Tuesday, November 13, 2012

Time and Impermanence in Middle Way Buddhism and Modern Physics


Time and Impermanence 
in Middle Way Buddhism and Modern Physics
Talk at the Physics and Tibetan Buddhism Conference
University of California, Santa Barbara January 30-31, 1998
Victor Mansfield: vic@lightlink.com ]
Department of Physics and Astronomy
Colgate University Hamilton, NY 13346

Time is the substance I am made of. Time is a river which sweeps me along, but I am the river; it is a tiger that devours me, but I am the tiger; it is a fire that consumes me, but I am the fire. - Jorge Luis Borges [1]

I. Introduction

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 (PrasangikacarrotMadhyamika, which I abbreviate by Middle Way) through a little story. Nearly thirty years ago a very holy man gave me some fresh carrot juice to drink. What a tasty elixir! I returned home determined to grow some fresh carrots of my own on our little farm. (Actually, I was determined to get my wife to grow them.) However, the soil in my part of the world is heavy and stony, and the carrots that first year were stubby and misshapen. I thought, "If only I had a garden tiller, I could whip that heavy soil into the most beautiful carrot bed." I could not afford one of those fancy tillers that a delicate ten-year-old girl can operate with one hand. My rototiller is a test of my manhood, a bucking bronco requiring strength and stamina. Of course, time destroys both people and equipment, and my tiller soon suffered from a long list of woes. It requires the patience of an advanced Bodhisattva to start, it only works at the deepest setting, it no longer has a reverse, and it cannot run in place and so bolts ahead . . . when you can manage to start it. However, I only use it a few hours a year, so I suffer with it and consider it a perverse sort of challenge.

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--------------------I
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 ----------------
Now imagine the following experiment illustrated in Figure 3. We just patiently monitor the system until its entropy spontaneously drops to the value S1 or below at a time t1. If we choose S1 low enough, this could take a long time. The virtue of choosing a small value of S1 is that once it occurs, we know we are very likely to be near the bottom of a dip in the entropy curve, rather then part way down a larger dip. This is simply because the even larger dips are so much less likely. At t1, when the low entropy, S1, occurs, since we are very likely at the minimum of a dip, an increase in entropy with time happens in either direction. At time t1 + e , where e is some small time interval, the entropy increases. We consider this the future. However, the entropy also increases in the past at t1 - e . Therefore, the symmetry of the underlying laws of physics gives no directionality to entropy increase or time.

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?

Acknowledgments
It is a pleasure to thank Professor B. Alan Wallace of the University of California at Santa Barbara for inviting me to present these ideas. As always, I offer special thanks to my consort, wife, and best friend, Elaine Mansfield, for her careful reading and suggestions for improvement on an earlier version of this manuscript. I warmly thank Devon Cottrell and Andrew Holmes of Carmel, CA for several useful comments and  encouragement on an earlier version of this paper. I offer my deep gratitude to His Holiness the Dalai Lama for encouraging the dialogue between Buddhism and Science and showing the power of wisdom and compassion in action. Finally, I offer my deepest gratitude to the late Anthony Damiani, founder of Wisdom’s Goldenrod and great exponent of dharma in many forms, who ignited our desire for some personal realization of wisdom and compassion.
  1. Borges, Jorge Luis, Labyrinths, selected stories and other writings, "A New Refutation of Time," Eds. D.A. Yates and J.E. Irby, New Directions Books, New York, 1964, p. 234.
  2. Gyatso, Kelsang, Heart of Wisdom, Tharpa Publications, London, 1986, p. 29.
  3. The time interval , where D t0 is the rest frame value (70 days in our example) and v/c is the relative velocity between the system and the observer divided by the speed of light, c.
  4. Mansfield, Victor, "Time in Madhyamika Buddhism and Modern Physics," The Pacific World
    Journal of the Institute of Buddhist Studies, Volumes 11 & 12, 1995 & 1996, p. 10.
     Available at http://www.lightlink.com/vic/time.html
  5. Davies, P.C.W., "Stirring up Trouble," in Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, England, 1994, pp. 119-130.
  6. Mansfield, Victor, Synchronicity, Science, and Soul-Making, Open Court Publishing, Chicago, 1995 and "Time in Madhyamika Buddhism and Modern Physics," see reference 4.
  7. Garfield, Jay, The Fundamental Wisdom of the Middle Way, Oxford University Press, New York, 1995, p. 257.
  8. Bohm, David, Wholeness and the Implicate Order, Routledge, & Kegan Paul, London, 1983, p. xi.



中觀佛教和量子力學:對話的開始

 (2009-09-27 09:29:46)

維克多·曼斯菲爾德 

 獨立於我們人類之外存在著這個巨大的世界,它在我們面前像是一個巨大的、永恆的謎團,但我們至少可以部分地檢查它。 ——阿爾伯特·愛因斯坦

一、導言

 在上述引言中,代表著經典物理學傳統頂峰的愛因斯坦,表達了他經常重申的對獨立的、客觀的世界的信仰。從一開始,量子力學就否定具有獨立於測量的確定屬性的客體,因此愛因斯坦總是發現他在反對自己協助創立的學科的基礎。他最著名的異議——EPR悖論,引發了一場關於量子力學的基本原理和物理世界根本性質的曠日持久和精力旺盛的爭論。多虧了約翰·貝爾在理論上的和Aspect等人在實驗上的出色工作,愛因斯坦的質問發展成了Abner Shimony稱為「可訴諸實驗的形而上學」的可能性。我們第一次能夠用現代實驗來真正解決重要的哲學問題。
既然發生在這場物理學基礎的巨大風暴所吹起的塵埃已開始落定,我們可以更加全面地理解這一實驗的哲學意義。我將不去關注實在論與量子力學的話題,這方面已經寫了如此多的內容。儘管在量子力學中有反實在論的傾向,然而量子力學現在似乎與經適當修正的非還原論的實在論是可以相容的。我將關注量子力學中有關不完備性和非局域性的論題,而不是實在論,在前一方面已有可靠的理論和實驗工作。這一工作令人興奮之處在於,感謝由愛因斯坦所引發的質疑,我們可以通過實驗來研究獨立於量子力學方程的完備性和局域性的哲學問題。Aspect等人所發現的對貝爾不等式的實驗否定,告訴我們的是關於世界的信息,而不僅僅是有關量子力學目前的方程。

 伴隨著物理學基礎方面的變化,部分地是由於西藏佛教徒進入西方,西方對於中觀佛教哲學內容的興趣也在迅速增長。感謝許多學術成就,尤其是Jeffrey Hopkins 和Robert Thurman的學術工作,具緣中觀派——藏傳佛教許多人認為是佛教思想的頂峰——的哲學原理,現在正被用西方語言在從未預想過的細緻程度上討論著。儘管對中觀的興趣與日俱增,我仍然同意David Loy的估計:「考慮到中觀的歷史意義,西方對中觀瞭解如此之少,真是一種思想的恥辱。」

