William L. Ames

Emptiness and Quantum Theory

Emptiness (śūnyatā) is a key concept in Buddhism, especially in Mahāyāna Buddhism; quantum theory is the heart of contemporary physics. Emptiness does not mean “nonexistence” but rather that all entities, including ourselves, lack the independent identity we tend to assume that they possess. Quantum theory has replaced the mechanistic worldview of nineteenth-century physics with a view that offers far less support to naive realism. To see what these ideas have in common, we begin by considering Buddhism.

SOME BASIC BUDDHISM

The Buddha’s lifetime (c. 560–480 B.C.E.) was a period of great social and political change in northern India. The use of iron led to an increase in population and wealth as people used iron axes to clear the forest and iron plows to put more land under cultivation. Cities grew, and large kingdoms replaced earlier small kingdoms and aristocratic republics. Urbanization and social change led to alienation and discontent and a questioning of older religious formulations. In this atmosphere new religious and philosophical teachings proliferated. The doctrines of the Upanisads profoundly transformed what we now call Hinduism; and from among the various new schools that arose at that time, Buddhism was to become a major world religion.

The major elements of the Buddha’s teaching were an analysis of the pervasive suffering in life and a proposal for a path leading to the end of suffering. The Buddhist First Noble Truth of suffering has often been misinterpreted as meaning that all of life is overtly painful, an assertion that contradicts common experience. Instead, the Buddha claimed that all conditioned phenomena are impermanent, and thus even our pleasure and happiness are unsatisfactory in that they are subject to change and loss. Even neutral experiences, which provoke neither pain nor pleasure, are unsatisfactory because of their conditionedness, which involves our supposed selves in a complex web of causes and conditions whenever we try to act.

Another famous Buddhist teaching is that all phenomena are “not a self” or “without a self” (anātman). In the case of a human being, this means that neither one’s body nor one’s mind is a self or under the control of a self. The notion of a self is in fact rather slippery. Although we sometimes identify with our bodies or our thoughts or feelings or other mental phenomena, at other times we speak of “my” body, thoughts, feelings, etc., implying that the self is something separate from these, something that possesses them. We can imagine a self without any one of these kinds of phenomena, though not without all of them.

In Buddhism body and mind are seen as a stream of impermanent physical and mental events. The body constantly changes and ages, while the mind, with its perceptions, thoughts, feelings, etc., changes at each moment. Body and mind are like a river. The flow goes on, but there is no enduring entity that we can point to. The flow itself is not a thing, and it is constantly changing.

Body and mind are not under the control of a self because they are impermanent and because their changes depend on various causes and conditions, many of which are independent of what the self may want. Moreover, most Buddhists hold that there is no self apart from the body or mind that could control them. When we observe ourselves, we find only the physical and mental phenomena we call body and mind. Thus there is no evidence for a self different from mind and body, and a self with neither a body nor a mind makes no sense.

DEPENDENT ORIGINATION

According to Buddhism, our minds and bodies and the external world are all made up of impermanent, changing phenomena. This idea is closely related to the Buddhist emphasis on causality. On the one hand, the fact that things are dependent on causes and conditions drives the process of change, because the causal factors are themselves constantly changing. On the other hand, causality provides a source of order that prevents impermanence from becoming arbitrary and chaotic. For example, given the necessary conditions, such as soil and water and warmth, a rice seed will give rise to a rice sprout, but never to a barley sprout.

Causality in Buddhism is expressed in the principle of dependent origination (pratityasamutpāda). This principle is often formulated as a succession of twelve factors beginning with ignorance and leading, via craving, to suffering such as old age and death. In its most general form, though, the idea of dependent origination is stated in the following way: “When this exists, that comes to be; because of the origination of this, that originates. When this does not exist, that does not come about; because of the cessation of this, that ceases.”

In other words, if A is one of B’s necessary conditions, then the occurrence of B is dependent on or conditioned by the occurrence of A. When A does not exist, B cannot exist. (We should note that in Buddhism multiple causal factors are always necessary to produce any given result.) To go back to the traditional example of a rice sprout, the rice seed is considered the cause (hetu) of the sprout, while the other necessary factors, such as soil, moisture, warmth, etc., are causal conditions (pratyaya). A rice sprout originates only when all the causal factors necessary to its existence occur. When the conditions necessary to maintain it are not all present, it ceases to exist.

