Using Analogies with Quantum Physics, Dispelling Doubts

The fact that a karmic tendency has the ability to give rise to many different “results, which are not yet happening,” suggests that the analogy of a probability function might be helpful in describing this situation. Modern Western physics uses this conceptual framework of a probability function to describe, for instance, the wave-particle dual nature of light.

• A “probability function” – a mathematical function of a variable, such as a photon, that gives the probability that a certain value will occur, such as the location of the photon
• A “probability density” – a particular value of a probability function; for instance, the probability of a photon being present in a specific location.

From the point of view of the photon functioning as a wave, a photon is a “wave-function” and thus a “quantum entity.” This means that before measuring the location of a photon, its present location can only be described as a probability density within a probability function. According to the Copenhagen interpretation of quantum mechanics, when the photon’s location is measured, however, the photon adopts a specific location. The photon’s wave-function “collapses” – meaning that the photon is no longer functioning as a wave. The photon is now functioning as a particle at a determined location.

• We cannot say that the photon actually “exists” in any of its probable locations until its wave-function collapses. But that does not mean that the wave-function does not exist before it collapses.
• More accurately, we would say that an indeterminate quantum system probabilistically collapses down onto one determinate outcome upon measurement by an observer.

Although an existent nonstatic affirmation phenomenon, such as a pot of yoghurt, does not have a wave-particle dual nature, the Buddhist analytical framework of valid and invalid phenomena describes the same scenario regarding valid cognition of the spatial location of a pot of yoghurt as is the case with valid cognition of a photon.

For the sake of simplicity of expression, let us refer to the pot of yoghurt simply as “yoghurt” and, of all the possible locations of the yoghurt, let us analyze its location as limited to being either on the table or in the refrigerator.

At the time of “milk in the pot, which is presently happening,” the “yoghurt, which is presently happening” is an invalid phenomenon and cannot be validly cognized. At that time, however, the “yoghurt, which is not yet happening” is a valid phenomenon and can be validly cognized.

Moreover, the “milk, which is presently happening and which is temporarily not giving rise to its result” has both the ability to give rise to “yoghurt on the table, which is presently happening” and the ability to give rise to “yoghurt in the refrigerator, which is presently happening.”

Thus, at the time of the “milk, which is presently happening,” the “yoghurt on the table, which is not yet happening” and the “yoghurt in the refrigerator, which is not yet happening” are both valid phenomena and may be validly cognized. These two “yoghurts, which are not yet happening” constitute something like an indeterminate quantum system regarding the yoghurt.

At the time of the “yoghurt in the refrigerator, which is presently happening” the “yoghurt on the table, which is presently happening” is an invalid phenomenon and cannot be an object of valid cognition.

• The “yoghurt on the table, which is presently happening” is a valid phenomenon only when the location of the yoghurt is nowhere other than the table. The “yoghurt on the table, which is presently happening” may then be validly known.

Only with valid cognition of the “yoghurt on the table, which is presently happening” does the “yoghurt in the refrigerator, which is presently happening” become an invalid phenomenon.

• For example, during the temporal interval of the “yoghurt on the table at noon today, which is presently happening,” the “yoghurt in the refrigerator at noon today, which is presently happening” is an invalid phenomenon and cannot be validly cognized.
• The state of all mental continuums, from noon today onwards, being parted from valid cognition of the “yoghurt in the refrigerator at noon today, which is presently happening at noon today” is a nonanalytical stopping – a “never-happened of something that could have happened, once something else has happened instead.”

Thus, valid cognition of the “yoghurt on the table at noon today, which is presently happening” ascertains the existence of both the “yoghurt on the table at noon today, which is presently happening” and the nonanalytical stopping of valid cognition of the “present-happening of the yoghurt’s location being in the refrigerator at noon today.”

If we examine the certainty factor of what result will arise from a network of causes and circumstances, the above Copenhagen interpretation of probability functions leads to the following conclusions:

• Certainty of what result arises occurs only with cognition of the “presently-happening result.”
• At the time of the multiple “results, which are not yet happening,” there can be no certainty of the final “result, which is presently happening” that arises.

