In order to find the right paradigm for our time, we shall now turn to Buddhism. In Buddhism the Pali term ditthi is the closest equivalent of the term paradigm in English. By ditthi we mean "view, belief, dogma, theory, speculation." Sammâditthi or right worldview does not presuppose any dualism between mind and body. Buddhism is a realism in the sense that it accepts the real existence of both mind and external things, including our body. Unlike dualistic philosophies, Buddhism does not take mind and body to be two separate and independent entities. Mind and body are interconnected in their nature. That is to say that a person (puggala) consists of both mental and bodily components called "nâma-rupa." Here, the term "nâma" refers to all mental phenomena whereas the term "rupa" refers to the bodily component of the person. Nâma and rupa taken together constitute a "whole" known as a person. Nâma and rupa (i.e. mind and body) are interconnected according to the law of Dependent Origination.
Both material and mental phenomena are non-substantial (anattâ), i.e. empty of self-reality. Nothing exists in itself, for each existence is conditioned by causes outside itself. All phenomena have nothing substantial in themselves, they are in a state of becoming (bhava), not that of static being. A belief in either absolute being or absolute non-being is considered to be an extreme view. The Buddha says:
Kaccana, "everything exists" is one extreme view. "Nothing exists" is another extreme view. Avoiding both these extremes, the Tathagata teaches a doctrine by the middle way.
The doctrine of the middle way refered here is the principle of Dependent Origination (Paticcasamuppada) which can be expressed by the following formula:
When this is, that is (Imasmiæ sati idaæ hoti)
This arising, that arises (Imassuppadâ idaæ uppajjati)
When this is not, that is not (Imasmiæ asati idaæ na hoti)
This ceasing, that ceases (Imassa nirodhâ idaæ nirujjhati)
To put it into a modern form:
When A is, B is
A arising, B arises
When A is not, B is not
A ceasing, B ceases
According to the law of Dependent Origination, all phenomena are dependently originated (Paticcasamuppada). Buddhists see the world, not as a collection of isolated objects, but as a network of phenomena that are fundamentally interconnected and interdependent. The Buddhist worldview, therefore, is holistic because it sees the world as an intgrated whole rather than as a dissociated collection of parts. It recognizes the fundamental inter-dependence of all phenmoena in the world. Everything is dependently originated.
The fundamental interdependence of all things in the world is not only the central characteristic of Buddhism, but is also one of the most important revelations of modern physics. Quantum theory studies the realm of subatomic particles and discovers that electron, proton, and neutron are interconnected, interrelated and integrated parts of the whole. Quantum theory dissolves the solid material objects of classical physics into wavelike patterns of probabilities. These patterns do not represent probabilities of things, but rather probabilities of interconnections.
Subatomic particles are always dependently originated. This can be seen from the way electrons orbit around protons and neutrons. If someone tries to split up the nucleus of an atom by fission, the atomic mass will turn into energy immediately; as we learn from Einstein's equation: E = mc2, in which c represents the speed of light. "E is the energy that is contained in a stationary body; m is its mass. The energy that belongs to the mass m is equal to this mass, multiplied by the square of the enormous speed of light." This equation tells us that the atomic mass is nothing but a form of energy. Even an object at rest has energy stored in its mass. From this it follows that all material objects which come into existence through the interconnection of atomic masses can be viewed as energy fields spreading all over the world. In these energy fields, there is no permanent entity. This is in conformity with the Buddhist view that all things are non-substantial (Sabbe dhamma anatta). When we shift our attention from macroscopic objects to the microscopic world of atoms, we find a complex web of relationships among subatomic particles. As Henry Stapp has pointed out, "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 following statement made by Werner Heisenberg, one of the founders of quantum theory, could be read as a description of the Buddhist principle of Dependent Origination:
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.
What follows from our discussion is that whereas quantum theory confirms the truth of the Buddhist principle of Dependent Origination, Einstein's equation, E = mc2, supports the Buddhist theory of non-substantiality (anatta). Buddhism and modern physics represent a realistic philosophy and a holistic worldview which can be taken as a new paradigm replacing the dualistic philosophy and mechanistic worldview of classical physics. This paradigm shift will enable us to view the world as a whole and to take a holistic approach to development. Such an approach will set a balanc
In the midst of working on this paper, I learned that a friend of ours, an extraordinarily beautiful woman in all senses of the word, found that her equally beautiful nine-month old boy has a virulent strain of muscular dystrophy. For that bright-eyed and laughing little boy with a genetic time bomb, the future points to progressive wasting, immobility, and death before adulthood.
It is easy to see in this little boy the transformations already affecting his body and to feel the sharp sting of how things will unroll in time. There is a clear sense of inevitability, of time being "a river which sweeps him along." Although just as true for ourselves, we easily see in him that time is a devouring tiger and a consuming fire.
I’ll show that understanding something about time in Buddhism and modern physics deepens our sense of how "Time is the substance I am made of." Such understanding also helps us appreciate how we are the devouring tiger and the consuming fire. Beyond its inevitability and destruction, time has other crucial features.
We can reflect on past events and learn from them, but we cannot influence them. The past has a fixity that contrasts sharply with the more malleable future, where we make choices and influence events. Therefore, we experience a directionality to time, expressed by a metaphorical arrow pointing from the past, through the present, and into the indefinite future.
In contrast, the fundamental equations of physics are all time symmetric, meaning that they have no directionality in time. All the fundamental interactions can proceed in the reverse direction without violating any laws of physics. For a simple example, bounce a ball off the floor and take a movie of it. If you run the movie backwards, nothing looks strange because the time-reversed motion violates no laws of physics. Or, take a movie of our solar system from a distant star and play it backwards. All the rotations and revolutions of the sun and planets will be reversed, but no laws of physics are violated and nothing looks strange. The same is true for quantum mechanical examples. Let an excited atom decay and emit a photon. Run the process backwards and you have an atom absorbing light and ending in an excited state.
Yet, many complex processes do display clear temporal directionality. The ruptured balloon, dangling from the tearful child’s hand never spontaneously reassembles itself back into its inflated condition. Such irreversible processes like the rotting of food and the decay of teeth are in sharp contrast to the time reversible laws of physics. Our little sick friend’s inevitable ride down the river of time, along with our own, is full of irreversible transformations, leading to death, the one we most fear. Therefore, despite the symmetry of the fundamental interactions, nature clearly has many asymmetric and irreversible processes. As we will see below, the physicist’s explanation for this asymmetry, within symmetric underlying laws, can help us understand some of the deepest lessons from Middle Way Buddhism.
The two decades that this little boy can look forward to seem criminally short from here, yet time may seem to crawl unendurably in his final days. However, in this digital age most believe that, despite such subjective experiences, time is absolute. Two decades is a well-defined interval that all observers can agree on, despite their subjective biases. Again, appreciating how physics destroys this apparent absoluteness can also deepen our understanding of Middle Way Buddhism.
I hope to show that understanding a little about time in modern physics helps us more deeply appreciate some of the most profound ideas in Buddhism. Furthermore, I will also suggest that some appreciation of Middle Way Buddhist ideas could aid in the development of physics. Thus a nontrivial synergy between these two very different disciplines is possible, one that results in deeper understanding and more compassionate action. While time may be a devouring tiger, appreciating these ideas might help us attain equanimity and encourage us to act more compassionately toward each other and the planet.
II. Carrots and Emptiness in the Middle Way
I’ll review the principle of emptiness within the Middle Way Consequence School (Prasangika
One beautiful spring day a few years ago the rototiller was taking me for my annual ride while it bathed me in the blue smoke of burning oil. I was musing on carrots and rototillers and suddenly had a tiny enlightenment. The second of Buddha’s Four Noble Truths tells us that suffering is caused by desire. My desire for that delicious carrot juice had chained me to this rototiller for a quarter of a century! A desire for fresh, sweet carrot juice initially seemed innocent and "spiritually correct," in that good health is an aid to practicing dharma, but look where it led. Desire does generate suffering. However, those blue clouds bellowing from the burned out muffler along with that shattering noise and vibration urged me to deeper reflection. Upon what is that carrot-desire based?
The Middle Way clearly answers that desires and aversions are based upon the false belief in independent existence, the idea that beyond my personal associations, relationship, and names for carrots, there is a real, substantial, inherently existent entity. This substantially existent object, that entity that "exists from its own side," is the basis upon which we project all our desires and aversions, all our craving for and fleeing from objects.