Dependent origination is related to the idea of no self. The world is composed of impermanent phenomena, but past and present phenomena are related by the principle of dependent origination. The causal relation between past and present provides for a degree of continuity and the possibility of relative permanence. That is, because of causal regularity, things may endure for some time with only minor changes, changes that we may be able to ignore when carrying out the activities of our daily lives. Thus, thanks to dependent origination, strict impermanence can be reconciled with the sort of regularity and persistence of things that we observe in our ordinary experience. Buddhists generally do not think that we need to invoke selves or essences to account for the continuity in our experience. In fact, they emphasize that our tendency to try to hold on to things as if they had a permanent essence and to regard ourselves as real, enduring entities is at the root of our suffering.

Dependent origination is also an impersonal process. Phenomena condition other phenomena without there being an agent of actions or an experiencer of results, though there may be mental and physical phenomena that we are accustomed to think of as being someone’s action or someone’s experience. Thus Buddhists have argued that our actions (karma means “action”) can have results, including rebirth through successive lifetimes, without there being any permanent self. What we call a self is a stream of impermanent phenomena, causally interrelated by the fact that each mental or physical event originates in dependence on other events.

ABHIDHARMA

The preceding survey of basic Buddhist teachings is very incomplete. For example, I have said nothing about liberation or the path leading to it. Nevertheless, the ideas mentioned so far will provide enough of a foundation for the purpose of comparing emptiness and quantum theory.

Within a few centuries after the death of the historical Buddha, various early Buddhist schools had developed elaborate descriptions of the mind and the world, called Abhidharma. Abhidharma takes an analytical approach to the world. Living beings and physical objects are not considered to be unitary entities. Instead, they are made up of more fundamental units, called dharmas. The Sanskrit word dharma has many meanings, including “law” and “teaching of the Buddha.” Here dharma is used in the sense that I have been translating as “mental or physical phenomenon.” Dharmas are impersonal phenomena, which may be either mental or physical.1

This use of the term dharma preceded the Abhidharma systems. The sūtras, or recorded discourses of the Buddha, as they have come down to us, speak of dharmas, perhaps because the doctrine of no self made it necessary to account for human experience in a way that did not appeal to the notion of a self. As time went on, there would have been a natural tendency to want to elaborate the teachings contained in the Buddha’s discourses in order to extend the description and classification of things in terms of dharmas. More ambitiously, there would have been a desire to explain everything in terms of dharmas and the relations among them. This desire to make the Buddhist picture of the world complete and systematic probably accounts for the rise of Abhidharma.

Thus Abhidharma can be thought of as an attempt to systematize the teachings in the Buddha’s discourses in terms of a consistent and complete dharma theory (including a theory of causes and conditions). In Abhidharma dharmas are considered to be ultimate in the sense that they cannot be analyzed further. Also, in Abhidharma, as in later Buddhism, dharmas are impermanent not merely in the sense of being “not permanent” but also in the sense of being strictly momentary. Dharmas last no more than an instant, and the impression of objects that endure through time is a sort of “cinematic” illusion produced by rapid sequences of similar dharmas.

While we cannot go into the intricacies of Abhidharma here, there are some more points that ought to be mentioned. One is that most of the dharmas enumerated in the Abhidharma systems are mental. Because of the overriding Buddhist concern with liberation from suffering, Abhidharma is primarily an analysis of our psychological experience rather than of our experience of the physical world. Within psychology the emphasis is on moral factors, on the psychology of meditation, and on the psychology of the spiritual path. Nevertheless, Abhidharma never questions the reality of the physical world, and a number of dharmas, such as sound and visible form, are physical.

The idea of “two truths” appeared first within Abhidharma. In ordinary language we describe the world in terms of objects like jars, but dharma theory analyzes them into dharmas. Thus there is no jar apart from its constituent dharmas of color, shape, texture, etc. Whatever disappears upon analysis, like a jar, is conventional, or superficial, truth. In contrast, the dharmas themselves cannot be analyzed into more basic constituents; if they could be, they would not be considered dharmas. Whatever withstands analysis (in other words, the dharmas) is considered to be ultimate truth.

Not only objects like jars but also persons like Bill Ames can be analyzed into dharmas and thus are merely conventional truths. In his teachings the Buddha often spoke about persons and objects, though at other times he spoke in terms of dharmas. According to the Abhidharmists, when the Buddha spoke in terms of conventional truth, he did so that his audience could understand him. Abhidharma, on the other hand, always speaks in terms of ultimate truth, that is, dharma theory. We will see the idea of the two truths reappearing later in the development of Buddhism, but with a quite different content.