 本文試圖利用中觀研究的最近發展,並利用同一時期量子力學哲學基礎上的澄清。我將把空性的核心教義和物理學中目前關於不完備性和非局域性的觀點進行比較,然後把中觀原理應用於對後者的理解。我要顯示,在空性的中觀概念與對貝爾不等式的實驗否定和量子力學的基本原理之間存在緊密的聯繫。我希望這些比較和應用,能夠激勵在量子力學的哲學後果和關於解脫的古老教義的現代研究之間的對話。第2節討論中觀佛教中的空性,尤其是從具緣中觀派的角度。通過嚴守當代西藏人關於具緣中觀派的觀點,——它主要是依據宗喀巴的解釋——我希望能避免目前關於早期中觀的激烈爭論。第3節簡述貝爾不等式的哲學背景。第4節和第5節給出一個批判性實驗的非技術的、然而是基本的討論,它顯示貝爾不等式的基本哲學內容。在此基礎上,第6 節作出比較和應用。第7 節包括概述與結論。

 最近的一些文章和專著,雖然其導向和焦點與本文不同,也都在現代物理學和佛教之間進行比較。為了盡量加強本文的可讀性,我只要求讀者具有最少的物理學背景知識,並給出中觀理論的相當詳盡的框架。

二、中觀佛教的空性

 佛教主要的興趣在於將有情從無窮無盡的生死輪迴(sansara)的無明和煩惱中解脫出來。正如一名好的佛教醫生一樣,具緣中觀派行者首先診斷出解脫的主要障礙——對固有存在的信念。然後他開出治療這種瘟疫的處方——空性的哲學教義。在本節中我要簡單描述具緣派治療者眼中的病症和治療方法。

 具緣派聲稱,不管我們可能會主張什麼樣的思想立場,當我們檢查我們在生存壓力下的行為時,我們就會發現一種堅固的信念,相信客體和主體是根源其自身而存在的,是獨立存在的,是象顯現出來那樣存在的;這些通過分析可以是發現的。(例如,假使一位學者的同行指責他剽竊抄襲,而他實際上是清白的,那麼似乎是固有地存在的「我」就輪廓鮮明地站出來了。)獨立於與其它客體關係或認知活動而存在著的客體,內在地非關係的客體,源自於自身存在的客體,——這些對於除了深悟空性者之外的所有人來說都是實在的本質。這些描繪存在的不同方式,被交替地用來刻畫具體的、獨立的實在的原則,這種實在我們誤認為是瀰漫在我們生活中的。從這些哲學錯誤中產生了一連串的煩惱和局限,因為我們過高地估計了表面上非聯繫的和固有的存在客體(也包括了我們自己的心靈和心靈狀態),將超出它們所包含的快樂和痛苦賦予它們。因此我們在煩惱的輪迴中追求或逃避這些客體。

 通過全面吸收終極真理——具緣中觀派空性的教義,可以醫治這種疾病。這種醫治使我們轉變成佛陀——徹底落實普遍慈悲教義的治療者,主要是為了其它人的緣故已獲得了解脫。具緣派通常使用三種力量逐漸增強的論證方式,來確立現象缺乏固有存在或現象空性,它們分別是:現象對原因和條件的依賴、整體與部分的關係、現象對心靈命名的依賴。建立這些依賴的方式,具緣派可以把緣起與缺乏孤立同一性等同起來(空性就是獨立的和固有的存在的缺乏)。現象缺乏固有存在,或者說它們的空性蘊涵著緣起;反之亦然。為表達這些觀念,我選取普通客體並分析之,它與經典的路線並非完全一致,但與之相容。在下面的段落中,我把在前一篇文章中的分析進行修改和擴展。

 設想一棵蘋果樹生長在我的窗外,並且為小鳥、蜜蜂和主人所珍視。有什麼能比這棵樹更算是固有的存在?當然它依賴於許多原因和條件,如肥沃的土壤、氣候和樹的栽培與嫁接。但是這些形式的依賴,似乎都沒有奪走樹的獨立存在。是的,我宣稱擁有它,我的孩子攀爬它,但是這些聯繫的屬性,對於其作為獨立存在的真實本質似乎是相當外在的或者偶然的。

 樹由樹幹、樹根、樹枝、樹葉和樹皮等等組成。中觀宗主張,樹既非這些組成部分本身,也不是所有這些部分的總和。但是,儘管存在整體和部分的複雜的內在關係,普通人還是毫不懷疑,作為獨立實體的樹,可以在其組成部分和相互關係中找到。

 當風兒輕輕吹動樹葉時,我的狗所聽的頻率比我聽到的要高,而享受花蜜的蜜蜂可以看到我所看不到的紫外線,但是卻看不到這些花朵後來所變成的蘋果的紅色。我們的感官機能對樹的表象當然有所貢獻。但是我們仍然堅定地相信存在一棵「真正的」樹——一棵獨立的、非關係的、固有存在的實體,它是這些感覺屬性的基礎,並且可以解釋我們共同具有的樹的經驗。讓我們仔細檢查這一「實在的原則」——這種固有的存在。

 對於一個在一段給定時間內固有存在的客體,在這段時間的任何時段中都應當是同樣內在存在的。客體在任何間隔(不管長短)都完全是其自身。按照佛教徒的觀點,時間的瞬間被當作是原子式的,沒有內在的轉變或改變。時間的轉變或時光之流就是瞬間的相繼。

 固有的存在是一種基本的屬性,一定是不受任何限制地永遠適合於對像全體的。既然對像在任何時刻是完全充實的和自足的,按照定義,該對像在任何時刻與在任何其它時刻的任何其它對象都沒有內在的和基本的關係。因為內在存在的對象與其它時刻都沒有基本的關係,而同時又延續了不止一個時刻,它必定是內在的無變化的,既不可能產生變化,也不可能接受變化。它是不受影響的和不能產生影響的,封閉在其永不改變的自性之中。任何內在存在的固體必定會凝固在永恆之中。

 分析據認為是沒有空間關係的對象,也可以進行類似的論證。它們在一個限定的空間範圍中也一定是完全地和自足地存在,和與其它範圍的相互作用無關的。正如基於時間的論證一樣,這一不可避免的推理導致無法接受的孤立化和不變性。

