# Information Physics—Towards a New Conception of Physical Reality

## Abstract

**:**

## 1. Introduction

## 2. The Role of Information in Quantum Physics

#### 2.1. Classical Physics

- A conception of the physical world, namely the mechanical conception of reality;
- A precise conceptual and mathematical framework, which formalizes this mechanical conception;
- Classical physical theories—in particular Newtonian mechanics and Maxwellian electrodynamics—which are built within this framework.

#### 2.2. Quantum Physics

#### 2.2.1. Quantum Model of the Measurement Process

- Discreteness. The number of possible outcomes of a measurement may be finite or countably infinite;
- Probabilistic Outcomes. The outcome of a measurement performed on a physical system is only predictable on a probabilistic level;
- Disturbance. A measurement almost invariably changes the state of the system upon which it is performed;
- Complementarity. A measurement only yields information about some of the parameters needed to specify the state of the system, at the expense of the others.

- (1) Limited information about future measurement outcomes.Given the state of the system and the measurement to be performed, the experimenter lacks information about the outcome that will be obtained. In the above example, prior to performing a Stern-Gerlach measurement in the -direction on the spin, the experimenter does not know which outcome (up or down) will occur, but only that the probabilities of the two possible outcomes are and , respectively.Quantitatively, prior to performing the measurement, the experimenter has uncertainty about which outcome will be obtained. The -function here is an uncertainty function, such as the Shannon entropy function, . After performing the measurement and obtaining a definite outcome, the experimenter’s uncertainty has been removed. Hence, the uncertainty, , can be interpreted as the amount of information the experimenter lacks prior to performing the measurement about which the outcome will be obtained.
- (2) Limited information about the unknown state of a physical system.If an experimenter is presented with a system in an unknown state and wishes to learn what that state is, the quantum framework imposes two kinds of fundamental limits. First, due to the probabilistic and disturbance features of measurements, the outcome of a single measurement performed on the system provides scant information about the state of the system. In practice, in order to build up any useful knowledge of the state, the experimenter must perform a large number of measurements on identically-prepared copies of the system. Furthermore, due to complementarity, a single type of measurement only provides access to one-half of the degrees of freedom of the state of the system, so that the experimenter must perform other types of measurement in order to build up information about all of the degrees of freedom in the state.In the electron spin example, the experimenter wishes to learn about the unknown state, . The experimenter’s information about the outcome probabilities, , prior to performing the Stern-Gerlach measurement is encoded in the Bayesian prior probability , where symbolizes the experimenter’s prior state of knowledge. After the experimenter has performed identical Stern-Gerlach measurements on identically prepared copies of the system, obtaining data which can be summarized in the data string of length , the prior can be updated to the posterior, , using Bayes’ rule:If the experimenter obtains cases of outcome up and of outcome down, thenThe amount of information the data thus provides the experimenter about can readily be quantified using, for example, the continuum form of the Shannon entropy,which is finite for finite . Hence, for finite , the experimenter only has finite, imperfect information about . Only in the practically unattainable limit as does the experimenter gain perfect knowledge of .Furthermore, the data string, , provides no information about the . In order to obtain information about the , the experimenter needs to perform Stern-Gerlach measurements in other directions.

#### 2.2.2. Quantum Description of Composite Systems

## 3. The Rise of the Informational View

#### 3.1. Mach and the Primacy of Experience over Concepts

“The goal which it (physical science) has set itself is the simplest and most economical abstract expression of facts.”

“In mentally separating a body from the changeable environment in which it moves, what we really do is to extricate a group of sensations on which our thoughts are fastened and which is of relatively greater stability than the others, from the stream of all our sensations. Suppose we were to attribute to nature the property of producing like effects in like circumstances; just these like circumstances we should not know how to find. Nature exists once only. Our schematic mental imitation alone produces like events.”

#### 3.2. Thermodynamics, Statistical Mechanics, and Maxwell’s Demon

#### 3.3. Shannon’s Theory of Information, and Its Applications

Principle of Maximum Entropy:In assigning a probability distribution , select the distribution which has maximum entropy, subject to the normalization constraint and any other constraints on .

