How Madhyamika Philosophy Explains the Mystery of Quantum Physics

Abstract:

The theory of relativity informs us that our science is a science of our experience, and not a science of a universe that is independent of us as conscious observers (see the explanation in this article: Why Relativity Exists). This nature of our science is also reflected in the formulation of quantum

mechanics, since the main formulation of quantum mechanics does not provide direct rules for the behaviour of particles. Instead, it provides rules that concern only the results of measurements by observers. This means that the observer is an intrinsic part of the main formulation of quantum mechanics, and what differentiates the observer from physical particles has to be mind and consciousness.

As John von Neumann and Eugene Wigner pointed out, this means that consciousness has an intrinsic role to play in quantum mechanics. Why then has there been so much resistance to recognizing this fundamental fact? And why have physicists, for more than a century, persistently tried to get rid of the observer, even if it meant—in defiance of Occam’s razor—having to insert, by hand, additional hypothetical ad hoc conditions to the basic formulation?

The underlying problem appears to be the need to fit this intrinsic role of consciousness, in quantum mechanics, into the prevailing view, in Western philosophy, of a mind-matter duality. An attempt to fit the role of consciousness into this framework of a mind-matter duality would unfortunately lead to

solipsism, and that is the main problem. So the vast majority of physicists gravitate, instead, to the stance of materialism, and hence the need for them to free quantum mechanics from the conscious observer.

The formulation of quantum mechanics actually does not, in any way, suggest a mind-matter dichotomy, and it certainly does not suggest either materialism or solipsism. Quantum mechanics actually points to a middle way between these two extremes of materialism and solipsism, a realization that both Werner

Heisenberg and Wolfgang Pauli eventually reached. This means that the formulation of quantum mechanics actually points to the philosophical viewpoint of the Buddhist Madhyamika philosophy, also known as the Middle Way philosophy. Madhyamika philosophy would allow us to include the role of consciousness in quantum physics without ending up in the extremes of either solipsism or materialism.

In this paper, the formulation of quantum mechanics is explicitly interpreted in terms of Madhyamika philosophy, and this can be done directly without any modifications to the original formulation of quantum mechanics, and without the need for additional ad hoc conditions. In other words, we can have a direct experiential interpretation of quantum mechanics that fits perfectly with Madhyamika philosophy. Thus, in addition to being supported by extremely precise logical analysis and deep meditational insight, there is now also concrete scientific evidence that the Madhyamaka view of reality is correct.

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1 Relativity and the Underlying Problem in Interpreting Quantum Mechanics

Even a whole century after the discovery of the mathematical formulation of quantum mechanics, there is still no universally accepted and consistent interpretation of what the formulation actually means. Instead, we have a wide array of differing interpretations of quantum mechanics, requiring additional ad hoc hypothetical conditions, inserted by hand, in order to make the formulation fit the particular interpretation favored. The absence of a general acceptance of any of these interpretations means, also, that none of these interpretations are actually free of conceptual problems.

So what exactly is the underlying problem here? How is it that we cannot even interpret, consistently, the formulation of quantum mechanics that, together with the theory of relativity, forms the foundation of all modern physics?

What we plan to explore, in this paper, is the possibility that the problem of interpretation may not actually reside in the basic mathematical formulation of quantum mechanics itself. The problem of interpreting quantum mechanics may, in fact, reside in having to fit the formulation into the prevailing

philosophical view of reality that physicists subscribe to. In other words, we are looking at the possibility that the prevailing philosophical view of reality may, in fact, be incorrect, and that this may be the actual cause of the problems in interpreting quantum mechanics.

Let us begin by looking at what the theory of relativity—which forms the other half of the foundation of modern physics—tells us about the nature of our reality. What the theory of relativity informs us is that our science is actually a science of how we experience the universe, and not a science of a

universe “out there” that is independent of us as observers. This realization enables us to explain why the speed of light is constant in all inertial frames of reference. Since this constancy of the speed of light is a crucial starting postulate in the theory of relativity, it means that, by acknowledging our science as a science of our experience, we can even explain, to a large extent, why the theory of relativity exists. (See Why Relativity Exists.)

On reflection, it is evident that our science must be a science of what we experience because the very data that is used for the formulation of our scientific theories comes from measurements made by conscious observers. Our scientific theories cannot be based on data that is free of the conscious observer, because unobserved data means no data! So our science must be a science of our experience.

Now, if our science is a science of our experience and quantum mechanics reflects this experience by correctly describing what we find in our measurements, it follows logically that quantum mechanics provides important information about how we experience our reality. Quantum mechanics, at least to some extent,

must be about the observer’s experience. This is reinforced by the fact that the very formulation of quantum mechanics is centered on the observer and the results of measurements by the observer. The role of the observer is, in fact, so pivotal in quantum mechanics that the whole formulation would not even make sense without the observer!

It is remarkable, then, that many physicists, instead of looking at what quantum mechanics tells us about our experience of reality, prefer to focus their efforts in trying to get rid of the observer. For more than a century now, physicists have repeatedly introduced new theoretical ideas to free quantum mechanics from the observer. As a result, there is now a whole array of interpretations of quantum mechanics, all aimed at negating the role of the observer, but with none of them fully succeeding in actually removing the observer.

It is time to correct, at least to some extent, this unbalanced situation by now studying what quantum mechanics actually tells us about how we experience the universe, as well as what it tells us about the nature of our reality. For this reason, we will here adopt a direct experiential interpretation of quantum mechanics.

What this means is that we will accept the reality that our science is a science of how we experience the universe, and not a science of a universe “out there” independent of us. We accept that the conscious observer necessarily plays a role in our science, and that quantum mechanics, in the first place,

was formulated to fit the results of measurements made by the conscious observer. This, in fact, is not an assumption. It is actually the truth. We choose here not to battle against this truth but to simply accept it and see what we find. This is what we mean by a direct experiential interpretation of quantum mechanics.

Imagine the scenario if we had, earlier in history, adopted the same approach concerning relativity, and accepted that the scientific definitions of time and space were, in the first place, designed to fit how we, the conscious observers, experience these entities. Again this would not have been an assumption. It would be the truth since the scientific concepts of time and space were actually constructed, in the first place, to fit the conscious observer’s experience of them.

Now, if we had accepted this truth, and had learned that the physiological mechanisms of our body all run via electromagnetic transmission, we would, in fact, have been able to predict that the speed of light would always remain constant, relative to us, regardless of our state of motion. The direct experiential interpretation of the concepts of time and space would then have led to this falsifiable proposition. And we would have confirmed that this

direct experiential interpretation did, in fact, correctly predict that the speed of light is constant relative to all frames of reference. In other words, theoretically, we could have predicted the results of the Michelson-Morley experiment even before it was performed if history had worked out differently! (See Why Relativity Exists.)

So now let us apply a similar direct experiential interpretation to quantum mechanics and see what we can learn from it. We shall do this without invoking artificially added ad hoc conditions to the basic rules of quantum mechanics. In other words, we will adopt an interpretation that accepts directly what the formulation of quantum mechanics is telling us about the reality that we experience.

