1.1 Introduction
The task of science is to construct theories and laws with which to predict the occurrence of events in nature. 'The task of science is both to extend the range of our experience and to reduce it to order', wrote Bohr [1934, p. 1]. Whether successful 'prediction' of occurrence of events naturally entails a causal status to such an explanation is a point that remains controversial. For, the famous Quine-Duheim hypothesis tells us that data under-determines theory such that more than one theory can adequately predict the same set of data, in principle. If so, no one theory can claim the status of a causal explanation merely by virtue of predictive success. Yet, causal thinking continues to form the 'implicit' basis of the physicists' successful thinking about the world even when they develop one theory to account for data. In this regard, Einstein's view is pertinent. He proposed that although under-determinism may hold in principle, only one theory always is found to be the right theory in practice.
[O]ne can think that arbitrarily many, in themselves equally justified systems of theoretical principles were possible; and this opinion is, in principle, certainly correct. But the development of physics has shown that of all the conceivable theoretical constructions a single one has, at any given time, proved itself unconditionally superior to all the others. No one who has really gone deeply into the subject will deny that, in practice, the world of perceptions determines the theoretical system unambiguously, even though no logical path leads from the perceptions to the basic principles of the theory [cited in Howard, 1991, p. 224-5].
We see Einstein's claim that, in practice, the empirical world unambiguously determines one theory over others as providing justification to distinguish between the ontological cause and explanations on the one hand, and between causal and non-causal explanations on the other. For now, there can be many explanations at the empirical level (since data under-determines the theory). One of them would be a causal explanation (based on physicists own extra-pragmatic considerations), and even that, according to this viewpoint, would not directly describe the ontological cause.
In justification of the last mentioned claim, I shall presently trace the diminishing ability of physicists to directly link explanation to cause at the level of experience, taking up relevant points in classical physics, thermodynamics, and relativity. I finally discuss quantum mechanics, where the classical notion of causality fails altogether. At each stage of the discussion, I shall relate the conclusions reached, to the proposal to distinguish between causality and causal explanation.
1.2 Causality in Classical Mechanics
By the term 'classical physics', I refer to all physics prior to quantum theory. The first stage of development of classical physics occurred between the sixteenth and nineteenth centuries in the form of mechanics developed by Newton. Newton's classical mechanics attempted to provide a grasp of the laws governing the motion of macroscopic bodies. Kepler had already given quantitative expression to such physical laws, but Einstein (1927) points out that Kepler's laws of planetary movement are concerned with movement as a whole, and not with the question 'how the state of motion of a system gives rise to that which immediately follows it in time' (emphasis his). That is to say, Kepler's laws described motion in terms of the yearly period of revolution and the major/minor axes of the elliptical motion, but not how this motion comes about, much less how this motion is the result of the state of the system itself. Thus, Einstein further remarks: "[B]efore Newton, there existed no self-contained system of physical causality which was somehow capable of representing any of the deeper features of the empirical world." [ibid., p. 290]
According to Einstein, Newton devised a formal system that could answer the question, 'how does the state of motion of a mass-point change in an infinitely short time under the influence of an external force?' Newton developed the mathematics of calculus to answer this question, and wrote down the formula in the form of the differential equation: . The acceleration of a body a is directly (i) proportional to the force F acting on it, and (ii) inversely proportional to its mass m. But even with this equation, according to Einstein, Newton was yet to arrive at a causal explanation of a (macroscopic) body's motion. Newton had to postulate the further idea of the force of gravitational attraction mutually acting on massive bodies, and only then was he able to show that the force acting on an individual mass was determined by the positions of all masses situated at a small distance from the mass in question. This alone provided the basis of a causal law in Newtonian system. To quote Einstein:
"[Initially] the motion was determined by the equation of motion in cases only where the force was given. Inspired by the laws of planetary motions, Newton conceived the idea that the force operating on a mass was determined by the position of all masses situated at a sufficiently small distance from the mass in question. It was not till this connection was established that a completely causal concept of motion was achieved'. The logical completeness of Newton's conceptual system lay in this, that the only causes of the acceleration of the masses of a system are these masses themselves."
