Emptiness and Form

The classical mechanistic world view was based on the notion of solid, indestructible particles moving in the void.

Modern physics has brought about a radical revision of this picture.

It has led not only to a completely new notion of ‘particles’, but has also transformed the classical concept of the void in a profound way.

This transformation took place in the “field theories”.

• It began with Einstein’s idea of associating the gravitational field with the geometry of space.
• It became even more pronounced when quantum theory and relativity were combined to describe the force fields of subatomic particles.

In these ‘quantum field theories’, the distinction between particles and the space surrounding them loses its original sharpness and the void is recognized as a dynamic quantity of paramount importance.

The Concept of Fields

The field concept was introduced in the 19th century by Faraday and Maxwell in their description of the forces between electric charges and currents.

An electric field is a condition in the space around a charged body which will produce a force on any other charge in that space.

Electric fields are thus created by charged bodies and their effects can only be felt by charged bodies.

Magnetic fields are produced by charges in motion, i.e. by electric currents, and the magnetic forces resulting from them can be felt by other moving charges.

In classical electrodynamics, the theory constructed by Faraday and Maxwell, the fields are primary physical entities which can be studied without any reference to material bodies.

Vibrating electric and magnetic fields can travel through space in the form of radio waves, light waves, or other kinds of electromagnetic radiation.

Relativity theory has made the structure of electrodynamics much more elegant by unifying the concepts of both charges and currents and electric and magnetic fields.

Since all motion is relative, every charge can also appear as a current in a frame of reference where it moves with respect to the observer.

Consequently, its electric field can also appear as a magnetic field.

In the relativistic formulation of electrodynamics, the two fields are thus unified into a single electromagnetic field.

The concept of a field has been associated not only with the electromagnetic force, but also with that other major force in the large-scale world, the force of gravity.

Gravitational fields are created and felt by all massive bodies, and the resulting forces are always forces of attraction, contrary to the electro-magnetic fields which are felt only by charged bodies and which give rise to attractive and repulsive forces.

The proper field theory for the gravitational field is general relativity.

In this theory, the influence of a massive body on the surrounding space is more far-reaching than the corresponding influence of a charged body in electrodynamics.

Again, the space around the object is ‘conditioned’ in such a way that another object will feel a force, but this time the conditioning affects the geometry, and thus the very structure of space.

Matter is the full.

Empty space is the void.

These were the 2 fundamentally distinct concepts on which the atomism of Democritus and of Newton was based.

In general relativity, these two concepts can no longer be separated. Wherever there is a massive body, there will also be a gravitational field, and this field will manifest itself as the curvature of the space surrounding that body.

We must not think, however, that the field fills the space and ‘curves’ it. The two cannot be distinguished; the field is the curved space! In general relativity, the gravitational field and the structure, or geometry, of space are identical.

They are represented in Einstein’s field equations by one and the same mathematical quantity. In Einstein’s theory, then, matter cannot be separated from its field of gravity, and the field of gravity cannot be separated from the curved space.

Matter and space are thus seen to be inseparable and interdependent parts of a single whole.

Material objects not only determine the structure of the surrounding space but are, in turn, influenced by their environment in an essential way.

The inertia of a material object is the object’s resistance against being accelerated.

According to the physicist and philosopher Ernst Mach, inertia is not an intrinsic property of matter, but a measure of its interaction with all the rest of the universe.

In Mach’s view, matter only has inertia because there is other matter in the universe.

When a body rotates, its inertia produces centrifugal forces (used, for example, in a spin-drier to extract water from wet laundry), but these forces appear only because the body rotates ‘relative to the fixed stars’, as Mach has put it.

If those fixed stars were suddenly to disappear, the inertia and the centrifugal forces of the rotating body would disappear with them.

This conception of inertia, which has become known as Mach’s principle, had a deep influence on Albert Einstein and was his original motivation for constructing general relativity.