CLASSICAL PHYSICS

Before going on to later developments in Buddhism, I would like to turn to physics and discuss classical physics because, as we shall see, it has some interesting parallels with Abhidharma. First of all, what do we mean by “classical” in the context of physics? Essentially, it refers to the body of experiment and theory that began in the seventeenth century with the work of Galileo and others and continued through the end of the nineteenth century. The publication of Albert Einstein’s paper on the special theory of relativity in 1905 marks the beginning of modern, postclassical physics, though a more radical break with classical physics came somewhat later in the twentieth century with the development of quantum theory.2

Compared to ancient and medieval physics, classical physics makes much greater use of mathematics in its description of how the physical world works. For example, Newton’s second law of motion is expressed as an equation: F = ma. This equation states that the force, F, acting on a body is equal to its mass, m, multiplied by its acceleration, a. Acceleration is the rate at which velocity changes. Thus the equation means that if the mass of a body is constant, then the greater the force applied to a body, the more rapidly its velocity changes.

One interesting point to note is that if the force is zero the acceleration will also be zero, and the body’s velocity remains constant. (This is, in fact, Newton’s first law of motion.) This principle stands in contrast to the sort of “gut-level” physics we use in daily life, where we generally assume that an object will slow down and eventually stop unless some force is applied to keep it moving. This happens because friction is pervasive in our environment. But Newton, generalizing an idea of Galileo’s, realized that a better theory of matter and motion could be constructed by making a different assumption, namely, that a body will keep moving in a straight line at a constant speed unless some force is applied to it. Friction is considered to be an applied force. If friction were always present, this way of looking at things might be somewhat artificial. Newton’s laws of motion, though, are vastly superior in accounting for the motion of celestial bodies in space, where friction is virtually nonexistent. Even where friction cannot be ignored, Newtonian physics provides a consistent, quantitative way of taking it into account.

Thus classical physics represents a step away from our everyday view of the world, though it is a small enough step that “common sense” can be made to accommodate it with relatively modest revisions. Another feature of classical physics that is already apparent from “F = ma” is that its mathematical description of the world permits quantitative calculations of, for example, the motion of a body under an applied force. In principle, the equations used in classical physics permit one to calculate exactly the future evolution of any collection of material bodies; in other words, classical physics is deterministic.

In practice, though, exact calculations are usually possible only in the simplest cases. Thus the predictions of scientific theories usually have some fuzziness because of the approximations made in doing calculations. Likewise, experimental measurements always contain some experimental error, and it is important to estimate the range of the error accurately. One is normally comparing, not only in classical physics but also in science generally, approximate measurements with the results of approximate calculations. Thus the predictions of scientific theories can be confirmed only as being “within experimental error.” An experiment will be unable to distinguish between two competing theories if the predictions of both lie within the range of experimental error.

Newton’s laws belong to the branch of classical physics known as mechanics, the study of matter moving under the influence of forces. Other areas developed later. In the nineteenth century it was realized that electricity and magnetism are closely related, and James Clerk Maxwell developed a mathematical theory of electromagnetism that gave a unified description of electricity and magnetism. Like Newton’s mechanics, Maxwell’s theory was deterministic, and, like Newton, Maxwell was able to use his theory to account for a wide range of phenomena. The greatest triumph of Maxwell’s theory was his insight that light is a form of electromagnetic radiation. Thus his theory was able not only to unify electricity and magnetism but also to unify both with optics, the study of light.

Besides classical mechanics and electromagnetic theory, other important areas of classical physics were thermodynamics (the study of heat) and statistical mechanics. Thermodynamics developed important concepts of energy and entropy, while statistical mechanics accounted for thermodynamic phenomena such as heat and temperature in terms of the motion of large numbers of particles.

Thus, by the end of the nineteenth century, the successes of classical physics were impressive indeed. Not only had new theoretical understanding of the physical world been achieved and new phenomena predicted and discovered, but scientific knowledge had also been applied to produce powerful technological achievements. The idea became widespread that the physical universe and perhaps all of reality could be explained as unchanging particles of matter interacting by means of forces described by deterministic mathematical laws.

CLASSICAL PHYSICS AND ABHIDHARMA

Despite some significant differences, Abhidharma and classical physics can be seen as broadly similar. Both reduce the world to impersonal, relatively simple units of analysis which are causally related to each other. Whether the units of analysis are particles and forces, on the one hand, or dharmas, on the other, physical objects and living organisms are seen as just complicated combinations of these simple units.3 In classical physics particles and forces are related by physical laws that are usually expressed as equations. In Abhidharma dharmas are related by the various kinds of causes and conditions summed up under the heading of dependent origination.

For example, in daily life we may say, “There is a book on the table.” For both Buddhism and physics this statement is only conventionally true. In classical physics the book and the table are fundamentally a collection of atoms interacting by means of forces. For Abhidharma the book and the table are made up of dharmas that influence each other according to various causes and conditions.