[1973, p.256, emphasis Einstein's]
Newton's laws thus proved important, not only because of their predictive precision but because of enabling the control of mechanical systems. The twin features of prediction and control afforded by early mechanics led many to propose the universal validity of Newton's laws to all systems, including the universe. The eighteenth century scientist Laplace, for example, famously believed that if we can specify the position and momentum of each particle constituting the universe at any one instant, then in principle, all the past and future states of the universe can be calculated and everything that we need to know about the universe at any time can be known. [Bohm, 1971, p.37] calls this an 'unlimited extrapolation' of the science of mechanics as necessitating a completely determinate prediction of the future behavior of the 'entire universe'.
The implication of such a large-scale mechanistic view is that any feature of the world that is not knowable under the mechanical conception is merely our subjective conceptions of the world and epiphenomenal, i.e. not having any causal significance. Thus, Laplace agreed that the various qualitative properties like hardness, color, texture, etc are not guided by basic laws governing the motions of atoms, but are to be 'regarded as subjective categories' mere concepts that we use about arrangement of an aggregate of molecules. The objective quantitatively specifiable (and hence, presumably causally significant) properties are positions, velocities, masses etc.
However, Bernays [1971] rightly points out that it is a fallacy to consider causality as a philosophical derivative of determinism. Bernays argues that our causal reasoning does not depend on strict mathematical preciseness that is peculiar to deterministic reasoning. The deterministic form exists in the theoretic description of a fixed mathematical system whereas causality is used in heuristic reasoning, in applications of physical theories, in commonsense reasoning and so on. He writes:
"In any case, the causal view is not bound to the theoretical scheme of mechanics or generally to the assumption of deterministic lawfulness. Indeed the causal aspect by itself does not include the element of strict generality and of mathematical preciseness, which is peculiar to deterministic reasoning. One might even observe that deterministic consideration tends to eliminate the proper causal aspect. In fact, in the presentation of a physical theory, the concept of causality has no proper place. The deterministic form exists only for the theoretical description of a fixed, definite system." [ p. 262]
The point that determinism does not translate into causality can also be made in the following manner. Classical mechanics predictively accounts for the motions of both the celestial planets and the more commonplace falling apple through a single set of simple empirical laws. The idea that these empirical laws also provide a causal explanation, where the term 'cause' carries the same meaning as in everyday heuristic reasoning (that one event causes another event) is connected to the feature of the formalism that an initial state determines any subsequent state.
This simplistic equating of Newtonian formal determinism with cause, however, overlooks a crucial disanalogy. In Newton's physics, there is no requirement that only an earlier state should determine a latter state. A so-called future state can also be used as an initial state to predict the state of the system at an earlier time instant. Evidently, the determinism is incompatible with the heuristic notion of cause in the world, namely the cause must always precede the effect. It is here that Einstein's above quoted point that the claim of causal explanation in mechanics comes from the fact that the formal specification of the state of a system completely determines the mutual motions of the bodies comprising the system gains significance. The notion of 'cause' invoked at the formal level in mechanics embodies an entirely formal idea of cause that works only at the level of explanation and is different from the notion of ontological cause. We see here the support for our proposal that the terms 'cause' in the ontological sense and in 'causal explanation' be considered different.
The principles of classical mechanics, involving the idea of 'causal' motion soon got extended to describe the behavior of gases, in the form kinetic theory of gases and the statistical explanations for the laws of thermodynamics. However, here statistical laws, not determinism, characterized scientific description.
1.3 Kinetic theory of Gases
The molecular theory of heat and the kinetic theory of gases were based on the postulation that heat is a form of random molecular motion. This random molecular motion is manifested externally as 'heat'. This motion as seen in gaseous molecules thus formed the basis of the kinetic theory of gases. The size of the molecules being much less than the mean distance of the molecules enables their random and free movement to allow a continuous motion. Frequent collisions however occur, causing sudden changes in velocity of the molecules. Their occasional collisions against the walls of the container (in which a gas is kept) lead to the buildup of pressure. In this way, observed macroscopic properties of gases, such as temperature and pressure were explained using the kinetic theory of molecular motion.
