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Quantum Mechanics

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website: https://www.fritjofcapra.net/

Excerpts from chapters 10 and 11 of Dr. Fritjof's book, The Tao Of Physics

The most important characteristic of the Eastern world view … is the awareness of the unity and mutual interrelation of all things and events … a basic oneness. It is called Brahman in Hinduism, Dharmakaya in Buddhism, Tao in Taoism… Buddhists also call it Tathata, or Suchness: What is meant by the soul as suchness, is the oneness of the totality of all things, the great all-including whole.

In ordinary life, we are not aware of this unity of all things, but divide the world into separate objects and events. This division is … not a fundamental feature of reality [but] an illusion. Hindus and Buddhists tell us that this illusion is based on avidya, or ignorance, produced by a mind under the spell of maya. The principal aim of the Eastern mystical traditions is therefore to readjust the mind by centering and quietening it through meditation.

The Sanskrit term for meditation samadhi means literally ‘mental equilibrium’. It refers to the balanced and tranquil state of mind in which the basic unity of the universe is experienced: Entering into the samadhi of purity, (one obtains) all-penetrating insight that enables one to become conscious of the absolute oneness of the universe.

The basic oneness of the universe is not only the central characteristic of the mystical experience, but is also one of the most important revelations of modern physics. It becomes apparent at the atomic level and manifests itself more and more as one penetrates deeper into matter, down into the realm of subatomic particles [which] are all interconnected, interrelated and interdependent; that they cannot be understood as isolated entities, but only as integrated parts of the whole.

The following discussion is based on the so-called Copenhagen interpretation of quantum theory which was developed by Bohr and Heisenberg in the late 1920s and is still the most widely accepted model. In my discussion I shall follow the presentation given by Henry Stapp of the University of California which concentrates on certain aspects of the theory and on a certain type of experimental situation that is frequently encountered in subatomic physics.

Stapp’s presentation shows most clearly how quantum theory implies an essential interconnectedness of nature, and it also puts the theory in a framework that can readily be extended to the relativistic models of subatomic particles to be discussed later on.

The starting point of the Copenhagen interpretation is the division of the physical world into an observed system (‘object’) and an observing system. The observed system can be an atom, a subatomic particle, an atomic process, etc. The observing system consists of the experimental apparatus and will include one or several human observers.

A serious difficulty now arises from the fact that the two systems are treated in different ways. The observing system is described in the terms of classical physics, but these terms cannot be used consistently for the description of the observed ‘object’.

We know that classical concepts are inadequate at the atomic level, yet we have to use them to describe our experiments and to state the results. There is no way we can escape this paradox. The technical language of classical physics is just a refinement of our everyday language and it is the only language we have to communicate our experimental results.

The observed systems are described in quantum theory in terms of probabilities. This means that we can never predict with certainty where a subatomic particle will be at a certain time, or how an atomic process will occur. All we can do is predict the odds. For example, most of the subatomic particles known today are unstable, that is, they disintegrate - or ‘decay’- into other particles after a certain time. It is not possible, however, to predict this time exactly. We can only predict the probability of decay after a certain time or, in other words, the average lifetime of a great number of particles of the same kind. The same applies to the ‘mode’ of decay.

In general, an unstable particle can decay into various combinations of other particles, and again we cannot predict which combination a particular particle will choose. All we can predict is that out of a large number of particles, 60 per cent, say, will decay in one way, 30 per cent in another way, and 10 per cent in a third way. It is clear that such statistical predictions need many measurements to be verified. Indeed, in the collision experiments of high-energy physics tens of thousands of particle collisions are recorded and analysed to determine the probability for a particular process.

It is important to realize that the statistical formulation of the laws of atomic and subatomic physics does not reflect our ignorance of the physical situation … [but] we have come to recognize probability as a fundamental feature of the atomic reality which governs all processes, and even the existence of matter. Subatomic particles do not exist with certainty at definite places, but rather show ‘tendencies to exist’, and atomic events do not occur with certainty at definite times and in definite ways, but rather show ‘tendencies to occur’.