The units of analysis in both classical physics and Abhidharma are taken to be ultimately real. The particles and forces of classical physics are held to be really, objectively there; the same holds for Abhidharma’s view of dharmas. Both dharmas, on the one hand, and particles and forces, on the other hand, have definite, knowable properties. Though there may be some practical problems, such as experimental error, the properties of both dharmas and particles/forces are in principle well defined, with no inherent fuzziness.

Of course, there are some important differences as well. The dharmas are closer to our immediate experience than the mathematically described particles and forces of classical physics. Dharmas are known through examining our own experience. Each dharma is said to “bear its own mark” by which it is known. Particles and fields are known through being part of a theory that is found to be consistent with experiment. The fact that the theory is formulated in mathematical terms makes it possible to derive quantitative predictions that can be compared with quantitative experimental results.

Another important point is that most of the dharmas are mental rather than physical, whereas physics deals exclusively with the physical world. (Whether life and consciousness can ultimately be explained in physical terms is a separate question.) Another difference between Abhidharma and classical physics is that dharmas are momentary, while the atoms of classical physics are unchanging. In classical mechanics change is due to the motion of atoms and to the forces that produce changes in motion. Finally, Abhidharma is part of the soteriological project of Buddhism. It helps us to gain insight into how things really are and is thus part of the path to liberation. While many people have had the idea that science contributes to human betterment, strictly speaking, such an idea is not part of physics.

QUANTUM THEORY

Classical physics saw the world as composed of particles with definite properties interacting according to deterministic laws, but by the early twentieth century it was clear that classical physics had difficulty in accounting for some phenomena. Some of these shortcomings of classical physics led Einstein to devise the special and general theories of relativity. Quantum theory was developed by a number of physicists, including Niels Bohr and Werner Heisenberg, in an effort to explain other phenomena, especially phenomena on the atomic and molecular level, which could not be accounted for classically.

Some of the predictions of quantum theory have been verified by the most accurate experiments ever performed in physics, and, as a mathematical framework for calculating the results of experiments, this theory is universally accepted by physicists. On the other hand, there is considerable disagreement about the interpretation of quantum theory, that is, what the theory is telling us about the way the world is. Probably most physicists simply use the theory while ignoring questions of interpretation, and here I will try to discuss the features of the theory that are relatively independent of one’s choice of interpretation.4

What are the most salient features of quantum theory? I think that any list would have to include the following: quantization, wave-particle duality, complementarity, uncertainty or indeterminacy, probabilistic prediction, the quantum measurement problem, and nonlocality.

Quantization means that, in many circumstances, physical quantities like energy, momentum, and so on can have only certain discrete or discontinuous values. For example, in the case of an electron bound in an atom, the electron in its orbit about the nucleus can have only certain discrete energies. This means that only certain orbits are possible and not others. In contrast, in classical mechanics, a planet can orbit at any distance from the sun.

In classical physics one has waves and particles, but there is no way that something can be both. In quantum theory particles such as electrons behave like waves under some circumstances, and electromagnetic waves, for example, sometimes manifest particle properties. One way of looking at the quantization of the energy of electrons bound in atoms is to say that the electrons are behaving as standing waves in a closed space. In such a case only certain wavelengths are possible; in quantum theory there is a one-to-one relationship between the wavelength of the wave aspect of a “particle” and the momentum of the particle. Thus because the bound electron as wave can have only certain wavelengths, the same electron as particle can have only certain orbits. Similarly, electromagnetic waves behave in some circumstances like particles called photons, with the momentum of the photon corresponding to the wavelength of the electromagnetic wave.

Even in quantum theory one never sees something behaving as a wave and a particle at the same time. This fact is known as complementarity. One can choose to do experiments that bring out either the wave nature or the particle nature of the object one is studying, but one will never observe both in a single measurement. For example, in some types of experiments an electron will act like a wave; in others it will act like a particle, but it will never act like a wave and a particle at once. The difficulty for common sense comes in trying to reconcile the wave behavior at one time with the particle behavior at another.

Another way of looking at wave-particle duality is to say that an electron in itself cannot be defined as either a wave or a particle. It can be said to have a wave nature or a particle nature only in relation to a given experimental situation. Thus at least some of the electron’s properties belong to the electron’s context as much as to the electron itself.