 對內在存在的非理性和根深蒂固的信念蘊涵了內在的無聯繫的實體。這種實體一定是自然的活力所無法觸動的,因此不能變化,沒有相互作用,也不能成為知識的對象。這種無聯繫的實體在我們流變的世界中不可能存在。雖然固有存在的客體確實不存在,習俗意義上的對象作為依存的和聯繫的客體則非常顯著地存在著。空性並非虛無主義。存在著關於世俗意義上的實體和正確行為的有效知識。「我」 作為對心靈和肉體的一種心智的命名,在世俗意義上確實存在。空性也不會落入常存的極端,因為對像缺乏內在的存在。對像既非作為不存在,也非作為內在的存在,而是作為緣起居於「中道」。

 這一論證或解毒劑的力量,在很大程度上取決於我們是否同意診斷。如果我們提煉正常的經驗,是否會發現人們信仰引誘其墮入生死輪迴的獨立存在?我們頭腦中可能會有疑問,但具緣派在這一點上是堅定不移的。正如Hopkins所指出的那樣「空性修證和生起領悟空性的智慧的關鍵,在於確認對像顯現出它們似乎是存在於自身和由自身而存在的。」或者隨後他說:「然而,具緣派回答道,『固有存在』或者『存在的自我模式』術語本身就暗示了獨立性。」這種獨立的、非聯繫的性質,我們誤認為它賦予對像如此實體性和現實性,恰恰導致固有的存在自相矛盾和自我廢棄。如果現象是依存性的,那麼它們依賴於什麼呢?

 現象通過它們的相互聯繫而獲得定義,並且依賴於這種聯繫。現象的本質是現象的聯繫性和依存性。內在的非聯繫性是一種自相矛盾的屬性。雖然我們錯誤地假定固有的存在是表象的本質,但是中觀派主張,正是一個對像缺乏固有的存在、它的空性、它的依存性,才使得現象可能產生並發揮功能。

 那麼現象為什麼顯現為固有存在呢?具緣中觀派主張除了建立感覺知覺的細節之外,心靈會把將經驗實體化和具體化,向我們呈現為主體和客體,它們錯誤地顯現為固有的存在。換言之,固有的存在不過是概念的命名和增益,——它從未存在過並且永遠不會存在。然而我們卻被深深地囚禁於不存在之中,囚禁於概念的命名和杜撰之中,這是我們本能地和被迫地所產生的思想的屬性。從經驗的模糊不清元素中,心靈杜撰出固有存在的客體,然後對此附加上貪戀和厭惡,——這是生死輪迴的兩個腳鐐。這種將經驗實體化為獨立存在的傾向,是我們與生俱來的無明的核心、痛苦的根源;對此可以用空性的教義驅除掉。

 但是,雖然增益是獨立存在客體錯誤顯現的根源,心靈在其命名活動中與對象的(與內在的意義相反的)世俗意義上的存在也有關聯。換句話說,伴隨著心靈對內在存在非法的增益活動,它在對世俗意義上存在命名活動中合法地發揮其作用。心靈及其客體相互依賴的習俗存在確保了它們彼此的空性。因此,具緣中觀派說,緣起——理性之王——在其最強有力的形式中是:「一切現象因為受到依存地增益,都沒有固有的存在。」所有其它證明沒有固有存在的推理都起源於這一理性之王,它可以徹底地克服常見和斷見兩種極端。

 按照具緣派的觀點,不僅沒有通往獨立於心靈的世界的道路,而且這樣的一個世界根本就不存在。然而必須立刻申明,這種觀點不是在其對手佛教唯識宗中可以找到的那種觀念論。具緣派鮮明地強調對像外在於心靈,但是這些對像缺乏內在的或獨立的存在。如果沒有這種與心靈聯繫的外在客體,則無論是心靈還是客體都不會有世俗意義上的存在,因為它們彼此依存。不僅如此,任何心靈都沒有內在的存在。如果它們內在地存在,則我們黑暗無明的心靈就不可能轉變為光明的標誌和佛陀的覺悟。

 也許在中觀陣營中最大的哲學競爭是具緣派和依自起派之間
的競爭。 近來由Hopkins 和Thurman所撰寫的最重要的專著全面地討論了這種辯論。雖然論證經常是冗長和技術性的,我將簡述依自起派的立場,並通過回答在這種辯論中可能產生的質疑來考慮一些批評的問題。依自起派同意具緣派的觀點:在終極意義上,一切現象缺乏內在的存在,在最終的分析中找不到顯現為內在存在的客體。但是,依自起派主張世俗意義上的對象確實內在地存在。他們在中觀的兩種真理的教義中作出他們的區分,宣稱有兩種互補的現象觀:一種是終極的,認為一切都是空的,而另一種是世俗的,認為對像在日常生活的領域中具有存在、作用和效果。我們的普通生活和話語處於世俗真理的範圍內,但是我們不幸地在世俗存在上增益內在的存在來玷污它。

 依自起派論證說,如果客體在世俗意義上不是內在地存在的話,那麼就無法解釋客體特殊的作用以及我們所經驗到的主體間的一致。我的樹上懸掛的紅色球體,是叫做蘋果的能吃的果實,而非致命的毒藥。心靈的命名、增益無法說明蘋果的營養價值與毒藥。按照依自起派的觀點,需要一些獨立的存在以說明這一特殊的性質,儘管最終一切現象都是空的。

 具緣派對此立場進行了雙重的否定:首先,以上的論證或者更加經典的論證顯示內在存在的自我矛盾性。內在存在的不一致性在終極和世俗層次上都是平等的,——僅僅為世俗層次保留內在的存在並不是將它恢復為一種有意義的原理。錯誤還是錯誤,——不管是世俗意義上還是終極意義上。

 其次,客體的空性、它的緣起性、以及它的各種關聯和聯繫恰恰賦予了它功用和效能。蘋果依賴於原因和條件、整體和部分、以及多方面的相互聯繫,——獨立存在的缺乏——確保了其世俗的存在、特殊性、以及我們主體間的一致性。將自相矛盾的內在存在賦予客體只會使得它們不能活動、永恆不變以及不能發揮作用。

 最後,對於所有中觀宗而言,空性是現象的終極真理。在內在存在的錯誤信仰之處,沒有頒布任何更高的或更超越的原則。空性是無肯定的否定——僅僅現象中的獨立存在。空性自身也是空的。

 伴隨著空性的原則,治療的一個基本組成部分是普遍慈悲的修行。空性及其對我們徹底的相互依存和聯繫的確認蘊涵了普遍慈悲的教義。如果我們,和每一種現象一樣,是緣起的,那麼痛苦和從痛苦中解脫出來都既不是孤立的也不是純粹個人的事情。個人從輪迴中解脫出來就不是目標。相反,認真的修行者發誓為了一切有情從輪迴的無知和痛苦中解脫出來而勤苦修行。菩薩為了其它受苦的有情毫無保留地奉獻自己。空性和慈悲之間有一種協同的關係——慈悲加深對空性的理解,而空性則為長養無限制的慈悲提供理智上的支持。中觀宗以空性和慈悲的巨大支柱建立起佛陀的全部教義——這裡表現了它的祝福。