#### 3.4. Black Hole Physics

#### 3.5. Computation as a Physical Process

## 4. Information Physics

“ ‘It from bit’ symbolizes the idea that every item of the physical world has at bottom—at a very deep bottom, in most instances—an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin, and this in a participatory universe.”

“What we call reality consists of a few iron posts of observation between which we fill an elaborate papier-mâché of imagination and theory.”

**Shift from the view of a physical theory as a description of reality in itself to a description of reality as experienced by an agent.**Mach’s emphasis on the primacy of the experience of an agent over the concepts of a physical theory, thermodynamics as a theory explicitly constructed to interrelate the macro-variables accessible to limited agents, and quantum theory with its highly non-trivial model of the measurement process have all helped to shift the focus of physical theory from being a description of reality in itself to a description of reality as experienced by an agent.**Breakdown of the classical notion of an ideal agent who has unfettered access to the state of reality.**Szilard’s proposal that there is a physical entropic cost associated with measurement (itself arising from the tension between the second law of thermodynamics and the reversible dynamics of classical mechanics), the quantum model of measurement (with its features of discreteness, probabilistic outcomes, disturbance and complementarity), and the limited access to information of the internal constitution of a black hole by an external observer all point to the breakdown of the classical notion of an ideal agent who has unfettered access to the state of reality without bringing about any reciprocal change as a result, and all suggest that the interface between an agent and the physical world is a highly non-trivial one governed by precise rules which we can come to know.**Recognition that the informational view might lead to new quantitative understanding of the reality described by existing physics.**Szilard’s quantification of the entropy generation associated with information acquisition, Shannon’s quantification of the information gain resulting from learning the outcome of a probabilistic process, Jaynes’ derivation of statistical mechanics on the basis of Shannon’s information measure, the quantification and statistical interpretation of black hole entropy, and the constructive use of the mathematical tools of information theory to discover and explore unexpected phenomena in the quantum world have all lent support to the hope that the informational view might lead to new quantitative understanding of the reality described by existing physics and that it is important that information be taken into account in the development of new physical theories.

#### 4.1. Understanding Quantum Theory

#### 4.1.1. Information-based Reconstruction of Quantum Theory

**Wootters’ derivation of Malus’ law**. One of the first attempts to reconstruct quantum theory using a small number of physically compelling postulates was carried out by Wootters [34]. Wootters considers the amount of information gained by an experimenter about the parameters of the state of a quantum system when identically-prepared copies of the system are analyzed, and postulates that, if one holds the experimental situation fixed but imagines varying the physical laws which govern the situation, then the actual laws are those which maximize the amount of information that the experimenter gains about the system.

Wootters’ Information Maximization Principle: The laws of quantum physics are such that the expected gain in the Shannon information about the state of a quantum system after analysis of a large number of identically-prepared systems is maximized. The average is taken over all possible data that can be obtained in a given number of analyses.

**Recent Reconstructions of Quantum Theory.**Following Wootters’ pioneering work, numerous attempts have been made to derive specific predictions of quantum theory, or to reconstruct the quantum formalism itself, from postulates inspired by an informational view, with much of the recent work inspired by the new perspective afforded by advances in the field of quantum information [35,36]. Almost without exception, these derivations take as a given the probabilistic nature of measurement outcomes, and formulate informationally-inspired postulates within this probabilistic framework.

## 5. Towards a New Conception of Reality

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- More generally, the knowledge that an agent (be the agent ideal or non-ideal) possesses about the state of a system can be represented by a probability distribution over the state space of the system. This distribution itself is often also referred to as “the state” of the system. If the distribution picks out a single state, as would it be in the case of an ideal agent, it is said to be pure.
- This characterization holds true for an N-dimensional quantum system. In that case, the state is represented by where V
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Goyal, P.
Information Physics—Towards a New Conception of Physical Reality. *Information* **2012**, *3*, 567-594.
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Goyal P.
Information Physics—Towards a New Conception of Physical Reality. *Information*. 2012; 3(4):567-594.
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**Chicago/Turabian Style**

Goyal, Philip.
2012. "Information Physics—Towards a New Conception of Physical Reality" *Information* 3, no. 4: 567-594.
https://doi.org/10.3390/info3040567