In classical physics all the properties of a particle are well defined. An electron’s position and momentum, for example, are influenced by external forces, but there is no doubt that the electron does have a definite position and a definite momentum at each moment. According to quantum theory, it is impossible to determine the position and the momentum of a particle simultaneously with absolute accuracy. (This is an example of Heisenberg’s famous uncertainty principle.) One often hears this fact explained by the idea that we unavoidably disturb something when we measure it. A closer analysis shows that quantum theory implies that the position and momentum of an electron, for instance, are objectively indeterminate.5 That is, it is not that the electron really has a definite position and momentum but we cannot know what they are; rather, the electron’s position and momentum have a certain irreducible “fuzziness.”

The uncertainty principle is closely related to wave-particle duality. To the extent that the electron can be considered as a wave, it is not surprising that it usually does not have a definite position, since waves are spread out in space.

In classical physics it is possible, at least in principle, to measure the present state of a physical system exactly and then, knowing the forces acting, to calculate exactly the future evolution of the system. (Here we overlook the practical difficulties of measurement and calculation.) Thus one would know precisely what the outcome of any future measurement performed on the system would be. Quantum theory, on the other hand, generally gives only probabilities for the outcome of a measurement. It is impossible to predict, for example, when a particular unstable atomic nucleus in a sample of a radioactive element will decay.

In other words, classical physics is deterministic, while quantum theory is probabilistic. Nevertheless, in the case of many repeated measurements or many individual quantum events of the same type, probabilities become exact percentages and yield exact patterns of events, even if individual events cannot be exactly predicted. In the case of a radioactive substance, one can predict with great certainty that a certain fraction of the nuclei will decay in a given amount of time, even though one does not know which nuclei those will be. Thus, despite the probabilistic nature of quantum theory, there is still room for certain kinds of definite predictions.

The probabilistic nature of quantum theory is reflected in its mathematical formulation. In quantum theory the state of a physical system is described mathematically by a “wave function.” For example, the wave function associated with an electron specifies the probabilities for different possible values of the position, momentum, etc., of the electron; but in most cases it does not give a single definite value. Thus the wave function does not so much represent the wave nature of the electron as it represents something more abstract, a sort of wave of probability associated with the electron.

As long as no measurement is made, the wave function changes in time according to an equation known as the Schrödinger equation.6 (Erwin Schrödinger was another of the founders of quantum theory.) Interestingly, the Schrödinger equation itself is a perfectly deterministic equation, just like the equations of classical physics. The probabilistic element comes in when a measurement is made. Just as an electron, for example, is never observed to be a wave and a particle at the same instant, so its position or momentum is never measured to have more than one value simultaneously. Rather, it will be measured to have one of the possible values allowed by the wave function; but if more than one value is possible it is impossible to say in advance with certainty which value the measurement will give. What one can predict are the probabilities of the different possible values, as given by the wave function. If one repeats the same measurement on many identical quantum systems, the probabilities give the percentage of the measurements that will show each of the possible values.

When a measurement is made on a quantum system, we get some definite value for a physical quantity such as energy or momentum. In between measurements the wave function for the system generally shows multiple possible values for a particular quantity. According to standard quantum theory, the wave function tells us all that there is to know about a quantum system. Thus, in between measurements, the physical quantities characterizing a system have to be considered to be indeterminate in most cases. This brings us to the quantum measurement problem. When a measurement is made, how and why does an indeterminate state turn into a definite measured value? (We should note that this is a problem in the interpretation of quantum theory. If we ignore the quantum measurement problem, we can still calculate probabilities for the outcomes of measurements.)

A somewhat more formal way of looking at the quantum measurement problem is the following: in between measurements, the wave function is usually one that corresponds to multiple possible values for any physical quantity. Immediately following a measurement, the wave function has changed to one in which the measured quantity has only the measured value. The wave function then continues to evolve in time according to the Schrödinger equation until the next measurement, usually returning to a state in which the quantity that was measured has more than one possible value.

The abrupt change in the wave function when a measurement is made is called the “collapse” or the “reduction” of the wave function. The wave function collapses from a state in which multiple values are possible to one in which only one value is possible. Thus the quantum measurement problem becomes, How and why does the wave function collapse when a measurement is made? In one sense it is the problem of reconciling the deterministic evolution of the wave function in the time interval between measurements with the probabilistic nature of wave function collapse.

The final aspect of quantum theory that I want to discuss is nonlocality. Classical physics conceives of the physical world as composed of separate and distinct physical objects that interact with each other. When one adds special and general relativity to classical physics, it becomes clear that none of these interactions can travel faster than the speed of light. This fact is called “locality,” meaning that a distant object cannot influence a physical system instantaneously or in less time than it takes light to travel the distance between them.