Due to the considerable mathematical complexity of Einstein’s theory, physicists have not yet been able to agree whether it actually incorporates Mach’s principle or not. Most physicists believe, however, that it should be incorporated, in one way or another, into a complete theory of gravity.

Thus modern physics shows us once again-and this time at the macroscopic level-that material objects are not distinct entities, but are inseparably linked to their environment; that their properties can only be understood in terms of their interaction with the rest of the world.

According to Mach’s principle, this interaction reaches out to the universe at large, to the distant stars and galaxies.

The basic unity of the cosmos manifests itself, therefore, not only in the world of the very small but also in the world of the very large; a fact which is increasingly acknowledged in modern astrophysics and cosmology.

In the words of the astronomer Fred Hoyle, Present-day developments in cosmology are coming to suggest rather insistently that everyday conditions could not persist but for the distant parts of the Universe, that all our ideas of space and geometry would become entirely invalid if the distant parts of the Universe were taken away.

Our everyday experience even down to the smallest details seems to be so closely integrated to the grand-scale features of the Universe that it is well-nigh impossible to contemplate the two being separated,’ The unity and interrelation between a material object and its environment, which is manifest on the macroscopic scale in the general theory of relativity, appears in an even more striking form at the subatomic level.

Here, the ideas of classical field theory are combined with those of quantum theory to describe the interactions between subatomic particles. Such a combination has not yet been possible for the gravitational interaction because of the complicated mathematical form of Einstein’s theory of gravity.

But the other classical field theory, electrodynamics, has been merged with quantum theory into a theory called ‘quantum electrodynamics’ which describes all electromagnetic interactions between subatomic particles.

This theory incorporates both quantum theory and relativity theory. It was the first ‘quantum-relativistic’ model of modern physics and is still the most successful.

The striking new feature of quantum electrodynamics arises from the combination of two concepts; that of the electro- magnetic field, and that of photons as the particle manifestations of electromagnetic waves. Since photons are also electro- magnetic waves, and since these waves are vibrating fields, the photons must be manifestations of electromagnetic fields.

Hence the concept of a ‘quantum field’, that is, of a field which can take the form of quanta, or particles. This is indeed an entirely new concept which has been extended to describe all subatomic particles and their interactions, each type of particle corresponding to a different field.

In these ‘quantum field theories’, the classical contrast between the solid particles and the space surrounding them is completely overcome.

The quantum field is seen as the fundamental physical entity; a continuous medium which is present everywhere in space. Particles are merely local condensations of the field; concentrations of energy which come and go, thereby losing their in- dividual character and dissolving into the underlying field.

The conception of physical things and phenomena as transient manifestations of an underlying fundamental entity is not only a basic element of quantum field theory, but also a basic element of the Eastern world view. Like Einstein, the Eastern mystics consider this underlying entity as the only reality: all its phenomenal manifestations are seen as transitory and illusory.

This reality of the Eastern mystic cannot be identified with the quantum field of the physicist because it is seen as the essence of a phenomena in this world and, consequently, is beyond all concepts and ideas.

The quantum field, on the other hand, is a well-defined concept which only accounts for some of the physical phenomena. Nevertheless, the intuition behind the physicist’s interpretation of the subatomic world, in terms of the quantum field, is closely paralleled by that of the Eastern mystic who interprets his or her experience of the world in terms of an ultimate underlying reality.

Subsequent to the emergence of the field concept, physicists have attempted to unify the various fields into a single fundamental field which would incorporate all physical phenomena.

Einstein, in particular, spent the last years of his life searching for such a unified field.

The Brahman of the Hindus, like the Dharmakaya of the Buddhists and the Tao of the Taoists, can be seen, perhaps, as the ultimate unified field from which spring not only the phenomena studied in physics, but all other phenomena as well.

In the Eastern view, the reality underlying all phenomena is beyond all forms and defies all description and specification. It is therefore often said to be formless, empty or void.

But this emptiness is not to be taken for mere nothingness. It is, on the contrary, the essence of all forms and the source of all life.

