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Ulrich Mohrhoff

Publications and source records attributed to Ulrich Mohrhoff.

33 records · Page 2Linked to original sources
arXiv2004

Probabilities from envariance?

Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's derivation it is argued that this claim is exaggerated if not wholly unjustified. In order to demonstrate that Born's rule arises noncircularly from deterministically evolving quantum states, it is not sufficient to assume that quantum states are somehow associated with probabilities and then prove that these probabilities are given by Born's rule. One has to show how irreducible probabilities can arise in the context of an ontological no-collapse interpretation of quantum states. It is argued that the reason why all attempts to do this have so far failed is that quantum states are fundamentally algorithms for computing correlations between possible measurement outcomes, rather than evolving ontological states.

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arXiv2003

Do quantum states evolve? Apropos of Marchildon's remarks

Marchildon's (favorable) assessment (quant-ph/0303170, to appear in Found. Phys.) of the Pondicherry interpretation of quantum mechanics raises several issues, which are addressed. Proceeding from the assumption that quantum mechanics is fundamentally a probability algorithm, this interpretation determines the nature of a world that is irreducibly described by this probability algorithm. Such a world features an objective fuzziness, which implies that its spatiotemporal differentiation does not "go all the way down". This result is inconsistent with the existence of an evolving instantaneous state, quantum or otherwise.

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arXiv2002

Reflections on the Spatiotemporal Aspects of the Quantum World

The proper resolution of the so-called measurement problem requires a "top-down" conception of the quantum world that is opposed to the usual "bottom-up" conception, which builds on an intrinsically and maximally differentiated manifold. The key to that problem is that the fuzziness of a variable can manifest itself only to the extent that less fuzzy variables exist. Inasmuch as there is nothing less fuzzy than the metric, this argues against a quantum-gravity phenomenology and suggests that a quantum theory of gravity is something of a contradiction in terms - a theory that would make it possible to investigate the physics on scales that do not exist, or to study the physical consequences of a fuzziness that has no physical consequences, other than providing a natural cutoff for the quantum field theories of particle physics.

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arXiv2002

Against "knowledge"

Quantum "states" are objective probability measures. Because their dependence on a time is not the time dependence of an evolving state, they are neither states of Nature nor "states of knowledge." There is no such thing as an evolving state. This disposes of the problem posed by the apparent existence of two modes of evolution. What essentially stands in the way of a consistent ontological interpretation of the quantum theory is our habit of projecting into the quantum world the detached, intrinsically differentiated spatiotemporal background of classical physics, for this is what entails the existence of an evolving state. An objective probability measure is the formal expression of an objective indefiniteness, such as the positional indefiniteness that contributes to "fluff out" matter. An objective indefiniteness entails that the values of certain observables are extrinsic (possessed because they are indicated) rather than intrinsic (indicated because they are possessed). This dependence on value-indicating facts is not a dependence on anything external to the quantum world. The latter constitutes a free-standing reality that owes nothing to observers, "information," or our interventions into "the course of Nature."

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arXiv2002

Why the laws of physics are just so

Does a world that contains chemistry entail the validity of both the standard model of elementary particle physics and general relativity, at least as effective theories? This article shows that the answer may very well be affirmative. It further suggests that the very existence of stable, spatially extended material objects, if not the very existence of the physical world, may require the validity of these theories.

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arXiv2002

Making sense of a world of clicks

In a recent article O. Ulfbeck and A. Bohr (Foundations of Physics 31, 757, 2001) have stressed the genuine fortuitousness of detector clicks, which has also been pointed out, in different terms, by the present author (American Journal of Physics 68, 728, 2000). In spite of this basic agreement, the present article raises objections to the presuppositions and conclusions of Ulfbeck and Bohr, in particular their rejection of the terminology of indefinite variables, their identification of reality with "the world of experience," their identification of experience with what takes place "on the spacetime scene," and the claim that their interpretation of quantum mechanics is "entirely liberated" from classical notions. An alternative way of making sense of a world of uncaused clicks is presented. This does not invoke experience but deals with a free-standing reality, is not fettered by classical conceptions of space and time but introduces adequate ways of thinking about the spatiotemporal aspects of the quantum world, and does not reject indefinite variables but clarifies the implications of their existence.