The situation is more complicated in quantum theory. Suppose two objects interact with each other, move off in different directions, and later become widely separated. According to quantum theory, the objects remain in a strange way intertwined, subtly influencing each other instantaneously. Due to the probabilistic nature of quantum theory, these “influences” cannot be controlled and used to transmit a message faster than light. Moreover, even though the “influences” seem to travel faster than light, no matter or energy is transported, so the theory of relativity’s ban on faster-than-light speeds is not violated. In fact, rather than something traveling faster than light between two distant objects, it may be that the objects are somehow not separate, somehow fundamentally connected even though separate in space.

This nonlocality, whether it is thought of as instantaneous influences between distant objects or as inseparability of distant objects, seems to be not only a property of quantum theory. In 1964 a physicist named John Bell proved a theorem that showed that, in certain types of experiments, any local theory would have to predict results that obeyed a certain restriction. Such experiments were eventually done, and it was found that the results violated the restriction Bell’s theorem placed on predictions of local theories. Thus the experimental results could not be accounted for by local theories; a nonlocal theory is required. The results agreed with the predictions of quantum theory (a particular nonlocal theory), but this is less significant than the fact that, even if quantum theory eventually turns out to be wrong, it seems any physical theory that hopes to agree with experiment will have to include nonlocality.7

MAHĀYĀNA

In discussing Abhidharma, I alluded to the existence of more than one early Buddhist school. Traditionally, there were said to be eighteen schools, which differed on various points of doctrine and monastic discipline. (For example, the Abhidharma of the Sarvāstivāda school recognized seventy-five dharmas, while the Theravāda school recognized eighty-two.) The only one of these early schools to have survived to the present day is the Theravāda school of Sri Lanka and Southeast Asia.

Thus there was diversity within Buddhist thought from an early stage, though the differences between the various early schools could be considered relatively minor. This diversity increased with the rise of Mahāyāna Buddhism. (The earliest Mahāyāna sūtras that still exist may date from the second or first century B.C.E.) Though firmly rooted in early Buddhism, Mahāyāna has its own characteristic emphasis on universal compassion, which aims to liberate all sentient beings from suffering, and on wisdom (prajñā), which comprehends the emptiness of all phenomena. The Mahāyāna ideal is exemplified by the bodhisattva, who, motivated by compassion, seeks to perfect wisdom and skillful means in order to attain complete enlightenment for the benefit of all beings. Here, because of its emphasis on the idea of emptiness, we will focus on the Mahāyāna philosophical school called Madhyamaka.

MADHYAMAKA

We have seen how classical physics was replaced by a theory that deviates much more sharply from commonsense ideas. In Buddhism, too, Abhidharma’s picture of the world was challenged by a more radical understanding. The Madhyamaka school was founded by Nāgārjuna, who lived around 150 or 200 C.E. Madhyamaka can be seen as a philosophy based on the perfection of wisdom (prajñāpāramitā) sūtras, some of which are among the earliest Mahāyāna sūtras. The sūtras expound emptiness in a discursive way, while the Mādhyamikas8 use systematic argument.

The Mādhyamikas agree with the Abhidharmists that living beings and material objects have only a conventional existence. But they go further and argue that even the dharmas themselves exist only conventionally. The Mādhyamikas base their argument on the fundamental Buddhist idea of dependent origination. All conditioned dharmas arise in dependence on causes and conditions. Thus, according to the Mādhyamikas, dharmas have no independent, self-contained existence and no intrinsic nature of their own. They are said to be “empty,” meaning “empty of intrinsic nature.”

Here it is important to realize that emptiness does not mean that nothing exists. This would amount to nihilism, a position that all Buddhists reject along with the existence of permanent conditioned entities. It is undeniable we have experiences as well as thoughts about whether the experiences are real or not. The question is how do phenomena exist, conventionally or absolutely? By using the term emptiness the Mādhyamikas deny any absolute or ultimate existence of phenomena, but they do not deny that phenomena exist conventionally.

Like Abhidharma, Madhyamaka speaks of two truths, but the content is not the same. For the Mādhyamikas the conventional, or superficial, truth is the existence of dharmas in dependence on causes and conditions. The ultimate truth is their emptiness or lack of intrinsic nature.

If emptiness means being empty of intrinsic nature, then a good way of understanding the meaning of emptiness is to look at what the Mādhyamikas mean by intrinsic nature. (“Intrinsic nature” translates svabhāva, literally, “own-nature” or “own-being.”) In his major work, the Mūlamadhyamaka-kārikā, Nāgārjuna says, “Intrinsic nature is not contingent and not dependent on another” (MMK 15–2ab) and “The alteration of intrinsic nature is never possible” (MMK 15–8cd). Thus the intrinsic nature of a thing is what that thing is inherently, independent of any causes and conditions. Intrinsic nature is unalterable because it is independent of all external circumstances.