Thus the Upanishads say,

Brahman is life. Brahman is joy. Brahman is the Void . . . Joy, verily, that is the same as the Void. The Void, verily, that is the same as joy.3

Buddhists express the same idea when they call the ultimate reality Sunyata-‘Emptiness’, or ‘the Void-and affirm that it is a living Void which gives birth to all forms in the phenomenal world. The Taoists ascribe a similar infinite and endless creativity to the Tao and, again, call it empty.

The Tao of Heaven is empty and formless’ says the Kuan-tzq4 and Lao Tzu uses several metaphors to illustrate this emptiness. He often compares the Tao to a hollow valley, or to a vessel which is for ever empty and thus has the potential of containing an infinity of things.

In spite of using terms like empty and void, the Eastern sages make it clear that they do not mean ordinary emptiness when they talk about Brahman, Sunyata or Tao, but, on the contrary, a Void which has an infinite creative potential. Thus, the Void of the Eastern mystics can easily be compared to the quantum field of subatomic physics. Like the quantum field, it gives birth to an infinite variety of forms which it sustains and, eventually, reabsorbs.

As the Upanishads say,

Tranquil, let one worship It As that from which he came forth, As that into which he will be dissolved, As that in which he breathes.5

The phenomenal manifestations of the mystical Void, like the subatomic particles, are not static and permanent, but dynamic and transitory, coming into being and vanishing in one ceaseless dance of movement and energy. Like the subatomic world of the physicist, the phenomenal world of the Eastern mystic is a world of samsara-of continuous birth and death. Being transient manifestations of the Void, the things in this world do not have any fundamental identity. This is es- pecially emphasized in Buddhist philosophy which denies the existence of any material substance and also holds that the idea of a constant ‘self’ undergoing successive experiences is an illusion. Buddhists have frequently compared this illusion of a material substance and an individual self to the phenomenon of a water wave, in which the up-and-down movement of the water particles makes us believe that a ‘piece’ of water moves over the surface.*

It is interesting to note that physicists have used the same analogy in the context of field theory to point out the illusion of a material substance created by a moving particle.

Thus Hermann Weyl writes:

According to the Field theory of matter1 a material particle such as an electron is merely a small domain of the electrical field within which the field strength assumes enormously high values, indicating that a comparatively huge field energy is concentrated in a very small space.

Such an energy knot, which by no means is clearly delineated against the remaining field, propagates through empty space like a water wave across the surface of a lake; there is no such thing as one and the same substance of which the electron consists at all times.6

In Chinese philosophy, the field idea is not only implicit in the notion of the Tao as being empty and formless, and yet producing all forms, but is also expressed explicitly in the concept of ch’i. This term played an important role in almost every Chinese school of natural philosophy and was particularly important in Neo-Confucianism; the school which attempted a synthesis of Confucianism, Buddhism and Taoism.

*The word ch’i literally means ‘gas’ or ‘ether’, and was used in ancient China to denote the vital breath or energy animating the cosmos. In the human body, the ‘pathways of ch’i’ are the basis of traditional Chinese medicine. The aim of acupuncture is to stimulate the flow of ch’i through these channels.

The flow of ch’i is also the basis of the flowing movements of T’ai Chi Ch’uan, the Taoist dance of the warrior.

The Neo-Confucians developed a notion of ch’i which bears the most striking resemblance to the concept of the quantum field in modern physics. Like the quantum field, ch’i is conceived as a tenuous and non-perceptible form of matter which is present throughout space and can condense into solid material objects.

In the words of Chang Tsai:

When the ch’i condenses, its visibility becomes apparent so that there are then the shapes (of individual things). When it disperses, its visibility is no longer apparent and there are no shapes. At the time of its condensation, can one say otherwise than that this is but temporary? But at the time of its dispersing, can one hastily say that it is then non-existent?’

Thus ch’i condenses and disperses rhythmically, bringing forth all forms which eventually dissolve into the Void.

