III Workshop sobre Filosofía, Lógica e Historia
de la Mecánica Cuántica en el Cono Sur
VIII Encuentro de Filosofía e Historia de la Ciencia del Cono Sur
16 al 20 de octubre de 2012 - Universidad de Santiago de Chile – CENI
La teoría cuántica permite predecir con exactitud sorprendente los resultados de experimentos y
desarrollar nuevas tecnologías, desde la criptografía cuántica y teleportación cuántica hasta el desarrollo
de nuevas computadoras cuánticas. Sin embargo, después de más de un siglo de su creación, muchas de
las preguntas planteadas originalmente permanecen sin respuesta: ¿de qué habla la mecánica cuántica?
Luego del VI Encuentro AFHIC en Montevideo y del VII Encuentro AFHIC en Canela-RS, Brasil, por
tercera vez nos encontramos varios grupos del cono sur para trabajar conjuntamente y discutir
cuestiones referentes a la interpretación de la mecánica cuántica: la lógica subyacente, las nociones de
posibilidad, determinación, indeterminación, substancia y objetividad, la lógica de la computación
cuántica, la posibilidad o no de una ontología de individuos, etc. Buscamos, en definitiva, analizar la
teoría cuántica para comprender su significado, su referencia y su alcance.
Organizado por: Décio Krause, Christian de Ronde y Hector Freytes.
TRABAJOS QUE SE DISCUTIRAN EN EL WORKSHOP:
The “Unreasonable” Effectiveness of Mathematics in Quantum Mechanics
Arezoo Islami - Stanford University.
Why does mathematics work so well in describing some parts of the world- in theories of modern
physics, for instance? In particular, can we provide an explanation for this phenomenon or is it
completely unreasonable? Eugene Wigner’s seminal paper (1960) has reformulated this problem as the
problem of ”The Unreasonable Effectiveness of Mathematics in Natural Sciences” . Since its
publication, this paper has created much controversy in the literature and has provoked many
philosophers, physicists and mathematicians alike to respond to this paper. In recent years, Mark
Colyvan (2009) and Penelope Maddy (2009) have made substantial contributions to Wigner’s problem
calling for further study of relevant history, e.g. history of Quantum mechanics, Maxwell equations, etc.
This paper is an exercise in the study of the development of Hilbert space formalism of quantum
mechanics, focusing on the employment of complex numbers in the postulates of quantum mechanics.
I will argue that once we scrutinize what exactly we mean by ”effectiveness” of mathematics, it
becomes rather clear that it is due to idealizations and approximations that mathematics plays such an
important role in quantum mechanics. Finally, I will defend Wigner against objections to his account,
most of which are based on a profound misunderstanding of his 1960 paper.
El Estatuto Epistemológico del Principio de Simetría en Weizsäcker
Cesar Fabián Ávila - Pontificia Universidad Católica de Chile.
Nuestro trabajo pretende investigar en el pensamiento de Weizsäcker – caracterizado como un
kantismo no estricto – el estatuto epistemológico del principio de simetría, principio que tendría lugar
en la razón en su función reguladora y unificadora sintética, proyectaría esta unidad a la naturaleza,
mostrando que la frontera entre la razón teórica y la practica no es tan rígida en el sentido kantiano.
Para Weizsäcker es la mecánica cuántica, en continuidad de la interpretación de Niels Bohr, el lugar
teórico adecuado para mostrar la libertad que posee el observador cuando define el tipo de explicación,
en contra de una estricta interpretación kantiana de los principios metafísicos de la ciencia de la
naturaleza.
Carl Friedrich von Weizsäcker, Die Einheit der Natur, München. 1971
Carl Friedrich von Weizsäcker, Aufbau der Physik, München, 1985
Carl Friedrich von Weizsäcker, Zeit und Wissen, München, 1992 .
Carl Friedrich von Weizsäcker, Der begriffliche Aufbau der theoretischen Physik, Stuttgart, 2004.
Carl Friedrich von Weizsäcker, Zum Weltbild der Physik, Leipzig, 2007
Quantum metaphysics and quantum logic
Hernán Pringe - Conicet-UBA-UDP
Transcendental approaches to modern physics have received renewed attention from scholars. The aim
of this talk is to contribute to this debate by investigating the possibility of providing quantum theory
with metaphysical principles in a Kantian sense. For this purpose, we will attempt to show how such
principles may be gained from the application to the quantum case of the general principles of
metaphysics of nature established by Kant. We shall begin by briefly discussing Kant’s views on these
principles (§1). We shall then analyze the transcendental status of quantum objectivity (§§2-3). This will
give us the clue to identify certain synthetic a priori judgments as metaphysical principles of quantum
theory, i.e., as the principles of quantum metaphysics (§4). Finally, we shall consider one of such
principles (§5) and we shall discuss its role in a philosophical foundation of quantum logic (§6).