This innate and unreflective belief in inherent existence divides into two pieces. First, that phenomena exist independent of mind or knowing. That "underneath" or "behind" the psychological associations, names, and linguistic conventions we apply to objects like carrot or rototiller, something objective and substantial exists fully and independently from its own side. Such independent objects appear to provide the objective basis for our shared world. Second, we falsely believe these objects to be self-contained and independent of each other.[2] Each object being fundamentally nonrelational, it exists on its own right without essential dependence upon other objects or phenomena. In other words, the essential nature of these objects is their nonrelational unity and completeness in themselves.
Since it is so critical to identify inherent existence carefully, let me say it in other words. Consider the carrot stripped of its sense qualities, history, location, and relation to its surroundings. All but an advanced practitioner of the Middle Way believes that this denuded carrot has some unique essence, some concrete existence that provides the foundation for all its other qualities. This core of its being, this independent or inherent existence, is what the Middle Way denies. The carrot surely has conventional existence; it attracts rodents and makes great juice. It functions as a food. However, it totally lacks independent or inherent existence, what we falsely believe is the core of its being. In other words, the object or subject we falsely believe independently exists is not actually "finable upon analysis." When we search diligently for that entity we believe inherently exists, we cannot actually find it. It’s independent being does not become clearer and more definite upon searching. Instead, phenomena exist in the middle way because they lack inherent existence, but do have conventional existence.
While reifying carrots, I simultaneously reify the one who desires carrots and consider him as inherently existent too. Out of the seamless flux of experience, I falsely impute or attribute inherent existence to both the subject and its object of desire and thereby spin the wheel of samsara. In this way, perception is a double act that simultaneously generates a false belief in inherently existent subjects and objects, gentleman farmers and their carrots. Then our time is occupied with cherishing our personal ego, putting its desires before all else, pushing others aside to satisfy those desires, and running after objects we falsely believe inherently exist. We think those objects will make us happy, but in fact they can never satisfy us. Perhaps time "is a fire that consumes me, but I am the fire." Was not this the point of the Buddha’s fire sermon?
According to the Middle Way, we can put out the fire by deeply appreciating the doctrine of emptiness, the lack of inherent existence in all subjects and objects, in all phenomena. This requires not only an intellectual formulation as given here, but a profound transformation of our whole being at many levels—a process that usually takes many life times.
Just so that you will have the whole story, I recently bought a new tractor to replace my 1934 hand-cranking model (also the source of many deep lessons). With the new tractor, I bought a huge rototiller that attaches to it and makes garden preparation a breeze. However, I have given the old rototiller, now called the dharma-tiller, to my son hoping that he will grow good vegetables and a deeper understanding of emptiness.
The description of emptiness given so far is negative, a thoroughgoing denial of what we wrongly believe is the core of existence. Next, let me turn to a more positive description of phenomena, including carrots. If phenomena don’t independently exist than how do they exist? The Middle Way tells us that they dependently exist in three fundamental ways. First, phenomena exist dependent upon causes and conditions. For example, carrots depend upon soil, sunlight, moisture, freedom from rodents, and so forth. Second, phenomena depend upon the whole and its parts. Carrots depend upon its greens, stem, root hairs, and so on and the totality of all these parts. Third, and most profoundly, phenomena depend upon mental imputation, attribution, or designation. From the rich panoply of experience, I collect the sense qualities, personal associations, and psychological reactions to carrots together, and name them or designate them as "carrot." The mind’s proper functioning is to construct its world, the only world we can know. The error enters because along with naming comes the false attribution of inherent existence, that foundation for desire and aversion.
For the Middle Way, dependent arising is a complementary way of describing emptiness. We can understand them as two different views of the same truth. Therefore, contrary to our untutored beliefs, the ultimate nature of phenomena is its dependency and relatedness, not isolated existence and independence.
One of the difficulties in understanding emptiness is that we can easily assent to the importance of relatedness, while falling prey to the unconscious assumption that relations are superimposed upon independently existent terms in the relation. In fact, it is the relationships, the interdependencies that are the reality, since objects or subjects are nothing but their connections to other objects and subjects.
We might ask what would phenomena be like if they did in fact inherently or independently exist. The Middle Way explains that inherently existent objects would be immutable, since in their essence they are independent of other phenomena and so uninfluenced by any interactions. Conversely, independently existent objects would also be unable to influence other phenomena, since they are complete and self-contained. In short, independently existent objects would be immutable and impotent. Of course, experience denies this since our world is of continuously interacting phenomena, from the growth of carrots nourished by sun, rain, and soil, to their destruction by rodents. From the subjective side, that we do not independently exist implies that it is possible to transform ourselves into Buddhas, exemplars of infinite wisdom and compassion.
Critics of the Middle Way often say that if objects did not inherently exist, they could not function to produce help and harm. Carrots lacking independent existence could not give sweet juice or make soup. The Middle Way turns this around 180 degrees, and answers that it is precisely because objects and subjects lack independent existence that they are capable of functioning. So the very attribute that we falsely believe is at the core of phenomena would, if present, actually prevent them from functioning.
Now how does all this relate to the Middle Way notion of time? As I mentioned above, if phenomena inherently existed then they would of necessity be immutable and impotent, unable to act on us or we on them. Since, in truth, phenomena are fundamentally a shifting set of dependency relations, impermanence and change are built into them at the most fundamental level. That the carrot exists in dependence upon causes and conditions, its whole and parts, and on our attribution or naming is what makes it edible, allows me to experience it and be nourished by it. More important for impermanence, these defining relations and co-dependencies and their continuously shifting connections with each other guarantee that all objects and subjects are impermanent, ceaselessly evolving, maturing, and decaying. In short, emptiness and impermanence are two sides of the coin of existence and therefore transformation and change are built into the core of all entities, both subjective and objective. In this way, the doctrine of impermanence is a direct expression of emptiness/dependent arising. Because I lack inherent existence and am most fundamentally a kinetic set of shifting experiences, with no eternal soul, as we normally understand it, then "Time is the substance I am made of." Borges’ compact sentence seems like a Middle Way aphorism. Being substantially of time guarantees my continuous transformation and death. Indeed, time "is a fire that consumes me, but I am the fire." These philosophic truths of emptiness and impermanence are central to Buddhist practice, and I return to them later. Now let us turn to physics and its view of time.
III. Time in Modern Physics
As mentioned in the introduction, we all have a natural belief in the absoluteness of time, meaning that, for example, one minute is the same for all observers. Let me again proceed by way of example.
My carrots take 70 days to harvest time. Our belief in the absoluteness of time or its independent existence appears in the view that this time is something intrinsic to the carrot. As long as the growing conditions are normal, it does not matter how this time is measured or who measures it. It has an independent or absolute nature. However, let an astronaut take the same seeds and grow them in a space ship traveling at 90 percent the speed of light relative to the Earth. Then relativity theory tells us that the days to harvest (as measured by an Earth-based observer) would be 161 days.[3] Figure 1 shows the days to harvest, as observed on Earth, plotted against the velocity of the space ship, relative to Earth, divided by the speed of light, c. So for example when v/c = .9 then we move straight upward from that point on the horizontal axis and intersect the curve at 161 days. Only in a reference frame at rest with respect to the observer (the rest frame) is the days to harvest 70 days.
------------------- Figure 1--------------------
Relativity emphatically states that no value of the days to harvest time is any more real or intrinsic than any other. For example, if the astronaut looked back at my garden she would correctly measure my time to harvest as 161 days. Since time intervals depend directly upon the relationship between the object and the observer, they are essentially relational. We cannot consider time independent of a particular reference frame. In Middle Way language, it lacks independent existence. If the seed manufacturers were devotees of relativity they would state on the package, "The time to harvest is 70 day only in the rest frame. For other reference frames consult the graph on the back." That graph would be Figure 1. We can attempt to evade this relational nature of time by saying that humans never travel at any significant fraction of the speed of light, and so this is just an academic consideration. This move denies the conceptual import of relativity’s view of time and the thousands of experiments done all over the planet every day that rely on it.
If we clarify the idea of the present moment, the essentially relational nature of time intervals, whether decades or microseconds, is complemented by a thoroughgoing relativity of the present. Take the reasonable definition that all the simultaneous events that take place for an observer at one time defines the present moment. Let’s say I plant my carrots at exactly 9:00 AM on a given day and at that moment a friend in New Deli boards a plane, while my son enters a classroom in a distant city. Relativity teaches that those simultaneous events defining the moment of carrot planting are only simultaneous in my garden’s reference frame. If our farmer-astronaut, moving at 90 percent the speed of light, passes directly over my garden at 9:00 AM he observers a different set of simultaneous events and thus his present moment differs from mine. While a second astronaut, traveling at a different speed over my garden at 9:00 AM, finds yet a third set of simultaneous events and thus a different present from mine or the first astronaut.
