In modern science we judge a theory by its ability to make detailed quantitative predictions within some domain (vertical coherence) and we also look for applications across various fields outside its original domain (horizontal coherence). In this way we generate a coherent network of concepts, laws and theories that is usually taken to be a sign of a correct representation of the phenomena of nature. The present chapter recapitulates our exposition of the discovery and development of the law of universal gravitation as a useful illustration of this process and discusses how this became interwoven with our ideas about space and time. Here we tell a retrospective story in which facts are selectively arranged in a sequence to produce a hopefully coherent narrative. This, of course, does not imply that there was any inherent need that events had to develop as they did.

A REVOLUTION

As we have seen (Sections 4.5 and 4.7), in the Aristotelian view of the cosmos the earth was at the center of the celestial sphere and all the space between these was divided into concentric regions (the homocentric spheres of Eudoxus), each region being the domain of one of the planets. This system of spherical regions turned one within the other to account for the observed motions of the stars and planets. The entire system was driven by the motion of the outermost shell, the celestial sphere.

In this chapter we present a prelude to the foundations of modern mechanics that is basically the study of the descriptions and of the causes of the motion of bodies. Aristotle and Galileo are the historical characters on whose work we focus. As we pointed out in Chapter 3, it is important to appreciate that all developments in science take place against the historical, philosophical and social backgrounds in which the scientists find themselves. All scientists, no matter how singularly gifted, build upon the work of their predecessors, even when they overturn old beliefs and theories. Unlike the Athena of Greek mythology who emerged full grown from the head of Zeus, new theories in science do not materialize in final form from one mind working in isolation, but are developed as part of a larger movement. That theme, to which we return often in this book, is well illustrated in the following.

THE IMPETUS THEORY

Over the centuries there were numerous transcriptions and translations of Aristotle's works, as well as endless commentaries upon them. Not all those who studied the Aristotelian tradition were uncritical of it. This was especially true for Aristotle's position that ‘unnatural’ motion required the action of an external agent. Hipparchus, perhaps the greatest astronomical observer of antiquity, expressed somewhat vaguely the concept of an impressed force that was transmitted to a moving body. This impressed force was gradually dissipated by the surrounding medium so that the body eventually came to rest.

In a physical theory we typically describe a system in terms of its state. We specify the relevant physical quantities or variables and then use dynamical laws to find the time evolution of these variables to predict their values in the future. For example, in classical particle mechanics, the state of a system is specified by the positions and velocities (or, equivalently for us, the momenta) of all of the particles in the system (that is, r(t) and v(t) for each particle). Newton's second law, F = ma, then determines the time evolution of the variables, or of the state, of the system. For electrodynamics, the state variables are the electric and magnetic fields, E and B, and Maxwell's equations govern the time evolution of these. In classical physics (including relativity here), the state variables that are the central entities of the dynamical equations (typically the positions and momenta of the particles) are also the directly observable physical quantities. That is, the state itself is specified in terms of the observables of the theory. The essential features of the classical world view (as modified by relativity) are that the present state of a system in principle determines its future state (as in the flight of a baseball under the influence of gravity) and that the agency responsible for this event-by-event causal structure must propagate from the cause to the effect at some rate no greater than the speed of light.

When it was first put forward, special relativity struck many people as counterintuitive and possibly inconsistent, as we saw when we considered the twin paradox in Chapter 17. Quantum mechanics had a similar effect, only to a much greater and longer lasting degree, from the time of its inception in the mid 1920s until the present. This reaction to quantum theory was not confined to an initial confusion that often accompanies a new subject, but remained a life-long puzzle for Einstein, to mention only the most prominent opponent of what he took to be the reigning orthodoxy. In this chapter we study a famous attempt by Einstein and two of his colleagues to show that quantum mechanics was, if not logically inconsistent, then at least an incomplete theory. This charge of incompleteness is just that raised by Schrödinger's cat paradox (Section 21.4).

THE EPR PARADOX

In 1935 Einstein, Boris Podolsky (1896–1966) and Nathan Rosen (1909–1995) (hereafter referred to as EPR) published a paper titled ‘Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?’. They take as their criterion for the completeness of a theory that it contains terms corresponding to every relevant entity found in reality. For example, in the classical description of a system, such as a planet going around the sun, there are symbols representing the position r, the momentum p and so forth for the various parts of the system.

