2,257 research outputs found
Black holes, complexity and quantum chaos
We study aspects of black holes and quantum chaos through the behavior of
computational costs, which are distance notions in the manifold of unitaries of
the theory. To this end, we enlarge Nielsen geometric approach to quantum
computation and provide metrics for finite temperature/energy scenarios and
CFT's. From the framework, it is clear that costs can grow in two different
ways: operator vs `simple' growths. The first type mixes operators associated
to different penalties, while the second does not. Important examples of simple
growths are those related to symmetry transformations, and we describe the
costs of rotations, translations, and boosts. For black holes, this analysis
shows how infalling particle costs are controlled by the maximal Lyapunov
exponent, and motivates a further bound on the growth of chaos. The analysis
also suggests a correspondence between proper energies in the bulk and average
`local' scaling dimensions in the boundary. Finally, we describe these
complexity features from a dual perspective. Using recent results on SYK we
compute a lower bound to the computational cost growth in SYK at infinite
temperature. At intermediate times it is controlled by the Lyapunov exponent,
while at long times it saturates to a linear growth, as expected from the
gravity description.Comment: 30 page
Knowing What We Know about IT and Business Value: Cause for Concern about Endogeneity Problems and Potential Solutions
Do IT investments deliver business value? This long-standing question of IS interest is a causal question. Answers to this question are often sought through the use of econometric methods, which require careful attention to the issue of endogeneity for valid causal inference. Yet, concerns about endogeneity problems in econometric research persist despite the many quantitative techniques available for addressing them. Recent publications in strategic management and accounting have offered a few non-quantitative solutions, such as better writing and reviewing norms, better theory selection, and use of descriptive quantitative and qualitative methods. Not considered in these prescriptions is a relatively little-known category of explicitly causal case study research methods that originated in sociology and political science. This paper describes these methods, shows how they address endogeneity problems, and explores how they might complement statistical methods in the study of IT business value
Temporal naturalism
Two people may claim both to be naturalists, but have divergent conceptions
of basic elements of the natural world which lead them to mean different things
when they talk about laws of nature, or states, or the role of mathematics in
physics. These disagreements do not much affect the ordinary practice of
science which is about small subsystems of the universe, described or explained
against a background, idealized to be fixed. But these issues become crucial
when we consider including the whole universe within our system, for then there
is no fixed background to reference observables to. I argue here that the key
issue responsible for divergent versions of naturalism and divergent approaches
to cosmology is the conception of time. One version, which I call temporal
naturalism, holds that time, in the sense of the succession of present moments,
is real, and that laws of nature evolve in that time. This is contrasted with
timeless naturalism, which holds that laws are immutable and the present moment
and its passage are illusions. I argue that temporal naturalism is empirically
more adequate than the alternatives, because it offers testable explanations
for puzzles its rivals cannot address, and is likely a better basis for solving
major puzzles that presently face cosmology and physics.
This essay also addresses the problem of qualia and experience within
naturalism and argues that only temporal naturalism can make a place for qualia
as intrinsic qualities of matter
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