4,454 research outputs found
On Probability and Cosmology: Inference Beyond Data?
Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data
Philosophical problems of space-time theories
I present a discussion of some open issues in the philosophy of space-time
theories. Emphasis is put on the ontological nature of space and time, the
relation between determinism and predictability, the origin of irreversible
processes in an expanding Universe, and the compatibility of relativity and
quantum mechanics. In particular, I argue for a Parmenidean view of time and
change, I make clear the difference between ontological determinism and
predictability, propose that the origin of the asymmetry observed in physical
processes is related to the existence of cosmological horizons, and present a
non-local concept of causality that can accommodate both special relativity and
quantum entanglement.Comment: 20 pages, small changes to match the version published by Cambridge
University Pres
The Mathematical Universe
I explore physics implications of the External Reality Hypothesis (ERH) that
there exists an external physical reality completely independent of us humans.
I argue that with a sufficiently broad definition of mathematics, it implies
the Mathematical Universe Hypothesis (MUH) that our physical world is an
abstract mathematical structure. I discuss various implications of the ERH and
MUH, ranging from standard physics topics like symmetries, irreducible
representations, units, free parameters, randomness and initial conditions to
broader issues like consciousness, parallel universes and Godel incompleteness.
I hypothesize that only computable and decidable (in Godel's sense) structures
exist, which alleviates the cosmological measure problem and help explain why
our physical laws appear so simple. I also comment on the intimate relation
between mathematical structures, computations, simulations and physical
systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs;
more details at http://space.mit.edu/home/tegmark/toe.htm
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