So far in this book we have studied several major advances in the history of physics. We can now look back and ask what the relation of physics to the other natural sciences is and attempt to draw some lessons about the nature of science and how it operates. For example, what are the hallmarks of science and what, if anything, makes scientific knowledge different from other types of knowledge? The traditional view of science, supported by nearly all scientists and by many philosophers of science, has been to treat the scientific knowledge finally arrived at as being valid largely independently of the details of how it was obtained, as long as it passes the scrutiny of logical analysis and agreement with further observations. Such a position has been called into question by a considerable body of recent work in the history and philosophy of science. We did touch on certain sociological or public aspects of science in our historical presentation of the formulation of quantum theory in Chapter 19. In this chapter we focus on attempts to identify a strictly rational side of science and to reconcile this with the larger social context within which science functions. We use physics as our prototypical science and also discuss at some length the views of Albert Einstein on reality, on a theory of knowledge and on the method and goals of science. Our first task is to delimit certain features of physics for consideration.

Since we hope to learn something about science and its operation and since science concerns itself with a certain type of knowledge and its attainment, let us begin with a brief consideration of how we arrive at knowledge. A common type of knowledge is that based on opinion or on the acceptance of another's authority. Most of our everyday knowledge used for dealing with the practicalities and necessities of life is gained in either of these fashions. Much of what one learns in the course of reading a book is taken as true simply because it has been presented on the printed page, although hopefully you will be more critical than that. Thus, we can merely have an opinion about a proposition and then decide to accept it as true or we can appeal to the authority of another, as ‘Einstein says’ or ‘Aristotle says,’ or to the authority of a text, as ‘The Bible says,’ or we can assert a fact to be ‘obvious’. Consider the following example:

In previous chapters we argued that the empirically successful formalism of quantum mechanics supports equally well two mutually incompatible general ontologies: the inherently indeterministic and generally accepted Copenhagen interpretation and Bohm's completely deterministic one. This underdetermination of the interpretation by the formalism is not simply an apparent one of two equivalent theories since there is no way to translate the terms of one of these ontologies into those of the other. This case could be seen as presenting a challenge to the scientific realist who seeks from successful scientific theories a true representation of the world. Furthermore, we suggest that the actual historical competition between these theories and the selection of Copenhagen over Bohm illustrate that such an historically contingent process is not meaningfully distinct from the rational reconstruction and logical judgment of the victorious theory. What is deemed successful and put on offer by the scientific community for the philosopher of science to justify after the fact is itself a contingent and nonunique product.

UNDERDETERMINATION

The origin of the underdetermination of scientific theories, what we refer to here as the so-called Duhem–Quine thesis, is typically located in Pierre Duhem's The Aim and Structure of Physical Theory (first published in 1906). There Duhem was quite explicit about what he took to be the basis for judging whether or not a given physical theory is acceptable.

In this chapter we consider several of the empirical implications that follow from Einstein's two postulates and relate these to experimental tests of special relativity. The emphasis is on how many diverse, quantitative predictions result from two verbal statements that appear so disarmingly simple and qualitative in nature. Just as Newton's system of classical mechanics and theory of gravity gained universal acceptance because of its many quantitative successes and its wide range of applicability to seemingly unrelated phenomena (recall Chapter 11), so Einstein's special theory of relativity soon became the dominant theory because of the great scope of its achievements.

RELATIVISTIC DOPPLER EFFECT

We begin by considering the effect that relative motion has on the measured frequency of light. In a classical, or nonrelativistic, context this was originally discussed by Christian Doppler (1803–1853) in 1842. The relativistic version was first treated by Einstein in his 1905 ‘relativity’ paper. In Figure 17.1 let observer B be moving parallel to and in the same direction as the propagation of the wave front, all as seen by observer A. From the point of view of A, for whom the wavelength (or distance between successive wave fronts) is λ, the time t that it takes for two successive wave fronts to pass the moving observer B is t = (λ + vt)/c. Denote by t′ (a proper time) the time B measures between the passage of these two wave fronts (past B).

In this chapter we study one of the dramatic clashes that took place during the overthrow of the Aristotelian world view that had given man a unified picture of himself and of his surroundings. In the Galileo episode this became hopelessly entangled with the issue of intellectual freedom versus institutional authority. However, there were other relevant factors as well: the personalities of Galileo and of those who opposed him and, possibly, the social structure of the patronage system of support for artists and scientists in those times.

THE BACKGROUND

Perhaps it will help the reader if we begin by listing several key events that preceded the direct confrontation between Galileo and the Church authorities.

1. March 1610 – Galileo published the Sidereus Nuncius (The Starry Messenger) in which he discussed his telescopic observations and discoveries. He showed that there were many more stars in the heavens than had been thought previously, that the surface of the moon was rough, containing mountains, plains and valleys, much like the surface of the earth itself, and that Jupiter had a set of moons orbiting the central planet, very much as the planets orbit the sun in the Copernican system. This work had great popular appeal and wide impact.

2. December 1613 – Galileo wrote a letter to one of his scientific pupils, the Benedictine monk Benedetto Castelli (1578–1643), concerning his own views on the relation between science and religion.

3. […]