9,529 research outputs found
Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule
I present a proof of the quantum probability rule from decision-theoretic
assumptions, in the context of the Everett interpretation. The basic ideas
behind the proof are those presented in Deutsch's recent proof of the
probability rule, but the proof is simpler and proceeds from weaker
decision-theoretic assumptions. This makes it easier to discuss the conceptual
ideas involved in the proof, and to show that they are defensible.Comment: 23 pages. This is a modified version of my 2003 paper, which
incorporates a completely rewritten and substantially improved proof of
Equivalence as well as a few other more minor change
A formal proof of the Born rule from decision-theoretic assumptions
I develop the decision-theoretic approach to quantum probability, originally
proposed by David Deutsch, into a mathematically rigorous proof of the Born
rule in (Everett-interpreted) quantum mechanics. I sketch the argument
informally, then prove it formally, and lastly consider a number of proposed
``counter-examples'' to show exactly which premises of the argument they
violate.Comment: 36 pages. To appear (under the title "How to prove the Born rule") in
Saunders, Barrett, Kent and Wallace, "Many Worlds? Everett, Quantum Theory,
and Reality" (Oxford University Press
Gravity, Entropy, and Cosmology: In Search of Clarity
I discuss the statistical mechanics of gravitating systems and in particular
its cosmological implications, and argue that many conventional views on this
subject in the foundations of statistical mechanics embody significant
confusion; I attempt to provide a clearer and more accurate account. In
particular, I observe that (i) the role of gravity \emph{in} entropy
calculations must be distinguished from the entropy \emph{of} gravity, that
(ii) although gravitational collapse is entropy-increasing, this is not usually
because the collapsing matter itself increases in entropy, and that (iii) the
Second Law of Thermodynamics does not owe its validity to the statistical
mechanics of gravitational collapse.Comment: 25 page
Why Black Hole Information Loss is Paradoxical
I distinguish between two versions of the black hole information-loss
paradox. The first arises from apparent failure of unitarity on the spacetime
of a completely evaporating black hole, which appears to be
non-globally-hyperbolic; this is the most commonly discussed version of the
paradox in the foundational and semipopular literature, and the case for
calling it `paradoxical' is less than compelling. But the second arises from a
clash between a fully-statistical-mechanical interpretation of black hole
evaporation and the quantum-field-theoretic description used in derivations of
the Hawking effect. This version of the paradox arises long before a black hole
completely evaporates, seems to be the version that has played a central role
in quantum gravity, and is genuinely paradoxical. After explicating the
paradox, I discuss the implications of more recent work on AdS/CFT duality and
on the `Firewall paradox', and conclude that the paradox is if anything now
sharper. The article is written at a (relatively) introductory level and does
not assume advanced knowledge of quantum gravity.Comment: 26 pages. Corrected error in one diagram; other minor revision
The case for black hole thermodynamics, Part II: statistical mechanics
I present in detail the case for regarding black hole thermodynamics as
having a statistical-mechanical explanation in exact parallel with the
statistical-mechanical explanation believed to underly the thermodynamics of
other systems. (Here I presume that black holes are indeed thermodynamic
systems in the fullest sense; I review the evidence for \emph{that} conclusion
in the prequel to this paper.) I focus on three lines of argument: (i)
zero-loop and one-loop calculations in quantum general relativity understood as
a quantum field theory, using the path-integral formalism; (ii) calculations in
string theory of the leading-order terms, higher-derivative corrections, and
quantum corrections, in the black hole entropy formula for extremal and
near-extremal black holes; (iii) recovery of the qualitative and (in some
cases) quantitative structure of black hole statistical mechanics via the
AdS/CFT correspondence. In each case I briefly review the content of, and
arguments for, the form of quantum gravity being used (effective field theory;
string theory; AdS/CFT) at a (relatively) introductory level: the paper is
aimed at students and non-specialists and does not presume advanced knowledge
of quantum gravity.. My conclusion is that the evidence for black hole
statistical mechanics is as solid as we could reasonably expect it to be in the
absence of a directly-empirically-verified theory of quantum gravity.Comment: 34 pages; minor revisions onl
The Everett Interpretation
The Everett interpretation of quantum mechanics - better known as the Many-Worlds Theory - has had a rather uneven reception. Mainstream philosophers have scarcely heard of it, save as science fiction. In philosophy of physics it is
well known but has historically been fairly widely rejected. Among physicists (at least, among those concerned with the interpretation of quantum mechanics in the first place), it is taken very seriously indeed, arguably tied for first place in popularity with more traditional operationalist views of quantum mechanics. In this article, I provide a fairly short (15,000 words) and self-contained introduction to the Everett interpretation as it is currently understood. I use little technical machinery, although I do assume the reader has encountered the measurement problem already (at about the level of the well-known discussions by Penrose or Albert)
Worlds in the Everett Interpretation
This is a discussion of how we can understand the world-view given to us by
the Everett interpretation of quantum mechanics, and in particular the role
played by the concept of `world'. The view presented is that we are entitled to
use `many-worlds' terminology even if the theory does not specify the worlds in
the formalism; this is defended by means of an extensive analogy with the
concept of an `instant' or moment of time in relativity, with the lack of a
preferred foliation of spacetime being compared with the lack of a preferred
basis in quantum theory. Implications for identity of worlds over time, and for
relativistic quantum mechanics, are discussed.Comment: Latex, 27 pages. To appear in Studies in the History and Philosophy
of Modern Physic
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