Buddhism agrees with the Copenhagen interpretation that, in our above example, at the time of "milk in the pot, which is presently happening", "yoghurt in the pot, which is presently happening" does not actually exist in any of its probable locations – on the table or in the refrigerator. This is because “yoghurt, which is presently happening” is an invalid phenomenon at the time of the “milk, which is presently happening” and thus cannot be validly cognized at all, let alone validly cognized in one location or another.

Buddhism also agrees that at the time of the “milk, which is presently happening,” the “yoghurt on the table, which is not yet happening” and the “yoghurt in the refrigerator, which is not yet happening” are only probability densities: they are only particular values of a probability function or indeterminate quantum system describing the location of the “yoghurt, which is presently happening” when it arises. However, Buddhism asserts that these two “yoghurts, which are not yet happening” are probability densities only from the point of view of ordinary beings. From the point of view of Buddhas, the two are not probability densities and all the “yoghurts in various locations, which are not yet happening” do not constitute a probability function or an indeterminate quantum system.

Buddhism agrees with the Copenhagen interpretation that, at the time of the “milk, which is presently happening,” a probability function and an indeterminate quantum system “exist” concerning the location of the “yoghurt, which is presently happening.” However, the existence of the probability function or the indeterminate quantum system is not truly established from the side of the probability densities of any of the components of the system. The existence of a probability function or an indeterminate quantum system is established merely in terms of mental labeling.

Mentally labeling all the “yoghurts in various locations, which are not yet happening” as a “probability function” or as an “indeterminate quantum system” does not create the probability function or the indeterminate quantum system. They are valid mental labels, however, because they fulfill the three criteria for validity of mental labeling:

• There are the conventional terms probability function and indeterminate quantum system coined and used by a certain class of beings – in this case, ordinary beings familiar with quantum physics.
• Valid cognition of the conventional truth of the network of all these “yoghurts, which are not yet happening” by this class of beings does not contradict its being labeled as a “probability function” or as an “indeterminate quantum system.” A statistically significant number of such beings would agree with these mental labels.
• Valid cognition of the deepest truth of the network does not contradict the manner with which this class of beings labels how its existence as a probability function or as an indeterminate quantum system is established. Valid cognition of the deepest truth about the network cognizes that its existence is devoid of being established in any impossible way, such as from the side of the probability densities of each of the components of the system.

From the point of view of Buddhas, however, the mental labels probability function and indeterminate quantum system are not appropriate to be applied to the basis for labeling. This is because the omniscient awareness of Buddhas validly cognizes every causal factor that will affect where the location will be of the “yoghurt, which is presently happening” when it arises. From the point of view of Buddhas, at the time of the “milk, which is presently happening,” the valid label for the network of all the “yoghurts in various locations, which are not yet happening” is a determinate system. This is a valid mental label by the same three criteria as above.

• Note that according to the third criterion, the network’s existence as a “determinate system” is not established from the side of any component of its basis for labeling.
• Nor does the action of a Buddha labeling the network as a “determinate system” in any way cause the system to be determinate.
• Moreover, valid cognition of the “result, which is presently happening” – such as “the yoghurt on the table, which is presently happening” – by anyone, whether an ordinary being, an arya bodhisattva, or a Buddha, does not establish, a posteriori, that the network of all the “yoghurts in various locations, which are not yet happening” was a determinate system.

The “many-worlds” or Everett interpretation of quantum mechanics rejects wave-function collapse and postulates, instead, “quantum decoherence” and “quantum superposition.” According to this explanation, with the measurement of a quantum entity, such as a photon’s wave-function, the quantum system of observer and what is observed “decoheres” or, in a sense, “splits” into simultaneously existent multiple systems, “superposed,” in a sense, upon each other.

The indeterminate system does not collapse into one determinate system upon measurement by an observer, while the other possible determinate systems cease to exist. Rather, all possible “worlds” or “universes” occur, in each of which an alternate observer measures an alternate location of what is observed. In each quantum universe, however, it appears to the observer as if a wave-function collapse has occurred, although that is not the case.

