Abstract: There is no way to reduce physics to information theory. Matter is not just empty space with isolated bits of information. The quantum is not digital data, logic, probability, or information. There is a long history of trying to understand the ethereal mysteries of quantum mechanics by reduction to discrete information, as if the universe were a giant ghostly digital computer without the hardware. These attempts have failed, and should be seen as evasions of the central truths of quantum mechanics. In short, there is no it from bit. Submitted to the FQXi.org 2013 Essay Contest answering: “It from Bit or Bit from It?” Author Bio: Roger Schlafly has a BSE from Princeton U, and a PhD in Mathematics from U California Berkeley, under I. Singer. He blogs at DarkBuzz.com.
Abstract: There is no way to reduce physics to information theory. Matter is not just empty space with isolated bits of information. The quantum is not digital data, logic, probability, or information. There is a long history of trying to understand the ethereal mysteries of quantum mechanics by reduction to discrete information, as if the universe were a giant ghostly digital computer without the hardware. These attempts have failed, and should be seen as evasions of the central truths of quantum mechanics. In short, there is no it from bit. Submitted to the FQXi.org 2013 Essay Contest answering: “It from Bit or Bit from It?” Author Bio: Roger Schlafly has a BSE from Princeton U, and a PhD in Mathematics from U California Berkeley, under I. Singer. He blogs at DarkBuzz.com.
Introduction Of John Wheeler's “Really Big Questions,” the one on which the most progress has been made is “It from bit?” – does information play a significant role at the foundations of physics? It is perhaps less ambitious than some of the other questions, such as “How come existence?”, because it does not necessarily require a metaphysical answer. And unlike, say, “Why the quantum?”, it does not require the discovery of new laws of nature: there was room for hope that it might be answered through a better understanding of the laws as we currently know them, particularly those of quantum physics. And this is what has happened: the better understanding is the quantum theory of information and computation. How might our conception of the quantum physical world have been different if “It from bit” had been a motivation from the outset? No one knows how to derive it (the nature of the physical world) from bit (the idea that information plays a significant role at the foundations of physics), and I shall argue that this will never be possible. But we can do the next best thing: we can start from the qubit. Qubits To a classical information theorist, a bit is an abstraction: a certain amount of information. To a programmer, a bit is a Boolean variable. To an engineer, a bit is a “flip-flop” – a piece of hardware that is stable in either of two physical states.
“I refute it thus!” Samuel Johnson famously dismissed Bishop George Berkeley's argument for the unreality of matter by kicking a large stone (Boswell, 1823). In the light of modern physics, however, Johnson's simple reasoning evaporates. Apparently solid matter is revealed, on closer inspection, to be almost all empty space, and the particles of which matter is composed are themselves ghostly patterns of quantum energy, mere excitations of invisible quantum fields, or possibly vibrating loops of string living in a ten-dimensional space–time (Greene, 1999). The history of physics is one of successive abstractions from daily experience and common sense, into a counterintuitive realm of mathematical forms and relationships, with a link to the stark sense data of human observation that is long and often tortuous. Yet at the end of the day, science is empirical, and our finest theories must be grounded, somehow, “in reality.” But where is reality? Is it in acts of observation of the world made by human and possibly non-human observers? In records stored in computer or laboratory notebooks? In some objective world “out there”? Or in a more abstract location? The ground of reality When a physicist performs an experiment, he or she interrogates nature and receives a response that, ultimately, is in the form of discrete bits of information (think of “yes” or “no” binary answers to specific questions), the discreteness implied by the underlying quantum nature of the universe (Zeilinger, 2004). Does reality then lie in the string of bits that come back from the set of all observations and experiments – a dry sequence of ones and zeros? Do these observations merely transfer really-existing bits of information from an external world reality to the minds of observers, or are the bits of information created by the very act of observation/experiment? And – the question to which this entire discussion is directed – are bits of “classical” information the only sort of information that count in the reality game, or does an altogether different form of information underpin reality? In short, where is the ontological ground on which our impression of a really-existing universe rests?