It is not possible, for example, to say with certainty where an electron will be in an atom at a certain time. Its position depends on the attractive force binding it to the atomic nucleus and on the influence of the other electrons in the atom. These conditions determine a probability pattern which represents the electron’s tendencies to be in various regions of the atom…

… these tendencies, or probabilities, are represented by the so-called probability [wave] function, a mathematical quantity which is related to the probabilities of finding the electron in various places at various times…

If we want to observe and measure such a particle, we must first isolate it, or even create it, in a process which can be called the preparation process. Once the particle has been prepared for observation, its properties can be measured, and this constitutes the process of measurement.

The situation can be represented symbolically as follows.

A particle is prepared in the region A, travels from A to B, and is measured in the region B. In practice, both the preparation and the measurement of the particle may consist of a whole series of quite complicated processes. In the collision experiments of high-energy physics, for example, the preparation of the particles used as projectiles consists in sending them around a circular track and accelerating them until their energy is sufficiently high. This process takes place in the particle accelerator. When the desired energy is reached, they are made to leave the accelerator (A) and travel to the target area (B) where they collide with other particles. These collisions take place in a bubble chamber where the particles produce visible tracks which are photographed. The properties of the particles are then deduced from a mathematical analysis of their tracks; such an analysis can be quite complex and is often carried out with the help of computers. All these processes and activities constitute the act of measurement.

The important point in this analysis of observation is that the particle constitutes an intermediate system connecting the processes at A and B. It exists and has meaning only in this context; not as an isolated entity, but as an interconnection between the processes of preparation and measurement. The properties of the particle cannot be defined independently of measurement these processes. If the preparation or the measurement is modified, the properties of the particle will change too.

On the other hand, the fact that we speak about ‘the particle’, or any other observed system, shows that we have some independent physical entity in mind which is first prepared and then measured. The basic problem with observation in atomic physics is, then - in the words of Henry Stapp – that ‘the observed system is required to be isolated in order to be defined, yet interacting in order to be observed.‘...

In the present case, this means that the concept of a distinct physical entity need not have a precise definition, but can be defined approximately. This is done in the following way.

The observed object is a manifestation of the interaction between the processes of preparation and measurement. This interaction is generally complex and involves various effects extending over different distances; it has various ‘ranges’, as we say in physics. Now, if the dominant part of the interaction has a long range, the manifestation of this long-range effect will travel over a large distance. It will then be free from external disturbances and can be referred to as a distinct physical entity. In the framework of quantum theory, distinct physical entities are therefore idealizations which are meaningful only to the extent that the main part of the interaction has a long range.

Such a situation can be defined mathematically in a precise way. Physically, it means that the measuring devices are placed so far apart that their main interaction occurs through the exchange of a particle or, in more complicated cases, of a network of particles. There will always be other effects present as well, but as long as the separation of the measuring devices is large enough these effects can be neglected. Only when the devices are not placed far enough apart will the short-range effects become dominant. In such a case, the whole macroscopic system forms a unified whole and the notion of an observed object breaks down.

Quantum theory thus reveals an essential interconnectedness of the universe. It shows that we cannot decompose the world into independently existing smallest units. As we penetrate into matter, we find that it is made of particles, but these are not the ‘basic building blocks’ in the sense of Democritus and Newton. They are merely idealizations which are useful from a practical point of view, but have no fundamental significance. In the words of Niels Bohr, ‘Isolated material particles are abstractions, their properties being definable and observable only through their interaction with other systems.‘...

The following passage from a recent article by David Bohm ... confirms this fact most eloquently.

“One is led to a new notion of unbroken wholeness which denies the classical idea of analyzability of the world into separately and independently existing parts . . . We have reversed the usual classical notion that the independent ‘elementary parts’ of the world are the fundamental reality, and that the various systems are merely particular contingent forms and arrangements of these parts. Rather, we say that inseparable quantum interconnectedness of the whole universe is the fundamental reality, and that relatively independently behaving parts are merely particular and contingent forms within this whole.”

At the atomic level, then, the solid material objects of classical physics dissolve into patterns of probabilities, and these patterns do not represent probabilities of things, but rather probabilities of interconnections. Quantum theory forces us to see the universe not as a collection of physical objects, but rather as a complicated web of relations between the various parts of a unified whole. This, however, is the way in which Eastern mystics have experienced the world, and some of them have expressed their experience in words which are almost identical with those used by atomic physicists.

Here are two examples:

“The material object becomes . . . something different from what we now see, not a separate object on the background or in the environment of the rest of nature but an indivisible part and even in a subtle way an expression of the unity of all that we see.”