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arXiv2001

Two theories of decoherence

Theories of decoherence come in two flavors---Platonic and Aristotelian. Platonists grant ontological primacy to the concepts and mathematical symbols by which we describe or comprehend the physical world. Aristotelians grant it to the physical world. The significance one attaches to the phenomenon of decoherence depends on the school to which one belongs. The debate about the significance of quantum states has for the most part been carried on between Platonists and Kantians, who advocate an epistemic interpretation, with Aristotelians caught in the crossfire. For the latter, quantum states are neither states of Nature nor states of knowledge. The real issue is not the kind of reality that we should attribute to quantum states but the reality of the spatial and temporal distinctions that we make. Once this is recognized, the necessity of attributing ontological primacy to facts becomes obvious, the Platonic stance becomes inconsistent, and the Kantian point of view becomes unnecessarily restrictive and unilluminating.

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arXiv2001

A space for the quantum world

Epistemic interpretations of quantum mechanics fail to address the puzzle posed by the occurrence of probabilities in a fundamental physical theory. This is a puzzle about the physical world, not a puzzle about our relation to the physical world. Its solution requires a new concept of physical space, presented in this article. An examination of how the mind and the brain construct the phenomenal world reveals the psychological and neurobiological reasons why we think about space in ways that are inadequate to the physical world. The resulting notion that space is an intrinsically partitioned expanse has up to now stood in the way of a consistent ontological interpretation.

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arXiv2001

Unveiled reality: comment on d'Espagnat's note on measurement

According to d'Espagnat we must choose between nonlinear breaks in quantum state evolution and weak objectivity. In this comment it is shown that this choice is forced on us by an inconsistent pseudo-realistic interpretation of quantum states. A strongly objective one-world interpretation of linear quantum mechanics is presented. It is argued that the weak objectivity favored by d'Espagnat is, in fact, inconsistent with quantum mechanics.

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arXiv2001

Objective probabilities, quantum counterfactuals, and the ABL rule

The ABL rule is derived as a tool of standard quantum mechanics. The ontological significance of the existence of objective probabilities is discussed. Objections by Kastner and others to counterfactual uses of the ABL rule are refuted. Metaphysical presumptions leading to such views as Kastner is defending in her Comment are examined and shown to be unwarranted.

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arXiv2000

Quantum Mechanics and the Cookie Cutter Paradigm

What has so far prevented us from decrypting quantum mechanics is the Cookie Cutter Paradigm, according to which the world's synchronic multiplicity derives from surfaces that carve up space in the manner of three-dimensional cookie cutters. This insidious notion is shown to be rooted in our neurophysiological make-up. An effort is made to liberate the physical world from this innate fallacy.

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arXiv2000

The One, the Many, and the Quantum

The problem of understanding quantum mechanics is in large measure the problem of finding appropriate ways of thinking about the spatial and temporal aspects of the physical world. The standard, substantival, set-theoretic conception of space is inconsistent with quantum mechanics, and so is the doctrine of local realism, the principle of local causality, and the mathematical physicist's golden calf, determinism. The said problem is made intractable by our obtruding onto the physical world a theoretical framework that is more detailed than the physical world. This framework portraits space and time as infinitely and intrinsically differentiated, whereas the physical world is only finitely differentiated spacewise and timewise, namely to the extent that spatiotemporal relations and distinctions are warranted by facts. This has the following consequences: (i) The contingent properties of the physical world, including the times at which they are possessed, are indefinite and extrinsic. (ii) We cannot think of reality as being built "from the bottom up", out of locally instantiated physical properties. Instead we must conceive of the physical world as being built "from the top down": By entering into a multitude of spatial relations with itself, "existence itself" takes on both the aspect of a spatially differentiated world and the aspect of a multiplicity of formless relata, the fundamental particles. At the root of our interpretational difficulties is the "cookie cutter paradigm", according to which the world's synchronic multiplicity is founded on the introduction of surfaces that carve up space in the manner of three-dimensional cookie cutters. The neurophysiological underpinnings of this insidious notion are discussed.

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arXiv2000

The Pondicherry interpretation of quantum mechanics

This article presents a novel interpretation of quantum mechanics. It extends the meaning of ``measurement'' to include all property-indicating 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 property-indicating 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 deep-seated 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. There 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.

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arXiv1999

Quantum mechanics and elements of reality

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 time-symmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have objected to Vaidman's time-symmetrized 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 quantum-mechanical 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 quantum-mechanical properties is that quantum mechanics presupposes property-defining 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 quantum-mechanical correlations, such as the spatial nonseparability of the world.

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