Therefore, relativity makes both time intervals and individual moments relative to a given reference frame, leaving our old absolute view of time far behind. There are similar things to say about other primary qualities of objects, but these points about time are enough for the present. A more interesting and profound quality of time comes from understanding how it has an arrow.
We store our carrots in the cellar where there is a cool, even temperature. However, even there, they rot after four to six months. We have never seen rotten food return to its fresh state. Rotting, whether of vegetables, teeth, or our entire bodies, is an irreversible process. Given that the quantum mechanical laws, which govern the chemical changes of rotting, are time symmetric, this is mysterious. The great Austrian physicist, Ludwig Boltzmann, made the first significant progress in understanding this mystery. He realized that irreversibility comes from reversible underlying laws only when you have large numbers of particles in the system.
Boltzmann started by considering a simple box containing many gas particles governed by Newton’s laws. In analyzing this system, he assumed that it was totally isolated from the rest of the universe. There were no influences of the universe on the box and its contents or vice versa. Now this should give anybody influenced by the Middle Way philosophy some real discomfort, since he is assuming that the system independently exists. More about that later.
Boltzmann then imagined a partition in the middle of the box with all the particles in just one half of the box. The other half is totally empty. To proceed further we need to understand the concept of entropy, or measure of disorder. The more disorder, the less knowledge we have about the details of the system, the higher the entropy. When the partition is removed, the overwhelmingly most probable configurations of the new equilibrium condition involve the gas spreading evenly throughout the box. In principle, it is possible for the gas to bunch up in only one quarter of the box. However, it is overwhelmingly more probable that it will attain a new equilibrium configuration diffused throughout the box. Such equilibrium states have maximum entropy. Through this reasoning, Boltzmann proved the famous Second Law of Thermodynamics, which says that any isolated system’s entropy must either stay the same or increase. Therefore, when the egg hits the floor it is overwhelmingly likely to go to a state of greater entropy. What is more, the increase in entropy defines the direction of the arrow of time. Time advances in the same direction in which entropy increases—what we call the future. This does not deny that there are local decreases in entropy, like the growth of a child, but the global entropy relentlessly increases with time.
For several years, I taught our junior-senior level course on statistical physics. We used the standard textbook and followed Boltzmann’s derivation of the Second Law of Thermodynamics, with the appropriate level of mathematical sophistication. In the last few years, I found that there were arguments as far back as 1877 that showed Boltzmann was deeply wrong. I review some of these problems elsewhere in nontechnical language..[4] Here, I take a different approach and follow an elegant and simple argument by P.C.W. Davies.[5] As we will shortly see, entropy increases, but not the way Boltzmann thought. Why several revisions of this famous text persist in the error is a mystery.
------------- Figure 2 ---------------
The basic difficulty, which can be seen in several independent ways, is that completely isolated systems, like the box of gas, can generate no directionality to time because of the time-symmetric laws governing the system. Figure 2 displays the entropy, S, of an isolated box of gas plotted versus time, t. We see that the random gas motions give occasional deviations below the maximum. Although it is unlikely, the random motions spontaneously generate states of greater order or lower entropy, which are then brought back to maximum disorder by the same randomization. This is like the shuffling of playing cards that, on rare occasions, puts them into states of greater order, with continued shuffling returning them to disorder.
---------------- Figure 3 ----------------
Even before I began getting instruction from my rototiller 25 years ago, the problem of the arrow of time had largely been resolved, although there are still technical subtleties. Much to the delight of the Middle Way, the main problem lies in assuming we have a totally isolated system independent of interaction with its environment.
We now understand that we must account for how Boltzmann’s box got into the low entropy state of all particles in just one half. This did not result from just waiting a long time for random motions to throw the gas all to one side, but from Boltzmann evacuating one half and placing gas in the other. Preparing the box in a low entropy state must generate more entropy elsewhere in the universe. For example, Boltzmann consumed calories from lunch and radiated energy from himself and his equipment that eventually went into deep space. In other words, the box had its entropy put into a low condition by processes outside itself, but at the expense of a much greater entropy increase elsewhere in the universe.
Let me give an example closer to the garden. I walk in the garden to check on whether the mice have eaten the carrots. My footprint in the soft soil gives it more order and structure, thus lowering its entropy. However, this lower entropy comes from a much greater generation of entropy from my metabolic processes, which eventually degrade to heat radiated to the universe.
As we have long known, the energy emitted into deep space from our activities can only radiate into space because the universe is expanding. If the universe were not expanding then it is so large that any line of sight from the Earth, when extended far enough, would land on a star surface. Then the effective temperature of deep space would be that of the surface of stars, which is typically 6000 °K, rather than the 3 °K it actually has. Since entropy can only increase when energy moves from high to low temperature regions, the simple process of radiating our body's energy into space would be blocked in a static universe. Thus, there would be neither a Boltzmann nor the ability to reduce entropy locally in the box by generating more entropy elsewhere in the universe.
All systems organizing themselves or decreasing their entropy, whether the growing of a carrot, a snowflake, or a child, are decreasing entropy in one location that must be accompanied by a greater entropy generation in another. Not only is the energy from Boltzmann’s food and his equipment eventually traced back to our sun, but the sun’s low entropy is critical. Energy generation processes, whether the digestion of our food or the workings of a nuclear power plant, are totally dependent upon our solar system being in a low entropy condition. What causes the sun and other stars to be in a low entropy condition? This occurs because the expansion of the universe was faster than the nuclear generation rates in the first three minutes of the big bang. Then, when nearly all the helium (about 25% of the total mass of the universe) was formed, the universe expanded so quickly that after three minutes it was too cool for nuclear reactions to occur. If the expansion and associated cooling were much slower, then all the matter in the universe would form into a very stable isotope of iron, an inert and high entropy condition. Then the stars would not shine, there would be no great entropy gradients in the universe, no time asymmetry, and, of course, no life.
Local time-asymmetry, such as the decay of any biological system, from carrots to our own bodies, must be accounted for by connecting it to the expansion of the universe and its earliest evolution. This extraordinary beautiful result has many technical twists and turns, but the central idea is clear: increasing entropy and time-asymmetry owe their existence to the largest and earliest processes in the universe and its continued expansion. This is a long way from the notion of an isolated and noninteracting system, so abhorrent to the Middle Way. In this way, when you put cold milk into your coffee and the mixture comes to the same temperature and a higher entropy than when the fluids were separated, you are profiting from the universe’s expanding and cooling before iron-56 could form. Similarly, that we must all face the irreversible process of death, with its massive entropy increase, is traceable to the earliest and largest processes in the universe. In other words, the impermanence and decay found all around us is due to the earliest and most distance process in the universe and its continued expansion.
On a more positive note, irreversible processes are also essential to life. If metabolic processes did not irreversibly transform my lunch, not only would I get indigestion, I would not live. That which sustains me also destroys me. Indeed, time "is a fire that consumes me, but I am the fire."
IV. Comparisons and Connections
As I have said in my recent ruminations[6] about the relationship between physics and Buddhism, it is a mistake to connect any Buddhist principle too closely with any particular phenomena from physics. Physical theories are prime examples of impermanence. What happens if I make an argument that some physical effect verifies some great principle of Buddhism and then the physics is replaced by a new theory? Does that damage Buddhism? Are the foundations of Buddhism to tremble at every scientific revolution?
A more fruitful dialogue between Buddhism and science can occur when comparisons and connections are done at a more philosophic level. For example, here I have tried to focus on emptiness, the philosophic heart of Buddhism, and make connections with questions of comparable philosophic significance in physics. If the connections mutually illuminate both the physics and the Buddhism, without trying to reduce one to the other, then our understanding of both disciplines deepens. In the present example, the erroneous assumption of a thermodynamic system being completely isolated from any form of external interaction was a critical error. This error could have been avoided if the philosophic principle of emptiness were more widely understood and appreciated in the scientific community. Physics is always done in a philosophic context. In the case of classical statistical physics and thermodynamics, it was done within Cartesian dualism. Although Descartes’ vision helped both physics and western philosophy, it has also hindered us in more ways than we can count. I suggest that the principle of emptiness, if more fully appreciated within science, could actually further the scientific enterprise.
What does Buddhism gain from such connections and comparisons as attempted here? I see at least two benefits. First, understanding such things as the relativity of time (the 70 days to harvest example) and the relativity of the present moment helps us appreciate the closely parallel arguments made in the Middle Way about time’s lack of inherent existence. There is a well-known and difficult section in Nagarjuna’s Mulamadhyamakakarika that analyzes time and leads to the modern interpretation, "Time is thus merely a dependent set of relations, not an entity in its own right, and certainly not the inherently existent vessel of existence it might appear to be."[7] Such critical, but difficult, points are illuminated by understanding Einstein’s relativity of time. In short, science can help us understand ancient, but pivotal, philosophic aspects of Buddhism.