Chang Tsai says again,

The Great Void cannot but consist of ch’i; this ch’i cannot but condense to form all things; and these things cannot but become dispersed so as to form (once more) the Great Void.8

As in quantum field theory, the field-or the ch’i-is not only the underlying essence of all material objects, but also carries their mutual interactions in the form of waves. The following descriptions of the field concept in modern physics by Walter Thirring, and of the Chinese view of the physical world by Joseph Needham, make the strong similarity apparent.

Modern theoretical physics . . . has put our thinking about the essence of matter in a different context. It has taken our gaze from the visible-the particles-to the underlying entity, the field. The presence of matter is merely a disturbance of the perfect state of the field at that place; something accidental, one could almost say, merely a ‘blemish’. Accordingiy, there are no simple laws describing the forces between elementary particles .., Order and symmetry must be sought in the underlying field.g

The Chinese physical universe in ancient and medieval times was a perfectly continuous whole. Ch’i condensed in palpable matter was not particulate in any important sense, but individual objects acted and reacted with all other objects in the world . . . in a wave-like or vibratory manner dependent, in the last resort, on the rhythmic

alternation at all levels of the two fundamental forces, the yin and the yang. Individual objects thus had their intrinsic rhythms. And these were integrated . . . into the general pattern of the harmony of the world.lO With the concept of the quantum field, modern physics has found an unexpected answer to the old question of whether matter consists of indivisible atoms or of an underlying continuum.

The field is a continuum which is present everywhere in space and yet in its particle aspect has a discontinuous, ‘granular’ structure. The two apparently contradictory concepts are thus unified and seen to be merely different aspects of the same reality. As always in a relativistic theory, the unification of the two opposite concepts takes place in a dynamic way: the two aspects of matter transform themselves endlessly into one another.

Eastern mysticism emphasizes a similar dynamic unity between the Void and the forms which it creates. In the words of Lama Govinda:

The relationship of form and emptiness cannot be con- ceived as a state of mutually exclusive opposites, but only as two aspects of the same reality, which co-exist and are in continual co-operation.11 The fusion of these opposite concepts into a single whole has been expressed in a Buddhist sutra in the celebrated words:

Form is emptiness, and emptiness is indeed form. Emptiness is not different from form, form is not different from emptiness. What isform that isemptiness, what isemptiness that is form.‘2

The field theories of modern physics have led not only to a new view of subatomic particles but have also decisively modified our notions about the forces between these particles. The field concept was originally linked to the concept of force, and even in quantum field theory it is still associated with the forces between particles. The electromagnetic field, for example, can manifest itself as a ‘free field’ in the form of travelling waves/photons, or it can play the role of a field of force between charged particles. In the latter case, the force manifests itself as the exchange of photons between the interacting particles. The electric repulsion between two electrons, for example, is mediated through these photon exchanges.

This new notion of a force may seem difficult to understand, but it becomes much clearer when the process of exchanging a photon is pictured in a space-time diagram. The diagram below shows two electrons approaching each other, one of them emitting the photon (denoted by ~4 at the point A, the other one absorbing it at the point B. When the first electror’ emits the photon it reverses its direction and changes its velocity (as can be seen from the different direction and inclination of its world line), and so does the second electron when it absorbs the photon. In the end, the two electrons fly apart, having repelled each other through the exchange of the photon. The full interaction between the electrons will involve a series of photon exchanges, and as a result the electrons will appear to deflect one another along smooth curves.

In terms of classical physics, one would say that the electrons exert a repulsive force on one another. This, however, is now seen to be a very imprecise way of describing the situation.

Neither of the two electrons ‘feels’ a force when they approach each other. All they do is interact with the exchanged photons. The force is nothing but the collective macroscopic effect of these multiple photon exchanges. The concept of force is therefore no longer useful in subatomic physics.

It is a classical concept which we associate (even if only subconsciously) with the Newtonian idea of a force being felt over a distance. In the subatomic world there are no such forces, but only inter- actions between particles, mediated through fields, that is, through other particles. Hence, physicists prefer to speak about interactions, rather than about forces.

