Quantum Foundations

The causal Markov condition relates statistical dependences to causality. Its relevance is meanwhile widely appreciated in machine learning, statistics, and physics. I describe the *algorithmic* causal Markov condition relating algorithmic dependences to causality, which can be used for inferring causal relations among single objects without referring to statistics. The underlying postulate "no algorithmic dependence without causal relation" extends Reichenbach's Principle to a probability-free setting. I argue that a related postulate called "algorithmic independence of initial state and dynamics" reproduces the non-decrease of entropy according to the thermodynamic arrow of time.

Remark to last week's participants: This will be a condensed version of last week's talks. I will drop many details (in particular on the relation to quantum theory) and also drop the introductory slides to algorithmic probability (for this, see Marcus Hutter's introductory talk on Tuesday afternoon, April 10). Motivated by the conceptual puzzles of quantum theory and related areas of physics, I describe a rigorous and minimal “proof of principle” theory in which observers are fundamental and in which the physical world is a (provably) emergent phenomenon. This is a reversal of the standard view, which holds that physical theories ought to describe the objective evolution of a unique external world, with observers or agents as derived concepts that play no fundamental role whatsoever. Using insights from algorithmic information theory (AIT), I show that this approach admits to address several foundational puzzles that are difficult to address via standard approaches. This includes the measurement and Boltzmann brain problems, and problems related to the computer simulation of observers. Without assuming the existence of an external world from the outset, the resulting theory actually predicts that there is one as a consequence of AIT — in particular, a world with simple, computable, probabilistic laws on which different observers typically (but not always) agree. This approach represents a consistent but highly unfamiliar picture of the world, leading to a new perspective from which to approach some questions in the foundations of physics.

The progression of theories suggested for our world, from ego- to geo- to helio-centric models to universe and multiverse theories and beyond, shows one tendency: The size of the described worlds increases, with humans being expelled from their center to ever more remote and random locations. If pushed too far, a potential theory of everything (TOE) is actually more a theories of nothing (TON). Indeed such theories have already been developed. I show that including observer localization into such theories is necessary and sufficient to avoid this problem. I develop a quantitative recipe to identify TOEs and distinguish them from TONs and theories in-between. This precisely shows what the problem is with some recently suggested universal TOEs.

In accordance with Betteridge's Law of Headlines, the answer to the question in the title is "no." I will argue that the usual norms of Bayesian inference lead the conclusion that quantum states are features of physical reality. The argument will involve both existing $\psi$-ontology results and extension of them that avoids the use of the Cartesian Product Assumption. As the usual norms of Bayesian inference lead to the conclusion of the reality of quantum state, rejecting it requires abandonment of virtually all of Bayesian information theory. This, I will argue, is unwarranted

The progression of theories suggested for our world, from ego- to geo- to helio-centric models to universe and multiverse theories and beyond, shows one tendency: The size of the described worlds increases, with humans being expelled from their center to ever more remote and random locations. If pushed too far, a potential theory of everything (TOE) is actually more a theories of nothing (TON). Indeed such theories have already been developed. I show that including observer localization into such theories is necessary and sufficient to avoid this problem. I develop a quantitative recipe to identify TOEs and distinguish them from TONs and theories in-between. This precisely shows what the problem is with some recently suggested universal TOEs.

In this talk I compare the normative concept of probability at the heart of QBism with the notion of probability implied by the use of Solomonoff induction in Markus Mueller's preprint arXiv:1712.01816.

Algorithmic information theory (AIT) delivers an objective quantification of simplicity-qua-compressibility,that was employed by Solomonoff (1964) to specify a gold standard of inductive inference. Or so runs the conventional account,that I will challenge in my talk.

In his famous thought experiment, Wigner assigns an entangled state to the composite quantum system made up of Wigner's friend and her observed system. While the two of them have different accounts of the process, each Wigner and his friend can in principle verify his/her respective state assignments by performing an appropriate measurement. As manifested through a click in a detector or a specific position of the pointer, the outcomes of these measurements can be regarded as reflecting directly observable "facts". Reviewing arXiv:1507.05255, I will derive a no-go theorem for observer-independent facts, which would be common both for Wigner and the friend. I will then analyze this result in the context of a newly derived theorem in arXiv:1604.07422, where Frauchiger and Renner prove that "single-world interpretations of quantum theory cannot be self-consistent". It is argued that "self-consistency" has the same implications as the assumption that observational statements of different observers can be compared in a single (and hence an observer-independent) theoretical framework. The latter, however, may not be possible, if the statements are to be understood as relational in the sense that their determinacy is relative to an observer.

A central fact in computer science is that there are universal machines, that is machines that can run any other program. Recently, a somewhat similar notion of universality has been discovered in physics, by which some spin models can simulate all other models. In this work we shed light on the relation between the two concepts of universality

Following Stefan Wolf’s talk, we address the doubts expressed on fundamental space-time causality. Usually it is assumed that causal structures represent a definite partial ordering of events. By relaxing that notion one risks problems of logical nature. Yet, as we show, there exists a logically consistent world beyond the causal, even in the classical realm where quantum theory is not invoked. We explore the classical correlations within and the computational limits of that world. It turns out that relaxing causality in that fashion does not allow for efficient computation of NP-hard problems. These results are related to closed time-like curves: Contrary to previous models of time travel, which necessitate quantum theory and violate the NP-hardness assumption, we obtain a computationally tame model for classical and reversible time travel where freedom of choice is unrestricted.

Landauer's principle claims that "Information is Physical." Its conceptual antipode, Wheeler's "It from Bit," has since long been popular among computer scientists in the form of the Church-Turing hypothesis: All natural processes can be simulated by a universal Turing machine. Switching back and forth between the two paradigms, motivated by quantum-physical Bell correlations and the doubts they raise about fundamental space-time causality, we look for an intrinsic, physical randomness notion and find one, namely complexity, around the second law of thermodynamics. Bell correlations combined with Kolmogorov complexity in the role of randomness imply an all-or-nothing nature of the Church-Turing hypothesis: Either beyond-Turing computations are physically impossible, or they can be carried out by "devices" as simple as individual photons. This latter result demonstrates in an exemplary way the fruitful interplay between physical and informational-computational principles.

An important ingredient of the scientific method is the ability to test alternative hypotheses on the causal relations relating a given set of variables. In the classical world, this task can be achieved with a variety of statistical, information-theoretic, and computational techniques. In this talk I will address the extension from the classical scenario to the quantum scenario, and, more generally, to general probabilistic theories. After introducing the basic hypothesis testing framework, I will focus on a concrete example, where the task is to identify the causal intermediary of a given variable, under the promise that the causal intermediary belongs to a given set of candidate variables. In this problem, I will show that quantum physics offers an exponential advantage over the best classical strategies, with a doubling of the exponential decay of the error probability. The source of the advantage can be found in the combination of two quantum features: the complementarity between the information on the causal structure and other properties of the cause effect relation, and the ability to perform multiple tests in a quantum superposition. An interesting possibility is that one of the "hidden principles" of quantum theory could be on our ability to test alternative causal hypotheses.