“Things derive their being and nature by mutual dependence and are nothing in themselves.”

If these statements could be taken as an account of how nature appears in atomic physics, the following two statements from atomic physicists could, in turn, be read as a description of the mystical experience of nature:

“An elementary particle is not an independently existing unanalyzable entity. It is, in essence, a set of relationships that reach outward to other things.”

“The world thus appears as a complicated tissue of events, in which connections of different kinds alternate or overlap or combine and thereby determine the texture of the whole.”

The picture of an interconnected cosmic web which emerges from modern atomic physics has been used extensively in the East to convey the mystical experience of nature. For the Hindus, Brahman is the unifying thread in the cosmic web, the ultimate ground of all being:

“He on whom the sky, the earth, and the atmosphere Are woven, and the wind, together with all life-breaths, Him alone know as the one SOUI.”

In Buddhism, the image of the cosmic web plays an even greater role. The core of the Avatamsaka Sutra, one of the main scriptures of Mahayana Buddhism, is the description of the world as a perfect network of mutual relations where all things and events interact with each other in an infinitely complicated way. Mahayana Buddhists have developed many parables and similes to illustrate this universal interrelatedness… The cosmic web, finally, plays a central role in Tantric Buddhism, a branch of the Mahayana which originated in India around the third century A.D. and constitutes today the main school of Tibetan Buddhism. The scriptures of this school are called the Tantras, a word whose Sanskrit root means ‘to weave’ and which refers to the interwovenness and interdependence of all things and events.

In Eastern mysticism, this universal interwovenness always includes the human observer and his or her consciousness, and this is also true in atomic physics. At the atomic level, ‘objects’ can only be understood in terms of the interaction between the processes of preparation and measurement. The end of this chain of processes lies always in the consciousness of the human observer. Measurements are interactions which create ‘sensations’ in our consciousness - for example, the visual sensation of a flash of light, or of a dark spot on a photographic plate - and the laws of atomic physics tell us with what probability an atomic object will give rise to a certain sensation if we let it interact with us. ‘Natural science’, says Heisenberg, ‘does not simply describe and explain nature; it is part of the interplay between nature and ourselves.‘

The crucial feature of atomic physics is that the human observer is not only necessary to observe the properties of an object, but is necessary even to define these properties. In atomic physics, we cannot talk about the properties of an object as such. They are only meaningful in the context of the object’s interaction with the observer. In the words of Heisenberg, ‘What we observe is not nature itself, but nature exposed to our method of questioning.‘

The observer decides how he is going to set up the measurement and this arrangement will determine, to some extent, the properties of the observed object. If the experimental arrangement is modified, the properties of the observed object will change in turn.

This can be illustrated with the simple case of a subatomic particle. When observing such a particle, one may choose to measure - among other quantities - the particle’s position and its momentum (a quantity defined as the particle’s mass times its velocity). We shall see in the next chapter that an important law of quantum theory - Heisenberg’s uncertainty principle - says that these two quantities can never be measured simultaneously with precision. We can either obtain a precise knowledge about the particle’s position and remain completely ignorant about its momentum (and thus about its velocity), or vice versa; or we can have a rough and imprecise knowledge about both quantities. The important point now is that this limitation has nothing to do with the imperfection of our measuring techniques. It is a principle limitation which is inherent in the atomic reality. If we decide to measure the particle’s position precisely, the particle simply does not have a well-defined momentum, and if we decide to measure the momentum, it does not have a well-defined position.

In atomic physics, then, the scientist cannot play the role of a detached objective observer, but becomes involved in the world he observes to the extent that he influences the properties of the observed objects. John Wheeler sees this involvement of the observer as the most important feature of quantum theory and he has therefore suggested replacing the word ‘observer’ by the word ‘participator’. In Wheeler’s own words,

“Nothing is more important about the quantum principle than this, that it destroys the concept of the world as ‘sitting out there’, with the observer safely separated from it by a 20 centimeter slab of plateglass. Even to observe so miniscule an object as an electron, he must shatter the glass. He must reach in. He must install his chosen measuring equipment. It is up to him to decide whether he shall measure position or momentum. To install the equipment to measure the one prevents and excludes his installing the equipment to measure the other. Moreover, the measurement changes the state of the electron. The universe will never afterwards be the same. To describe what has happened, one has to cross out that old word ‘observer’ and put in its place the new word ‘participator’. In some strange sense the universe is a participatory universe.”