三、貝爾不等式的哲學背景

 本節中,我說明量子力學的爭論是圍繞著中觀宗稱之為內在存在的問題而進行的。把獨立存在增益給現象的先天傾向,在經典物理學中發現了一個徹底的和量化的表達。另一方面,量子力學最革命的方面是其否認客體的某些屬性具有獨立的存在。這個側面已經激發了許多批評和修正的嘗試,儘管量子力學在實驗和理論上已獲得了意想不到的成功。最著名的批評就是由愛因斯坦所發起的,在最近對貝爾不等式的實驗否定中達到了頂點。

 愛因斯坦對量子力學的基礎的偉大批評是從他在1927年的挑戰開始的。批評的核心論文由愛因斯坦、波多爾斯基和羅森(EPR)於1935年撰寫。尼爾斯·波爾迅速反駁了這篇文章,基本上大多數物理學家都同意他,這在後來成為量子力學的標準解釋。但是這一科學的某些最重要的創始人如薛定鄂和德·布羅依都同意愛因斯坦。從關於量子力學的解釋的論文的份量和爭論的激烈程度上看,所有的關鍵問題都還沒有徹底解決。

 令人吃驚的是,儘管愛因斯坦是對量子力學進行批評的轉折點,但直到最近幾年學術界才澄清了愛因斯坦的批評和立場究竟是什麼。EPR論文並沒有包含愛因斯坦對這一問題上最清楚的表述。愛因斯坦的哲學立場最好的表達出自Dialectia 。下面的引證出自Howard出色的翻譯和評論:

 如果要問,獨立於量子理論的物理觀念領域的特點是什麼,那麼下面的一切首先就會引起我們的注意:物理概念指涉一個真實的外部世界,即觀念賦予號稱獨立於感知著的主體的『真實的存在』的事物上···這些事物的特點是被確定在一個時空連續統中。不僅如此,對於引入物理學的這種安排,最基本的似乎是:在一個特定的時間中,這些事物號稱彼此相互獨立,從而這些事物『處於空間不同的部分。』沒有這種有空間距離的事物彼此之間相互獨立的假定,——這種假定起源於日常思維,——我們所熟悉的物理學思想就不可能。沒有這種分離,就看不出物理學定律如何表達和檢驗。場論將這一原則推到極至,把彼此獨立存在的基本元素定位於無限小的(四維)空間元素中,似乎是基本的定律對它們的要求。

 對於相對論意義上獨立的有空間距離的事物A和B而言,這種觀點是有特點的:即在A上施加的外在影響對B沒有直接的效果,這被稱為定域作用的原則,只在場論中才有一致的應用。

 定域作用的原則恰好表示光速是一切物理作用傳播速度的上限。局域性在本文後面還要扮演一個角色。儘管在本節中沒有討論,所提到的『基本定律』是嚴格決定論的,——相似的條件總是導致同樣的結果——,這個觀點在量子力學中必須作重大修改。

 對本文來說,比定域作用或決定論更為核心的是,「有空間距離的事物的存在,彼此之間相互獨立,這種假定源自日常思維。」Howard稱之為愛因斯坦的分離原則。在空間中分離並且沒有物理學相互作用的客體,被看作是獨立存在的,具有內在的、確定的屬性。正是在這種基本存在的基礎上,關係才得以建立;但是與關係者「彼此之間相互獨立的存在」相比,關係的實在性較少,基礎性較弱。當然,這種「源自日常思維的」對獨立存在的信仰,中觀宗毫不驚奇,因為他們說對內在存在的信仰是我們最深厚的與生俱來的無明。愛因斯坦也相信,彼此之間相互獨立存在是對不同於習俗的客體作出一致定義所必須的個體化原則。這在中觀宗的立場上看也是自然的,因為他們主張,缺乏獨立存在才使得我們可能通過我們體現於命名或語言的習俗確保客體具有相對的存在,——這正是愛因斯坦所想要避免的情形。(在俱緣中觀派中體現於語言中的習俗的重要性,及其與維特根斯坦的語言哲學的關係,有關的詳細討論,參見Thurman)

 有人嘗試將愛因斯坦的觀點構建不同於標準量子力學的理論。通過假定局域性(沒有任何通訊超過光速)和隱變量(目前還無法測量)的存在,局域隱變量理論嘗試在量子領域重新恢復決定論和獨立存在。為了檢驗這些理論,約翰·貝爾正是假定一切局域隱變量的核心,即局域性和獨立存在,從而推導出預測這些理論在一組實驗中相關結果的一個不等式。我下面要考察一個實驗。(標準量子力學不遵循貝爾不等式。)實驗否定了建立在這些聽上去如此有道理假定上的貝爾不等式,我將要說明,這對我們的世界觀產生了深遠的影響。與此同時,實驗與量子力學精確的一致強化了我們對於已確立的理論的信心。

 這種「相互獨立存在」,或愛因斯坦的分離性,在貝爾不等式的語境中擁有一種嚴格的(邏輯-數學的)表達形式。Howard已經顯示愛因斯坦的彼此相互獨立存在與完備性密切相關——一切可測量的屬性在獨立於測量的理論中得到全面說明的觀點。我不對這些嚴格的結果進行評論,而是使用對上面解釋的分離原則更加直覺的理解,並在下一節中將此觀念應用於貝爾不等式的一個簡單派生物中。

 Paul Teller把這種對客體的孤立和獨立存在的無所不在的信念稱之為個別論,他確信這是我們在量子力學上遇到的許多困難的根源。他特別有效地指出,量子客體之間基本的聯繫性,以及要達到對量子力學的正確理解必須拋棄個別論。D.Howard1985年的論文也包含了類似的觀點。

 我認為,彼此之間獨立存在的觀念,——Howard稱之為愛因斯坦的分離性、Teller稱之為個別論,——以及完備性的觀念,在中觀宗確定的內在存在中都是基本的成分。內在存在及其否定是比科學哲學所關注的更加寬廣的一組問題。但是在現代科學哲學家和中觀宗行者共同關注的領域中,他們所討論的完全是同一個問題,不管你稱之為內在的存在、分離性、完備性或者個別論。以下兩節討論實驗和量子力學是如何否定內在存在的。

四、相關性實驗

 本節包含一個有關檢驗量子力學概念基礎實驗的非技術的討論。雖然描述是經過調整的,但它忠於實驗的物理學精神。感謝David Mermin,我們可以不受物理學和數學的技術限制而嚴格地表述貝爾不等式的哲學精神。在本節及下節中,我把他的著作中的內容抽提出來並予以擴展。