¿Qué prueba un experimento? El caso del efecto Compton
Alejandro Cassini - CONICET-Universidad de Buenos Aires
El efecto Compton se consideró en su momento, y todavía se considera, como una evidencia
experimental decisiva acerca de la composición cuántica de la luz, esto es, como una prueba
experimental de la existencia del fotón. Sin embargo, en los experimentos de Compton no se realiza
ninguna observación o medición de partículas o sus propiedades. Todas las magnitudes físicas
observadas pueden describirse enteramente en términos ondulatorios: dirección, frecuencia y longitud
2 de onda de los rayos X dispersados por la materia. El fotón no es observado, sino postulado para
explicar los resultados experimentales. En principio, sería posible explicar los mismos resultados
mediante hipótesis que no postularan la existencia de fotones. Argumentaré que todos los experimentos
existenciales en física de partículas tienen la misma estructura: la partícula “descubierta” constituye la
mejor explicación causal, disponible en un momento determinado, de los resultados observados en el
experimento en cuestión. Este hecho lleva a preguntarse qué es lo que prueba un experimento en
general y cómo deben interpretarse las afirmaciones de existencia en física teórica.
Sobre el pensamiento físico y epistemológico de Paul Dirac
Nahuel Sznajderhaus - Universidad de Buenos Aires
Paul Dirac fue uno de los físicos más importantes en la revolución cuántica. Entre sus trabajos
fundacionales se encuentra la ecuación que determina la evolución de una partícula relativista de spin ½
y el desarrollo de la primera versión matemáticamente consistente de la mecánica cuántica presentada
en su famoso libro de 1930. Dirac participó de las profundas discusiones referidas a la interpretación de
la teoría sosteniendo una posición fundada en una concepción pragmática y positiva de la física. En este
trabajo nos interesa exponer y analizar el pensamiento de Paul Dirac, señalando la importancia de su
obra en la formulación e interpretación actual de la mecánica cuántica.
Aspectos transcendentais do estruturalismo científico
Patrícia Kauark-Leite - Departamento de Filosofia da Universidade Federal de Minas Gerais
O realismo estrutural foi introduzido no debate contemporâneo sobre o realismo científico em 1989
por John Worrall. Quase dez anos depois, James Ladyman (1998) propôs uma distinção entre duas
formas de interpretar o realismo estrutural: uma ôntica e outra epistêmica. A primeira, nomeada de
realismo estrutural ôntico, defende que as teorias físicas contemporâneas só podem se comprometer
com a existência de estruturas e relações e não com objetos, indivíduos e propriedades. Assim, a
máxima: tudo o que existe são as estruturas. A segunda, nomeada realismo estrutural epistêmico, tem
sido muita vezes identificada como uma posição kantiana, por enfatizar que só podemos conhecer as
estruturas. O nosso objetivo é mostrar que essa última versão, por ser fundamentalmente uma posição
realista, não é consistente com perspectiva transcendental. Procuraremos defender o estruturalismo
transcendental como uma alternativa entre o realismo estrutural, defendido entre outros por James
Ladyman e Steven French e o empirismo estrutural, de Bas van Fraassen e Otávio Bueno.
Paraconsistent Quasi-Set Theory
Décio Krause - Department of Philosophy, Federal University of Santa Catarina, Florianópolis, SC - Brazil
Paraconsistent logics are logics that can be used to base inconsistent but non- trivial systems. In
paraconsistent set theories, we can quantify over sets that in standard set theories (that are based on
classical logic), if consistent, would lead to contradictions, such as the Russell set, R = {x : x ∉ x}.
3 Quasi-set theories are mathematical systems built for dealing with collections of indiscernible elements.
The basic motivation for the development of quasi-set theories came from quantum physics, where
indiscernible entities need to be considered (in most interpretations). Usually, the way of dealing with
indiscernible objects within classical logic and mathematics is by restricting them to certain structures,
in a way so that the relations and functions of the structure are not sufficient to individuate the objects;
in other words, such structures are not rigid. In quantum physics, this idea appears when symmetry
conditions are introduced, say by choosing symmetric and anti-symmetric functions (or vectors) in the
relevant Hilbert spaces. But in standard mathematics, such as that built in Zermelo-Fraenkel set theory
(ZF), any structure can be extended to a rigid structure. That means that, although we can deal with
certain objects as they were indiscernible, we realize that from “outside” of these structures these
objects are no more indiscernible, for they can be individualized in the extended rigid structures: ZF is a
theory of individuals, distinguishable objects. In quasi-set theory, it seems that there are structures that
cannot be extended to rigid ones, so it seems that they provide a “natural” mathematical framework for
expressing quantum facts without certain symmetry suppositions. There may be situations, however, in
which we may need to deal with inconsistent bits of information in a quantum context, even if these
informations are concerned with ways of speech. Furthermore, some authors think that superpositions
may be understood in terms of paraconsistent logics, and even the notion of complementarity was
already treated by such a means. This is, apparently, a nice motivation to try to merge these two
frameworks. In this work, we develop the technical details, by basing our quasi-set theory in the
paraconsistent system C1. For the finalities of this work, some philosophical questions are outlined, but
this topic is left to a future work.