The idea of ‘participation instead of observation’ has been formulated in modern physics only recently, but it is an idea which is well known to any student of mysticism. Mystical knowledge can never be obtained just by observation, but only by full participation with one’s whole being. The notion of the participator is thus crucial to the Eastern world view, and the Eastern mystics have pushed this notion to the extreme, to a point where observer and observed, subject and object, are not only inseparable but also become indistinguishable.

The mystics are not satisfied with a situation analogous to atomic physics, where the observer and the observed cannot be separated, but can still be distinguished. They go much further, and in deep meditation they arrive at a point where the distinction between observer and observed breaks down completely, where subject and object fuse into a unified undifferentiated whole. Thus the Upanishads say,

“Where there is a duality, as it were, there one sees another; there one smells another; there one tastes another . . . But where everything has become just one’s own self, then whereby and whom would one see? Then whereby and whom would one smell? then whereby and whom would one taste?”

This, then, is the final apprehension of the unity of all things. It is reached - so the mystics tell us - in a state of consciousness where one’s individuality dissolves into an undifferentiated oneness, where the world of the senses is transcended and the notion of ‘things’ is left behind. In the words of Chuang Tzu,

“My connection with the body and its parts is dissolved. My perceptive organs are discarded. Thus leaving my material form and bidding farewell to my knowledge, I become one with the Great Pervader. This I call sitting and forgetting all things.”

Modern physics, of course, works in a very different framework and cannot go that far in the experience of the unity of all things. But it has made a great step towards the world view of the Eastern mystics in atomic theory. Quantum theory has abolished the notion of fundamentally separated objects, has introduced the concept of the participator to replace that of the observer, and may even find it necessary to include the human consciousness in its description of the world. It has come to see the universe as an interconnected web of physical and mental relations whose parts are only defined through their connections to the whole. To summarize the world view emerging from atomic physics, the words of a Tantric Buddhist, Lama Anagarika Govinda, seem to be perfectly apropos:

“The Buddhist does not believe in an independent or separately existing external world, into whose dynamic forces he could insert himself. The external world and his inner world are for him only two sides of the same fabric, in which the threads of all forces and of all events, of all forms of consciousness and of their objects, are woven into an inseparable net of endless, mutually conditioned relations.”

When the Eastern mystics tell us that they experience all things and events as manifestations of a basic oneness, this does not mean that they pronounce all things to be equal. They recognize the individuality of things, but at the same time they are aware that all differences and contrasts are relative within an all-embracing unity. Since in our normal state of consciousness, this unity of all contrasts-and especially the unity of opposites-is extremely hard to accept, it constitutes one of the most puzzling features of Eastern philosophy.

It is, however, an insight which lies at the very root of the Eastern world view. Opposites are abstract concepts belonging to the realm of thought, and as such they are relative. By the very act of focusing our attention on any one concept we create its opposite. As Lao Tzu says, “When all in the world understand beauty to be beautiful, then ugliness exists; when all understand goodness to be good, then evil exists.”

The mystic transcends this realm of intellectual concepts, and in transcending it he becomes aware of the relativity and polar relationship of all opposites. He realizes that good and bad, pleasure and pain, life and death, are not absolute experiences belonging to different categories, but are merely two sides of the same reality; extreme parts of a single whole. The awareness that all opposites are polar, and thus a unity, is seen as one of the highest aims of man in the spiritual traditions of the East.

‘Be in truth eternal, beyond earthly opposites!’ is Krishna’s advice in the Bhagavad Gita, and the same advice is given to the followers of Buddhism. Thus D. T. Suzuki writes, “The fundamental idea of Buddhism is to pass beyond the world of opposites, a world built up by intellectual distinctions and emotional defilements, and to realize the spiritual world of non-distinction, which involves achieving an absolute point of view.”

The whole of Buddhist teaching-and in fact the whole of Eastern mysticism-revolves about this absolute point of view which is reached in the world of acintya, or ‘no-thought’, where the unity of all opposites becomes a vivid experience…

The notion that all opposites are polar-that light and dark, winning and losing, good and evil, are merely different aspects of the same phenomenon-is one of the basic principles of the Eastern way of life. Since all opposites are interdependent, their conflict can never result in the total victory of one side, but will always be a manifestation of the interplay between the two sides. In the East, a virtuous person is therefore not one who undertakes the impossible task of striving for the good and eliminating the bad, but rather one who is able to maintain a dynamic balance between good and bad.