Why then do the Mādhyamikas say that things have no intrinsic nature? A good example is the heat of fire. Conventionally, and in the Abhidharma, heat is the intrinsic nature of fire because fire is always hot. Heat is invariably present in fire, independent of any other causes and conditions. In contrast, water may or may not be hot, depending on causes extraneous to the water itself. Thus heat is not the intrinsic nature of water.

The Mādhyamikas do not deny this conventional usage of the term intrinsic nature, but they deny that heat is the intrinsic nature of fire in any ultimate sense. The heat of fire depends for its existence on precisely those causes and conditions responsible for the existence of the fire itself. The heat of fire is thus contingent and dependent; and so, for the Mādhyamikas, it cannot be the intrinsic nature of fire or anything else. Likewise, no other properties of fire qualify as an ultimately real, intrinsic nature. Fire ultimately has no intrinsic nature, no independent and unchanging essence that makes it what is.

The Mādhyamikas hold that, as with fire, so all phenomena, all dharmas have no intrinsic nature. Conditioned dharmas and all their properties occur in dependence on causes and conditions. Thus dharmas and their characteristics are dependent and contingent. The existence of each dharma is sustained by dharmas other than itself; no dharma is self-sufficient.

Another way of saying this is the following: because a dharma depends for its existence on dharmas other than itself, it is nothing in itself, that is, when it is considered in isolation from everything else. If we focus on a particular dharma in an effort to distinguish its own intrinsic nature from that of other dharmas, we find that it disappears. The process of excluding from consideration everything but the dharma in question removes the very conditions on which its existence depends. Thus we do not find any inherent identity in it, any intrinsic nature that makes it what it is and that is independent of everything else.

We might also say that a dharma’s identity is not self-contained but relational. And since the other dharmas to which it is related also exist only relationally, there is no “fixed point,” no self-established entity anywhere. Even dependent origination, even emptiness, the absence of intrinsic nature, are conventional, relational facts and not ultimate entities. Emptiness is itself empty of intrinsic nature.

As we have seen, the Mādhyamikas deny that things exist by an intrinsic nature, but they do not deny that things exist in any sense. Nāgārjuna compares the way in which things do exist to the mode of existence of mirages and magical illusions. Like such illusions, things appear in dependence on causes and conditions, but they are not appearances of intrinsically existing entities. This is not to say that there is no distinction on the conventional level between, say, physical objects and optical illusions. The point is that both occur dependently and have no independent essence.

Thus emptiness, lack of intrinsic nature, in no way excludes causal regularity, expressed in Buddhism by the principle of dependent origination. In fact, most of the arguments that Mādhyamikas give to support the idea of emptiness rest on the fact of causality. Looking at it another way, one can say that if things had intrinsic nature causal relations would be impossible because everything would be independent of everything else. In this sense, it is emptiness that makes causality possible.

COMPARISON WITH QUANTUM THEORY

There is much more to say about Madhyamaka, but this should be enough for the purpose of comparing it with quantum theory. We recall that in quantum theory many of the properties of, for instance, an electron are not intrinsic to the electron itself. They depend not only on the electron but also on the type of experiment that is being performed.

In Madhyamaka, too, attributes are relational and not intrinsic. A dharma by itself has no nature, any more than an electron can in itself be said to be either a wave or a particle. The major difference is that Madhyamaka is more complete in its negation of intrinsic nature. In quantum theory some of the properties of an electron, such as its rest mass, are intrinsic to it; and, of course, physics deals only with the physical world. For the Mādhyamikas all phenomena without exception are empty of intrinsic nature.

There are other aspects of quantum theory that can be compared with Madhyamaka. In quantum theory the observer does not play a purely passive role. Whether an electron behaves as a wave or a particle depends on the type of experiment being done, and it is the observer who decides what sort of experiment to do. Thus quantum theory seems to be describing what the physicist John Wheeler calls a “participatory universe.”9 The observer does not simply record an objectively existing electron. Instead, he or she is partially responsible for determining what the electron is. As Wheeler puts it, “No elementary phenomenon is a phenomenon until it is a recorded phenomenon.”10

Madhyamaka has its own version of the “participatory universe.” In line with the general principle of dependent origination, subject and object, knower and known, observer and observed exist only in relation to each other. Neither has an independent, “objective” existence. They are all empty of any self-contained, intrinsic nature. Again, Madhyamaka is more thoroughgoing than quantum theory. Not all the properties of an electron are affected by the conditions of observation, whereas, for the Mādhyamikas, subject and object are fully relative.