Some physicists interpret quantum superposition to mean that all the quantum universes have equal reality; some assert that only one is real and the others are “metaphorical”; and others adopt an agnostic approach that we cannot know whether or not alternate quantum universes to the one we are in are real.

In each quantum universe, however, the observer and the observed system are “entangled subsystems.” This means that what the observer observes and the state of the observed system are relative to each other and correlate. In other words, they correspond to each other.

Once an observation or measurement occurs, each quantum universe contains one element – meaning, one configuration – of a combined subject-object wave-function. The subsequent evolution of each pair of entangled, relative subject-object pairs proceeds without being affected by the subsequent evolutions of alternate subject-object pairs in alternate universes.

Evolution in each quantum universe entails further decoherence of subject-object wave-functions with each observation or measurement that is made.

For each observer in each quantum universe, alternate “parallel universes” are unobservable.

Nevertheless, the information concerning an electron, for instance, in one quantum universe – such as the location and spin-state of the electron – is “entangled” with the information concerning the electron in alternate quantum universes. When a piece of information concerning the electron is measured or observed in one quantum universe as having a certain value, the same value for that piece of information is not measured in alternate quantum universes.

Let us transpose the “many-worlds” interpretation to our example of valid cognition of the location of the pot of yoghurt at noon today. Let us also consider the case of various observers of an event all traveling at the same speed, so that we do not need to take into consideration relativistic time in our analysis.

According to the “many-worlds” interpretation, at the time of the “yoghurt on the table at noon today, which is presently happening,” the “yoghurt in the refrigerator at noon today, which is presently happening” can also be validly cognized. It cannot be validly cognized, however, by someone who is validly cognizing the “yoghurt on the table at noon today, which is presently happening.”

According to the Buddhist analysis, valid cognition of the “yoghurt on the table at noon today, which is presently happening” ascertains the existence of both the “yoghurt on the table at noon today, which is presently happening” and the nonanalytical stopping of valid cognition of the “present-happening of the yoghurt’s location being in the refrigerator at noon today.”

• There can be never be valid cognition of the “present-happening of the yoghurt’s location being in the refrigerator at noon today” because the “yoghurt in the refrigerator at noon today, which is presently happening” is an invalid phenomenon from noon today onwards.
• “Yoghurt in the refrigerator at noon today, which is presently happening” is an invalid phenomenon not only at the time of the “yoghurt in the refrigerator at noon today, which is not yet happening,” but also at the time of the “yoghurt on the table at noon today, which is presently happening” and at the time of the “yoghurt on the table at noon today, which is no longer happening.”

Several questions arise at this point. We have seen that the certainty factor of what result will arise from a network of causes and circumstances arises dependently in terms of mental labeling. For different classes of beings, different certainty factors are valid labels. Is it likewise the case that for different classes of beings observing the arising of a “presently-happening result” from a “karmic tendency with the abilities to give rise to a variety of results, which are not yet happening,” each class may validly cognize a different “presently-happening result?”

According to the Buddhist analysis, this is possible. Based on valid cognition of “milk in the pot, which is presently happening,” then at the time of the arising of the “result of the milk, which is presently happening,” humans may validly cognize the result as yoghurt, clutching ghosts as pus, and celestial beings as nectar. As in the “many-worlds” interpretation, each of the classes of beings would be unable to validly cognize what the result is that any of the others validly cognize. Buddhism would add, however, that some humans with advanced awareness are able to validly cognize what a clutching ghost or celestial being sees.

Buddhism clarifies this “many-worlds” interpretation, however:

• From its own side, the “abilities to give rise to pus, yoghurt, or nectar, all of which are not yet happening” are not established on the side of the “milk, which is presently happening.”
• These abilities arise dependently in terms of the mental labeling of each of the three above-mentioned classes of beings.
• Thus, each of the three abilities is a valid phenomenon only with respect to the class of beings that validly labels it.