Decoherence, Indivisibility and Complementarity
Jairo Roldan – Universidad del Valle, Facultad de Ciencias, Cali
Decoherence is considered as a solution to the measurement problem in quantum mechanics and, in
general, as an answer to the problem of the kind of reality that can be assigned to the macroscopic
bodies in a manner consistent with the consideration of quantum mechanics as a complete and
universal theory. Niels Bohr is considered as one of founders of the “orthodox” interpretation of
quantum mechanics, an interpretation that is also known as the Copenhagen interpretation. One of the
basis of Bohr’s thought is his linguistic thesis about the language of classical physics. It will be shown
that his linguistic thesis does not advocate any dualism between the macroscopic domain and the
microscopic one; neither denies the universal validity of quantum physics and let alone claims a logical
primacy of the classical physics over the quantum physics. It will be shown also how the theory of
decoherence gives support to the linguistic thesis of Bohr. With the purpose of showing the coherence
of his thought an analysis is also presented of Niels Bohr’s thesis about the interpretation of quantum
mechanics. Two ideas are identified that can be considered as fundamental in Bohr’s interpretation: the
indivisibility and the complementarity, which was considered by Bohr as an epistemological principle
which has its clearest application in quantum mechanics, but could also be applied in other contexts
with the same logical structure of quantum phenomena. A general conception of complementarity is
finally presented which includes a definition of that notion as precise as possible.
4 Infinitary logic associated to the event structure of probability spaces
Hector Freytes - Department of Mathematic FCEyA - UNR/CONICET
Department of Philosophy - University of Cagliari - Italia
A probability space is a triple < Ω, F, µ > consisting on the sample space Ω, an arbitrary nonempty set,
the sigma-algebra F ⊆ ℘(Ω) whose elements are called events and a probability measure µ: F [0,1].
Recently, the theory of sigma-algebras, was studied by several authors [1,2,3] in the attempt to extend
classical results related to the more general event structures as many valued sigma-algebras, etc. The
event structure F is a Boolean algebra admitting denumerable suprema and infima. Thus, denumerable
suprema and infima can be seen as infinatry operations in F. The aim of this work is to investigate, an
infinitary logical system for the event structure of probability spaces. A standard completeness theorem
is provided.
[1] A. Di Nola and M. Navara, “A characterization of _-complete MV - algebras with enough states
Colloq. Math. 103 (2005), 121-130.
[2] A. Dvurecenskij, “Loomis-Sikorski Theorem for _-complete MV - algebras and l-groups” J. Austral.
Marth. Soc. (Series A) 68 (2000), 261-277.
[3] D. Mundici and B. Riecan, “Probability on MV-algebras”, In: Handbook of Measure Theory (E. Pap
Ed.), 869-909, North Holland, Amsterdam, (2002).
Representation and Causality in Quantum Mechanics
Christian de Ronde - Dto. de Filosofía "Dr. A. Korn" UBA/CONICET
Center Leo Apostel and Foundations of the Exact Sciences - Brussels Free University
It is well known that both notions of 'causality' and 'representation' are problematic within quantum
mechanics [Foreman 1971, Cassirer 1956, Kauark-]. We shall discuss the relation between these notions
and both classical and quantum physics. More specifically, in this work we discuss these questions form
a general realistic perspective according to which a physical theory must provide an answer to the
question: 'what is the theory talking about?' In particular, as argued in [de Ronde 2011], by considering
the two main problems of quantum mechanics, namely: i) the problem of contextuality and ii) the problem of
superpositions; we discuss in what sense both causality and representation expose the limits of an
interpretation of quantum mechanics in terms of a classical metaphysical scheme.
Cassirer, E., 1956, Determinism and Indeterminism in Modern Physics, New Haven, Yale University Press.
Foreman, P., 1971, “Weimar Culture, Causality, and Quantum Theory, 1918-1927: Adaptation by
German Physicists and Mathematicians to a Hostile Intellectual Environment”, Historical Studies in the
Physical Sciences, 3, 1-115.
Kauark-Leite, P., 2012, “Causalidade e teoria quântica”, Scientiae Studia, Vol. 10., No. 1.
5 de Ronde, C., 2011, The Contextual and Modal Character of Quantum Mechanics: A Formal and Philosophical
Analysis in the Foundations of Science, PhD Dissertation, Utrecht University.