2 The Formulation of Quantum Mechanics

2.1 Introduction

At the beginning of his paper on quantum physics, entitled “Toward ‘It From Bit,’” renowned physicist, John Wheeler, made the following comment: “If these questions verge on philosophy, then perhaps we can adopt as motto, ‘philosophy is too important to be left to the philosophers.’” Given that most physicists have little interest in actually studying what quantum mechanics tells us about how we experience our reality, it is appropriate here that we also apply the reverse form of the motto: ‘quantum physics is too important to be left to the physicists’!

So let us begin now by outlining the formulation of quantum mechanics, in a way that the general reader can understand, and also demonstrate how pivotal the role of the observer is to this formulation. Fortunately, it is possible to present the formulation of quantum mechanics without the use of actual mathematics, and yet convey how and why the crucial philosophical problems arise from it.

Keep in mind that even a full understanding of the mathematics behind quantum theory will not tell us why the mathematical formulation works in this way. As Richard Feynman says, nobody actually understands quantum physics. Physicists know how to compute the results of experiments using quantum mechanics, but we have no idea why the mathematics work. That may seem odd, but it is the truth. In a sense, physicists are like technicians who know how to operate a machine without actually knowing why the machine works.

So readers need not feel that they do not understand something because they are not well versed in the mathematics. Take comfort that even those who are fully conversant with the mathematics also do not know why it works!

2.2 The Quantum Wave Function

In order to make this presentation—of the formulation of quantum mechanics—easier to understand, I will describe each point twice—first using the actual scientific and mathematical terminology, and then repeating the same point using an analogy (which involves a special kind of cake and how we cut it!). Let us begin.

Quantum mechanics basically involve a mathematical entity (often in the form of a matrix) known as the quantum wave function (also called the quantum state). This quantum wave function is a mathematical entity that appears to encapsulate all the information we have about a particle. The quantum wave function actually presents us with the probability distribution of measurement results that can occur if and only if a measurement is made on the particle involved.

Note, right from the onset, that quantum mechanics is about measurements by an observer and what the observer may find. Quantum mechanics does not provide us with direct rules governing the behaviour of particles. Incredibly, they only tell us about the particle indirectly, through rules governing the results of measurements made on the particle by an observer! That is why the very formulation of quantum mechanics would not even make sense without an observer.

Let us simplify this idea of the quantum wave function with an analogy. Imagine the quantum wave function to be a special kind of cake (of the birthday cake variety), which has within its structure, all the information we can possibly obtain about a particle if we make measurements on the particle. What is

strange about this information found in the cake, though, is that it does not tell us anything definite about the particle. It only gives us a probability distribution of what we may find if we make an actual measurement on the particle. So how do we obtain this probability information about the particle from this cake? We have to follow a certain procedure, which in scientific language is as follows:

If a measurement is made on a particle—let us say, an electron—an operator is applied to the quantum wave function. An operator is a mathematical procedure, and different operators correspond to different properties—known as observables—of the particle that we want to measure. Thus, if we want to

measure the particle’s position, we apply the position operator that corresponds to the position observable. If we want to measure the particle’s momentum, we apply a different operator—the momentum operator that corresponds to the momentum observable—to the quantum wave function.

Now what happens to the quantum wave function when we apply a particular operator is this. The operator effectively informs us how to divide the quantum wave function into separate components known as eigenstates (also known as eigenfunctions or eigenvectors). The set of eigenstates corresponding to a particular operator is known as its preferred basis.

If we are looking at this in terms of our cake analogy, the operator is like a set of instructions on how to divide up our cake (the quantum wave function). For measurement of different properties (or observables) of the particle (our electron), we have different sets of instructions on how to divide

up the cake. In other words, different operators divide the quantum wave function (our cake) into different types of eigenstates (our parts of the cake). For example, one operator may tell us that the cake is to be divided into rectangular parts, while another operator may tell us that the cake is to be divided into triangular slices.

Note that we are not actually cutting the cake yet, but are only marking out the divisions (we only actually cut the cake when we make an actual measurement of the particle). The portions of the cake, so marked up for division, according to the instructions provided by the operator, are the

eigenstates. The set of these parts of the cake—that the operator instructs us to mark out—is known as the preferred basis of that particular operator. Each different operator therefore has a different preferred basis. The preferred basis for dividing up the quantum wave function is thus determined by the operator employed, which, in turn, is determined by the observable we choose to measure.

Let us now add a new scientific term to our exposition of quantum mechanics: the word superposition. In scientific terminology, we say that different operators instruct us to consider the quantum wave function as a superposition of different sets of eigenstates. The word superposition essentially means a

combination, where all the parts are basically added up (or superimposed upon each other) to form a whole. As long as we have not yet made an actual measurement, we can consider the quantum wave function to be a superposition of its eigenstates.

Let us return to our cake analogy to illustrate the situation. Recall that we can imagine the quantum wave function to be like a birthday cake. When we apply an operator, it tells us how the cake is to be divided into parts, which are the eigenstates. In scientific terminology, we say that the quantum wave function (our cake) is formed by a superposition (combination) of all its eigenstates (the parts of the cake).

Note that the word superposition can only be used here if and only if we have not yet cut the cake. In other words, the parts of the cake—that we have marked out—are actually still joined together. Once we actually cut the cake (i.e., make an actual measurement), the parts are no longer in a

superposition. The important point is this: if we have not actually made a measurement (i.e., actually cut the cake), the parts are still joined together, and we can change our mind and decide to cut the cake in a different way.

Going back to the actual situation, what this means is that, if we have not made an actual measurement, of say, the position of our electron, we can change our mind and decide to measure something else like the electon’s momentum instead. In other words, without an actual measurement being made on the electron, its quantum wave function is still intact, and we can still decide to change the operator we want to apply to it.

To reiterate: As long as we have not made an actual measurement on the electron, we say that its quantum wave function (our cake) is a superposition (combination) of its eigenstates (the parts of the cake). If we make an actual measurement, something unusual happens, and we can then no longer consider

the quantum wave function as a superposition of its eigenstates. As we shall explain later, this is because something dramatic (known as the collapse of the wave function) happens to the quantum wave function once we actually make a measurement on the particle concerned.

Let us now add something more (the concept of eigenvalues) to our exposition of the formulation of quantum mechanics, using scientific terminology: Recall that, for each different observable, when we apply its corresponding operator, the quantum wave function yields up a set of eigenstates. Now we learn that each eigenstate has a particular number or value attached to it, known as its corresponding eigenvalue.

These eigenvalues represent the possible results of the measurement of that particular observable (that the preferred basis of eigenstates correspond to). The complete set of eigenvalues of all the eigenstates represent the complete set of possible measurement results of the observable that we choose to

measure. In other words, each eigenstate has an eigenvalue, and these eigenvalues are the different possible results or values that the observable can have (if we were to actually measure that observable of the particle).