The kinetic theory of gases marked the beginning of the departure of classical physics from the emphasis on individual processes to make way for the statistical regularities of an ensemble. Although properties such as temperature and pressure belonged to the 'gas' as a whole (the ensemble of molecules), these properties were nevertheless predicated to the gas on the basis of average properties (such as mean free path, average time between collisions etc.), which presuppose underlying motions of individual particles governed by the deterministic Newtonian laws of motion. The randomness is a result of unpredictability of the motion of individual gas atoms or molecules, and the unpredictability in turn is due to the unavailability (to us) of their complete state information at any instant in time. The statistical mode of description is used to tide over this ignorance and thus the probabilities governing the statistical laws are epistemic. Ontologically, there is causal motion. Thus, the validity of the mechanistic, deterministic point of view underwrote these new formulations of physical laws, retaining the distinction in the two different senses of the terms 'cause' as feature of the world, and at the level of explanation.
Determinate mechanists considered chance as ontologically (though not epistemically) reducible to determinate laws. The need to invoke chance or probability based description, they hold, is only due to the knowledge of the underlying causal factors. Bohm's own viewpoint is also that 'Chance is reducible completely and perfectly to an approximate and purely passive reflection of determinate law' [1971, p. 64].
However, Bohm cites von Mises who considered determinism as an approximation of probability, an idea in the reverse direction. In such a view, 'the laws of probability are regarded as having more fundamental character than is possessed by determinate laws' [1957, p.64]. Reichenbach [1962] also held the same view. Our viewpoint, distinguishing cause and explanation, allows for multiple explanations (none of which need be causal in the ontological sense) to exist for the same given ontological world underlying a set of experiences. From this viewpoint, we can attempt to bridge between the above two opposing lines of interpretation of the relation between deterministic and probabilistic descriptions. We can say that deterministic and probabilistic description are not two distinct modes of description (such that we must find out the relation between them) but differ only in degree in describing epistemically the same underlying causal feature of the world.
1.4 Causality and Electromagnetic Field Theory
During Newtonian times, it was not completely known whether light was made up of waves or particles. However, Young demonstrated conclusively in 1800 the wave nature of light. When light was passed through two slits the interference pattern of white and dark bands suggested that light is a form of wave. Light also showed diffraction, which confirmed its wave nature. Since all waves were thought of as waves in a medium, the question of the material medium for carrying light waves, namely the 'ether' entered science. Maxwell's laws however established the electromagnetic field as a wave without a medium.
Bohm [1971, p. 41] considered electromagnetic field theory as an important type of 'causal law'. Classical electromagnetic theory introduced the concept of electric and magnetic fields, which are continuously distributed through space. However at each instant of space and time the components of the fields have definite values, which act locally at that point. Electric charges in motion would create a magnetic field and vice versa. Thus both electric and magnetic fields determine each other. Faraday discovered a set of quantitative relations between electric and magnetic fields and Maxwell determined equations that showed the interdependence of charged bodies and the fields [ibid., p.42]. Bohm suggested that the combined laws (Newton's equations and Maxwell's equations) formed the basis of a new set of causal laws within classical mechanics that were not only determined by motions of bodies but by both fields and bodies. He wrote: since the electric and magnetic fields contribute to forces acting on the bodies, it is clear that fields and bodies co-determine each other. [ibid., p. 42]
The introduction of field was a revolutionary step in the physics of matter and space. Even when space contains no bodies, the fields could carry momentum, energy and have properties like moving bodies and Einstein had suggested that the fundamental particles of physics might consist of the modes of motion of the fields [ibid., p. 44]. Thus physical laws were formulated not only on the basis of the motions of bodies through space but also in terms of changing amplitudes of fields at different points in space. Bohm further wrote that the concept of field did not make the adherents to mechanism go away, as they still assumed that the entire universe is reducible to quantitative changes in bodies and fields or fields alone. Yet, Bohm argued that such a mechanistic philosophy is also still based on a false assumption, as the earlier Laplacian mechanistic view was. Such a view presupposed the field being continuous, and thus would require an infinite number of variables for its adequate mathematical expression.
