arXiv subjects
Publications and source records attributed to Karl Svozil.
A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.
Physical entities are ultimately (re)constructed from elementary yes/no events, in particular clicks in detectors or measurement devices recording quanta. Recently, the interpretation of certain such clicks has given rise to unfounded claims which are neither necessary nor sufficient, although they are presented in that way. In particular, clicks can neither inductively support nor "(dis)prove" the Kochen-Specker theorem, which is a formal result that has a deductive proof by contradiction. More importantly, the alleged empirical evidence of quantum contextuality, which is "inferred" from violations of bounds of classical probabilities by quantum correlations, is based on highly nontrivial assumptions, in particular on physical omniscience.
In this highly speculative Letter it is argued that, under certain physical conditions, Maxwell's demon might be capable of breaking the second law of thermodynamics, thereby allowing a perpetual motion machine of the second kind, by accessing single particle capabilities.
Despite provable unknowables in recursion theory, indeterminism and randomness in physics is confined to conventions, subjective beliefs and preliminary evidence. The history of the issue is very briefly reviewed, and answers to five questions raised by Hector Zenil are presented.
The amount of contextuality is quantified in terms of the probability of the necessary violations of noncontextual assignments to counterfactual elements of physical reality.
This review is about the convenience, the benefits, as well as the destructive capacities of money. It deals with various aspects of money creation, with its value, and its appropriation. All sorts of money tend to get corrupted by eventually creating too much of them. In the long run, this renders money worthless and deprives people holding it. This misuse of money creation is inevitable and should come as no surprise. Abusive money creation comes in various forms. In the present fiat money system "suspended in free thought" and sustained merely by our belief in and our conditioning to it, money is conveniently created out of "thin air" by excessive government spending and speculative credit creation. Alas, any too tight money supply could ruin an economy by inviting all sorts of unfriendly takeovers, including wars or competition. Therefore the ambivalence of money as benefactor and destroyer should be accepted as destiny.
If the unitary quantum mechanical state evolution is universally valid, quantized systems evolve uniformly, deterministically, and reversible; that is, one-to-one. Hence, what is considered an irreversible measurement might be a purely subjective, conventional, and convenient abstraction of the situation that, although in principal totally reversible, for all practical purposes (fapp), measurements cannot be undone. If this is granted, then Schroedinger's "quantum jellification" arises because of the inevitability of the physical co-existence of classically mutually exclusive states through quantum coherence. It is suggested to take the rather unique human cognitive and perceptive experience as evidence that, at least at the level of apperception, quantum jellification does not exist at all. Otherwise the problems of how to characterize the ambivalence of perception and cognition induced by quantum coherence on a fundamental level of cognition, and why this ambivalence appears to be rather weak and can be ignored fapp, remain unsolved.
The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum alone. We discuss possible interpretations and consequences for quantum oracles.
In this paper we propose a quantum random number generator (QRNG) which utilizes an entangled photon pair in a Bell singlet state, and is certified explicitly by value indefiniteness. While "true randomness" is a mathematical impossibility, the certification by value indefiniteness ensures the quantum random bits are incomputable in the strongest sense. This is the first QRNG setup in which a physical principle (Kochen-Specker value indefiniteness) guarantees that no single quantum bit produced can be classically computed (reproduced and validated), the mathematical form of bitwise physical unpredictability. The effects of various experimental imperfections are discussed in detail, particularly those related to detector efficiencies, context alignment and temporal correlations between bits. The analysis is to a large extent relevant for the construction of any QRNG based on beam-splitters. By measuring the two entangled photons in maximally misaligned contexts and utilizing the fact that two rather than one bitstring are obtained, more efficient and robust unbiasing techniques can be applied. A robust and efficient procedure based on XORing the bitstrings together---essentially using one as a one-time-pad for the other---is proposed to extract random bits in the presence of experimental imperfections, as well as a more efficient modification of the von Neumann procedure for the same task. Some open problems are also discussed.
Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may "compute the hard or even the incomputable" by measuring observables which correspond to computationally hard or even incomputable problems.
We propose to "boost" the speed of communication and computation by immersing the computing environment into a medium whose index of refraction is smaller than one, thereby trespassing the speed-of-light barrier.
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an asymptotic property --- of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
The quantum correlations of two or more entangled particles present the possibility of stronger-than-classical outcome coincidences. We investigate two-partite correlations of spin one, three-half and higher quanta in a state satisfying a uniqueness property in the sense that knowledge of an outcome of one particle observable entails the certainty that, if this observable were measured on the other particle(s) as well, the outcome of the measurement would be a unique function of the outcome of the measurement performed. We also investigate correlations of four spin one-half particles.
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a necessary, but not sufficient "symptom" of "true randomness". We base our experimental approach on algorithmic information theory which provides characterizations of algorithmic random sequences in terms of the degrees of incompressibility of their finite prefixes. Algorithmic random sequences are incomputable, but the converse implication is false. We have performed tests of randomness on pseudo-random strings (finite sequences) of length $2^{32}$ generated with software (Mathematica, Maple), which are cyclic (so, strongly computable), the bits of $π$, which is computable, but not cyclic, and strings produced by quantum measurements (with the commercial device Quantis and by the Vienna IQOQI group). Our empirical tests indicate quantitative differences, some statistically significant, between computable and incomputable sources of "randomness".
The noncontextuality of quantum mechanics can be directly tested by measuring two entangled particles with more than two outcomes per particle. The two associated contexts are "interlinked" by common observables.
We have recently introduced the two new computing models of self-similar cellular automata and self-similar Petri nets. Self-similar automata result from a progressive, infinite tessellation of space and time. Self-similar Petri nets consist of a potentially infinite sequence of coupled transitions with ever increasing firing rates. Both models are capable of hypercomputations and can, for instance, ``solve'' the halting problem for Turing machines. We survey the main definitions and propositions and add new results regarding the indeterminism of self-similar cellular automata.
Some quantum cryptographic protocols can be implemented with specially prepared chocolate balls, others protected by value indefiniteness cannot. Similarities and differences of cryptography with quanta and chocolate are discussed. Motivated by these considerations it is proposed to certify quantum random number generators and quantum cryptographic protocols by value indefiniteness. This feature, which derives itself from Bell- and Kochen-Specker type arguments, is only present in systems with three or more mutually exclusive outcomes.
Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of "steps" involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper-) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the self-contradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.