For example, if we choose to measure the electron’s position, we apply the position operator to the quantum wave function of the electron, and the set of eigenstates and their corresponding eigenvalues (that the operator produces) tell us that these are the possible results of the measurement. For example, that particular electron’s quantum wave function may inform us that the position of the electron can be, for example, at values of 2, 3, or 7 on our position scale. The values of 2, 3, or 7, would be the eigenvalues of the position observable, for that particular electron’s quantum wave function. Remember that each eigenvalue has its own eigenstate. So, in our example, when we apply the position operator, we find that the quantum wave function can be divided into three eigenstates. There are then three eigenvalues, one eigenvalue for each of the three eigenstates. [for simplicity, we ignore those cases with degenerate eigenvalues, since it will not affect our understanding of how quantum mechanics works]

In terms of our cake analogy, the situation is this. When we apply our rules for dividing the cake (the operator), we notice that the different parts of the cake (the eigenstates) each contain a label, which is a number or value (the eigenvalues). Each part of the cake has a different label (eigenvalue)

stuck to it. If the cake has been divided into three parts, there are three different labels—one for each part of the cake. These labels, which are numbers (the eigenvalues), represent the possible measurement results if we measure that particular observable of the particle concerned (i.e., our electron).

Let us now move on, in scientific terminology, to something new, which is the one other important piece of information (apart from the eigenvalues) that we can obtain from the quantum wave function when we apply an operator. A particular operator not only informs us of what eigenstates we can divide the

quantum wave function into (i.e. its preferred basis), it also informs us of the “size” of each of these eigenstates. This “size” is given by the expansion coefficients of the eigenstates. These expansion coefficients are essentially numbers that tell us how big each of the eigenstates are—i.e., they give each of the eigenstates a weightage. (Note that these numbers are not the eigenvalues. The expansion coefficients form another set of numbers that informs us of the size of each eigenstate.)

The expansion coefficient of a particular eigenstate reflects the probability that our measurement will yield the result given by the eigenvalue of that particular eigenstate. In other words, the bigger the expansion coefficient is, the more likely will its corresponding eigenvalue be the measurement result. Thus, the expansion coefficients of the eigenstates provide us with a probability distribution of the possible results of a measurement.

Looking again at the analogy of our birthday cake, we can now see that the application of an operator not only tells us how the cake is to be divided (i.e. what its eigenstates are), what the label of each part is (i.e., its eigenvalue), but also how big each of those parts (the eigenstates) are going to be

(indicated by the expansion coefficient of each eigenstate). In summary, each part of the cake (i.e. each eigenstate) has a label (its eigenvalue) that informs us of a possible measurement result; and each part of the cake (i.e. each eigenstate) has a particular size (represented by its expansion coefficient) that tells us of the probability that its particular label (the eigenvalue) would be the actual measurement result.

Thus the way the quantum wave function is to be divided (upon applying an operator) tells us two things:

(1) The corresponding eigenvalues of the eigenstates inform us of the possible results of our measurement.

(2) The corresponding expansion coefficient of each eigenstate informs us of the probability that our measurement would yield that particular eigenvalue of the eigenstate.

That is why we say that the quantum wave function represents the probability distribution of the possible results of a measurement of an observable. For example, if we want to measure an electron’s position, the application of the position operator will give us a probability distribution of the electron’s possible positions.

It is important to realize, however, that the quantum wave function actually does not tell us exactly where the particle is. It only gives us the possible positions where we would find the particle if and only if we choose to actually measure its position. That is why the quantum wave function is called a probability wave, and that is the peculiarity of quantum mechanics: All we can know about a particle’s observable from its quantum wave function is simply a probability distribution of the possible results, if we actually make the measurement. If we do not make an actual measurement, the particle does not seem to even decide where it actually is!

2.3 A Note for Readers Without a Mathematics Background

If, by now, you feel puzzled by the mysterious nature of the quantum mechanics formulation, and begin to think that you may be missing something because you lack the required mathematical ability, let me assure you, once again, that the mathematics do not help, in any way, to explain the mysterious nature of the formulation.

The mathematics merely enables us to compute the results of applying a particular operator to a particular quantum wave function. It allows us to compute the eigenstates and their corresponding eigenvalues and expansion coefficients, and we do this by manipulating the numbers according to certain mathematical procedures. Unfortunately, we have no idea why these particular mathematical procedures work.

We only know that the mathematical procedures work because the eigenvalues we obtain do match the possible experimental results. But we have no clue why these mathematical procedures do this. This is a fact. We also know experimentally that the expansion coefficients do provide us with the correct probability distribution of the measurement results. But again, we have no idea why these mathematical procedures (for obtaining the expansion coefficients) do what they do. We are truly like technicians who know how to push the correct buttons to get the machine to work, but actually have no idea why the machine works.

That is why this ability to manipulate the numbers does not help, in any way, to explain the formulation of quantum mechanics. Physicists are as equally puzzled by the mysterious nature of the formulation as you are. Our mathematical ability does not help, in any way, to reduce this puzzlement. This is because we actually have no idea at all why the mathematics work!

Unfortunately, some physicists do try to suggest that they understand quantum mechanics simply because they can compute the results. Do not be fooled by this. This would be like claiming to understand how a car works by simply being able to drive it. The ability to compute, by merely following certain mathematical procedures, is not the same as understanding why it works.

If physicists really understand why the mathematics work, we would not have all these differing interpretations of quantum mechanics that we find today. Furthermore, these interpretations should also then not contain conceptual problems. But they do. It is therefore a fact, as Richard Feynman says, that nobody understands why the mathematics in quantum mechanics work!

2.4 The Collapse of the Wave Function

It should be evident, by now, how pivotal the role of the observer is, in the formulation of quantum mechanics. The quantum wave function deals with possible results of measurements by the observer, and with the probability distribution of these possible results upon measurement by the observer. Quantum

mechanics does not provide rules for the behaviour of a particle, directly, on its own right, independent of the observer, but only rules for the results of measurements of the particle by the observer. That essentially explains why physicists have still not succeeded in freeing quantum mechanics from the observer, even after repeated attempts at it for more than a century!

We now arrive at the one single part of the original formulation of quantum mechanics that disturbs physicists the most; and that is what happens when the observer actually makes a measurement. This event is known as the collapse of the wave function.

What happens when the observer makes an actual measurement is this. The quantum wave function suffers an abrupt and discontinuous change. It collapses into one of its eigenstates. In other words, one of the eigenstates replaces the quantum wave function and becomes the new quantum wave function. All the other eigenstates disappear. This is what is meant by the term “collapse of the wave function.”

Following our analogy of the birthday cake, making an actual measurement of an observable is like actually cutting the cake (not just marking out the divisions) into its appropriate parts (its preferred basis) according to the instructions provided by the operator corresponding to the observable we are measuring. The collapse of the wave function is then akin to only one slice of the cake (the eigenstate with the eigenvalue that corresponds to our measurement result) being chosen by chance and the rest of the cake being thrown away. This slice of the cake, that is chosen by chance, then becomes our new cake, and the parts of the cake that have been thrown away are irretrievable. They are gone. We now have to live with the slice of cake that survived (the eigenstate with the correct eigenvalue) as the new cake (the new quantum wave function).