 這個實驗包含了三個主要成分。圖1顯示一個產生相關光子對的光子源置於在兩個同樣的偏振檢測器中間,成一直線。(相關意味著什麼下面就清楚了。現在我們可以說一開始在一起的光子之間即使在分開之後也能保持某種確定的關係。)相關光子對同時由光子源發射,每一個朝向一個偏振檢測器。

 貝爾分析的一個魅力是,它不需要描述或理解偏振性或檢測器的物理性質。關於實驗裝置,我們所需要知道的是,每一次光子進入檢測器都會記錄下+或-。雖然如此,如果知道這點就會更好:即每一個檢測器象偏振太陽鏡一樣作用,只會透過落到其上的某些光線。如果光子通過,檢測器記錄+,要是沒通過,就記錄-。正如偏振太陽鏡一樣,偏振檢測器的效果隨其圍繞光子運行的路線旋轉而改變。每一個檢測器可以在A、B、C位置之間迅速切換,從光子源看過去方向依次相差120度。(見圖1)一次只能有一個切換。任何一次切換每一個光子落在檢測器上都只能記錄+或-。

 實驗以下述方式進行:相關光子對同時送往每一個檢測器。在光子達到檢測器之前每一個旋鈕獨立地和隨機地重新調整。每一個偏振檢測器獨立和隨機地調整意味著9種可能的組合將會平等地發生。它們分別是A-A、A-B、A-C、B-A、B-B、B-C、C-A、C-B、C-C,其中第一個字母代表左邊檢測器的旋鈕,第二個字母代表右邊的旋鈕(例如B-C表示左邊檢測器定於B,而右邊檢測器定於C)。數量極多的光子對送往檢測器,反應被記錄下來。任何一次我們只可以測量到如下的檢測器反應:++、+-、-+、和--;其中例如+-意味著左邊光子通過了檢測器而右邊則沒通過。這些就是實驗的主要思想。

 與實際的實驗一致,把距離和旋鈕確定的準確時間安排成在旋鈕確定之後,信號以光速運行傳播也無法從左邊檢測器在右邊被檢測之前到達檢測器。既然光速被假定為任何影響或信息傳播速度的上限,這就保證了在不同檢測器上旋鈕確定和測量之間不可能存在通訊,一個檢測器的旋鈕確定和測量不會對另一個檢測器旋鈕確定和測量產生影響。例如,假設檢測器相距一光年之遙,檢測器重新隨機確定1秒之後進行測量。檢測器重新確定在一邊,測量的事件發生在另一邊,依照相對論在四維時空中具有類空(space-like)分離性,在類空分離的事件之間通訊行為不可能發生。假定光速是物質作用或通訊傳播速度的上限,這是對局域隱變量理論和量子力學同樣適用的普遍假定。這得到了理論和實驗的壓倒性支持。正如下面將清楚顯示的那樣,排除兩次測量或旋鈕確定之間的物理關聯或「共謀」的能力在解釋中是至關重要的。

五、局域隱變量解釋:貝爾不等式

 局域隱變量理論在物理實在論中有其根源——對應於一個獨立於觀察者的世界,一個具有確定的、在測量之外完全可以說明的屬性的世界。這自然導致對於一個完備性理論的要求,即一個系統所有可以測量的屬性在獨立於測量的理論中可以得到完全的說明。或者用EPR的使用可以保證系統的屬性獨立於類空分離事件的局域性原則,來建立物理實在的要素。

 在眼下的事例中,完備性和局域性允許我們假定偏振性(它決定一個光子是否可以通過特定位置上的檢測器,檢測器是否記錄+或-),對於光子是內在或固有的,是獨立於類空分離的旋鈕確定或事件的。換言之,我們是在體現愛因斯坦的要求「空間上有距離的事物之間的相互獨立存在。」在一邊的一個光子按假定具有一種確定的偏振性,它是先於並獨立於在另一邊的測量的。假定光子的這種內在屬性獨立於特定的旋鈕確定和遠處的測量結果,這自然得我們對此不加思考;但這種「起源於日常思維的」似乎清白無辜的假定,按照愛因斯坦的觀點,正是局域隱變量理論的核心。

在附錄中,我提出了貝爾不等式的一個簡單形式的非技術的變種,它僅僅假定了局域性和相互獨立存在(確定的偏振性獨立於測量)。雖然這個變種是嚴格的,它只要求基本的高中數學。這種簡單形式的貝爾不等式預測至少1/3的光子應該記錄為同樣的符號,如果在兩個檢測器中隨機設定的旋鈕是不同的話。測量的結果準確地顯示只有1/4的光子記錄了同樣的符號,當旋鈕不同的時候。

 但是我們如何來理解實驗對建立在這種似乎「不證自明」假定基礎上的不等式的破壞呢?作為準備的嘗試,我們可能會說,當對相關光子對中第一個光子進行測量時,第二個光子迅速變為相關的狀態,從而改正了統計結果(1/4)。但是在實驗中,時間的安排使得第二個光子的測量與第一個光子的測量之間具有一種類空的分離,因此有關什麼是「合適的相關狀態」的信息傳播一定比光速更快——這在任何人看來都是嚴重的問題。問題甚至更為嚴重,因為正如我在附錄中所顯示的那樣,假定局域性和獨立存在就蘊涵著第二個光子已經具有了完全確定的、與第一個光子同樣的偏振狀態。在這兩個假定下,光子不能只是簡單地象變色龍一樣在最後時刻改變其偏振狀態,從而改正統計結果。局域性或獨立存在(或者二者)在自然中一定遭到了破壞。

在下一節中,我檢查更加精緻的相關光子模型,但是結論仍然成立。在光子之間存在著神秘的關聯性或非局域性。它們的表現不像分離的實體而更像相互聯繫的整體——但是我們在每一個檢測器上測量粒子般的實體。正如我在下一節中所強調的,我們本能地把光子實體化為具有「相互間獨立存在的」完全確定的實體。這使得要從我們在如此徹底投入了獨立存在信念的世界的經驗中建立一個相關光子的模型根本不可能。雖然如此,在下一節中,我嘗試用空性的觀點來詳細闡明我們對這一神秘現象的理解。

這裡必須強調兩點:首先,對貝爾不等式的否定並不依賴於量子理論,雖然對這種實驗的考慮當然是由量子理論的特殊性質所激發的。其次,這些結果並非局限於亞-微觀領域,因為檢測器分離達13米之遠。這裡討論的量子效應通常並不在宏觀領域中出現,但是在原則上和在實際上,它們並非局限於微觀世界中。
 對於局域隱變量理論及其局域性和完備性的假定,量子客體獨立於類空分離的事件具有一個
完全確定的性質,換句話說,它們內在地存在著。實驗對貝爾不等式的否定要求對這些假定放寬一個或全部放寬。正如我下面所強調的,放寬這些假定其中之一就是承認量子客體具有根本的相關性或相對的相關性——這是對它們空性或缺乏內在存在的斷言。

