Bit from It

Abstract

With his aphorism ‘it from bit’, Wheeler argued that anything physical, any it, ultimately derives its very existence entirely from discrete detector-elicited information-theoretic answers to yes or no quantum binary choices: bits. In this spirit, many theorists now give ontological primacy to information. To test the idea, I identify three distinct kinds of information and find that things, not information, are primary. Examination of what Wheeler meant by ‘it’ and ‘bit’ then leads me to invert his aphorism: ‘bit’ derives from ‘it’. I argue that this weakens but not necessarily destroys the argument that nature is fundamentally digital and continuity an illusion. There may also be implications for the interpretation of quantum mechanics and the nature of time, causality and the world (For publication in this volume, I have added some new footnotes, dated 2014, in which I indicate developments in my thinking since the essay competition, giving details of any appropriate publications. I also take the opportunity, omitted at the time, to respond to some of the comments that were made of my essay in FQXi posts (at http://fqxi.org/community/forum/topic/911). I have also, without noting them, made a few trivial changes to the text for the sake of greater clarity and precision).

Appendices

Appendix A: Maximal Variety

In the body of the essay, I describe ‘time capsules’ as configurations that carry intrinsic semantic content. Here I give another example. It does not suggest history, but the notion of a structured configuration is all important.

Leibniz told princesses that we live in the best of all possible worlds, but in his serious philosophy he argued that we lived in the one that is more varied than any possible alternative (Monadology, §58). Some years ago, Lee Smolin and I found a way to express this idea in a simple mathematical model. One representation is in terms of a ring of $N$ slots (here $N=24$) into which balls of different colours (or darkness in grey shades) can be placed (Fig. 17.1).

Fig. 17.1

The most varied two-colour (dark-light) 24-slot universe

The diagram is maximally varied in the sense that, without pointing to a particular ball or naming colours or sense of direction, each ball is more readily identified than for any other occupation of the slots. The rule of creation is minimization of indifference (the inverse of variety). Balls are identified by their neighbourhoods: the seven-slot neighbourhood centered on ball $x$ at noon is either the string $SDDxDSD$ or $DSDxDDS$ (left-right symmetry), where $S$ and $D$ are same ($S$) or different ($D$) neighbours (colour symmetry). The indifference $I_{ij}$ of slots $i$ and $j$ is equal to the length (3, 5, 7,$\ldots$) of the respective strings needed to distinguish them. The total indifference of a distribution is $I=\sum _{i<j}\,I_{ij}$. The most varied distribution is the one for which $I$ has its smallest value. The relative number of balls of each colour is not fixed in advance but found by the minimization of $I$. Figure 17.1 is typical of the maximal-variety configurations (in general there are 2 or 3 for each $N$, though for 24 Fig. 17.1 is the unique configuration). Interestingly, the symmetric rule of creation invariably leads to markedly asymmetric configurations. The maximally—and near-maximally—varied configurations ‘proclaim their own sematics’ in the sense that smart enough mathematicians could deduce the law that creates them. For more details and the results of calculations up to $N=27$ see [17].

Appendix B: Best Matching

This appendix describes the motion of particles without the props of absolute space and time. Position and time are treated relationally. The basic idea—best matching—also leads to general relativity (GR) [18]. The further requiremnt of relativity of size leads to GR with a distinguished definition of simultaneity [11]. I relied on this result in Sect. Holism and Reductionism to argue that identifying instants of time with confgurations is not in conflict with Einstein’s theory.

Consider $N$ gravitating particles (masses $m_i$) in Euclidean space. For $N=3$, Fig. 17.2 shows the three particles at the vertices of the triangles representing two possible relative configurations ‘held in imagination’ somehow relative to each other. This generates apparent displacements $\delta \mathbf x _i$ of particle $i$. Calculate (17.2):

Fig. 17.2

A trial placing of the two triangles generates apparent displacements $\delta \mathbf x _i$. Minimization of the trial action (17.2) leads to the best-matched displacements

$$\begin{aligned} \delta A_{trial}=2\sqrt{(E-V)\sum _i{m_i\over 2}\delta \mathbf x _i\cdot \delta \mathbf x _i}, ~ V=-\sum _{i<j}{m_im_j\over r_{ij}}. \end{aligned}$$

(17.2)

Here $E$ is a constant. The action (17.2) is clearly arbitrary with no significance, but, using Euclidean translations and rotations, we can move either triangle relative to the other into the unique best-matched position that minimizes (17.2). For any two nearly identical triangles, the best-matched value of (17.2) defines a ‘distance’ between them and a metric on $\mathcal S$, the space of all possible relative configurations of the particles. One can then find the geodesics in $\mathcal S$ with respect to this intrinsically—and holistically—defined metric of the $N$-body universe.

It can be shown [17] that the relative motions which the particles undergo as the representative point of the system moves along the geodesic are identical to the observable relative motions of particles in the Newtonian $N$-body problem with total energy $E$ and vanishing total angular momentum. Moreover, the increment $\delta t$ of ‘Newtonian’ time is derived [19]:

$$\begin{aligned} \delta t=\sqrt{\sum _i\,m_i\delta \mathbf x _i\cdot \delta \mathbf x _i\over {2(E-V)}}. \end{aligned}$$

(17.3)

The combination of best matching and the geodesic requirement, which dispenses with Newton’s absolute time as independent variable, leads to recovery of Newtonian behaviour of subsystems in a large $N$-body ‘island universe’. Newton’s first law, the basis of reductionism, is holistic in origin.