A similar analysis can be made regarding the location of the “presently-happening result of the milk.” Its location will appear and be validly labeled differently by humans and by ants, for example. For clutching ghosts, the location of the “pus in the pot, which is presently happening” may appear and be validly labeled as being in a pool of acid. Again, the classes of beings would be unable to validly cognize the location of the result that any of the others validly cognize. Buddhism would again add that some humans with advanced awareness are able to validly cognize what a clutching ghost sees.

Buddhism clarifies:

• Within one class of beings, such as humans, all would validly cognize the same location, at noon today, of the “yoghurt, which is presently happening.”
• It is impossible for some humans to validly cognize its location at noon today as on the table and some to validly cognize it as in the refrigerator.
• Some humans, however, may incorrectly think that the “yoghurt, which is presently happening at noon today” is in the refrigerator, when in fact it is on the table. Their distorted cognition and mental labeling of the location does not make the yoghurt be in the refrigerator for them. Their distorted cognition may cause them, however, to go to the refrigerator to fetch the yoghurt.

Let us now restrict our analysis to the valid cognition of humans. Within these parameters, let us examine further their valid cognition and labeling of the location of the “yoghurt, which is presently happening” as being on the table at noon today.

The question arises as to whether, at the time of the “present-happening of yoghurt on the table at noon today” or at the time of the “no-longer-happening of yoghurt on the table at noon today,” there is a valid phenomenon no-longer-happening of yoghurt in the refrigerator at noon today, which can be validly cognized by humans?

According to the Buddhist assertions, the answer is “no.” There can only be a “no-longer-happening of a presently-happening phenomenon.” The “no-longer-happening” arises with the perishing of the “presently-happening phenomenon” and then continues to give rise to further moments of “no-longer-happenings.”

Consider the case of the “milk, which is presently happening before noon today.” It has facets of the “ability to give rise to yoghurt on the table at noon today, which is not yet happening” and the “temporarily not-giving-rise to yoghurt on the table at noon today.” The latter is the basis for labeling the “not-yet-happening of the yoghurt on the table at noon today.” The “milk, which is presently happening before noon today” also has facets of the “ability to give rise to yoghurt in the refrigerator at noon today, which is not yet happening” and the “temporarily not-giving-rise to yoghurt in the refrigerator at noon today.” The latter is the basis for labeling the “not-yet-happening of the yoghurt in the refrigerator at noon today.”

When the “milk, which is presently happening before noon today” and its facet of “temporarily not-giving-rise to yoghurt on the table at noon today” perish with the arising of the “yoghurt on the table at noon today, which is presently happening,” the milk’s two facets of its “ability to give rise to yoghurt on the table at noon today, which is not yet happening” and the “not-yet-happening of the yoghurt on the table at noon today” also perish. That perishing occurs simultaneously with the arising of:

• The “no-longer-happening of milk”
• The “no-longer-happening of the milk’s ability to give rise to yoghurt on the table at noon today”
• The “present-happening of yoghurt on the table at noon today.”

The first two of these three are valid nonstatic phenomena and give rise to endless further moments in their stream of continuity, during which they maintain their essential natures. When the “present-happening of yoghurt on the table at noon today” perishes after noon, it gives rise to the “no-longer-happening of yoghurt on the table at noon today.” That “no-longer-happening” is also a valid nonstatic phenomenon and also gives rise to endless further moments in its stream of continuity, during which it maintains its essential nature.

By way of contrast, when the “milk, which is presently happening before noon today” perishes with the arising of the “present-happening of yoghurt on the table at noon today,” the milk’s facets of its “ability to give rise to yoghurt in the refrigerator at noon today, which is not yet happening” and its “temporarily not-giving rise to yoghurt in the refrigerator at noon today” – the basis for labeling the “not-yet-happening of the yoghurt in the refrigerator at noon today” – cease to exist. Simultaneous with their ceasing is the attainment of the nonanalytical stopping of valid cognition of the “present-happening of the yoghurt’s location being in the refrigerator at noon today” on the mental continuums of everyone.

• The difference between perishing (‘jig-pa) and ceasing (‘gog-pa) is that a cause perishes when the circumstances are complete for it to function as the obtaining cause of its result by giving rise to that result.