This notion of dynamic balance is essential to the way in which the unity of opposites is experienced in Eastern mysticism. It is never a static identity, but always a dynamic interplay between two extremes. This point has been emphasized most extensively by the Chinese sages in their symbolism of the archetypal poles yin and yang. They called the unity lying behind yin and yang the Tao and saw it as a process which brings about their interplay: “That which lets now the dark, now the light appear is Tao.” …

One of the principal polarities in life is the one between the male and female sides of human nature. As with the polarity of good and bad, or of life and death, we tend to feel uncomfortable with the male/female polarity in ourselves, and therefore we bring one or the other side into prominence.

Western society has traditionally favoured the male side rather than the female. Instead of recognizing that the personality of each man and of each woman is the result of an interplay between female and male elements, it has established a static order where all men are supposed to be masculine and all women feminine, and it has given men the leading roles and most of society’s privileges. This attitude has resulted in an over-emphasis of all the yang-or male-aspects of human nature: activity, rational thinking, competition, aggressiveness, and so on. The yin-or female-modes of consciousness, which can be described by words like intuitive, religious, mystical, occult or psychic, have constantly been suppressed in our male-oriented society.

In Eastern mysticism, these female modes are developed and a unity between the two aspects of human nature is sought. A fully realized human being is one who, in the words of Lao Tzu, ‘knows the masculine and yet keeps to the feminine’…

Examples of the unification of opposite concepts in modern physics can be found at the subatomic level, where particles are both destructible and indestructible; where matter is both continuous and discontinuous, and force and matter are but different aspects of the same phenomenon. In all these examples … it turns out that the framework of opposite concepts, derived from our everyday experience, is too narrow for the world of subatomic particles. Relativity theory is crucial for the description of this world, and in the ‘relativistic’ framework the classical concepts are transcended by going to a higher dimension, the four-dimensional space-time. Space and time themselves are two concepts which had seemed entirely different, but have been unified in relativistic physics. This fundamental unity is the basis of the unification of the opposite concepts mentioned above.

Like the unity of opposites experienced by the mystics, it takes place on a ‘higher plane’, i.e. in a higher dimension, and like that experienced by the mystics it is a dynamic unity, because the relativistic space-time reality is an intrinsically dynamic reality where objects are also processes and all forms are dynamic patterns…

In some situations the particle aspect is dominant, in others the particles behave more like waves; and this dual nature is also exhibited by light and all other electromagnetic radiation. Light, for example, is emitted and absorbed in the form of ‘quanta’, or photons, but when these particles of light travel through space they appear as vibrating electric and magnetic fields which show all the characteristic behavior of waves. Electrons are normally considered to be particles, and yet when a beam of these particles is sent through a small slit it is diffracted just like a beam of light-in other words electrons, too, behave like waves.

This dual aspect of matter and radiation is indeed most startling and gave rise to many of the ‘quantum koans’ which led to the formulation of quantum theory. The picture of a wave which is always spread out in space is fundamentally different from the particle picture which implies a sharp location.

It has taken physicists a long time to accept the fact that matter manifests itself in ways which seem to be mutually exclusive; that particles are also waves, waves also particles… The particle is not present at a definite place, nor is it absent. It does not change its position, nor does it remain at rest. What changes is the probability pattern, and thus the tendencies of the particle to exist in certain places. In the words of Robert Oppenheimer,

‘If we ask, for instance, whether the position of the electron remains the same, we must say ‘no’; if we ask whether the electron’s position changes with time, we must say ‘no’; if we ask whether the electron is at rest, we must say ‘no’; if we ask whether it is in motion, we must say ‘no’.’

The reality of the atomic physicist, like the reality of the Eastern mystic, transcends the narrow framework of opposite concepts. Oppenheimer’s words thus seem to echo the words of the Upanishads,

‘It moves. It moves not. It is far, and It is near. It is within all this, And It is outside of all this.’

Force and matter, particles and waves, motion and rest, existence and non-existence-these are some of the opposite or contradictory concepts which are transcended in modern physics. Of all these opposite pairs, the last seems to be the most fundamental, and yet, in atomic physics we have to go even beyond the concepts of existence and non-existence…