六、比較與應用

 中觀宗和實驗對貝爾不等式的破壞二者,都向我們最珍視的實在性原則——獨立的或者內在的存在——提出了尖銳的挑戰。但是物理學只研究物質領域,而中觀則分析一切人類經驗;所以比較能走多遠呢?不僅如此,雖然局域隱變量理論及其完備性和局域性的假定是站不住腳的,但就實驗對貝爾不等式否定的後果並未達到完全的一致意見。對於量子力學的哲學意義也還有許多爭論。在我們對貝爾不等式破壞的理解這個階段上,以及我們目前對量子力學本身的理解水平,我們可以有理由肯定什麼呢?在本節中,我將部分地回答這些問題,強調這些事實依賴於我們目前對物理學的理解,開始將中觀的空性教義應用於對貝爾不等式和量子力學的解釋,並將其與由Paul Teller和其他人發展的量子力學的哲學結合在一起。

 在接下來的段落中,我只提供反對決定論的局域隱變量的例子,正如貝爾在他1964年的分析中所做的那樣。在這些理論中,假定光子離開光子源之後偏振性具有一種確定值。例如,附錄表1中第一列顯示光子8種可能的偏振性確定狀態,光子完全決定了檢測器對於一個給定的位置反應。在稍後的工作中,貝爾和其他人分析了更加普遍的局域隨機隱變量理論。這些同樣被實驗所排除的理論,只給出了檢測器反應的這樣的概率,它們依賴於光子和檢測器位置的一些更加普遍的狀態。光子不是被看作攜帶一種偏振性的確定狀態;所以我們將我們的注意力轉移到檢測器反應的概率上來。現在完備性和局域性的概念變得更加微妙了,但是感謝Jarret和Shimony,我們準確地知道在這些局域隨機隱變量理論中獨立性的假定如何進入了貝爾不等式。假定了三種型式的獨立性:
1, 一側檢測器反應的概率獨立於另一側開關的位置。
 2, 光子源發出的概率的統計混合獨立於兩側檢測器的開關位置。
 3, 一側檢測器反應的概率獨立於另一側檢測器的反應。

 分析顯示,局域性只要求第一種和第二種獨立性,這同樣也為量子力學理論所遵循。但是結果獨立性(第三種)卻不為量子力學所遵循。考慮到局域性的壓倒性證據,結果獨立性是一種自然和量子力學似乎都破壞的假定。要將檢測器反應的概率或者一側結果的概率隔離出來,並認為它與另一側的結果分離開來是不可能的,即使在兩側的測量之間不可能有物理或信息的關聯。這對大多數人來說是神秘的。按照中觀所激發的評論,這種神秘觀可能會有所減弱。

 儘管在量子力學中,光子是最瞬時的實體,從幽靈般的概率中噴發出來接受測量,我們還是傾向於將它們當作沿著確定的軌跡在空時中旅行的具體的實體。我們太過經常地隱含地假定,它們是完備和自足的,獨立於間隔的狀況和事件。例如在教室、實驗室、或者在目前這篇文章中,我們差不多總是這樣來談論貝爾實驗:「兩個相互關聯的光子被送往相反的方向······」。理智上我們完全知道,相互關聯的光不可能嚴格地在這種分離的意義上來考慮,但是我們幾乎總是陷入這種思維習慣中。我們經常實用地辯護說,這會使得特殊的應用更加容易。但是即使通常關於局域性的討論,經常隱含地假定一個完全確定的粒子般的實體,其在軌跡上瞬間的位置與另一個事件是或不是類空(space-like)分離的。(施加局域性的限制並不一定牽涉這一概念上的謬誤。)換言之,我們通過將光看成是一種在完全確定的軌跡上運行的粒子般的光子,積習難改地將內在的、非關係的存在增益給光。這種與生俱來的傾向就是Teller所說的「個別論」的毛病。這種思維習慣如此強大,以至於它甚至也體現在John Weller經常重複的嘮嘮叨叨命令中:「以今天話說,波爾觀點(和量子理論的核心內容)可以歸納為一個單一的、簡單的語句『任何一個現象,除非是一個被觀察到的現象,否則就不是一個現象。』」雖然光除非被觀察到否則不是一個光子,我們通常還是把它看成是一種獨立存在著的實體,具有完全獨立於遙遠的事件和結果的屬性。

 雖然是我們器官活動正常通常模式的劇烈顛倒,中觀斷言現象的最高真理,其最基本的性質,是其內在的依存性和彼此的關聯性。現象的基本性質是其關聯和聯繫,而不是其孤立的同一性。通常的思維習慣承認對象的聯繫,例如相互聯繫,但是認為這些屬性對於光的基本屬性來說是偶然的。或者象Teller可能會說的那樣,某些量子屬性(例如相關光的性質)是內在聯繫的——其基本聯繫不會超越於其非聯繫的屬性。Teller不會從全面的角度來考慮個別性與內在聯繫,即不會像中觀應用類似概念——內在的存在與空性——那樣。在他思維的這個階段,他只把他的原則應用於解釋科學哲學問題,而沒有確定其可應用的範圍。

 實驗顯示了,相關性對於光來說在最基本的意義上是內在的——一側檢測器測量的結果與在另一側發現的結果精密相連。在現象的終極真理是內在存在的空性、其依存性和相關性這一意義上,我們不能也不應該用試圖通過各種(超出光之外的或其它的)聯繫使內在存在的實體發生關係來尋求對這些相關屬性的解釋。換言之,總是這麼說是令人厭煩的:「本質上聯繫的實體在一邊,它在測量時被命名為『光子』,它與另一邊的關係性實體的聯繫是如此本質性的,它們必須被整體性地考慮。」但是量子的形式化及其疊加的原則在數學上告訴我們的正是這種類似的內容,儘管我們在將其應用於我們正常的實體化或個別化思維方式時會感到困難,這種思維不加反思地將現象增益為內在的存在。

 如果局域性在未來的物理學中需要修改的話,那麼這對物理學將是極端重要的,但是與我們今天的討論沒有直接的關係。因為那時說檢測器的反應是一個依賴性相關事件仍然是正確的,它將會是以類空分離的事件為條件的或者說瞬間依賴的。這種對類空分離事件的依存性將會是對其獨立存在的斷然否定。內在的存在,至少在貝爾類型的實驗中,在未來的物理學中是不可能復辟的。

 儘管量子力學在過去60年中取得了意想不到的成功,包括最近令人震驚的強、弱相互作用和電磁作用的統一,量子力學目前的形式可能會比實驗對貝爾不等式的否定還要短暫。即使如此,簡要地描述量子力學最基本的概念原理並將其與中觀的分析聯繫起來還是值得的。