The eigenstate that takes over as the new quantum wave function is the eigenstate whose corresponding eigenvalue is what the observer finds as the result of an actual measurement of the observable involved. The process proceeds in this manner. If an observer chooses to measure, for example, an electron’s position, the possible outcomes are determined by the set of eigenstates and their corresponding eigenvalues, according to the position operator’s preferred basis. Then when the observer actually measures the electron’s position, and finds the electron, for example, at position marked 3 on his position scale, the quantum wave function collapses into (and becomes) the eigenstate that has the corresponding eigenvalue of 3. All the other eigenstates disappear.

The expansion coefficients for any future preferred basis of this new quantum wave function are all readjusted, in a mathematical procedure known as normalisation, so that they again reflect the probability distribution of any future measurement results. In other words, the expansion coefficients are scaled up proportionately to again reflect the new probability distribution provided by the new quantum wave function.

In terms of our analogy with the cake, this process of normalisation is akin to blowing up, proportionately, the size of our surviving slice of cake (the chosen eigenstate) until it is about the same size as the original cake (the original quantum wave function that is to be replaced by this surviving eigenstate).

Note that there are actually two ways that an actual measurement by the observer affects our reality. First, the observer affects our reality by choosing what he wants to measure. This observable that he chooses to measure determines the operator, which in turn determines the preferred basis. Thus, by his choice of what to measure (by choosing the appropriate experimental set-up), the observer determines the set of possible eigenstates that the original quantum wave function can collapse into. The second way the observer affects our reality is by actually making the measurement, and that is when the observer causes the original quantum wave function to transform into one of these possible eigenstates.

The collapse of the wave function, which is an abrupt and discontinuous change, occurs if and only if an observer makes an actual measurement and observes the result. If no actual measurement is made, the quantum wave function does not collapse, but instead evolves over time in a continuous and orderly fashion according to the Schrodinger Equation. This equation, discovered by Erwin Schrodinger, tells us how the quantum wave function gradually changes over time depending on certain properties of the particle concerned, like its energy and momentum.

This gradual change, according to the Schrodinger Equation, is somewhat akin to how a wave would evolve over time and is continuous and deterministic (i.e., predictable). Using the Schrodinger Equation, we can tell ahead of time what the quantum wave function will be like, provided no observer actually makes a measurement.

If an observer actually makes a measurement, the collapse of the wave function occurs instead, and this change is abrupt, discontinuous and unpredictable. The question of what exactly causes the collapse of the wave function is known as the measurement problem, and it is still, arguably, the most prominent unresolved issue in quantum physics.

In terms of our cake analogy, this is what happens. If we do not make an actual measurement, our cake seems to change shape in a predictable fashion—like a soft jelly wobbling in a wave-like motion. This is akin to the quantum wave function (our cake) evolving according to the Schrodinger Equation. Here we can predict how the shape of our cake will change over time.

If we make an actual measurement, however, something very different happens to our cake. We then get a collapse of the wave function that is akin to our actually cutting our cake. Now, by chance, only one slice of cake (the “chosen” eigenstate) survives, while the rest of the cake disappears. This single slice that we are left with then magically enlarges itself until it is the same size as the original cake (the process of normalization), and becomes our new cake (the new quantum wave function).

If we do not make any further measurements, this new cake (the new quantum wave function) will also change shape continuously by wobbling in jelly-like fashion (i.e., by evolving according to the Schrodinger Equation), but of course, it is now a new and different cake, and not the same as the original cake we cut. Therefore, our cutting of the cake has actually given us a new cake (i.e., a new quantum wave function).

In the collapse of the wave function, the probability concerning which eigenstate actually takes over as the new quantum wave function follows the probability distribution reflected by the expansion coefficients of the original quantum wave function (before its collapse). Note that, from the quantum wave function, we only have a probability distribution of the possible results of the measurement. We cannot predict exactly what the actual result will be. In other words, the surviving eigenstate gets “chosen” by chance. This unpredictability of the wave function collapse upset Einstein so much that he made the famous comment, “God does not play dice with the universe,” to which Niels Bohr was said to have responded: “Einstein, stop telling God what to do!”

What actually upsets many physicists over this collapse of the wave function, however, is not its probabilistic nature, but the fact that the observer now seems to actually have a role in determining our reality. If there is no collapse of the wave function, the formulation of quantum mechanics only appears to accord the observer a passive role. The part of the quantum mechanics formulation concerning the quantum wave function, the eigenstates, and their corresponding eigenvalues and expansion coefficients, of course, do necessarily involve the observer, but the observer appears, so far, to be just passively observing.

The collapse of the wave function changes all that. Now the observer, upon choosing what to measure and actually making a measurement, causes an abrupt change to the quantum wave function. The observer now not only observes, but actually changes our reality by the act of making an actual measurement and taking note of the results. The observer is thus no longer just an observer. He or she actually becomes a participant in shaping our reality!

In terms of our cake analogy, what all this amounts to is this. Einstein’s concern is that when we actually cut the cake (i.e. make an actual measurement and cause a collapse of the wave function), the piece of cake (the eigenstate) that becomes the new cake is chosen randomly, a choice that cannot be predicted. It is purely a probabilistic event, thus prompting Einstein’s comment that “God does not play dice.”

Other physicists, however, appear more concerned with the fact that the observer actually gets to decide whether or not to cut the cake (i.e. whether or not to make an actual measurement), and in the process, decide whether or not to end up with a new cake (i.e. a new quantum wave function). This new cake (the new quantum wave function) represents a dramatic change in our external reality. In other words, the observer is now not only a passive observer, but an active participant in altering our reality by actually cutting the cake!

Not only that, the observer can choose to affect our external reality differently by deciding how to cut the cake. The observer can do this simply by choosing to measure different observables. Each different observable the observer chooses to measure means a different operator (i.e. a different rule on how to cut the cake), which results in a different preferred basis with different possible eigenstates (i.e. a different set of possible cake parts) from which a random selection is made. In other words, the observer can actively affect our reality by choosing whether or not to make a measurement (i.e. cut the cake) and also by choosing exactly what observable to actually measure (i.e. how to actually cut the cake).

This means, of course, that our science is not a science of a universe “out there” independent of us as observers. If anything, this evidence from quantum physics is even more compelling than that provided by the theory of relativity, in informing us that our science is an observer-dependent science. The theory of relativity informs us that time and space are really entities defined by us, observers, to reflect how we experience the universe. Here, in quantum physics, the observer, by the very act of observation, actually changes our reality!

Before continuing, we have to note that some physicists insist that the collapse of the wave function should no longer be considered part of the quantum mechanics formulation. They justify this by stating that there exists an interpretation of quantum mechanics, known as the “many-worlds interpretation,” that claims that the collapse of the wave function does not occur. However, this many-worlds interpretation has to introduce something new to take the place of the collapse of the wave function; and in this case, it posits the splitting of the universe into an infinite number of alternate universes, none of which can ever be directly verified experimentally!