According to quantum field theory, all interactions take place through the exchange of particles. In the case of electro- magnetic interactions, the exchanged particles are photons; nucleons, on the other hand, interact through the much stronger nuclear force-or ‘strong interaction’-which manifests itself as the exchange of a new kind of particles called ‘mesons’. There are many different types of mesons which can be exchanged between protons and neutrons. The closer the nucleons are to each other, the more numerous and heavy the mesons they exchange. The interactions between nucleons are thus linked to the properties of the exchanged mesons and these, in turn, interact mutually through the exchange of other particles. For this reason, we shall not be able to understand the nuclear force on a fundamental level without understanding the whole spectrum of subatomic particles.

In quantum field theory, all particle interactions can be pictured in space-time diagrams, and each diagram is associated with a mathematical expression which allows one to calculate the probability for the corresponding process to occur.

The exact correspondence between the diagrams and the mathematical expressions was established in 1949 by Richard Feynman, since when the diagrams have been known as Feynman diagrams. A crucial feature of the theory is the creation and destruction of particles. For example, the photon in our diagram is created in the process of emission at point A, and is destroyed when it is absorbed at point B. Such a process can only be conceived in a relativistic theory where particles are not seen as indestructible objects, but rather as dynamic patterns involving a certain amount of energy which can be redistributed when new patterns are formed.

The creation of a massive particle is only possible when the energy corresponding to its mass is provided, for example, in a collision process. In the case of the strong interactions, this energy is not always available, as when two nucleons interact with one another in an atomic nucleus.

In such cases, the exchange of massive mesons should therefore not be possible.

Yet, these exchanges do take place. Two protons, for example, may exchange a ‘pi-meson’, or ‘pion’, whose mass is about one seventh of the proton mass:

The reason why exchange processes of that kind can happen, in spite of the apparent lack of energy for creating the meson, is to be found in a ‘quantum effect’ connected with the uncertainty principle. As discussed previously,* subatomic events ocurring within a short time span involve a large uncertainty of energy. The exchange of mesons, i.e. their creation and subsequent destruction, are events of that kind.

They take place during such a short time that the uncertainty of energy is enough to allow for the creation of the mesons. These mesons are called ‘virtual’ particles. They are different from the ‘real’ mesons created in collision processes, because they can only exist during the period of time allowed by the uncertainty principle. The heavier the mesons are (i.e. the more energy is required to create them), the shorter is the time allowed for the exchange process. This is why nucleons can exchange heavy mesons only when they are very close together.

The exchange of virtual photons, on the other hand, can take place over indefinite distances because the photons, being massless, can be created with indefinitely small amounts of energy. This analysis of nuclear and electromagnetic forces enabled Hideki Yukawa in 1935 not only to predict the existence of the pion, twelve years before it was observed, but also approximately to estimate its mass from the range of the nuclear force.

In quantum field theory, then, all interactions are pictured as the exchange of virtual particles. The stronger the inter- action, i.e. the stronger the resulting ‘force’ between the particles, the higher the probability of such exchange processes; the more frequently will virtual particles be exchanged.

The role of virtual particles, however, is not limited to these interactions. One nucleon alone, for example, may very well emit a virtual particle and reabsorb it shortly afterwards. Provided the created meson disappears within the time allowed by the uncertainty principle, there is nothing to forbid such a process.

The corresponding Feynman diagram for a neutron emitting and reabsorbing a pion is reproduced overleaf. The probability for such ‘self-interaction’ processes is very high for nucleons because of their strong interaction. This means that nucleons are, in fact, emitting and absorbing virtual particles all the time. According to field theory, they have to be regarded as centres of continuous activity surrounded by clouds of virtual particles. The virtual mesons have to disappear very shortly after their creation, which means they cannot move very far away from the nucleon. The meson cloud is thus very small. Its outer regions are populated by light mesons (mostly pions), the heavier mesons having to be absorbed after a much shorter time and therefore being confined to the inner parts of the cloud.