ENGLISH ABSTRACT: What are the information processing capabilities of physical systems? As recently as the first half of the 20th century this question did not even have a definite meaning. What is information, and how would one process it? It took the development of theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate mathematically what it means to compute or communicate. Yet these theories were abstract, based on axiomatic mathematics: what did physical systems have to do with these axioms? Rolf Landauer had the essential insight - "Information is physical" - that information is always encoded in the state of a physical system, whose dynamics on a microscopic level are well-described by quantum physics. This means that we cannot discuss information without discussing how it is represented, and how nature dictates it should behave. Wigner considered the situation from another perspective when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences". Why are the computational techniques of mathematics so astonishingly useful in describing the physical world [1]? One might begin to suspect foul play in the universe's operating principles. Interesting insights into the physics of information accumulated through the 1970s and 1980s - most sensationally in the proposal for a "quantum computer". If we were to mark a particular year in which an explosion of interest took place in information physics, that year would have to be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be solved easily on a quantum computer. But the applications of information in physics - and vice versa - have been far more widespread than this popular discovery. These applications range from improved experimental technology, more sophisticated measurement techniques, methods for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight into quantum theory and nature. In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.
Can Reality be simulated by a huge Quantum Computer? Do we believe that Reality is made of something more than interacting quantum systems? The idea that the whole Physics is ultimately a quantum computation—a strong quantum version of the Church-Turing hypothesis well synthesized by the Wheeler’s coinage It from bit—is very appealing. It is theoretically very parsimonious: an Occam razor’s quality-guaranteed description of the world. But, if this is the case, then we need to understand the entire Physics as emergent from the quantum computation. Here I will make a short exploration on how this may come about. Ask a physicist what does he thinks the world is made of. Very likely the first impetuous answer will be: it is made of particles! But, at a second thought the answer will be: it is a Quantum Field. Particles are just states or the Field: they can be created and annihilated. We have indeed a beautiful Grand Unified Field Theory, and we are looking forward to see the Higg’s boson at the LHC. But what is the Quantum Field made of? Ultimately, it is made of quantum systems that are interacting, each system located at a different position in space. Things may be indeed more complicated than that, because the field is a continuum. But is Reality actually continuous? We don ’ t know: but it looks easier to think to Reality as a continuum. Now, suppose that this is not the case, namely Reality is ultimately discrete, and the continuum is only a mathematical fiction. Then, what else is out there more than interacting quantum
What is information? A short answer could be: Anything that changes our minds and states of thinking! Information is virtual. It can be carried by speech, an image, scratches on a stone, patterns in a photon field, the connections of neurons in our brains or even by the wavefunction of an electron. Information does not depend on the actual means of transmission nor does its identity change when changing the carrier. Information is physical. It needs to be sustained by a physical substrate and rearranging that substrate to contain the wanted information requires to spend energy or work. Without a physical world, information can not be stored, processed, or transmitted. Our world is permeated with different representations of information. Actually Information about the physical laws governing our Universe can be found everywhere and in everything. Could it then be that the real fundamental elements of this world are tiny bits of information? Could we get it from bit?1 A number of researcher investigate this possibility, and several of their attempts to recover physical laws from the principles governing information are reported about in this special issue on physics of information. The articles by Gregg Jaeger,2 by Ariel Caticha,3 and by John Skilling and Kevin Knuth4 address the reconstruction of quantum mechanics from information theory. Furthermore, Kevin Knuth and James Walsh5 show how to recover space-time from particles sending each others signals in an initially geometry-free setting. A central element of most works on information is the concept of a probability. Probabilities can be defined via various routes. Most familiar might be their definitions by the frequentists school as relative frequencies of events (in the limit of infinite amounts of such). A more general definition of probabilities is the Bayesians' one, which regards probabilities as quantifiers of statements, expressing how much those should be expected to be true. Although this definition looks subjective on the first glance, it rests on a solid mathematical theorem by Richard Cox6 that any extension of binary logic to a continuum of single valued truthfulness quantifier that respects a minimum of requirements must be isomorphic to probability theory. And this definition turns out to embrace the frequentists' definition in case that infinite numbers of comparable events are actually available and can be counted. The majority of authors of this special issues seem to favor the Bayesian perspective, which is probably