Second, Buddhism is a portable religion that has wandered far from the home of the original Prince. In each movement, whether to China, Japan, or Cambodia, it takes on the hues of the local culture without losing its original spiritual impulse. Science is clearly a cultural dominant in the West. Therefore, if Buddhism is to come to the West, in the best and fullest sense of the term, then interaction with science is both inevitable and necessary for a real transplant to take place. The present effort at understanding some common ground and even synergy between Buddhism and science can be part of the effort to translate Buddhism into terms that are easier for a Westerner to assimilate.
V. Summary and Conclusions
Reflecting on the relativity of time and how the irreversible nature of my little friend’s disease connects to the first few minutes of the universe and its continued expansion gives me little comfort. Yes, intellectually these ideas strongly support the principle of emptiness, that both the mother and the little boy along with the one who writes these words lack independent existence. Yes, we are all a system of interdependent relations and thereby subject to the law of impermanence. Nevertheless, the heartache remains. That little boy will be consumed by the "fire of time" before he reaches the age of my two sons.
According to the Middle Way, my inveterate projection of that false quality of independent existence is the foundation for my attachment and consequent suffering. It all comes back to my inability to put these ideas fully into practice. This is often the plight of those who can articulate ideas but not fully live them. Or being kinder to myself, perhaps I have assimilated just enough of the principle of emptiness to give me a deep appreciation of the mother’s sorrow, but not enough to dispassionately see it all as an embodiment of the First Noble Truth, that all experience is suffused with suffering. What then do we do?
The Middle Way advises us to take refuge in the Three Jewels: the Buddha or fully enlightened One, the Buddha’s teaching, and the community of those seeking enlightenment. The Buddha shows that we can do it. We suffering humans, nurtured and destroyed by time, can become full embodiments of wisdom and compassion and break free from the suffering of samsara, the endless torment of repeated death and rebirth. The Buddha’s teaching, which includes emptiness and much more, is the work at hand among those who support our efforts at realizing these great truths—including the mother and her sick child.
If I could reflect deeply enough on the relativity of the twenty years as the maximum allotted to this child and that the very irreversibility of his condition, and my own, is due to deep cosmological connections, then perhaps my sense of connectedness to others and the cosmos could increase. Could I realize more deeply that my ego and yours are dependent, not inherently existent, but fundamentally co-dependent systems of relationships? Could I profoundly appreciate that there is no speaker without a listener, no griever without a dependently related object of grief? If I could, then the centrality of my own ego and my self-cherishing would surely diminish. Such a realization of my ego’s emptiness and our mutual co-dependency must result in compassion, not just for this little boy and his mother, but for all sentient beings. Assimilating these great truths and shifting my ego off center stage is surely not easy, but the promised increase in understanding and compassion keeps me trying.
If I could deeply appreciate that any irreversible process, whether the rotting of carrots or my body, is due to the earliest and largest scale structure of the cosmos, then how much easier it would be to appreciate that my neighbor’s loss or gain is not separate from mine. Then the suffering in one cell of the body of humanity is truly the suffering of all. Perhaps, we could even realize that compassion is actually in our own enlightened self-interest and that the survival of our very planet requires a profound understanding of our co-dependence.
In contrast, we could ask what happens when our philosophic view embraces the false notion of independent existence. The late David Bohm, known for both the depths of his physics and philosophy, said it very directly when he wrote:
It is proposed that the widespread and pervasive distinctions between people (race, nation, family, profession, etc., etc.), which are now preventing mankind from working together for the common good, and indeed, even for survival, have one of the key factors of their origin in a kind of thought that treats things as inherently divided, disconnected, and "broken up" into yet smaller constituent parts. Each part is considered to be essentially independent and self-existent.[8]
According to Bohm, many of the evils of our modern world are traceable to a view where "Each part is considered to be essentially independent and self-existent." In other words, one in which things inherently exist. I tried to show above that, although we commonly assume for simplicity that a system, such as Boltzmann’s box, is independent from its surroundings, such a view misleads us. This is bad enough in physics, but when a race, nation, or person views themselves as fundamentally independent, then the stage is set for calamity—the stuff of our daily headlines.
As we stand on the threshold of ever more powerful theories in science, it is more urgent then ever that we find a coherent world view that can guide our science as well as our moral actions. Consider how the advent of quantum mechanics and relativity brought about the wonders of the information age, along with our horrendous weapons of mass destruction. Then imagine what wonders and horrors might be released by a grand unified theory or "theory of everything" that today occupies some of the best minds in physics. What benefits and horrors can we expect from the revolution already underway to understand the complete genetic code?
I’ll conclude with one small example. Despite it not being "spiritually correct," I enjoy watching professional football on TV. I usually hope for a close game with plenty of action. Occasionally, I find myself rooting for one team. I urge them on to victory, and even try to exert mental influence through my TV set. I catch myself and wonder what I am doing. "Hey, these guys are getting millions of dollars to beat each other up, what do I care who wins?" After a little reflection, I realize that "my teams" are those I have some connection with, even it if is only because they are from the State of New York or I go through the Pittsburgh airport on most of my flights. These flimsiest of connections give me affection and concern for those gladiators.
What would happen if I could more deeply appreciate the profound interdependence implied by the Middle Way? What would happen if I could more deeply appreciate, as more than interesting physics, how the irreversible processes that sustain and destroy my life occur because of my connection to the first few minutes of the big bang and the continuing expansion of the universe? Then how much do my loyalties expand? If I could appreciate that the relativity of time is logically extended to all my subjectivity, then how could I rationally support my selfishness and self-cherishing?
It is overwhelming to think about extending my loyalties beyond a small circle of family and friends to the cosmos. Now that we know of more planets outside our solar system than within, does the Bodhisattva vow of working for the liberation of all sentient beings, embrace even those beyond our solar systems? Surely, experiencing the sadness of more parents and their mortally sick children would crush me. How then can I possibly cultivate compassion on a cosmological scale?
Perhaps the ecological activists can offer guidance. In the face of daunting global ecological problems, they advise us to "think globally and act locally." Following their counsel, I try to keep the cosmological picture in mind and simultaneously act in the present with the person in front of me. Then it seems small ripples of compassionate action gradually flood beyond my little circle of family and close friends. The ideal is to extend our concern out in ever widening radii, until it encompasses more and more of the great suffering body of humanity. If in fact, I lack inherent existence then my present limitations are not fixed, in place for eternity, and I can work toward this ideal. Let us begin to widen the circle of concern beyond the narrow confines of "our team" and "our friends." How else can we live with that devouring tiger of time, that inexorably includes our final irreversible process?
Perhaps because I began writing this paper a few days after my fifty-fourth birthday, while my human and animal friends are gravely ill all around me, my awareness of time has become so acute. Yet anybody inspired by the doctrine of impermanence realizes that reflection on time is central to both the theory and practice of Buddhism. Since the no-self doctrine denies us any refuge in the notion of an eternal soul, as we commonly understand it, there is nowhere to hide from the truth of impermanence. Here I'll review the principle of emptiness in Prasangika Madhyamika, the Consequence School of Middle Way Buddhism so prominent in Tibetan Buddhism, and discuss how it bears on impermanence. Perhaps in the process we can glimpse how reflection on time is a liberating activity that must express itself in compassion.
In modern physics time also plays a central role, yet subjectively experienced or psychological time is not identical to the physicist's conception of time. Psychologically we are very clear about the radical distinction between the past and the future. We try to learn from the past, but these events are unalterable, while those in the future are unknown and the possibility for influencing them is greater. In contrast, in modern physics microscopic processes are entirely reversible--there is no fundamental distinction between the past and the future. Physical processes can run in what we consider the backwards order and not violate any laws of physics. Yet in the world where we and the Buddha have experience, there are clearly irreversible processes on all sides from the rotting of fruit in my refrigerator to the death of stars in deep space, and of course, to the death of loved ones. In our experience, the temporal notions of past and future are not symmetric like the spatial ideas of left and right. In this sense, time is asymmetric--an arrow of time points from the past into the future. Here I'll nontechnically review how modern physicists have dealt with this dichotomy between the symmetric microscopic level with its reversible time and the asymmetric macroscopic level where we are keenly aware of the difference between past and future and where decay and impermanence surround us.