 量子力學的哥本哈根標準解釋有兩個緊密聯繫的核心原理。首先,量子對像不具有客觀的或者具體空時的存在,即不具有獨立於整個測量狀態的完全確定的可測量的屬性。永遠必須要在進行測量的具體實驗安排的背景下才能考慮對象。在上述實驗中,一側檢測器的反應雖然與另一側檢測器的反應是類空分離的,必須要與它整合起來考慮。未經測量的對象,獨立於其被觀察的確切實驗狀態的對象,根本就不存在一個確定的客觀狀態。觀測儀器和被觀測對象是一個按照量子力學所涉及的無形整體或系統的互相補充的組成部分。按照波爾的觀點:「孤立的物質粒子是一種抽像,只有通過其與其它系統的相互作用才能確定並觀察其屬性。」在中觀中類似的思想運動是確立所有對象都缺乏獨立的存在。

 在上述的實驗中,按照量子力學的標準觀點,光子並不具有完全確定或外在的性質(偏振性組合如+-+或者-+-),即不具備先於或者獨立於現實的測量事件的性質。在測量事件前,對像只有的抽像「存在」, 即只有作為由波函數所描述的相互貫通的概率或者相關的潛在可能性,只有包含了有關量子體系的所有可能知識的量子力學的數學結構。雖然波函數是我們所能獲得的有關體系的最多的知識,但是它並不涉及到任何具體存在於空時中的物質的、客觀的實體。相反,疊加原則是內在的聯繫在數學上的一種表現。雖然在檢測器的反應之間不存在任何物理的或信息的聯繫,一側檢測器檢測的可能性依賴於另一側檢測器的反應:內在的聯繫具有可測量的後果。
即使在對量子力學的各種解釋之間對有關量子測量過程的細節存在著爭論,許多人(如在哥本哈根解釋中)都斷言:測量是量子事件向宏觀世界中的事件的一次不可逆地放大。因此看上去俱緣中觀強調對存在的增益與量子力學是有矛盾的。當然,總是可以像許多人爭辯的那樣,說一切科學都是一種心靈構造的世界,它是從人與自然之間複雜的相互作用中產生出來的;但這不是現在的關鍵問題。量子力學根本不像中觀派那樣把意識置於核心位置。這種明顯的分歧可以通過欣賞中觀的認識論和形而上學觀點的區別而得以緩和。認識論對於為什麼對像表現出獨立存在的解釋是用增益的術語給出的,而習俗對像被理解為由心靈命名的;但是形而上學的真理卻是:即使拋開心靈的作用,對象也是依存地相互關聯的。對佛陀而言,世界被真實地看作是空的、依存地相互關聯的,並且不存在施加於現象之上的獨立的增益活動。事實上,傳統宣稱佛陀甚至連一個可以將名義上的存在增益於對象的概念意識都沒有,儘管佛陀所感知的一切只是名義上的存在。

 這種量子力學的非意識解釋的一位著名捍衛者,John Wheeler也清楚地理解心靈增益內在存在或(Teller可能會說的)個別化的傾向。Wheeler說,「我們稱為實在的內容包含了幾個觀察的標竿,我們用一種精緻的想像和理論的人為構造物填充於其中。儘管在日常的環境中說世界獨立於我們而『外在地』存在是有用的,但這種觀點是再也站不住腳的。在這是一個『共同參與的宇宙』說法中有一種奇異的感覺。」

 這牽涉到哥本哈根解釋的第二個原理:對像由測量活動本身帶到了客觀的存在。對像只有通過測量活動才能變成空時現象。或者,如Wheeler所說:「除非是被觀察的現象,沒有一個基本的現象是現象。」在中觀的語言中,實體僅作為緣起的種屬而存在。在中觀中發現的空性與緣起的親密關係,與量子力學中發現的很相像,解釋中的這兩個主要原則總是保持緊密相連。

七、概括與結論

 量子力學60年來在權力、可應用性和優雅方面穩步地增長和加強。從20年代末和30年代初波爾、海森堡、波恩和其它人發展量子力學的哥本哈根解釋以來,其哲學原理只經受了適度的修正。儘管如此,關於量子力學的意義仍然存在熱烈的辯論,其中許多由這裡評述的最近貝爾的分析所加強。量子力學缺乏合適的哲學框架確實是量子革命如此緩慢和痛苦的主要原因之一。我已嘗試表明,對中觀關於空性觀點的同情理解可以幫助消化量子力學的意義。像Teller一樣,我主張將我們的哲學立場從個別論或對內在存在的信念轉移到基本的關係性,而不是修改量子力學的數學結構。

 一方面中觀可能對理解量子力學有所幫助,同時量子力學也可以幫助理解中觀。如果這種古代的教義要征服現代人,它需要更多的當代例證,而不是「龜毛的外套」或者將繩子誤認為蛇。量子力學可以提供強有力的例證來說明中觀的某些側面。它也可以復活例如俱緣中觀派和依自起派古代的爭論,後者主張在習俗意義上有內在的存在,這種立場在實驗對貝爾不等式的否定面前更加難以堅持。

 然而,目前這篇文章決非要通過物理學來證明中觀佛教的有效性。使用科學證明或者否定各種宗教或世界觀的主張有一個命運不濟的漫長歷史。撮合一種世界觀與科學婚姻的嘗試注定會過時。相反,我所做的是嘗試理解重要的和經實驗證實的哲學論斷,使得關於某些量子屬性缺乏獨立存在的個別化理論獨立化,並將其與中觀的空性原理結合起來。

 雖然許多哲學體系可以與實驗對貝爾不等式的否定結合起來,我主張(中觀的關鍵概念)空性,談論量子力學的核心問題具有獨一無二的直接性和力量。我已嘗試應用空性來理解實驗。然後我給出量子力學的標準觀點,並因此建立與中觀進一步的聯繫。我希望用這種方式去獲得對古代解脫哲學和現代物理科學結果的一種更深層次的欣賞。考慮到科學-技術世界觀的壓倒性主導地位,目前形式的比較工作當然是中肯的,如果它能避免將中觀或任何其它類似的思想主體部分還原為科學的一個分支的罪惡的話。

附錄:貝爾不等式的非技術性推衍

 假定上述包括到第五節前兩段的討論,我們可以推導出貝爾不等式的一個簡單形式。現在我給出一個非技術的推導,它只需要基本的高中數學。
 為方便起見,以第四節中描述的方式所收集的數據可以分為兩種情形:情形1,兩個檢測器具有相同的開關設置,情形2,開關設置不同。下面逐一探討。

