nontrivial normpreserving linear maps. Second, if we relax the demand that norm be preserved, we end up with a
The Complexity of Proving Chaoticity and the ChurchTuring Thesis
, 2010
"... Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may “compute the hard or even the incomputable” by measuring observables which correspond to computationa ..."
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Cited by 2 (1 self)
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Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may “compute the hard or even the incomputable” by measuring observables which correspond to computationally hard or even incomputable problems.
On the Brightness of the Thomson Lamp. A Prolegomenon to Quantum Recursion Theory
, 2009
"... Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accele ..."
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Cited by 1 (1 self)
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Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the selfcontradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.
COMPLEX AND UNPREDICTABLE CARDANO
, 806
"... Abstract. This purely recreational paper is about one of the most colorful characters of the Italian Renaissance, Girolamo Cardano, and the discovery of two basic ingredients of quantum theory, probability and complex numbers. The paper is dedicated to Giuseppe Castagnoli on the occasion of his 65th ..."
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Cited by 1 (0 self)
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Abstract. This purely recreational paper is about one of the most colorful characters of the Italian Renaissance, Girolamo Cardano, and the discovery of two basic ingredients of quantum theory, probability and complex numbers. The paper is dedicated to Giuseppe Castagnoli on the occasion of his 65th birthday. Back in the early 1990s, Giuseppe instigated a series of meetings at Villa Gualino, in Torino, which brought together few scattered individuals interested in the physics of computation. By doing so he effectively created and consolidated a vibrant and friendly community of researchers devoted to quantum information science. Many thanks for that! 1. Gambling scholar I always found it an interesting coincidence that the two basic ingredients of modern quantum theory, namely probability and complex numbers, were discovered by the same person, an extraordinary man of many talents, a gambling scholar by the name of Girolamo Cardano.
On classical, fuzzy classical, quantum, and fuzzy quantum systems
 IFSAEUSFLAT
, 2009
"... In this paper we consider physical systems and the concept of their states in the context of the theory of fuzzy sets and systems. In section 1 we give a brief sketch on the fundamental difference between the theories of classical physics and quantum mechanics. In section 2 and 3 we introduce very s ..."
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In this paper we consider physical systems and the concept of their states in the context of the theory of fuzzy sets and systems. In section 1 we give a brief sketch on the fundamental difference between the theories of classical physics and quantum mechanics. In section 2 and 3 we introduce very shortly systems and their states in classical and quantum mechanics, respectively. Section 4 presents the concept of fuzzy systems. We propose to fuzzify the classical systems in section 5 and quantum systems in section 6. In section 7 we start to consider a fuzzy interpretation of the uncertainty principle.