There is no question of physics proving the great doctrine of Buddhist impermanence nor the worldview implied. Furthermore, since physical theories are a prime example of impermanence, it is a guarantee of obsolescence to bind Buddhism or any philosophic view too tightly to a physical theory. What happens when the theory changes? Do the foundations of our closely linked worldview tremble at each scientific revolution? Nevertheless, science is the reigning worldview in modern culture and so there is a demand to ask how a philosophic or religious view relates to this dominant scientific view. In addition, the Dalai Lama is correct when he says in the opening quotation, "there is a growing interest among the scientific community in Buddhist philosophical thought."
Perhaps a fruitful dialogue can develop between Buddhism and science, one that deepens our appreciation of such ancient truths as impermanence and also fertilizes modern physics, which despite its enormous successes, still suffers from serious conceptual difficulties at its philosophic foundations. Of course, if such a dialogue is to be more than merely drawing pleasant parallels between such diverse subjects as Buddhist emptiness and nonlocality in quantum mechanics,[3] then revision of views must occur in both camps. The dialogue must bear fruit in the normal activities of each discipline. Otherwise, it is difficult to imagine how "there will be a great change in our worldview both from the material and the spiritual perspectives." I hope this paper contributes to the developing dialogue between science and Buddhism and makes some small progress toward a cross-fertilization. In the process we may learn how reflections on time can be, as Sir Eddington says in the opening quotation, a bridge between the spiritual and the physical.
II. Emptiness and Time in Prasangika Madhyamika
To begin my brief sketch of emptiness and time in the Prasangika Madhyamika (abbreviated to Madhyamika in this paper), I'll present two little stories and some comments on them from the Buddhist section of my forthcoming book, Synchronicity, Science, and Soul-Making.[4] Let me begin with a story that relates directly to the objective side of Madhyamika emptiness.
Several years ago I was returning graded term papers (worth about one third of the final course grade) and noticed one student was not receiving a paper. "Jay, I have no paper for you. Did you turn one in?" He said, "Oh yes, I submitted it along with everyone else." I apologized profusely and told him it must be in one of my offices. I would dig it out and grade it for him by the next class. (Then I also held the rotating chairmanship of our department and thus had the chairman's office along with my own in which to spread out and create havoc.)
I searched both offices at school and my office at home and could not find the student's paper anywhere. I could even vaguely recall seeing the paper at some time, but it just would not turn up, no matter how carefully I searched. My guilt started eating at me. Writing a term paper of that size is a very big piece of work, especially for someone as careful as Jay, and I, Mr. Chaos, cannot find his paper. "It must be here somewhere!" I vowed to reform my sloppy practices. Meanwhile, I would use this guilt driven opportunity to clean out all three offices in my desperate attempt to find the student's paper. During my search I would get the clear sensation it was going to turn up in the very next pile. I could almost see the title page now. . . . Nothing, no paper, and no evidence for ever receiving it. "How could I lose that paper?"
Defeated, I returned to the student and confessed I could not find the paper. I asked whether he had another copy or an earlier draft. He said that the one he turned into me was the only copy. I apologized again and offered him an additional two weeks to turn his research notes into another version of the paper. Meanwhile, I would keep an eye out for the paper, despite my having lost hope of finding it.
Early one morning while preparing for class, Jay came into my office. He looked like he had not slept for the last two nights. Before I could even say hello he blurted out, "I lied. I never did turn in a paper. I am sorry." I'll skip the long conversation we had and what came of it. That is not the point.
The point is that in my frantic and fruitless search for the term paper I was sure it was around somewhere, and that I would warmly embrace it with a mix of relief and satisfaction when it appeared. My vague image of the paper would be clarified and objectified. When found, the term paper would sit there and accuse me of my stupidity. In fact, my expectations instantly dissolved from the negative realization that the paper never existed and so could never be found. I had expectations and fantasies, but nothing to support them.
My belief in the false existence of that term paper is precisely analogous to the false belief in what the Madhyamika calls inherent or independent existence--the denial of which is their doctrine of emptiness. The major translators and commentators, such as Hopkins[5] and Thurman[6] and Tibetan scholar-monks such as Tenzin Gyatso, the fourteenth Dalai Lama,[7] or Geshe Kelsang Gyatso[8] who teach extensively in the West, use a variety of words to describe what is denied in the emptiness doctrine or the "negatee" as they call it. They use inherent existence (svabhavasiddhi) interchangeably with such terms as independent existence, intrinsic existence, substantial existence, intrinsic essence, or intrinsic self-nature to mean our most innate, unreflective, and pragmatic belief about the way subjective and objective phenomena exist.
We may divide this innate and unreflective belief in inherent existence into two pieces: First, that phenomena exist independent of mind or knowing, that "underneath" or "behind" the psychological associations, names, and linguistic conventions we apply to objects like bell or tree or term paper that something objective and substantial exists fully and independently from its own side. Such objects seem to provide the objective basis for our shared world. Second, these objects are also believed to be self-contained and independent of each other. Each object being fundamentally nonrelational, it exists on its own right without essential dependence upon other objects or phenomena. In other words, the essential nature of these objects is their nonrelational unity and completeness in themselves.
Our false belief in inherent or independent existence is the basis upon which we generate our desires and aversions. As we are taught in the second of the Four Noble Truths, these cravings and aversions, these desires, are what generate the suffering permeating all experience--the first Noble Truth. Madhyamika claims that only when we root out this false belief in inherent existence can we realize our potentiality for Buddhahood, for becoming beacons of wisdom and compassion.
The trouble with the false belief in inherent existence is that it includes a conviction that a diligent search will reveal it clearly before us where we can embrace it. The object's essence, its self-standing nature, will transparently shine forth. But in truth this self-standing nature is no more existent than that term paper. While something inherently existent has never been found in the past and will never be found in the future, the paper eventually did exist--although not the one I was initially seeking, but rather its replacement. (Can we truly replace something that never existed?)
The arguments denying inherent existence are extensive and occupy much of the Madhyamika Buddhist literature on emptiness. Rather than review these arguments in detail, I'll boil these brain-splitters down to their essence. They all amount to showing that inherent existence is "unfindable upon analysis." This means that when you search deeply for the object or subject believed to exist inherently, you come up with no more than I did when searching for the student's paper. Rather than find an independently existent phenomenon, these searches reveal an object or subject deeply and inextricably involved with its surroundings and the searcher, the person doing the analysis. (Any general object or subject can be considered a phenomenon, something we can know.)
The searches never yield independently existent objects, but rather those that are deeply dependent in three related ways. First, all phenomena are dependent upon "causes and conditions" or upon the vast network of causal factors and conditions that make a thing possible. The apple tree outside my window depends deeply upon favorable soil, light, water, disease control. For these reasons it lacks independent existence.
Second, all phenomena are dependent upon the whole and its parts and their relationships. For example, my apple tree depends upon having branches, trunk, leaves, all arranged in some well-defined way that we recognize as a tree. Consider the definition of an intrinsically existent object. Because an independent essence or self-nature must be self-contained and isolatable, by its very definition, an inherently existent phenomenon must be a partless essence. It cannot therefore be distributed over parts or shared between the whole and the parts. Yet, since we can always analyze phenomena into whole and parts, independent existence cannot inhere in them. Although we unreflectively consider inherent existence to be the touchstone of reality, its deep logical inconsistencies condemn it to nonexistence.
Third, and most profoundly, all phenomena are dependent upon imputation or mental designation. We continuously receive an immense avalanche of information that we organize, distill, and coordinate with other experiences. We cut up the seamless rush of experience into units of intelligibility (color, texture, memories, associations). Then we collect these items together and designate or name it a tree. Mind is constructive of its world, the only world we can know. We mentally designate, impute, or name that complex of sensations, memories, and expectations to be a tree. This is part of the mind's normal job. The problem comes when the mind erroneously invests the designated object with the nonexistent property of inherent existence. In other words, we illegitimately project the false notion of inherent existence into phenomena and then suffer the consequences of this projection.
It's quite an extraordinary idea that inherent existence, what we erroneously consider the core reality of an object, is simply nonexistent and furthermore that we falsely invest objects with this nonexistent. Upon that false projection we build our cravings and aversions and keep spinning the wheel of samsara. We must awaken from this ignorance if we are permanently to break out of the realm of suffering.
In truth, all objects exist only as sets of relationships or dependencies--between various objects and between the object and the knower who mentally designates them. No core of self-nature or intrinsic essence supports our names, linguistic conventions, and projections. Nothing exists "underneath" our imputations or mental designations. Objects are none other than dependency relationships and names. In other words, all phenomena exist as a species of dependent arising--dependent upon causes and conditions, whole and part, and mental designation. This view thoroughly denies the mind-matter split of Cartesian dualism, the core of many of our Western prejudices that impede both our philosophic and scientific understanding.