The big disadvantage with this many-worlds interpretation is that, even with such an extravagant ad hoc addition, by hand, to the theory (i.e. infinite alternate universes), there still remains many unresolved problems. One problem is that the probability distribution provided by the expansion coefficients no longer apply; another problem is the unresolved question of what exactly causes the universe to split if it does not involve the observer; yet another problem is the unresolved question of how we determine the preferred basis for the splitting of the universe (and in fact, why there should even be a preferred basis at all, when there is no observer involved). In other words, it remains to be seen whether the many-worlds interpretation can ever resolve all these problems, and adequately explain quantum mechanics without involving the observer. It has definitely not succeeded yet.

Since we are aiming for a direct experiential interpretation of quantum mechanics without having to introduce, by hand, artificial ad hoc additions to the formulation, we will keep to the original formulation of quantum mechanics that includes the collapse of the wave function. This issue of the collapse of the wave function was, in fact, the crucial focus of discussion and debate among the original founders of quantum mechanics, physicists like Werner Heisenberg, Erwin Schrodinger, Albert Einstein, Niels Bohr, Wolfgang Pauli, Max Planck, John von Neumann, and others.

3.1 The Copenhagen Interpretation

Our aim, in this paper, is to eventually look at what quantum mechanics is directly telling us about our reality. So, since we are aiming for this direct experiential interpretation of quantum mechanics—an interpretation that accepts the role of the conscious observer in our reality—we will dispense with all the ad hoc hypothetical additions, introduced by many physicists over the last century, in attempts to deny the conscious observer a role in quantum physics.

These include ideas like infinite parallel universes, hidden variables, spontaneous wave function collapses, or collapses upon consistent histories being achieved, and so on. These ad hoc hypotheses are designed mainly to negate the role of the observer, rather than to learn what quantum mechanics actually tells us about our experienced reality. In contrast, our aim here—in looking for a direct experiential interpretation of quantum mechanics—is to specifically learn what quantum mechanics actually tells us about our experienced reality and about the possible role of the conscious observer.

It is helpful for our purpose to look, first, at an early interpretation of quantum mechanics, known as the Copenhagen interpretation, because it probably came the closest to actually interpreting the formulation of quantum mechanics as it is. Because the Copenhagen interpretation is almost (but not entirely)

free of artificially added ad hoc assumptions—introduced to force the formulation to conform to some preconceived idea of reality—the interpretation provides us with a reasonable starting point as a basis for an eventual direct experiential interpretation of quantum mechanics. The Copenhagen interpretation is, in fact, still considered the standard interpretation of quantum mechanics.

This Copenhagen interpretation was devised mainly by two of the original founders of quantum physics, Niels Bohr and Werner Heisenberg. They were prominent pioneers of quantum physics, and they certainly wished to interpret the formulation of quantum mechanics as it is, if possible, without further hypothetical ad hoc embellishments. Unfortunately, as we shall see, Bohr and Heisenberg still ended up inserting one ad hoc assumption—that was never suggested in the formulation of quantum mechanics in the first place—purely to constrain the role of the observer.

Werner Heisenberg (left) with Niels Bohr at the Copenhagen Conference in 1934 To begin with, Niels Bohr and Werner Heisenberg, in the Copenhagen interpretation of quantum mechanics, clearly acknowledged the role of the observer. In the words of Niels Bohr:

There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we can say about Nature.

We can see that, right from the beginning, Niels Bohr already had the idea that quantum mechanics merely represents our knowledge or information about the external world. “What we can say about Nature,” of course, acknowledges the role of the observer, and basically supports the fact that our science is a science of our experience, and not a science of a universe “out there” independent of us observers.

However, Bohr also emphasizes that there is no actual quantum world. This may appear odd, but the reason why he does that can be found, here, in what Werner Heisenberg writes, concerning the quantum wave function (which he calls the probability function):

… the theoretical interpretation of an experiment requires three distinct steps:

(i) the translation of the initial experimental situation into a probability function;

(2) the following up of this function in the course of time;

(3) the statement of a new measurement to be made of the system, the result of which can then be calculated from the probability function. …

The second step cannot be described in terms of the classical concepts; there is no description of what happens to the system between the initial observation and the next measurement. It is only in the third step that we change over again from the ‘possible’ to the ‘actual’.

This is essentially the problem. There appears to be no way of describing what a particle is doing in between the initial measurement and the next measurement. If we measure, say, the position of an electron, we can obtain both its position and the initial quantum wave function (i.e. the probability function) of the electron, and we can obtain the electron’s subsequent position by a further measurement. The problem is that, in between these two

measurements, we only have the quantum wave function, which provides us with the probability of where we would find the electron if and only if we make a measurement. But since we are not making a measurement during this interim period, it means that the electron does not even “decide” where it is at this time. Only upon the second measurement does this, in Heisenberg’s words, “change over again from the ‘possible’ to the ‘actual’.” Heisenberg goes on to say:

… there is no way of describing what happens between two consecutive observations. It is of course tempting to say that the electron must have been somewhere between the two observations and that therefore the electron must have described some kind of path or orbit even if it may be impossible to know which path. This would be a reasonable argument in classical physics. But in quantum theory it would be a misuse of the language which … cannot be justified.

Heisenberg goes on to question, in his own words,… whether this warning is a statement about the way in which we should talk about atomic events or a statement about the events themselves, whether it refers to epistemology or to ontology.

This is a highly pertinent question that Heisenberg poses, and that is the question of whether this refers to our inability to know (epistemology) or to the fact that the electron is not actually manifesting as a real entity (ontology) during this interim period between the measurements.

3.2 The ]]Double-Slit Experiment}}

Here we will look more closely at Heisenberg’s question of whether the situation of the particle between two measurements is one of epistemology or ontology.

If quantum mechanics merely represents our knowledge or “what we can say about” the external world, it would suggest that there is an external world to talk about. But that does not seem to be the case here. The electron cannot be said to be at any particular place during the period between the measurements. It is not just a case of our ignorance of where it is; the electron actually does not “decide” where it is! That is why Heisenberg refers to this state as the ‘possible’ and not the ‘actual’. There does not seem to be a reality for the electron in the interim period between the measurements.

In his book “Physics and Philosophy,” Heisenberg elaborates why we cannot even propose a possible path for a particle during the interim period between two measurements. In other words, it is not just that we do not know where the particle is, we cannot even come up with a possible path that the particle could have been taken. In Heisenberg’s words:

… it is necessary to explain quite clearly why one would get into hopeless difficulties if one tried to describe what happens between two consecutive observations.

For this purpose it is convenient to discuss the following ideal experiment: We assume that a small source of monochromatic light radiates toward a black screen with two small holes in it. The diameter of the holes may be not much bigger than the wavelength of the light, but their distance will be very much bigger. At some distance behind the screen a photographic plate registers the incident light. If one describes this experiment in terms of the wave picture, one says that the primary wave penetrates through the two holes; there will be secondary spherical waves starting from the holes that interfere with one another, and the interference will produce a pattern of varying intensity on the photographic plate. [This is the double-slit experiment. See Figure 1.]