Uma Axiomatização Empirista da Teoria Quântica
Osvaldo Pessoa Jr. - Depto. Filosofia – FFLCH – Universidade de São Paulo
Apresenta-se uma axiomatização “empirista” ou operacional da teoría quântica, ou seja, uma que busca
definir os conceitos a partir de observações e operações físicas, postergando a introdução de estruturas
matemáticas mais sofisticadas, como o espaço de Hilbert (que, nas axiomatizações usuais, é
incorporado já no primeiro postulado). A motivação para tal abordagem é didática. A presente proposta
envolve nove definições operacionais e quatro postulados. Após a definição de “medição”, apresenta-se
o Postulado 1, que é um “postulado empírico” que caracteriza um sistema quântico, distinguindo-o de
sistemas clássicos. O “estado” de um sistema quântico é definido pelo arranjo experimental
macroscópico de sua preparação, e não por sua correspondência com vetores de um espaço de Hilbert.
Um estado quântico é “puro” se satisfizer os postulados seguintes (senão será uma “mistura
estatística”). Um “autoestado” é definido como um estado para o qual existe um arranjo experimental
que leva um certo detector a disparar com probabilidade 1. Define-se também autovalor,
ortogonalidade e base completa. O “observável” sendo medido em um experimento consiste da base
completa de autoestados e dos correspondentes autovalores. O Postulado 2 exprime o princípio
quântico de superposição, afirmando que qualquer estado acessível de um sistema quântico é ou um
dos autoestados si da base completa, ou uma combinação linear desses autoestados, envolvendo
quaisquer coeficientes ai escolhidos de tal maneira que satisfaçam a normalização e a regra de Born. O
Postulado 3 enuncia o postulado da projeção, se o objeto quântico não é absorvido pelo detector
(numa medição de não-demolição ou numa medição de resultado nulo). O Postulado 4 exprime a
evolução contínua, determinista e reversível do estado quântico, entre a preparação e a medição, regido
pela equação de Schrödinger. Na apresentação, pretendo mencionar outros sistemas operacionais de
axiomatização propostos na literatura, e espero que a plateia encontre furos (corrigíveis) na presente
abordagem, que ainda está em desenvolvimento.
Quantum entities as objects?
Jonas R. Becker Arenhart - Department of Philosophy Fronteira Sul Federal University, Chapecó, SC- Brazil
Great part of the recent metaphysical debate about the nature of quantum entities focuses on the
problem of their objecthood. Some philosophers claim that quantum entities are individual objects
(Saunders (2006), Dorato and Morganti (2011)), others that they are objects, but are not individuals (see
French and Krause (2006) chaps. 3 and 4), and a third party claim that they are not objects at all
(French and Ladyman (2003)). The main motivation for the third option, a version of eliminativist ontic
structural realism (OSR), concerns the desire to avoid falling in the dilemma of having to choose
between individuals and non-individuals: to overcome the underdetermination situation created by both
options, friends of OSR argue that it is better to leave particular objects behind and commit ourselves
only with the relations posed by the theory, leaving the relata without any metaphysical priority.
However, the precise meaning of objecthood, individuality, and non-individuality, are tied in such a way
6 that it is difficult to evaluate in a rigorous fashion the merits of the distinct proposals. To make matters
worse, it is not as clear as some have claimed that quantum mechanics itself should be seen as
endorsing one of the above proposals. That is, some version of ontological naturalism, the idea that
quantum mechanics tells us all about the (metaphysical) nature of quantum entities, does not seem to
be very promising concerning this particular problem, and yet it is usually assumed without much
question in those contexts. We shall propose that a definition of what it is for something to be an
object will in general encapsulate some metaphysical commitments that are hard to justify on the basis
of quantum mechanics, but that should be debated rather on a metaphysical basis if we are to make
some kind of progress in the debate. That is, the debate about the nature of quantum entities, mainly
the one concerning whether they are objects or not, must necessarily make a detour through some kind
of previous metaphysical discussion about the nature of objects, and such a debate is still missing when
it comes to matters concerning quantum objecthood and the problem of the metaphysical nature of
quantum entities in general.
Dorato, M. and Morganti, M., Grades of Individuality. A pluralistic view of identity in quantum
mechanics and in the sciences. Forthcoming in Philosophical Studies 2011.
French, S., Krause, D., Identity in Physics. A historical, philosophical and formal analysis, Oxford:
Oxford University Press, 2006.
French, S. Ladyman, J., Remodelling structural realism: quantum physics and the metaphysics of
structure. Synthese, 136, pp. 31-56, 2003.
Saunders, S., Are Quantum Particles Objects?, Analysis 66, pp. 52-63, 2006.
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