a result of our own, the guest editors', preference and not necessarily a reflection of the prevailing position of contemporary scientists. The different views on probabilities of frequentists and Bayesians are addressed by the article of Allen Caldwell.7 He builds a bridge between these antagonistic camps by explaining frequentists' constructions in a Bayesian language. In particular, his argumentation why the omnipresent p-value in statistical and experimental literature might often capture a relevant signal of model misfit is reassuring, given that a large fraction of our medical system is based on decisions backed up by p-values. A Bayesian might add that it would be even more reassuring, if a system rigorously build on logic and its continuous extension would be used for decisions affecting live-or-death questions. The laws governing probabilities themselves seem to reflect that of more elementary mathematical structures. Kevin Knuth shows how these emerge from lattice theory, which deals with relations in partially ordered sets like that of collections of possibilities.8 The sum rule of probability theory is a direct consequence of the underlying lattice structure. Interestingly, a number of other theories are resting also on such lattices and therefore exhibit their own versions of sum rules: measures of sets, mutual information, the Euler characteristics of topological spaces, as well as quantum mechanical interactions that are quantified by pairs of numbers, the real and imaginary parts of complex probability amplitudes (see also4). The theory of information has very practical application in physics and elsewhere. Manfred Opper discusses how the solutions of stochastic differential equations can be inferred via variational methods, which have their origin in thermodynamics.9 Torsten Enßlin introduces information field theory (IFT), the information theory for fields, as a means to infer the configuration of a physical field from incomplete and noisy data.10 The mathematical apparatus for this is that of quantum field theory (QFT), just with ordinary probabilities instead of complex probability amplitudes as in the latter. Could it be that the difference between IFT and QFT is just be the same as between classical information theory and quantum mechanics, the transition from real valued to complex valued quantifier for statements? Anyhow, any practical inference machinery, be it for dynamical systems or for fields, requires sophisticated numerical methods. Michael Betancourt reviews Markov Chain Monte Carlo Methods to calculate expectation values over high dimensional probabilities.11 Theo Steininger and coworkers present the NIFTy3 software package for numerical information field theory calculations, which can handle very high dimensional field inference problems.12 Finally, in an article focused on the subtleties of the Monty Hall problem and mostly aiming at information theoretical entertainment, Torsten Enßlin and Margret Westercamp investigate the possibility that human intuition might be more rational than contemporary psychology thinks.13 A number of possible topics for an issue on physics of information are not addressed here. We would have loved to have articles on Landauer's principle, which states that erasing information has to cost energy, on QBism, a Bayesian version of quantum mechanics, on artificial and biological neural networks, as well as any other aspect of the information-soaked biological world. What has a reader of this special issue to be equipped with in order to follow the lines of thoughts? In addition to the usual physicist's education, the minimal additional equipment are the basics of probability theory and the concept of entropy. Most of the other concepts used in the articles rest on those and are introduced there. Let A, B, and C be propositions (or possibilities). The probability P ( A | B ) of A being true assuming that B is true is a number between 0 and 1, with P ( A | B ) = 1 expressing certainty of A under B ( B ⇒ A ) and P ( A | B ) = 0 expressing certainty of not A being the case under B ( B ⇒ ¬ A ).
It is broadly believed that everything in the universe is found to be made from a few basic building blocks called fundamental particles, governed by four fundamental forces. However, physicists such as John Archibald Wheeler suggested that information is fundamental to the physics of the universe. According to this it from bit doctrine, all things physical are information-theoretic in origin. This doctrine is based in the old Copenhagen interpretation of quantum mechanics; an interpretation which is internally inconsistent and no applicable to the cosmos as a whole. Modern consistent interpretations of quantum mechanics eliminate the old myths about measurement processes and observers' consciousness and reintroduce the idea of a wholly physical reality, invalidating the it from bit doctrine. Utilizing a new phase space formulation of quantum mechanics developed recently by the author, the concepts of bit and it are reconsidered. We introduce the new states D as quantum bits and the new Hamiltonians H as quantum its. The new concepts of it and bit introduced in this work have a well-defined and rigorous definition, unlike Wheeler's concepts. Moreover, the new concepts apply on situations where the traditional wavefunction theory does not work. The it H is not derivable from the bit D and, as a consequence, the old it from bit doctrine gets substituted by the new it and bit. After showing why the physical entropy used in the science of thermodynamics is not a measure of the ignorance of human observers, the final part of this Essay is devoted to emphasize the importance that the bit acquires in modern science when confronted to the delicious multiplicity of the far-from-equilibrium regimes, where the certainty of Newtonian and Schrodinger motion begin to fade in favour of a complex non-geometrical, 'living', conception of Nature: an it and bit conception.