The Constants of Nature

A Realist Account

Peter Johnson

• Publisher: Routledge
• Year: 2019
• ISBN:
  9780429790706
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

First published in 1997, this volume constitutes an attempt to resolve certain misunderstandings and ignorance concerning the constants of Nature. Its purpose is to look closely at the philosophical arguments made to support the customary conventional view of measurement, particularly with regard to constants. Peter Johnson argues that historic accounts provide only a partial understanding of the nature of constants, and that the conventionalism that rises relates only to the numerical representations used to quantify the measurement of quantities.

1 Introduction and overview

Contrasting perspectives

Between 1880 and 1950 a good deal was written about the nature of physical quantities, dimensions and, obliquely, physical constants. Much of this interest stemmed from the practical need to understand the issues at stake in the choice of a system of basic quantities to be used uniformly across the scientific community in order to make the results of experiments consistent and comparable. Since the 1950s little has been written in this area, perhaps because the issues were thought to be resolved, and because scientists have settled on the S.I.¹ system of basic measurement quantities.

If there was a prevailing opinion at the end of the 1950s, it was that the choice of quantities, the assignment of dimensions and the nature of constants were entirely matters of scientific convention. Such views were a natural consequence of the operational concept of measurement championed by Bridgman (1926), according to which the conceptual content of a quantity is exhausted by its definition in terms of the carrying out of specified measurement operations in precisely described circumstances. Such a view of measurement clearly had much in common with the philosophical programme of the positivists. These views held sway well into the 1960s, and in the field of measurement they were fully expounded by Dingle (1942, 1943), and most recently by Ellis (1966).

The purpose of the present work is to look closely at the philosophical arguments made to support the customary conventional view of measurement, particularly with regard to constants. It will be argued that these historic accounts provide only a partial understanding of the nature of constants, and that the conventionalism that arises relates only to the numerical representations used to quantify the measurement of quantities. The story of conventional numerical representation needs to be supplemented by an account of the empirical foundations of constants. A modest realist account of constants will be developed under the auspices of Fine’s Natural Ontological Attitude (NOA), and this account will be articulated and defended in the context of other prevailing philosophies of science. The intention will not be to defend Fine’s particular form of modest realism per se, but to describe critically the emergence of NOA and to see whether it forms a suitable home for the empirical notions of constants developed in the first part of the work. It will be argued that NOA can accommodate constants, and that NOA may allow for the possibility that the physical grounding of constants may be underdetermined by tolerating a limited relativism in its account.

To give a sense of the strength of feeling expressed by philosophers and scientists concerning the status of constants, and to illustrate some of the interesting philosophical issues under discussion, it is helpful to contrast perspectives.

The current prevailing orthodoxy of the scientific community is well captured by Barrow, the astrophysicist:

Real advances in our understanding of the physical world always seem to involve either:

1. The discovery of a new fundamental constant of Nature,
2. A formula showing how the value of one constant of Nature is determined by the numerical values of others, or,
3. The discovery that a quantity believed to be a constant of Nature is not constant.

…. To most physicists the ultimate goal of their subject is nothing less than the determination of the numerical values of all these universal constants: the demonstration that they can possess only one possible set of self-consistent values, and that this requirement of self-consistency, together with a minimum of symmetry principles, will be enough to determine the structure of the world uniquely. (Barrow 1988 p. 322)

One of the great goals of fundamental physics is to find the reason for the precise numerical values of the constants that appear in the equations that prescribe the laws of Nature. Many physicists believe that, eventually, we will be able to calculate the values of the fundamental constants, and specify the initial conditions of the Universe by some principle of internal consistency that reveals there to be one, and only one, logical choice for all of them. (Barrow 1988 p. 280)

The view that the values of the constants might be obtainable from theory was also held by Einstein:

[Einstein] expressed his anticipations concerning the true universal constants … also in the following way: “In a reasonable theory, there are no (dimensionless) numbers whose values are only empirically determinable.” He stressed again, however, that he, naturally, had no proof for this, but that he could not imagine a unified and reasonable theory explicitly to contain a number which the mood of the creator could just as well have chosen differently, whereby a world of a qualitatively different lawlessness would have resulted. (Rosenthal-Schneider in Schilpp 1949 p. 144)

Eddington went further than theoretical deducibility, and spent many years working on a priori proofs of the values of constants:

I believe that the whole system of fundamental hypotheses can be replaced by epistemological principles. Or to put it equivalently, all the laws of nature that are usually classed as fundamental can be foreseen wholly from epistemological considerations. They correspond to a priori knowledge, and are therefore wholly subjective. (Eddington 1939 p. 57)

My conclusion is that not only the laws of nature but the constants of nature can be deduced from epistemological considerations, so that we can have a priori knowledge of them. (Eddington 1939 p. 58)

While at first sight Eddington’s views may seem curious, in fact modern unified field theorists are working along similar lines: Eddington’s fundamental theory attempted to integrate quantum mechanics and general relativity by postulating the cosmological consequences of a universe of a finite number of elementary particles, governed by quantum mechanics, and described by his quaternion calculus. Constraints upon the nature of such a system emerged from the simultaneous need to satisfy relativity and quantum mechanics and from constraints imposed by a priori features of the mathematical representation Eddington posited. This approach seems similar in outlook to the group-theoretic gauge symmetries that comprise the Standard Model used as the starting point for modern unified approaches.