It is natural to ask that if things lack inherent existence, if they are empty, then how can they function? How can an ultimately empty tree bear fruit that we eat? According to the Madhyamika, the very emptiness of independent existence of all phenomena is what allows them to function through their relationships and be sources of help and harm. In contrast, if objects inherently existed then they would of necessity be immutable and impotent, unable to act on us or we on them. Within this ultimately empty but conventionally existent world we must win our Buddhahood and thus they call our world the "womb of the Buddhas." Philosophically we must be able to move back and forth between the ultimate and conventional truth of phenomena.
Next let me turn to the subjective side of emptiness, again via a little story from my book. A few years ago I got the strong urge to go canoeing on a nearby lake. I've always enjoyed canoeing since my childhood and the beautiful late spring day seemed to cry out for it. A friend lent me his canoe and my wife and I were soon paddling along the shoreline enjoying the beauty and peace of nature. We were both extolling the beauties of Seneca Lake and saying how conducive canoeing was to a relaxing and aesthetic appreciation of nature. Suddenly a water skier was heading straight for us at top speed. He veered to the side at the last possible moment thereby completely drenching me and my wife with cold water. Sputtering disbelief, shock, indignation, then rage--all exploded inside me. "That damn kid! If he tries it again, I'll stand up in the canoe and whack him with the paddle! How could he do that to me. . . . to me?!" After a few moments of intense indignation I began to laugh heartily, marveling at how quickly my feelings changed from nature mystic to Attila the Hun, from the aspiring Bodhisattva to bloodthirsty monster. I also guiltily recalled how often Buddhism emphasize the control of anger. For example they say, "How are we harmed by our anger or hatred? Buddha has said that hatred decreases or destroys all our collections of virtue and can lead us into the lowest of the hell realms."[9]
However, the main point here is a philosophic one, rather than a moral one--although in Buddhism they always closely connect. From the philosophic perspective, the Madhyamika notes that right at the height of my indignation there was a clear experience of the I--the one we all firmly believe inherently or independently exists. Certainly I had no concern for "turning the other cheek" or for the doctrine of Universal Compassion or any such pious principles. But the critical thing is the I, the "me" believed to exist independently, standing in bold relief in the light of my indignation.
It is easy to be led astray by the anger in my story, but that is not the point. The important thing is that at these times we can most easily see the powerful sense of I or me. Perhaps another simple example will make this clear. Imagine an academic who is wrongly accused of some gross form of plagiarism. His shock and disbelief will quickly turn to indignation. "I would never do such a thing! I am scrupulously honest about that sort of thing," he might exclaim. Right at the height of his indignation there is a very strong sense of an I, one unjustly accused, honest, and thinking frantically how he can clear his good name.
This I or me that we instinctively believe inherently or independently exists is thoroughly denied in the doctrine of emptiness. The Madhyamika also goes well beyond denying this coarse or low level of the ego. That is just the beginning of their no-self doctrine. They claim that any identifiable level of subjectivity is empty of independent existence. Tenaciously clinging to the false belief in an independently existent subject or a self is the primary cause of our suffering, of our bondage to samsara.
For the Madhyamika, belief in inherently existent objects and subjects is the taproot of the pervasive suffering mentioned in the Four Noble Truths. Falsely believing that objects or subjects inherently exist, we ascribe more attractiveness or unattractiveness, generate more craving or aversion, to them then they actually deserve. Upon this foundation of the false belief in inherent existence we build all our emotional attachments, our chains to samsara. These attachments drive us endlessly toward or away from objects and people. We compulsively quest after or flee from objects we falsely believe inherently exist.
We may think inherent existence provides us with our most fundamental reality, but this belief in an inherently existent subject or I, this "self-grasping," is the millstone dragging us to the bottom of the ocean of samsara. This self-grasping leads directly to pervasive egotism, self-love, or "self-cherishing," that is putting our own concerns and desires before all else. Philosophic views, whether conscious or not, always have powerful consequences: wrong ones lead to suffering, correct ones to liberation or enlightenment. Because this false conception of inherent existence is the root of suffering, it must be pulled out, painfully extracted.
Of course, it is no easy matter to deny inherent existence in all objects and at every level of subjectivity. We have the great danger of a largely imaginary view of our attainment and only fattening our ego rather than realizing it as empty. Therefore, a competent guru or spiritual guide is usually a necessity when attempting to realize emptiness.
The denial of inherent existence does not mean that objects do not exist (the extreme of nihilism). They surely have a conventional or nominal existence and they function to provide help and harm, but they totally lack independent or inherent existence. They formalize this idea in the doctrine of the two truths. From the ultimate point of view, all subjective and objective phenomena are totally lacking in independent existence or in their own self-nature. This is the Ultimate Truth--that emptiness or selflessness of phenomena is their highest quality, their most profound nature. However, from the everyday realm of action, commerce, and spiritual practice, objects have a conventional nature. They function; they are efficacious and must be dealt with on this level. For example, ultimately, Tibet is totally without inherent existence; nevertheless, when discussing its political future and that its citizens have suffered mightily, then we are to treat it as people conventionally treat things in the world. Ultimately all phenomena are empty of inherent existence, yet in practical or conventional living we must treat them with the respect conventionally granted such objects. However, always keeping their emptiness in mind, we do not become slaves to our attachments--whether to a country or a person or our own life.
With this sketch of emptiness, let me briefly comment on impermanence. As I mentioned above, if things inherently existed then they would of necessity be immutable and impotent, unable to act on us or we on them. But the ultimate truth of objects is their emptiness, their lack of inherent existence. Objects exist conventionally and are effective in the world of action because of their relationships and interdependence with other objects and the knower. That the apple exists in dependence upon its whole and parts, causes and conditions, and on our mental designation or naming is what makes it an edible fruit, what allows us to experience it and be nourished by it. More important for impermanence, these very defining relations and co-dependencies and their continuously shifting connections with each other guarantee that all objects and subjects are impermanent, ceaselessly evolving, maturing, decaying, and transforming. In short, emptiness and impermanence are two sides of the coin of existence and therefore transformation and change are built into the core of all entities, both subjective and objective.
III. Asymmetric Time in Modern Physics
1. Symmetric time at the microscopic level
Imagine a pool table with a video camera mounted on the ceiling above the table and pointing down. Now make a video of a ball bouncing off a cushion at any angle. Then run the video backwards and notice that if we are not told the conventional order of events we would have no way to distinguish the usual order of events from the reversed order. This follows because no laws of mechanics are violated in this reversed collision of the ball with a cushion. Here is an example of a time symmetric process--a process that looks the same or obeys the same physical laws whenever the time order of events is reversed.
Let's make a video of the more complicated example of starting the pool game by shooting the cueball at the initial triangular array of balls. In this more complicated set of interactions the balls collide off each other and the cushions and some go into the pockets. Now if we ran this video backwards, it would be easy to tell it is being run backwards because we know quite well what a cueball does when it strikes the rack of balls. Nevertheless, all these complicated motions are still time-symmetric. If by some elaborate contrivance we launched each ball with its reversed velocity just after the break, then the balls would execute a complicated series of collisions, form into a perfect triangle, and eject the cueball back toward its starting point. Now if this contrived video were run backwards then a viewer would see it as just the normal break that begins a pool game--nothing special--even though it is actually a time reversal of the normal break. Such are the consequences of time-symmetric or time reversible laws seen throughout all physics at the microscopic level.[10]
However, if someone cracked an egg on the pool table, then a reversed video in which the spread out egg pulls together and fits itself back into the shell would be easy to spot as a fake. Nobody could reverse such a video and confuse the viewer about the correct time sequence. To understand this obviously asymmetric process, one with a clear "arrow" pointing from the past to the future, one built upon time-symmetric underlying laws, we must study more complicated systems than a few colliding balls. We need to understand a little modern statistical physics.
2. Understanding Time Asymmetry in Statistical Physics
The modern discussion of how we could understand the obvious asymmetry of time when the underlying laws are symmetric began with Ludwig Boltzman in the late nineteenth century. He was deriving the laws of thermodynamics, the laws governing the steam engine and the energy conversions at the heart of the Industrial Revolution, from the statistical properties of gases governed by Newton's Laws of mechanics--from statistical mechanics. Boltzman and others developed a precise notion of entropy as a measure of disorder. The greater the disorder in a system, the greater the entropy. Thermodynamics has the famous Second Law, which states that all systems isolated from their environments have a constant or increasing entropy. (The meaning of "isolated" will become clear below.) An important consequence of this Second Law is that any energy generation process must create some entropy. It cannot be 100% efficient. What is more, entropy increase always corresponded with the usual direction of time, the asymmetric distinction between the past and the future. Thus, if we can understand what entropy is and why it always increases with time, then we can understand how time-asymmetric process arise from the underlying symmetric laws.