Every nucleon is surrounded by such a cloud of virtual mesons which live only for an exceedingly short period of time. However, virtual mesons may become real mesons under special circumstances. When a nucleon is hit by another particle moving with a high velocity, some of the energy of motion of that particle may be transferred to a virtual meson to free it from the cloud. This is how real mesons are created in high-energy collisions.

On the other hand, when two nucleons come so near to each other that their meson clouds overlap, some of the virtual particles may not go back to be absorbed by the nucleon which originally created them, but may ‘jump across’ to be absorbed by the other nucleon. This is how the exchange processes arise which constitute the strong interactions.

This picture shows clearly that the interactions between particles, and thus the ‘forces’ between them, are determined by the composition of their virtual clouds. The range of an interaction, that is, the distance between the particles at which the interaction will set in, depends on the extension of the virtual clouds, and the detailed form of the interaction will depend on the properties of the particles present in the clouds.

Thus the electromagnetic forces are due to the presence of virtual photons ‘within’ charged particles, whereas the strong interactions between nucleons arise from the presence of virtual pions and other mesons ‘within’ the nucleons. In field theory, the forces between particles appear as intrinsic pro- perties of the particles. Force and matter, the two concepts that were so sharply separated in Greek and Newtonian atomism, are now seen to have their common origin in the dynamic patterns that we call particles.

Such aview of forces is also characteristic of Eastern mysticism which regards motion and change as essential and intrinsic properties of all things. ‘All rotating things’, says Chang Tsai with reference to the heavens, ‘have a spontaneous force and thus their motion is not imposed on them from outside’;13 and in the I Ching we read,

The natural laws are not forces external to things, but represent the harmony of movement immanent in them.14

This ancient Chinese description of forces as representing the harmony of movement within things seems particularly appropriate in the light of quantum field theory, where the forces between particles are seen as reflecting dynamic patterns (the virtual clouds) inherent in these particles.

The field theories of modern physics force us to abandon the classical distinction between material particles and the void. Einstein’s field theory of gravity and quantum field theory both show that particles cannot be separated from the space surrounding them. On the one hand, they determine the structure of that space, whilst on the other hand they cannot be regarded as isolated entities, but have to be seen as con- densations of a continuous field which is present throughout space.

In quantum field theory, this field is seen as the basis of all particles and of their mutual interactions. The field exists always and everywhere; it can never be removed. It is the carrier of all material phenomena. It is the ‘void’ out of which the proton creates the pi-mesons.

Being and fading of particles are merely forms of motion of the field.15

The distinction between matter and empty space finally had to be abandoned when it became evident that virtual particles can come into being spontaneously out of the void, and vanish again into the void, without any nucleon or other strongly interacting particle being present. Here is a ‘vacuum diagram’ for such a process: three particles-a proton (p), an antiproton Cp), and a pion (x)-are formed out of nothing and disappear again into the vacuum. According to field theory, events of that kind happen all the time. The vacuum is far from empty.

On the contrary, it contains an unlimited number of particles which come into being and vanish without end.

Here then, is the closest parallel to the Void of Eastern mysticism in modern physics. Like the Eastern Void, the ‘physical vacuum’-as it is called in field theory-is not a state of mere nothingness, but contains the potentiality for all forms of the particle world. These forms, in turn, are not independent physical entities but merely transient manifestations of the underlying Void. As the sutra says, ‘Form is emptiness, and emptiness is indeed form.’

The relation between the virtual particles and the vacuum is an essentially dynamic relation; the vacuum is truly a ‘living Void, pulsating in endless rhythms of creation and destruction.

The discovery of the dynamic quality of the vacuum is seen by many physicists as one of the most important findings of modern physics. From its role as an empty container of the physical phenomena, the void has emerged as a dynamic quantity of utmost importance.

The results of modern physics thus seem to confirm the words of the Chinese sage Chang Tsai:

When one knows that the Great Void is full of ch’i, one realises that there is no such thing as nothingness.‘6