情形1:兩個檢測器具有相同的開關設置。

 現在數據是在開關設置為A-A,B-B,C-C的情形下收集的。這是EPR1935年在挑戰量子力學的論文中所考慮的實驗的基本精神,儘管那時只是一個思想實驗而已。其數據可以簡單概括如下:

 1, 兩個檢測器總是記錄到以同樣的概率隨機產生的相同記號++和--
 2, +-和-+從不產生。
 首先,必須確立兩個關鍵的事實:在情形1中,對於三個檢測器設置A-A、B-B、C-C中的任意一個,測量總是產生「+」「+」或「-」「-」而從不產生「+」「-」或「-」「+」。從這一點,我們可以推斷出第一個關鍵事實:光子對的每一個成員在一個選定的方向上一定有相同的極性。如果在選定的方向上極性不相同,則可能會測量到+-或-+的結果,和情形1的結果相衝突。通過回憶一側的開關設置與測量和另一側的之間具有類空分離來確立第二個關鍵事實。它們之間不可能發生通訊,右側粒子和檢測器無法知道左側檢測器的位置和測量。因此我們可以選擇沿著B或C測量右側光子的極性,不會有充足時間將此信息通過任何方式傳回給左側光子來影響左側的測量。例如說,我們用設於A的左側檢測器測量得+,設於B的右側檢測器測量得—。依靠著一對光子在一個給定的方向上觀察到相同的極性,我們實際上測量了右側光子的2個成分(沿A +和沿B-)。當然,這還利用了完備性或左右兩側光子存在彼此相互獨立的假定。
我們同樣還可以選擇沿著C測量右側光子,從而獲得沿著A和C兩個方向的兩個值。這樣我們推斷右側光子在A、B、C三個方向上一定同時具有完全特殊的極性,不管開關的設置如何。既然論證對於左側和右側來說是對稱的,這就確立了第二個關鍵事實:兩個粒子一定對於三個可能位置中任何一個都具有完全特定的極性。這兩個關鍵的事實聯繫起來意味著,極性設置在三個方向上完全是特定的,並且它們與每一個光子對同一。情形1的數據連同局域性、彼此相互獨立存在的假定,以及歸納推理的使用要求這一結論。
在前述的分析中,標準的推廣是從以相同開關設置測量相同極性光子對的案例到不同開關設置的案例。既然一側的測量或者檢測器不可能影響到另一側的測量或者檢測器,我們基於彼此相互獨立存在推斷所有光子對在三個方向上一定具有相同的極性,不管其開關設置如何。
 使用一個簡單的符號來列舉極性可能的不同種類,例如+--代表了一個光子在方向A上測量極性的結果是+(通過),在方向B上-(沒通過),方向C上-;而+-+代表一個光子在方向A上+,方向B上-,方向C上+。有八種可能的極性組合:+++,++-,+-+,-++,---,--+,-+-,和+--。現在該考察開關設置不同時所收集的數據。

情形2:兩個檢測器具有不同開關設置

 考慮一下開關設置為A-B,A-C,B-A,B-C,C-A,和C-B的情形。約翰·貝爾1964年的顯赫成就是EPR思想實驗的推廣。正如下面所顯示的那樣,通過考慮開關設置不同的情形,實驗可以直接與局域性隱變量理論對質。情形2的數據如下:

 1:在1/4時間中檢測器記錄到以相同幾率隨機產生的相同符號++和--。
2:在3/4時間中檢測器記錄到以相同幾率隨機產生的不同符號+-和-+。

情形1和2的數據的獨特型式起源於成對光子間相關性——一側檢測器測量的結果相關於,或者說關聯到另一側檢測器檢測的結果。

表1列舉了情形2的測量的可能性。8行對應於可能的極性組合。6列對應於可能的開關組合。表中每一條目或是「同」或是「異」,表示條目的極性組合對於特定開關設置時,光子對產生相同或不同的測量結果。例如,表中下劃線的條目表示當極性組合為+-+而開關設置為A-B時,兩個光子被檢測為不同的記號(左側光子在A方向上為+,右側光子在B方向上為-)。表1顯示除了+++和---的極性組合外,總是有2個開關組合產生相同的結果,4個組合產生不同的結果。

相關表1
A-B A-C B-C B-A C-A C-B
極性 +++ 同 同 同 同 同 同
++- 同 異 異 同 異 異
+-+ 異 同 異 異 同 異
-++ 異 異 同 異 異 同
--- 同 同 同 同 同 同
--+ 同 異 異 同 異 異
-+- 異 同 異 異 同 異
+-- 異 異 同 異 異 同

 既然開關是獨立和隨機地設置的,我們知道對於一個給定的極性,6種開關組合發生的幾率是相同的。暫時假定我們有一大群相同的光子——每一種極性組合都有相同的可能性。換句話說,在一個相同的樣本中光子+--的可能性會像+++或者任何別的極性一樣。按照這中假定,表中的每一個條目都具有相同的統計權重。表中有同樣數量的「同」和「異」,因此如果測量這一相同樣本的大量光子,有一半時間會產生同樣的測量結果。

由於很快就會清楚的原因,接下來假定一個不一致的樣本,其中的光子中沒有+++或者---的極性,但是其它的極性表現是相同的。通過這種方式,我們去除那些對於所有開關設置總是產生相同結果的極性。現在對於所有剩餘的極性有2個「相同」和4個「不同」,因此具有這些極性的光子(我們假定的不一致的樣本)將總是只能記錄到1/3的同樣結果。對表1的思考顯示任何極性的組合都將會產生至少1/3的相同的測量結果。換句話說,假定在一個測量樣本的任意選擇極性的混合,一定至少產生1/3的相同測量結果。

 以上簡單的記數練習顯示(假定局域性和存在是相互獨立的)至少1/3的光子應該記錄到相同的符號。這是一個貝爾不等式的簡化形式。另一方面,實驗的結果是1/4——這正是標準量子力學所預言的結果。

 上述結果如此重要而又優雅簡潔,值得總結概括:情形1的數據顯示當開關設置相同時(A-A,B-B,C-C),檢測器的反應總是相同的。因為開關設置的時間安排,在局域性和相互獨立存在的假定下,極性完全是特定的和等同於相關光子對的每一個成員。表列舉了8種可能的極性及其對於6種不同的開關設置所產生的測量結果。它顯示當開關設置不同時,沒有任何極性組合所產生的測量結果中相同記號占檢測器反應的比例低於1/3的;然而實驗結果是1/4。實驗對貝爾不等式的嚴格否定,上述記數的一種推廣,迫使我們拋棄局域性隱變量理論。

 在這篇論文的主體部分,尤其是在第5節和6節,我嘗試了說明實驗對於違反貝爾不等式的哲學和物理學意義。

 譯自International Philosophy Quarterly Vol.XXIX.No.4 Issue No. 116(December 1989) PP371-387

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