Figure 1. Diagram illustrating the double-slit experiment (as described by Heisenberg). The interference pattern—with bright and dark fringes—is what is shown on the right side of the diagram.

The blackening of the photographic plate is a quantum process, a chemical reaction produced by single light quanta [note: a light quanta is a particle of light called a photon]. Therefore, it must also be possible to describe the experiment in terms of light quanta. If it would be permissible to say what happens to the single light quantum between its emission from the light source and its absorption in the photographic plate, one could argue as follows:

The single light quantum can come through the first hole or through the second one. If it goes through the first hole and is scattered there, its probability for being absorbed at a certain point of the photographic plate cannot depend upon whether the second hole is closed or open. The probability distribution on the plate will be the same as if only the first hole was open. If the experiment is repeated many times and one takes together all cases in

which the light quantum has gone through the first hole, the blackening of the plate due to these cases will correspond to this probability distribution. If one considers only those light quanta that go through the second hole, the blackening should correspond to a probability distribution derived from the assumption that only the second hole is open. The total blackening, therefore, should just be the sum of the blackenings in the two cases; in other words,

there should be no interference pattern. But we know this is not correct and the experiment will show the interference pattern. Therefore the statement that any light quantum must have gone either through the first or through the second hole is problematic and leads to contradictions. This example shows clearly that the concept of the probability function does not allow a description of what happens between two observations. Any attempt to find such a description would lead to contradictions; this must mean that the term ‘happens’ is restricted to the observation.

Now, this is a very strange result, since it seems to indicate that the observation plays a decisive role in the event and that the reality varies, depending upon whether we observe it or not.”

Heisenberg has described the famous double-slit experiment, an experimental set-up that is often used to illustrate the weirdness of quantum physics. This same experiment can now be carried out using electrons or even larger particles, like bucky-balls (i.e., the buckminsterfullerene molecules).

Essentially what happens is this. If we randomly send electrons through two slits towards a screen without measuring exactly which slit the electron travels through, the electrons will form an interference pattern on the screen, which is a pattern of bright and dark fringes. This suggests that the electrons are behaving like a wave, since only waves are supposed to form interference patterns. This, in turn, suggests that the electrons are actually passing through both slits at the same time.

Figure 3. How electrons on the screen, accumulated over time, form an interference pattern. (picture credit: Dr. Tanamura) Even if we shoot the electrons, one at a time, through the two slits without making any measurement of which slit they pass through, we will still get an interference pattern on the screen. Each electron will register as a single dot on the screen, but as more and more electrons arrive, an interference pattern, made up of all these individual dots, will clearly form on the screen (see Figure 3).

The real peculiarity of the double-slit experiment is this. If, while shooting electrons through the two slits, we make measurements that tell us which slit each electron actually passed through, an interference pattern would not form on the screen. This is because our observation of which slit the electron passed through “forces” the electron to manifest as a particle at that particular slit. This means that it is no longer functioning as a wave, and hence there is no interference pattern.

So what actually is happening? How can an electron, which we know is a particle, behave like a wave simply because we do not observe which slit it passed through? We know now that this wave is actually the quantum wave function, which is a probability wave. Since we did not measure which slit the electron passed through, we only have the quantum wave function and all that tells us is merely the probability distribution of where the electron would be found if and only if we make a measurement of its position.

Since we did not make a measurement, we only have the probability distribution of its possible position. For example, one particular electron may have a 50% chance of passing through one slit and a 50% chance of passing through the other slit. The key point is this: we cannot assume that the electron passed

through one or other slit. Since we did not make any measurement at all, the electron has not even “decided” which slit it passed through. Effectively it passed through both slits and that is the only way the interference pattern could have formed! That is what Heisenberg meant by his statement: “one would get into hopeless difficulties if one tried to describe what happens between two consecutive observations.”

Thus, the situation concerning the electron between two measurements is actually a question of ontology rather than epistemology. It is not just a question of us not knowing where the electron is during this interim period; it is as though the electron did not actually manifest as a particle during that time!

3.3 Attempts to Deny a Role for Consciousness Although Niels Bohr and Werner Heisenberg both acknowledged the role of the observer in quantum mechanics, neither of them wanted to acknowledge that consciousness actually influenced the external world, although Heisenberg, under the influence of Wolfgang Pauli, probably came close to acknowledging this later on.

Let us explore, here, how Bohr and Heisenberg tried to avoid giving consciousness an active role in quantum physics. The Copenhagen interpretation certainly acknowledges the collapse of the wave function upon the act of measurement. How then does it avoid giving consciousness a role in this act of measurement?

In his description of the Copenhagen interpretation, Heisenberg has this to say:

… the transition from the ‘possible’ to the ‘actual’ takes place during the act of observation. If we want to describe what happens in an atomic event, we have to realize that the word ‘happens’ can apply only to the observation, not to the state of affairs between two observations. It applies to the physical, not the psychical act of observation, and we may say that the transition from the ‘possible’ to the ‘actual’ takes place as soon as the

interaction of the object with the measuring device, and thereby with the rest of the world, has come into play; it is not connected with the act of registration of the result by the mind of the observer. The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change of our knowledge in the instant of registration that has its image in the discontinuous change of the probability function.

The “discontinuous change in the probability function,” that Heisenberg mentions above, is the collapse of the wave function. This makes the passage somewhat puzzling because Heisenberg states that the collapse of the wave function takes place with the act of registration of the result by the mind of the observer. That would seem to imply that the conscious mind does have a role to play in this collapse of the wave function, which would, in turn, mean that it has an influence on the external world.

How then does Heisenberg avoid this implication? What he does is to artificially divide the world into the microscopic atomic world and the macroscopic “rest of the world.” Then the claim is that, somehow, the interaction, between the microscopic world of, say, an electron with the macroscopic “rest of the world” represented by the measuring equipment, triggers off the collapse of the wave function.

Thus, Heisenberg divides the process of the collapse of the wave function into two parts. The first part is the transition from the ‘possible’ to the ‘actual’, which takes place during the interaction of the object with the measuring device. He then assigns the discontinuous change in the probability wave as the second part, where the knowledge of this process is registered in the observer’s mind.

This then is the way Heisenberg and Bohr attempt to avoid giving an active role to consciousness in the collapse of the wave function. This further statement by Heisenberg reiterates this hypothetical idea:

Certainly quantum theory does not contain genuine subjective features, it does not introduce the mind of the physicist as a part of the atomic event. But it starts from the division of the world into the ‘object’ and the rest of the world, and from the fact that at least for the rest of the world we use the classical concepts in our description.

How this interaction—between an elementary particle (like an electron) and the “rest of the world”—triggers off the collapse of the wave function is never made clear in the original Copenhagen interpretation. This hypothetical idea is also not part of the basic formulation of quantum mechanics, so it would have to be considered an ad hoc hypothetical addition to the formulation, designed purely to deny consciousness an active role in quantum mechanics.