In contrast to the views of scientists who accorded much importance to constants and their values, we may cite the violently opposing operationalist view of Ellis, one of the natural successors to Bridgman and Dingle:

We may conclude, then, that simply by adopting different conventions concerning the expression of equations, universal scale-dependent constants may be created or eliminated at will. We cannot, therefore, attach to these constants anything other than a conventional existence; and it is quite absurd to suppose that these constants represent the magnitudes of peculiar invariant properties of space or of matter. (Ellis 1966 p. 125)

Perhaps the best summary of the perplexities posed by constants that give rise to such radically differing views came from Palacios:

Universal constants have one disturbing feature. They appear in the expressions for the laws of physics without being previously defined either qualitatively or quantitatively. They are independent of the nature of the bodies to which these laws are applied. Further, they are not physical quantities since they always occur with the same value; and to imagine that in another universe they can take other values is an unjustified and useless metaphysical speculation. As there exists only one example of each, if they were physical quantities they would themselves be their own units and their value would be the number one. Nevertheless, they are not mere numbers since their value depends on the system of units adopted to measure the magnitudes which occur in the equations. Finally their existence is in some respects precarious since, for example, what has been called the dynamical constant is not mentioned in any physics textbook, whilst the mechanical equivalent of heat, which used to be discussed at great length in textbooks at the beginning of the century, is hardly mentioned in present day works … In the introduction to the present thesis it was indicated that there is a tendency to reduce the number of universal constants in use. The simplest thing would be to get rid of them all, but as there are not enough disposable units to do this, each author suppresses those which he likes least and a certain amount of published work exists in which, thanks to the suppression of such and such constants, a certain esoteric sense is supposed to be given to the laws of physics so obtained. (Palacios 1964 p. 23)

In the chapters that follow many of the issues raised by these differing perspectives will be explored. Thorough analysis will reveal the extent to which these views are correct, incomplete or misguided.

Summary of principal findings

In advance of detailed reading of the text, it may be helpful to list the principal findings that emerge from this research as a guide and aide-memoire through what is at times a complex and indigestible account.

1 It is possible to distinguish between two separate categories of universal constants: those measured by fundamental means and those given by derived measurement relying on a supporting law.

2 The most primitive fundamental universal constants are the charge, mass and magnetic moments of elementary particles; the most primitive derived constants are c, h, G, e and k.

3 All other universal constants customarily regarded as significant can be obtained from this set of primitive constants.

4 The fundamental universal constants can function as the standard objects within a formal axiomatic system of extensive measurement, and are properties of particles.

5 The derived universal constants can be defined within a formal system of derived measurement and characterise the interactions of particles.

6 The distinction between fundamental and derived quantities is not undermined by substitution of derived for fundamental quantities nor the possibility of alternative representations of fundamental quantities.

7 The conventionality that extends to the dimensional representation of derived quantities does not undermine the status of primitive universal derived constants, which can be grounded in an alternative empirical notion of dimensions.

8 NOA seems to offer a number of advantages compared with traditional realism, internal realism, instrumentalism and constructive empiricism. The potential vulnerability of NOA to problems arising from underdetetermination can be overcome by employing a notion of relativism that finds its origins in Quine’s work on the indeterminacy of translation.

9 The choice of alternative empirical systems to ground primitive derived constants represents a case of underdetermination that can be happily accommodated by NOA.

10 NOA provides a modestly realist account of science in which we may embed our notions of primitive constants.

Overview

With the list of key findings in hand, the structure and content of the various chapters fall more easily into place:

Chapter 2 Constants and measurement

In this chapter we review the principal traditional accounts of measurement in so far as they relate to constants. By drawing a distinction between system-dependent parameters and scale-factors, we are able to explain aspects of the physical and numerical systems in which constants are embedded without the confusion evident in the account of Campbell, nor the operationalist dogma of Ellis. There is a readily intelligible account of the physical meaning of constants, which can be formalised in the assignment of single values to system-independent parameters in a systematic account of the numerical representation of extensive quantities based upon the axiomatic scheme provided by Suppes. Important differences exist between fundamental and derived system-independent parameters, which give rise to further questions relating to the numerals and ratios are identified. We argue that no particular importance attaches to composite ratios that turn out to be dimensionless numbers, since it is always possible to use the results of dimensional analysis to turn a dimensioned composite ratio into a dimensionless ratio. The remaining primitive constants can be separated into those obtained by derived measurement and those by fundamental means. Support for this distinction lies in the particulate vs. field aspects of the categories so defined. The account given of primitive fundamental constants is defended against criticisms that it is a meaningless distinction in application and undermined by the possibility of alternative, non-standard representations. Conventionalist arguments against primitive derived constants based upon the theory of dimensions are addressed in Chapter 4.

Chapter 4 Constants, conventionality and dimensions

In this chapter we analyse in detail the arguments that have been made for a conventional status for derived constants. While it is true that constants can be made to appear or disappear at will, and to have whatever dimensions may be desired, these seemingly arbitrary features of constants are entirely aspects of the numerical representation employed, and apply equally to all quantities. It is possible, however, to specify an optimal representation of a formula that does not result in a redundancy of dimensional quantities or of constants. Manipulation of the numerical representation does not affect the unde...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Figures and tables
• Preface
• Acknowledgements
• 1 Introduction and overview
• 2 Constants and measurement
• 3 The taxonomy of constants
• 4 Constants, conventionality and dimensions
• 5 Constants and reality
• 6 Constants and underdetermination
• 7 Constants and NOA
• Bibliography