94 research outputs found
The Gibbs Paradox Revisited
The Gibbs paradox has frequently been interpreted as a sign that particles of
the same kind are fundamentally indistinguishable; and that quantum mechanics,
with its identical fermions and bosons, is indispensable for making sense of
this. In this article we shall argue, on the contrary, that analysis of the
paradox supports the idea that classical particles are always distinguishable.
Perhaps surprisingly, this analysis extends to quantum mechanics: even
according to quantum mechanics there can be distinguishable particles of the
same kind. Our most important general conclusion will accordingly be that the
universally accepted notion that quantum particles of the same kind are
necessarily indistinguishable rests on a confusion about how particles are
represented in quantum theory.Comment: to appear in Proceedings of "The Philosophy of Science in a European
Perspective 2009
The Logic of Identity: Distinguishability and Indistinguishability in Classical and Quantum Physics
The suggestion that particles of the same kind may be indistinguishable in a
fundamental sense, even so that challenges to traditional notions of
individuality and identity may arise, has first come up in the context of
classical statistical mechanics. In particular, the Gibbs paradox has sometimes
been interpreted as a sign of the untenability of the classical concept of a
particle and as a premonition that quantum theory is needed. This idea of a
quantum connection stubbornly persists in the literature, even though it has
also been criticized frequently. Here we shall argue that although this
criticism is justified, the proposed alternative solutions have often been
wrong and have not put the paradox in its right perspective. In fact, the Gibbs
paradox is unrelated to fundamental issues of particle identity; only
distinguishability in a pragmatic sense plays a role (in this we develop ideas
of van Kampen [10]), and in principle the paradox always is there as long as
the concept of a particle applies at all. In line with this we show that the
paradox survives even in quantum mechanics, in spite of the quantum mechanical
(anti-)symmetrization postulates
Is There a Unique Physical Entropy? Micro versus Macro
Entropy in thermodynamics is an extensive quantity, whereas standard methods
in statistical mechanics give rise to a non-extensive expression for the
entropy. This discrepancy is often seen as a sign that basic formulas of
statistical mechanics should be revised, either on the basis of quantum
mechanics or on the basis of general and fundamental considerations about the
(in)distinguishability of particles. In this article we argue against this
response. We show that both the extensive thermodynamic and the non-extensive
statistical entropy are perfectly alright within their own fields of
application. Changes in the statistical formulas that remove the discrepancy
must be seen as motivated by pragmatic reasons (conventions) rather than as
justified by basic arguments about particle statistics.Comment: To appear in "New Challenges to the Philosophy of Science", PSE
Volume 4, Springer 201
Probability in modal interpretations of quantum mechanics
Modal interpretations have the ambition to construe quantum mechanics as an
objective, man-independent description of physical reality. Their second
leading idea is probabilism: quantum mechanics does not completely fix physical
reality but yields probabilities. In working out these ideas an important motif
is to stay close to the standard formalism of quantum mechanics and to refrain
from introducing new structure by hand. In this paper we explain how this
programme can be made concrete. In particular, we show that the Born
probability rule, and sets of definite-valued observables to which the Born
probabilities pertain, can be uniquely defined from the quantum state and
Hilbert space structure. We discuss the status of probability in modal
interpretations, and to this end we make a comparison with many-worlds
alternatives. An overall point that we stress is that the modal ideas define a
general framework and research programme rather than one definite and finished
interpretation
How Classical Particles Emerge from the Quantum World.
The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that quantum particles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state--in clear conflict with what we know about classical particles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles emerge, as new entities that do not correspond to the "particle indices" defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises the question of whether the discussions about the status of identical quantum particles have not been misguided from the very start
Complementarity in the Bohr-Einstein Photon Box
The photon box thought experiment can be considered a forerunner of the
EPR-experiment: by performing suitable measurements on the box it is possible
to ``prepare'' the photon, long after it has escaped, in either of two
complementary states. Consistency requires that the corresponding box
measurements be complementary as well. At first sight it seems, however, that
these measurements can be jointly performed with arbitrary precision: they
pertain to different systems (the center of mass of the box and an internal
clock, respectively). But this is deceptive. As we show by explicit
calculation, although the relevant quantities are simultaneously measurable,
they develop non-vanishing commutators when calculated back to the time of
escape of the photon. This justifies Bohr's qualitative arguments in a precise
way; and it illustrates how the details of the dynamics conspire to guarantee
the requirements of complementarity. In addition, our calculations exhibit a
``fine structure'' in the distribution of the uncertainties over the
complementary quantities: depending on \textit{when} the box measurement is
performed, the resulting quantum description of the photon differs. This brings
us close to the argumentation of the later EPR thought experiment
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