Thus, while these pioneers of quantum mechanics, Niels Bohr and Werner Heisenberg, largely acknowledged the role of the observer, they, nonetheless, tried to limit this role to that of a mere passive observer, whose consciousness somehow did not influence the external world. Significantly, the only way they

could do this was to introduce, by hand, the idea of a “microscopic-macroscopic divide” in the material world—an ad hoc hypothetical idea that is not at all suggested by the formulation of quantum mechanics. (There is actually also a problem with this hypothetical microscopic-macroscopic divide, as we shall see in the next section.)

Over the last century, there have been many more ad hoc hypothetical additions, introduced by different physicists, to the formulation of quantum mechanics, aimed specifically at attempting to deny a possible active role for consciousness. None of these ad hoc hypothetical additions (and their corresponding interpretations) have actually fully succeeded in getting rid of the conscious observer, without running into serious problems.

Later, we will look more closely at why so many physicists felt such a persistent need to free quantum mechanics from the conscious observer. We will, however, take note, first, that there were prominent physicists who did accept the role of consciousness in quantum physics.

4.1 The von Neumann Chain

While other physicists, like Erwin Schrodinger, did contemplate according consciousness an active role in the collapse of the wave function, the man generally credited with formally introducing consciousness into the formulation of quantum mechanics is the eminent mathematician, John von Neumann. He is acknowledged as the man who first laid down the formal mathematical foundations of quantum mechanics.

John von Neumann

The reasoning, introduced by John von Neumann, as to why consciousness must play a role in the collapse of the wave function involves what is now known as the von Neumann chain. It is based on the fact that the measurement apparatus is also composed of elementary particles and hence must also satisfy the principles of quantum mechanics. The reasoning of von Neumann is as follows:

In order to measure an observable of an object, the measurement apparatus has to interact with the object. As a result of the interaction between the object and the measurement apparatus, the object becomes entangled with the measurement apparatus. What entanglement means is that the quantum wave function of each of the entities cannot be described independently of each other. The properties of the object and the measurement apparatus must now be correlated, so the two entangled entities essentially become one system. This one system can now theoretically be described by a new quantum wave function for the whole system. There is still no collapse of the wave function.

Thus, being merely entangled with the measurement apparatus means that the object is still not in an eigenstate, since the measurement apparatus has yet to indicate a definite result. In order to collapse the wave function of this system comprising of the object together with measurement apparatus, we now need

to make a measurement of this whole system. But then, the new measurement apparatus for this purpose, in turn, merely becomes entangled with the system it is meant to measure. And we still do not have a collapse of the wave function. Theoretically, this can go on indefinitely, in a process now known as the von Neumann chain.

Von Neumann then reasons that there must be a break or cut (schnitt in German) somewhere to bring about the collapse of the wave function, and that this break must be achieved by an entity that is different from systems that are merely composed of elementary particles. That different entity needed to bring about this break in the von Neumann chain, according to him, must be our subjective perception (apperzeption in German).

In other words, the ad hoc hypothetical idea of a “microscopic-macroscopic divide”—introduced by Bohr and Heisenberg to constrain the role of consciousness in the Copenhagen interpretation—cannot adequately account for the collapse of the wave function. An observation by the conscious mind is still required.

The man who gave us the Schrodinger Equation, Erwin Schrodinger himself, clearly shares the same sentiments as John von Neumann. In Schrodinger’s words:

… the observer is never entirely replaced by instruments; for if he were, he could obviously obtain no knowledge whatsoever …. Many helpful devices can facilitate this work … But they must be read! The observer’s senses have to step in eventually. The most careful record, when not inspected, tells us nothing.

Shortly after von Neumann introduced the von Neumann chain, Fritz London and Edmond Bauer explicitly pointed to the role played by consciousness, when they wrote this concerning the interaction between the object and the measurement apparatus (From “The Theory of Observation in Quantum Mechanics” 1939):

So far we have only coupled one apparatus with one object. But a coupling, even with a measuring device, is not yet a measurement. A measurement is only achieved when the position of the pointer has been observed. It is precisely this increase in knowledge, acquired by observation, that gives the observer the right to choose among the different components of the mixture predicted by theory, or reject those which are not observed, and to attribute thenceforth to the object a new wave function, that of the pure case which he has found.

We note the essential role played by the consciousness of the observer in this transition from the mixture to the pure case. Without this effective intervention, he would never obtain a new ψ function [i.e., a new quantum wave function].

4.2 Schrodinger’s Cat and Wigner’s Friend

In the early 1960s, acknowledging the insight of John von Neumann and even citing the book by London and Bauer, Physics Nobel Laureate, Eugene Wigner, brought the whole issue of consciousness into prominence. In his paper “Remarks on the Mind-Body Question,” Eugene Wigner wrote:

Eugene Wigner

When the province of physical theory was extended to encompass microscopic phenomena, through the creation of quantum mechanics, the concept of consciousness came to the fore again: it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the

consciousness. All that quantum mechanics purports to provide are probability connections between subsequent impressions (also called “apperceptions”) of the consciousness, and even though the dividing line between the observer, whose consciousness is being affected, and the observed physical object can be shifted towards the one or the other to a considerable degree, it cannot be eliminated.

Referring specifically to the way quantum mechanics functions, Wigner writes:

The important point is that the impression which one gains at an interaction may, and in general does, modify the probabilities with which one gains the various possible impressions at later interactions. In other words, the impression which one gains at an interaction, called also the result of an

observation, modifies the wave function of the system. The modified wave function is, furthermore, in general unpredictable before the impression gained at the interaction has entered our consciousness: it is the entering of the impression into our consciousness which alters the wave function because it

modifies our appraisal of the probabilities for different impressions which we expect to receive in the future. It is at this point that the consciousness enters the theory unavoidably and unalterably. If one speaks in terms of the wave function, its changes are coupled with the entering of impressions into

our consciousness. If one formulates the laws of quantum mechanics in terms of probabilities of impressions, these are ipso facto the primary concepts with which one deals.

Wigner even introduced a further refinement to the Schrodinger Cat problem—a modification now known as Wigner’s Friend—to illustrate the importance of consciousness in quantum physics. Let us, however, first look at the original Schrodinger Cat problem. Erwin Schrodinger first introduced his famous cat in 1933 with the following passage:

Erwin Schrodinger

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer

which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The ψ function of the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

Rest assured that there has been no feline casualty because of Schrodinger’s words. It is only a thought experiment, and no actual experiment, with the set-up suggested, will resolve the problem in any way. The purpose behind the Schrodinger Cat scenario is to illustrate the fact that the strange probability distribution, represented by the quantum wave function, can be brought from the atomic realm into the macroscopic world—in this case, in the form of a live and/or dead cat.

The question posed is this: What is happening to the cat if we do not actually look at it (i.e., make no measurement)? Can it be in a strange combination of being both alive and dead, as suggested by the probability distribution of the quantum wave function that has not collapsed? That would be similar to the situation of an electron passing through both slits simultaneously in the double-slit experiment. The problem here, of course, is that a cat is a living thing. So how can a living thing, like a cat, be both alive and dead at the same time, simply because we choose not to look?