[A]s field theories came to be an accepted part of the structure of modern physics, a great many physicists began to give them what is, in its essence, a mechanistic interpretation. For instead of assuming that the whole of nature can be reduced to the motions of a few kinds of bodies, they assumed that the whole of nature can be reduced to nothing more than a few kinds of bodies and a few kinds of fields it is true that the fields, being continuous, required a non-countable infinity of variables for their mathematical expression Thus the mechanistic program of predicting the future behavior of the universe by knowing the initial values of all mechanical parameters involved was now clearly impossible in practice.[1971, p. 46]
Bohm's emphasis on a physics that is less mechanistic yet causal [p. 66], is compatible with our position that our notion of ontological cause and the 'causality' implied by determinism at the level of explanation are different. Yet, Bohm had considered 'prediction' of events, the feature that is peculiar to determinism as a means to understanding ontological causality. According to him, the very fact that predictions are possible, even of qualitative properties of certain substances (as from chemical reactions) show that causal processes are inherent aspects of these substances considered, i.e. ontological feature of the world. This position too is compatible with our move since we do distinguish between causal explanations as containing more explanatory truth than other (pragmatically equivalent) explanations.
1.5 Causality and Relativity
Relativity rendered both time and space relative, i.e. dependent on reference frames, though not on the observer. Thus, the 'length' of an object as a physical magnitude is no longer an absolute feature of the object but depends on the relative motion between the object and the frame of reference within which the measurement is made. Similarly, the time order of certain events can also be reversed. Thus, two signals can reach two different reference frames in a reverse order, and even the time interval between the two events might differ from one reference frame to another. Bunge [1979, p. 67] wrote: 'relativity admits the reversal of time series of physically disconnected events but excludes the reversal of causal connections'. Thus concepts 'before' and 'after' have significance in causally connected events, but the mutable temporal succession of events precludes the mutability of causal connections.
Even though the theory of relativity exposed the arbitrariness even in the concept of simultaneity and judgment of events by observers mutually in relative motion, the recognition of the dependence of a physical phenomena on the frame of reference did not necessarily lead to the abandonment of the notion of causality because causality is maintained at every individual frame of reference. Indeed, in the general theory of relativity, the trajectory of a planet is given a causal explanation as being due to the space-time curvature and this sense of causal explanation is same as Newtonian Mechanics, we contend, since in relativity theory in fact, the same Newtonian idea, namely the distribution of the masses, instead of directly being the basis of causal explanation, now determine the curvature of the space-time which in turn provides the causal account of phenomena. Thus one can say that although the relativistic idea that physical properties (such as length, or time of occurrence of an event) are no longer absolute but dependent on the reference frame was startlingly non-classical, at the basis, the theory of relativity was compatible with the Newtonian notion of cause at the level of explanation. As Bohr put it:
'It is true that, from the point of view of relativistic argumentation, such attributes of physical objects as position and velocity of material bodies, and even electric and magnetic field intensities, can no longer be given absolute content. Still, relativity theory, which has endued classical physics with unprecedented unity and scope, has just through its elucidation of the conditions for the unambiguous use of elementary physical concepts allowed a concise formulation of the classical principle of causality along the most general lines.' [Bohr, 1950, p. 51]
1.6 Causality and Quantum Theory
If relativity theory retained the classical ideal of causality along the most general lines, quantum theory can be said to have had more revolutionary impact on the notion of causality than even the theory of relativity. Quantum theory began with Max Planck's explanation of the black-body radiation toward the end of the nineteenth century, by proposing that the black-body was modeled in terms of a discrete number of oscillators each of which radiated energy at a specific frequency E=hn, where n; being the frequency of radiated energy. It was called the quantum postulate. This was a startling departure from the classical electromagnetic theory radiation in which energy was related to amplitude, not frequency. In 1905, Einstein applied the same postulate to account for the photoelectric effect, in which electrons knocked off from a metal surface require the energy of the incident light to be in bundles rather than continuous. In such an effect, Einstein proposed that each electron gains the same amount of energy E=hn;, which depended on the frequency of light and not on its intensity. Thus if the incident light is very weak, fewer electrons would be liberated compared to incident light of a higher intensity, but in both cases the electrons will all gain the same energy as long as the frequency remained the same. At this level, the steep problem that the postulate poses for causal explanations along the classical lines was not so well appreciated.