• A causal phenomenon ceases when it is impossible for any circumstances to occur that would enable it to function as the obtaining cause of its result by giving rise to that result. With the ceasing of that causal phenomenon, all mental continuums become parted (bral-ba) from valid cognition of the result of that causal phenomenon and gain the attainment of a nonanalytical stopping of valid cognition of that result.
• Thus, simultaneously with a perishing is an arising of a nonstatic phenomenon, namely the result of the cause. Simultaneously with a ceasing is the attainment, on a mental continuum, of a static parting and nonanalytical stopping. That parting and nonanalytical stopping last forever and never change.
• Note that someone does not need to validly cognize the ceasing of “something that never happened” in order to attain on his or her mental continuum a parting and a nonanalytical stopping of valid cognition of that something.

Because, in our example, the milk’s facet of “temporarily not-giving-rise to yoghurt in the refrigerator at noon today” does not perish with the simultaneous arising of the “present-happening of yoghurt in the refrigerator at noon today” – because that “present-happening” never happens – there can be no “no-longer-happening of yoghurt in the refrigerator at noon today.” This is because a “no-longer-happening of a phenomenon” can only arise simultaneously with the perishing of that phenomenon.

• In other words, there cannot be a “no-longer-happening” of “something that never-happened.” There can only be a “no-longer-happening of something that actually happened.”

According to the “many-worlds” interpretation of quantum mechanics, when someone observes one possible “presently-happening result” of a causal situation, that person cannot simultaneously cognize the “present-happening of any of the other possible results.” This is because the other “presently-happening results” occur in unobservable “parallel universes.” Presumably, that person would also be unable to cognize the “no-longer-happenings of any of the other possible results” and would experience on his or her mental continuum the arising of the attainment of the nonanalytical stopping of valid cognition of these other results. Thus, Buddhism agrees with the “many-worlds” interpretation on this point.

When Buddhas validly cognize the milk in our above example, they valid cognize the milk’s “abilities to give rise to both yoghurt on the table and yoghurt in the refrigerator at noon today, neither of which is presently happening.” Before noon today, at the time of that cognition, Buddhas also validly cognize the “yoghurt on the table at noon today, which is not yet happening,” and the “yoghurt in the refrigerator at noon today, which is not yet happening.” Buddhas also know the certainty factor that the milk will give rise to “yoghurt on the table at noon today, which is presently happening.”

When validly knowing this certainty factor, Buddhas, however, do not also have on their mental continuum a nonanalytical stopping of valid cognition of “yoghurt in the refrigerator at noon today, which is presently happening.” Before Buddhas have valid cognition of “yoghurt on the table at noon today, which is presently happening,” not only is “yoghurt in the refrigerator at noon today, which is presently happening,” an invalid phenomenon; the nonanalytical stopping of valid cognition of “yoghurt in the refrigerator at noon today, which is presently happening,” is also an invalid phenomenon. Neither phenomenon can be validly known, since neither can be happening before noon today. Similarly, Buddhas can never validly cognize, in this example, a “no-longer-happening of yoghurt in the refrigerator at noon today.”

Thus, despite the fact that Buddhas have complete certainty about what the results will be of all causal phenomena, this does not render as invalid the ability of causal phenomena to give rise to various results, some of which will never happen. All these abilities are valid phenomena, validly knowable during the temporal interval of their “presently-happening.”

Therefore, in terms of karma, the karmic tendencies on our mental continuums have the abilities to give rise to a variety of karmic results, depending on whether or not we repeat or regret the causal actions that gave rise to them, whether or not we apply opponent forces, and so on. Before we are Buddhas, we can validly cognize, or at least know with presumption, that these abilities exist. Based on that understanding, we have choices of how we will act and thus we can affect which result will arise from these karmic tendencies.

Because (1) our karmic tendencies have these abilities and because (2) we can affect what these tendencies give rise to, and because (3) all these abilities and the choices we make are based on previous causes, all of which Buddhas validly cognize, Buddhas are certain of which result will actually arise. Thus, we limited beings affect the “future,” while Buddhas validly cognize “the future” without predetermining what “the future” will be.