Figure 1. Gas confined to half the box.
In preparation for the simple and elegant ideas that began with Boltzman let me briefly discuss the seating of patrons in a movie theater. Imagine a theater in which an aisle divides the seats such that half are on the left and half are on the right. Consider the case when the patrons occupy only half the seats--those just on the left. Even with all the patrons sitting just on the left, there are many different ways of seating individuals. Let's call each distinct way of distributing individuals in seats a microstate. To be general we'll not be constrained to seating people next to their friends. Even in a small theater many microstates are possible that satisfy the constraint of only filling just the seats on the left. For example, just interchanging the seating of any two patrons gives another distinct microstate. However, if we allowed the same number of people to sit anywhere in the theater there would be a much larger number of available microstates, since there are many more possible ways of getting the patrons seated when the entire theater is used. In my idealized example, each acceptable microstate is equally likely. My ideal patrons are neither concerned with whom they sit nor where they sit in the theater. They randomly distribute themselves in the seats and thereby make each acceptable microstate equally likely of realization. Given the equal probability of any microstate and the overwhelmingly greater number of microstates available when we permit seating on both sides, it is exceedingly unlikely that all the patrons would be found sitting on just one side. With these ideas we are now ready to understand some statistical physics of the gas in the box we were just considering.
Figure 2. Evenly diffused gas.
We can enumerate the total possible number of ways, or microstates, for which individual particles could distribute themselves in half the box and keep the energy fixed. For any significant amount of gas this will be an enormous number of microstates. For example, for just two grams of hydrogen gas there are 6.02217x1023 hydrogen molecules (H2), so there are an immense number of ways to arrange the gas in half the box with the required energy. The greater the number of acceptable microstates the greater the entropy, since the less we can specify about the state (which microstate it is in), the greater the disorder, the greater the entropy. Just as in the movie theater, we know that each acceptable microstate is equally likely of realization, of being the microstate that actually obtains at a given time. Now remove the partition between the halves of the box. Since there are many more microstates compatible with being in both halves of the box and each microstate is equally likely, then it is vastly more probable that the gas will be evenly distributed throughout the box as in Figure 2. (This is completely analogous to my idealized movie patrons.)
In summary, the overwhelmingly greater number of microstates for the gas occupying both halves of the box instead of only half and the equal likelihood of each microstate guarantees the overwhelming improbability of ever seeing a gas spontaneously arrange itself in just half the box. Since the states with the gas evenly distributed throughout both halves is more disordered (we can specify less about the gas location) entropy increases. This direction of entropy increase after removing the partition corresponds to our usual sense of the arrow of time. That is, in isolated systems entropy increases with what we consider advancing time.
For many years I followed the text book of choice for a junior-senior level course in statistical physics and thermodynamics and presented, with appropriate mathematical detail, the above argument to my students for why entropy should increase and why time has the observed past-future asymmetry. Unfortunately, I recently found that the argument is wrong! The basic problem is how from the dynamics of many particles undergoing time-symmetric motion do you actually get time-asymmetric motion? Let's return to the theater to illustrate the point.
Imagine another movie theater, samsara cinema. Here start with all the patrons sitting on the left and allow them to follow their whims for moving around. Perhaps the guy next to me is spilling his buttery popcorn all over me or the kids behind me are squirming around too much. I move to avoid them. Likewise for everybody else. However, in samsara cinema, although everybody can choose new seats and move to them, they never sit down. As soon as they move to another seat they find it not to their liking and move to a new one without sitting--samsara is a restless condition. There is thus constant motion from one seat to another. Then a full characterization of a microstate after the start of moving around gives each person both a location and a velocity.
Consider the initial microstate, S0, with everybody on the left (the low entropy one). After an arbitrary time a state S1 is generated with people spread throughout the theater (a higher entropy state). For each S1 there is another microstate, which is equally likely, call it, S1*, with everybody in the same location, but with their velocities reversed (all velocities vectors, V, changed to -V). Assuming reversible interactions for movie patrons (a patently false assumption), these velocity reversed microstates will, in whatever time it took to generate them from S0, result in the original condition with everybody on the left. Each velocity reversed patron simply retraces their steps and gets back to their original position. This must follow if we assume that all patrons move and interact only with time-symmetric dynamics. If we translate this argument to Boltzman's gas we see that after a very short time (the particles move and interact quickly) there is a significant probability of the particles being in just half the box as in Figure 1. So the original argument for entropy increase and time-asymmetric processes collapses in a heap.
Physicists have good reasons for being deeply committed to the Second Law of thermodynamics and controversy surrounds the details of the proper argument for entropy increases. However, in the last four decades the main issues have become clear.[11] We now understand that the whole notion of a system permanently and completely isolated from its environment is the root of the problem. (Are the Madhyamika grinning?) We now realize that we must account for how the box got into the low entropy state of all particles in just one half. This did not result from just waiting a long time for random motions to throw the gas all to one side, but from some lab technician evacuating one half and placing gas in the other. This preparing the box in a low entropy state must generate more entropy elsewhere in the universe. For example, the technician consumed calories from rice and tofu and radiated energy from herself and her equipment that eventually went into deep space. In other words, the box had its entropy put into a low condition by processes outside itself, but at the expense of a much greater entropy increase elsewhere in the universe.
As we have long known, the energy emitted into space from her activities can only radiate into outer space because the universe is expanding. If the universe were not expanding then any line of sight when extended far enough would land on a star surface. Then the effective temperature of deep space would be that of the surface of stars. Then space would typically have a temperature comparable to the surface of our sun (5800 °K) rather than the 3 °K it actually has. Since entropy can only increase when energy moves from high to low temperature regions, the simple process of radiating our body's energy into space would be blocked in a static universe. Thus the technician could not locally reduce the entropy in the box by generating more entropy elsewhere in the universe--unless her body temperature were higher than the average temperature of the surface of stars!
All systems organizing themselves or decreasing their entropy, whether it is the growing of a soy bean or the crystallization of a snowflake, are decreasing entropy in one location that must be made up by a greater entropy generation in another. Not only is the energy from the technician's food and her equipment eventually traced back to our sun, but the sun's low entropy is critical. Energy generation processes, whether the digestion of our food or the workings of a nuclear power plant, are totally dependent upon our solar system being in a low entropy condition. What causes the sun and other stars to be in a low entropy condition? This occurs because the expansion of the universe was faster than the nuclear generation rates in the first three minutes of the big bang. This means that in the first three minutes of the big bang, when nearly all the helium (about 25% of the total mass in the universe) was formed, the universe expanded so quickly that after three minutes it was too cool for nuclear reactions to occur. If the expansion and cooling were much slower then all the matter in the universe would form into a very stable isotope of iron, an inert and high entropy condition. Then the stars would not shine, there would be no great entropy gradients in the universe, no time asymmetry, and, of course, no life as we know it.
Local time-asymmetry, such as the decay of any biological system, including our own bodies, must be accounted for by connecting it to the expansion of the universe. This extraordinary result has many technical twists and turns, but the central idea is clear: increasing entropy and time-asymmetry owe their existence to the largest and earliest processes in the universe and its continued expansion. This is a long way from the notion of an isolated and noninteracting system, so abhorrent to a Madhyamika. In this way, when you pour milk into your coffee and the mixture comes to the same temperature and a higher entropy than when the fluids were separated, you are profiting from the universe's expanding and cooling before iron-56 could form. Similarly, you can trace the decay of your tooth, and the resulting entropy increase, to the earliest and largest processes in the entire universe. (You thought it was all about flossing!)
IV. Summary and Conclusions
While I was completing the section above on Madhyamika emptiness-impermanence, Leo, the best dog I ever had, died. Of course, it is a small loss compared to losing a loved one. Nevertheless, here in the womb of the Buddhas this sorrowful loss drives home again the asymmetry of time, the reality of impermanence. There will be no more long walks in the woods with Leo, no more enthusiastic greetings after a long day at work, no more solace from an affectionate friend. The future holds out the possibility of another dog, but Leo is irreversibly gone. I outlined something of the Madhyamika idea of emptiness-impermanence, which shows how the emptiness of all phenomena, their lack of independent existence, implies that they must exist though continually changing relationships, co-interdependence with their surroundings and the knower. My playful wrestling on the floor with Leo and my sons, Leo's stealing our socks, the wild chases though the house to retrieve them that Leo so loved, defined us all, made us who we are. Ultimately Leo is only a complex set of relationships, of actions and reactions, of history, psychological projections on those beautiful sad eyes, or reactions of disgust at the body parts of wild animals dragged into the yard. Although I know (intellectually) that the lack of independent existence in all things, emptiness, implies impermanence, I inveterately impute inherent existence on Leo and build my attachments and aversions on that false imputation, that false projection. Not only does this false attribution of independent existence chain us to the wheel of samsara, but it also is the basis of our self-cherishing, our egotism, and our inability to act compassionately.