Finally, we ought to remember that Madhyamaka, like all of Buddhism, is intended as a means to liberation,11 whereas physics has more modest aims. Buddhism and Western physics have come out of different cultures, and they have different starting points, methods, and goals. This makes it all the more remarkable that they have produced some very similar ideas.

Notes

1. Some Abhidharma schools recognized another category of dharmas, “conditioned factors dissociated from matter and mind,” for phenomena that seemed to be neither material nor part of the conscious operation of mind. Also, all schools recognized at least one unconditioned dharma: nirvāa.

2. The beginnings of quantum theory can be traced to a paper by Max Planck published in 1900. It took time, however, for the theory to be developed; and it was not until the late 1920s that (nonrelativistic) quantum theory was reasonably complete. It took even longer for its radical implications to be understood.

3. Strictly speaking, physics is concerned only with nonliving matter; but the view is widespread, among scientists and others, that living organisms can be explained in purely physical terms.

4. For a more detailed presentation of the crucial discoveries and unresolved problems in quantum mechanics, see George Greenstein and Arthur G. Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics (Boston: Jones and Bartlett, 1997).

5. The position can be exact if the momentum is totally indeterminate and vice versa.

6. The Schrödinger equation applies under circumstances where the effects of special relativity are negligible, that is, when relative velocities are small compared to the speed of light.

7. Some physicists have attempted to preserve locality by abandoning other cherished assumptions, such as “counterfactual definiteness.”

8. Generally, Madhyamaka is the name of the school and its philosophy; a follower of the school is called a Mādhyamika.

9. John Archibald Wheeler, “The ‘Past’ and the ‘Delayed-Choice’ Double-Slit Experiment,” in A. R. Marlow, ed., Mathematical Foundations of Quantum Theory (New York: Academic, 1978), p. 41.

10. John Archibald Wheeler, “Beyond the Black Hole,” in Harry Woolf, ed., Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein (Reading, Mass.: Addison-Wesley, 1980), p. 356.

11. For this reason, it is considered necessary in Buddhism to experience ultimate truth personally rather than simply to understand it intellectually. Intellectual understanding is very helpful on the path to liberation, but it is not able to take one the whole distance.

In the interface between Buddhism and psychology, it can be very useful to compare specific theories and methods in both disciplines, for they are deeply concerned with many common issues. Moreover, the first-person introspective methodologies of Buddhism may well complement the third-person modes of empirical inquiry of the cognitive sciences, thereby enhancing insights in both fields. But, as Victor Mansfield points out in the following essay, when bringing Buddhism and physics into dialogue, it is more fruitful to focus on philosophical issues. These are not at all irrelevant to physics itself, for theoretical and empirical research in physics always takes place within a philosophical context, which has a strong influence on the type of questions that are posed.

In this paper Mansfield draws out the deeply human elements of the Buddhist Madhyamaka view, explaining how the predilection to grasp onto the seemingly real, inherent nature of phenomena, including oneself and others, lies at the root of desire, aversion, and their resultant suffering. In rejecting the notion of “essences,” which Western philosophy inherited from Plato and later Descartes, the Prāsagika Madhyamaka vision of reality emphasizes the relative nature of all phenomena. Einstein’s theory of special relativity is explained here, providing empirical, scientific evidence demonstrating the noninherent nature of time (as well as mass and spatial dimension). But such relativity is confined to objective, inertial frames of reference, whereas the Madhyamaka theory asserts that the nature of all phenomena is also relative to the conceptual identification or designation or phenomena. In other words, all imaginable phenomena arise into existence relative to the conceptual framework in which they are conceived. That is what is meant by “conventional existence,” but this does not imply the existence of phenomena is merely a matter of personal or cultural whimsy. For all conditioned phenomena arise as dependently related events, dependent upon their own causal factors. And a central concern of Buddhism and science is to discover the regular patterns of those causal interactions, often called in science the “laws of nature.”

One of the meanings of the Sanskrit term dharma is “law,” and Buddhism strongly emphasizes the exploration of the laws of causality as they pertain to human conduct and experience. Here is where Mansfield draws out the practical applications of the Madhyamaka view for the cultivation of compassion and altruistic service. For if self and others are not inherently different, if we all live in interdependence, then compassionate concern for all beings is the only authentic way to relate to others and lead a meaningful life. Thus, Mansfield points out in his concluding comments, “as we stand on the threshold of ever more powerful theories in science, it is more urgent then ever that we find a coherent worldview that can guide our science as well as our moral actions.”