In 1913, Neils Bohr applied the quantum postulate to explain the observed spectra of hydrogen by proposing a semi-quantum model of the hydrogen atom. The electron was allowed to shift from one energy state (called conventionally, though misleadingly as orbit) to another by emitting or absorbing energy whose frequency was proportional to the differences between the two energy states. However, if the electron were to go from the same state to another state , then the energy it would emit be at a different frequency . This meant that in Bohr's model, in order to radiate energy, the electron has to first know beforehand which state it was going to go to! This was astutely made by Rutherford as early as 1913, while reviewing a draft of Bohr's paper.
'How does an electron decide what frequency it is going to vibrate at when it passes from one stationary state to another? It seems to me that you would have to assume that the electron knows beforehand where it is going to stop.' [Rutherford's letter to N. Bohr in 1913, quoted in Bohr, 1963, p. 40-1]
This is to say, unlike previous mechanical theories in which the state of the system in principle was adequate to determine the effect, in quantum postulate, the state of the electron in any given energy state E was insufficient in principle to determine the frequency of the emitted radiation. This means, the classical notion of cause that we previously pointed out, failed in quantum theory, even at the level of formal explanation.
David Bohm suggested a similar 'deeper level causality' for quantum events, as quantum mechanics according to him is in a stage of development so probabilistic laws within the quantum theory might not be the ultimate explanation of the quantum processes.
Between 1913 and 1926, the phase now referring to as 'old' quantum theory, the piecemeal application of the quantum postulate continued. In 1926, Heisenberg and then soon afterward Schrodinger, taking two different but mathematically equivalent routes, established the formalism of modern quantum theory. Their respective formulations are known as matrix mechanics, and wave mechanics. Of the two, Schrodinger's wave mechanics has emerged the preferred form in which the theory is used.
At the core of this new formalism are two features, indeterminacy relations and the state of superposition, both of which showed how QT is incompatible with any notion of causal explanation along classical lines. Heisenberg derived the indeterminacy relations. Formally, the relations can be stated as: where is Planck's constant, is the uncertainty in the momentum due to particle and is the uncertainty in the position of the electron. The physical meaning of this relation can be understood as follows.
Let us say we are trying to ascertain the position and momentum of an electron by bouncing light off of it. In order to determine the position of a particle accurately, we would need light of short wavelength. The concomitant high frequency would mean a high energy of the photon (since E=hn;) and this high energy of a single quantum implies, due to the statistical nature of quantum predictions, that the electron might absorb different quanta of this energy, resulting in an unpredictable change in the momentum of the electron. Thus, after measuring the position accurately, we will be no longer certain what the electron's momentum is, even if we knew what it was prior to the measurement. Similarly, in order to determine the momentum of a particle we would need a light of low energy (low frequency) but due to the concomitant long wavelength, however, our knowledge of the position of the particle would become approximate. This reciprocal indeterminacy entails that the more accurately one determines the position of a quantum particle, the less precise will be its momentum, as indeterminacy principle states that one cannot determine with arbitrary accuracy both these properties simultaneously.
As a result of the indeterminacy relations, the classical concept of causality as understood fails, because classical causality hinges upon the view that specifying the initial values of all mechanical variables defining the state of a given system would determine the future behavior of the system. Yet per indeterminacy relations, we would be unable to define the initial values of all the parameters in question, so that the future states or values could not be determined for such a system within quantum theory. The so-called standard or Copenhagen interpretation of quantum theory arose by accepting the final limit to knowability imposed by the uncertainty relations.