I also sketched above how, according to modern physics, the very connection that each object has with the earliest events in the universe and its present largest scale expansion guarantees the Second Law of thermodynamics, the inevitability of increased entropy, disorder, decay, and time-asymmetry from underlying time-symmetric laws. From the Madhyamika point of view, this extraordinary result beautifully illustrates how emptiness, the deep dependency and interrelatedness with the universe, brings about impermanence. In retrospect we can see that assuming systems, such as the box of gas, have an isolated existence, free from interactions with its environment, led us astray and prevented us from understanding how time-asymmetric processes could ever result from underlying time-symmetric laws. Perhaps if Madhyamika emptiness inspired the physicists working in statistical mechanics, they would never have made this assumption and the progress of statistical physics would have been more rapid.
We always pursue science within a matrix of philosophic and cultural beliefs--not all of which are helpful for its progress. I believe there are other areas in physics, especially the conceptual foundations of quantum mechanics, where inspiration by Buddhist philosophic principles might also be fruitful for the development of physics. On the other hand, reflecting on some fundamental topics from modern physics can enliven and deepen our understanding of Buddhist principles. Certainly more effective examples from modern physics can illustrate Buddhist principles than such quaint notions as "sweaters made of turtle hair."
Yet, however beautiful the parallels and fruitful the synergy between pivotal Buddhist doctrine and modern physics, we clearly cannot fall into the trap of binding them too tightly. Physical ideas and theories are evanescent and so we should not link any philosophic view too tightly to them, otherwise the next scientific revolution will make all our efforts obsolete. On the other hand, I applaud the Dalai Lama when he says that if scientific analysis convincingly refutes a core Buddhist position then Buddhism must give up the view. For example,
Buddhists believe in rebirth. But suppose that through various investigative means, science one day comes to the definite conclusion that there is no rebirth. If this is definitively proven, then we must accept it and we will accept it. This is the general Buddhist idea.[12]
Such a nondogmatic attitude that is open to revising even the most sacred beliefs of Buddhism is obviously appealing to modern Westerners.
Perhaps even more important than a potential synergy between Buddhism and physics is the possibility that through reflecting deeply upon the great truths of emptiness-impermanence, we will increase our compassion. In this day of rampant nationalism, fundamentalism, and zeal for tax cuts rather than securing a quality life for all, we could use more compassion. If, as physics claims, our distinction between past and future, the increase of entropy all around us, is dependent upon the first three minutes of the universe and its continuing expansion, how much more are we deeply related to all inhabitants on "spaceship earth?" If my interrelatedness to persons in the ghetto or a refugee camp is as profound as the doctrine of emptiness maintains, then suffering in one part of the great body of humanity affects us all. As the Dalai Lama puts it:
Each of us has responsibility for all humankind. It is time for us to think of other people as true brothers and sisters and to be concerned with their welfare, with lessening their suffering. Even if you cannot sacrifice your own benefit entirely, you should not forget the concerns of others. We should think more about the future and benefit of all humanity.
Also, if you try to subdue your selfish motives--anger, and so forth--and develop more kindness and compassion for others, ultimately you yourself will benefit more than you would otherwise. So sometimes I say that the wise selfish person should practice this way. Foolish selfish people are always thinking of themselves, and the result is negative. Wise selfish people think of others, help others as much as they can, and the result is that they too receive benefit.
“You often hear cosmologists say that the Big Bang is the moment when space and time began, there’s no such thing before the Big Bang. The truth is the Big Bang is the moment where our understanding ends. We don’t know what happened before the Big Bang, but it’s absolutely possible that something did.”
So says Caltech theoretical physicist, Sean Carroll. Carroll’s proposal that there once was a realm of space and time that preceded our universe’s Big Bang is part of a cosmological model first toyed with by theoretical physicists, including Einstein, in the 1930s. It is known as the Cyclic Model or Oscillatory Universe. A basic form of the theory posits that the universe we live in is one component of an interconnected, dual system of bouncing universes. The first begins with a Big Bang and expands for a period of time. Upon reaching some thermodynamic limit of expansion, it then experiences a “Big Crunch”, as the universe begins to shrink back toward a singularity. This force then propels the Big Bang of a second universe outward in the “opposite direction”, and the cycle continues back and forth perpetually. Within this framework, a Big Bang can therefore be defined as the event after a period of contraction and before a period of expansion. Furthermore, our universe may be the first, sixth, billionth, or some infinite number universe to exist in this cycle.
Let’s consider what exactly is meant by a universe sprouting in the “opposite direction” of our own. This directional plane is best conceptualized not as direction in physical space, but rather, as direction in time. Thus, one universe exists in the realm of “forward” moving time, and the other in the realm of “backward” moving time. Of course, these terms are completely relative, which is why they have been placed in quotations. The Cyclic Model therefore paints a universe perfectly symmetrical in time. Astonishingly, this so-called “time symmetry” or “time parity” offered by the Cyclic Model theory better reflects what the laws of physics say about time than the more widely accepted and standard Big Bang theory does.
The Big Bang theory, along with our own intuitive observations of the world, suggests a reality that is controlled by a relentless, unilateral arrow of time, moving in one direction and one direction only—forward. We cannot turn back the universal clock to reverse a glass cup falling to the ground and shattering, having the tiny pieces of broken glass return back into our hand to reform the whole. It all seems very obvious. Yet, many of the most important and fundamental laws of physics exhibit time-symmetry, working equally well regardless of time’s direction, and suggest that the master clock we perceive may be an illusion.
In addition to resolving the time problem, the Cyclic Model also allows physicists to circumvent the troublesome conditions of the singularity theorized to be the origin of the Big Bang. The singularity is a point of zero volume and infinite density, and at it the current laws of physics break down. Barring a major advance in a quantum theory of gravity, we have no tools with which to understand it, which may suggest that the phenomenon isn’t actually physically realizable to begin with.
So the Cyclic Model has its group of legitimate supporters in the scientific community, and continues to gain credibility, at least as part of a larger and more complex Multiverse theory. But such a conception of reality existed long before Einstein and others, guided by reason, ruminated about it in the 1930s. Since before the seventh century CE, a cyclic universe has been described by the cosmology of Tibetan Buddhism, bearing striking similarity to the candidate theory developed today by modern physics. A passage from Professor of Buddhist Studies Reginald Ray’s “Indestructible Truth” provides a succinct overview:
“The life span of the worlds is called a great kalpa and is divided into four. In the kalpa of creation, the worlds come into being; in the kalpa of duration, they have their life and support sentient beings; in the kalpa of dissolution, they are destroyed in a final conflagration; in the final kalpa, there is nothing but empty space. Then the entire process of manifestation begins again. The process of creation, duration, and destruction goes on and on, repeating itself ad infinitum throughout endless time.”
The analogy to the scientific terminology of universal progression, from Big Bang to period of expansion to Big Crunch to period of contraction, all within an eternal, timeless reality, is just about perfect. Even the physical details accounting for cause of the process in both frameworks resemble each other. Unlike other spiritual belief systems, for example, Hinduism, which attributes the cycles of the universe to the supernatural interaction of deities, Tibetan Buddhism explains the oscillations as a result of natural processes. It describes five particles—earth, water, wind, fire and space—that conglomerate and disassociate in a systematic fashion when a universe forms or is destroyed. We’ll start with the stage of emptiness, in which there are only space particles. When a sufficient amount of karma has accumulated from the sentient beings of the previous universe, the space particles begin the creation stage, allowing air particles to coagulate to form “wind”. Then fire particles join to make “lightning”, causing water particles to bond and create “rain”. Finally, the resulting “rainbows” herald in the joining of earth particles. After a duration period, the particles come apart in the period of dissolution, and result once more in the emptiness defined only by space particles.
A strong analogy can be drawn between “wind”, “lightening”, “rain” and “rainbows” and modern scientific terminology used to describe the events after the Big Bang, such as the initial clouds of randomly drifting matter (wind), the forming of electromagnetic fields (lightning) and the other fundamental forces, the particles shot off into space from dying stars (rain), and the eventual conglomeration of cooled matter to form planets (earth particles/rainbows).
Whether these similarities are purely coincidental or indicative of something more significant is left for personal speculation. However, it is becoming more and more evident how eerily the findings and predictions of modern physics are beginning to coincide with long-established beliefs of the Orient. For a seminal text on this topic, check out “The Tao of Physics”.
