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Notes on a Paulian idea: foundational, historical, anecdotal and forwardlooking thoughts on the quantum
"... This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of l ..."
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Cited by 13 (4 self)
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This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of letters written to various friends and colleagues
From Heisenberg to Gödel via Chaitin
, 2008
"... In 1927 Heisenberg discovered that the “more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa”. Four years later Gödel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. A ..."
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Cited by 11 (9 self)
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In 1927 Heisenberg discovered that the “more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa”. Four years later Gödel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. As both results express some kind of impossibility it is natural to ask whether there is any relation between them, and, indeed, this question has been repeatedly asked for a long time. The main interest seems to have been in possible implications of incompleteness to physics. In this note we will take interest in the converse implication and will offer a positive answer to the question: Does uncertainty imply incompleteness? We will show that algorithmic randomness is equivalent to a “formal uncertainty principle ” which implies Chaitin’s informationtheoretic incompleteness. We also show that the derived uncertainty relation, for many computers, is physical. This fact supports the conjecture that uncertainty implies randomness not only in mathematics, but also in physics.
The world according to quantum mechanics (or, the 18 errors of Henry P. Stapp)
, 2001
"... 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,” ePrint quantph/0103043, to appear in Foundations of Physics) are pointed out. An interpretation of (standard) QM that avoids these ..."
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Cited by 10 (4 self)
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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,” ePrint quantph/0103043, to appear in Foundations of Physics) are pointed out. An interpretation of (standard) QM that avoids these errors is presented.
Foundational, Historical, Anecdotal and ForwardLooking Thoughts on the Quantum Selected Correspondence, 1995–2001
, 2001
"... This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of l ..."
Abstract
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This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of letters written to various friends and colleagues
The Pondicherry interpretation of quantum mechanics
, 1999
"... This article presents a novel interpretation of quantum mechanics. It extends the meaning of “measurement ” to include all propertyindicating facts. Intrinsically space is undifferentiated: there are no points on which a world of locally instantiated physical properties could be built. Instead real ..."
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This article presents a novel interpretation of quantum mechanics. It extends the meaning of “measurement ” to include all propertyindicating facts. Intrinsically space is undifferentiated: there are no points on which a world of locally instantiated physical properties could be built. Instead reality is built on facts, in the sense that the properties of things are extrinsic, or supervenient on the facts. The actual extent to which the world is spatially and temporally differentiated (that is, the extent to which spatiotemporal relations and distinctions are warranted by the facts) is necessarily limited. Notwithstanding that the state vector does nothing but assign probabilities, quantum mechanics affords a complete understanding of the actual world. If there is anything that is incomplete, it is the actual world, but its incompleteness exists only in relation to a conceptual framework that is more detailed than the actual world. Two deepseated misconceptions are responsible for the interpretational difficulties associated with quantum mechanics: the notion that the spatial and temporal aspects of the world are adequately represented by sets with the cardinality of the real numbers, and the notion of an instantaneous state that evolves in time. The latter is an unwarranted (in fact, incoherent) projection of our apparent “motion in time ” into the world of physics. Equally unwarranted, at bottom, is the use of causal concepts. Therer nevertheless exists a “classical ” domain in which language suggestive of nomological necessity may be used. Quantum mechanics not only is strictly consistent with the existence of this domain but also presupposes it in several ways. I.
Undecidability in quantum mechanics
, 1998
"... The logical structure of quantum mechanics is investigated. After some remarks on formal systems and interpretations, it is shown that Bohr’s complementarity can be seen as an undecidable proposition. The flowing of the time prevents the birth of contradictions in nature, because it poses a cut betw ..."
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The logical structure of quantum mechanics is investigated. After some remarks on formal systems and interpretations, it is shown that Bohr’s complementarity can be seen as an undecidable proposition. The flowing of the time prevents the birth of contradictions in nature, because it poses a cut between two different, but complementary aspects of the reality. PACS03.65.Bz Foundations, theory of measurement, miscellaneous theories PACS02.10.By Logic and foundations
Quantum Mechanics and Elements of Reality
, 1999
"... It is widely accepted that a Born probability of 1 is sufficient for the existence of a corresponding element of reality. Recently Vaidman has extended this idea to the ABL probabilities of the timesymmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several auth ..."
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It is widely accepted that a Born probability of 1 is sufficient for the existence of a corresponding element of reality. Recently Vaidman has extended this idea to the ABL probabilities of the timesymmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have objected to Vaidman’s timesymmetrized elements of reality without casting doubt on the widely accepted sufficiency condition for ‘ordinary ’ elements of reality. In this paper I show that while the proper truth condition for a quantum counterfactual is an ABL probability of 1, neither a Born probability of 1 nor an ABL probability of 1 is sufficient for the existence of an element of reality. The reason this is so is that the contingent properties of quantummechanical systems are extrinsic. To obtain this result, I need to discuss objective probabilities, retroactive causality, and the objectivity or otherwise of the psychological arrow of time. One consequence of the extrinsic nature of quantummechanical properties is that quantum mechanics presupposes propertydefining actual events (or states of affairs) and therefore cannot be called upon to account for their occurrence (existence). Neither these events nor the correlations between them are capable of explanation, the former because they are causal primaries, the latter because they are fundamental: there are no underlying causal processes. Causal connections are something we project onto the statistical correlations, and this works only to the extent that statistical variations can be ignored. There are nevertheless important conclusions to be drawn from the quantummechanical correlations, such as the spatial nonseparability of the world.
From Heisenberg to Gödel via Chaitin
, 2005
"... In 1927, Heisenberg discovered that the “more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa. ” Four years later Gödel showed that a finitely specified, consistent formal system which is large enough ..."
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In 1927, Heisenberg discovered that the “more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa. ” Four years later Gödel showed that a finitely specified, consistent formal system which is large enough