Heisenberg?s uncertainty relation is often seen as a proof towards our final limitation of knowledge not only with regard to quantum theory, but also for all other sciences.
Bohm [1971] wrote:
'[T]he assumption of the indeterminacy principle as an absolute and final law that is supposed to apply to all processes that can possibly take place in the world implies a breakdown of causality in connection with phenomena that depend significantly on the laws of the atomic domain' [p. 86].
Despite the experimentally demonstrated validity of the indeterminacy relations, a number of physicists, notably Einstein among them, have considered the present quantum theory, though predictively accurate, as being incomplete. They expect that this theory would be replaced by a more sophisticated version, which would be able to describe and predict the behavior of 'individual' system and thus lay claim to a causal explanation.
On the contrary, de Broglie Bohm have suggested that present quantum theory itself could be fitted with a causal interpretation via the idea of 'hidden variables' at the sub-quantum level that determine the particle behavior at the quantum level. These state variables are 'hidden' in the sense that even though they determine the observed behavior of the particle, they cannot be themselves observed. Bohm wrote:
[O]ne might suppose that in its present state of development, the quantum theory is not complete enough to treat all precise details of the motion of individual electrons, light quanta, etc., to treat such details we should have to go to some as yet unknown deeper level. [1971, p. 80].
However, John Bell proved a theorem in 1964 that shows that hidden variable theories, in order to make the same predictions as present QT, would have to be grossly nonlocal, such that in the case of certain two particle systems in which the particles are arbitrarily far way, measurements carried out on one system can instantaneously affect the state of the other system, thus undermining the very purpose of formulating hidden variables, namely to preserve classical notion of causal explanations.
Indeed, Einstein had already argued in 1947, much prior to Bell's theorem, if non-locality is a feature of quantum theory, then the free choices of a conscious observers (as to which of the many possible experiments he will perform), would have a causal bearing on the course of events in the world. This squarely brings QT not only to demonstrate the failure of classical notions of causal explanations, but a direct nexus between causality and consciousness.
1.7 Causality and Complementarity
Neils Bohr, one of most famous and elusive interpreters of quantum theory, conceded that in atomic physics, there are 'new uniformities which cannot be fitted into the frame of ordinary causal description.' [Faye & Folse, 1998, p. 83] Nevertheless, he held the idea that quantum theory does not so much signal the failure of the classical ideal of causality as showing that different parts of the classical causal paradigm have to be used to explain different experimental results. Since the experimental arrangements leading to these results are mutually exclusive, using different causal pictures (such as wave and particle pictures of motion) in different experiments are not contradictory. He suggested that these different partial causal accounts be seen as complementary. He wrote:
'However contrasting such phenomena may at first appear, it must be realized that they are complementary in the sense that taken together they exhaust all information about the atomic object which can be expressed in common language without ambiguity.' [Bohr, 1963, p. 60]
He defined complementarity as a 'rational generalization of the classical ideal of causality. However, Bohr's complementarity is taken to have a very elusive content. Debate still goes on over whether Bohr's interpretive ideas really contain any true insights about quantum theory, or whether he merely ended up rationalizing away the deep problems to causality that QT poses.
1.8 Consciousness and the Physics of Causation
Although Bell originally showed that only hidden variable theories that try to make the same predictions of QT would be nonlocal, subsequent refinements have shown that just the predictions of quantum theory entail the consequence that quantum theory itself is nonlocal, if the observations are interpreted along classical lines. [See Stapp, 1993]
As a result, many workers, starting with Wigner in the 1960s, have tried to see a causal role for consciousness in quantum theory. Others, considering quantum nonlocality to be an objective feature of the natural world, have tried to provide a quantum theoretic account of consciousness itself. For example, Hameroff and Penrose [1996] suggest that the quantum mechanical processes within the microtubules in the neurons might form the basis of consciousness. I would say that to try and use quantum theory, whose ontological underpinnings is yet to be fathomed, to explain ontological consciousness is premature, and might amount to no more than explaining one mystery, namely consciousness, with another mystery, quantum theory.
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