That is the problem posed by Schrodinger, and up till this day, there is still no agreed resolution to the problem among physicists. Wigner added to this intrigue by proposing the following scenario: Suppose we place the cat and the devilish contraption inside a room together with a friend who will look at the cat after an hour. Now suppose further that the room allows no possible communication between our friend and us.

The weirdness of the situation has now been amplified. If we are not able to communicate with our friend, what is happening to the cat and our friend? Did our friend look at the cat and found it dead, or did our friend look at the cat and found it alive, or incredibly, is it a combination of both scenarios at the same time? That strange combination of both scenarios would be suggested by the quantum wave function that has not collapsed. But now we have a conscious person involved, so how can his consciousness be in a state of both seeing the cat alive and seeing the cat dead? This is the Wigner’s Friend problem.

How did Wigner resolve this issue of the friend?

In his own words:

In this case, in which the observation was carried out by someone else, the typical change in the wave function occurred only when some information (the yes or no of my friend) entered my consciousness. It follows that the quantum description of objects is influenced by impressions entering my consciousness.

Nonetheless, Wigner states that “the being with a consciousness must have a different role in quantum mechanics than the inanimate measuring device.” So how then does Wigner deal with this idea in the Wigner’s Friend problem? He essentially suggests the possible solution that an interaction of a conscious observer with the object changes the quantum wave function:

The simplest way out of the difficulty is to accept the conclusion which forced itself on us: to assume that the joint system of friend plus object cannot be described by a wave function after the interaction—the proper description of their state is a mixture.

What Wigner is suggesting here, as a possible solution, is that the quantum wave function should be altered upon interaction with a conscious observer: in technical terms, it is transformed from a superposition into a mixed state. (For those not conversant with these technicalities, the technical meaning is actually not important for our purpose. The only point we are making here is that Wigner suggests, as a possible solution, that an encounter with a conscious observer changes the quantum wave function in some way.)

It is well known, however, that Eugene Wigner, towards the end of his life, changed his views on the issue of consciousness in quantum physics. Regardless of this fact, it must be realized that the logical arguments that he put forth in his papers in the early 1960s stand on their own right. In order to consider them invalid, we need to actually refute these arguments themselves.

The reason, why Wigner changed his views later in life, is particularly important in our quest of reaching a direct experiential interpretation of quantum mechanics. As we shall see, the reason for Wigner’s change of mind regarding consciousness has actually little to do with the formulation of quantum mechanics per se. It has mainly to do, instead, with the prevailing Western philosophical ideas about mind and matter, an issue that we will now explore closely.

4.3 [[[The Problem of Mind-Matter Duality]]

If Wigner was aware that consciousness does play a role in quantum mechanics, as illustrated in his writings above, why then did he, later in life, change his view on this? The problems for Wigner were actually those arising from trying to fit the role of consciousness, suggested by quantum mechanics, into the prevailing Western philosophy that posits a duality between mind and matter.

This idea, of a duality between mind and matter, stems from the philosophical writings of Descartes who introduced, in the seventeenth century, the terms res cogita and res extensa. Res cogita can be translated as “thinking substance,” and res extensa as “extended substance.” Hence, res cogita represents the mind, and res extensa the external world composed of matter.

Over the years, this idea of a mind-matter duality in Western philosophy generated much discussion and debate among philosophers, resulting in many variations and refinements. The one common factor is that they all, nonetheless, revolve around this idea of a duality between mind and matter.

It would probably be reasonable to state, however, that most physicists actually have little interest in philosophy, and some have even openly expressed their aversion to it. Nonetheless, their thinking is still influenced by the broad philosophical views prevalent in their culture, and therefore their thoughts are still largely tailored to fit within this framework of a mind-matter duality.

Having little interest in philosophy per se, physicists generally resolve this issue of a mind-matter duality by adopting the stance of materialism, which is the idea that matter is the fundamental substance in nature, and that even consciousness is derived from matter. In fact, most physicists insist that consciousness must be derived from matter somehow, even though there is no actual scientific evidence for it, and no actual scientific theory on how this can possibly come about.

It is to counter this insistence—that consciousness must somehow be derived from matter—that left Wigner little choice but to put forth an argument against materialism:

The principal argument against materialism is not … that it is incompatible with quantum theory. The principal argument is that thought processes and consciousness are the primary concepts, that our knowledge of the external world is the content of our consciousness and that the consciousness, therefore,

cannot be denied. On the contrary, logically, the external world could be denied—though it is not very practical to do so. In the words of Niels Bohr, “The word consciousness, applied to ourselves as well as to others, is indispensable when dealing with the human situation.” In view of all this, one may well

wonder how materialism, the doctrine that “life could be explained by sophisticated combinations of physical and chemical laws,” could so long be accepted by the majority of scientists.

In the same paper “Remarks on the Mind-Body Question,” Wigner then proceeds to actually suggest a reason why the majority of scientists are so adamant in sticking to materialism:

The reason is probably that it is an emotional necessity to exalt the problem to which one wants to devote a lifetime. If one admitted anything like the statement that the laws we study in physics and chemistry are limiting laws, similar to the laws of mechanics which exclude the consideration of electric

phenomena, or the laws of macroscopic physics which exclude the consideration of “atoms,” we could not devote ourselves to our study as wholeheartedly as we have to in order to recognise any new regularity in nature. The regularity which we are trying to track down must appear as the all-important regularity—if we are to pursue it with sufficient devotion to be successful.

Wigner was probably aware that any physicist, insisting on the idea that consciousness must be derived from matter, would almost certainly reject, offhand, any active role for consciousness in quantum mechanics. Wigner himself, however, was able to consider a role for consciousness in quantum physics because he did not support such a materialistic view, and in fact, considered the content of consciousness to be the primary reality.

The problem for Wigner, however, was that he still had to fit his idea—that consciousness is responsible for the collapse of the wave function—into the framework of a mind-matter duality. In the framework of a mind-matter duality, making the content of consciousness the primary reality would imply that the

external world essentially lacks this same reality. This leads to solipsism, and that is the problem that induced Wigner, towards the end of his life, to change his mind regarding the role of consciousness in quantum mechanics.

In its extreme form, solipsism is the idea that only the conscious content of the mind is real and that there is no genuine external reality. In other words, everything is only happening in one’s mind.

Wigner had become unhappy with this idea that the only thing that can register reality is your own mind. This would mean, Wigner argues, that reality would also be limited to what your mind can register, but practically everyone accepts that reality is much larger than what a mind can directly observe.

Wigner was also troubled with the problem of errors in observation. If solipsism is the correct scenario, why would any perception be considered mistaken at all? While we know that it is possible to hear things that are not there, and that our eyesight gets worse when we get older, in a solipsistic

interpretation, every observation would be reality. Indeed, if everything is only happening within one’s mind, whatever is perceived or experienced should constitute the reality. In solipsism, there is no concept of “error in observation,” a point that Wigner considered very unsatisfactory.

Another problem with solipsism is the fact that all the different minds seem to agree with what is happening in the external world. They all perceive the same blue sky, the same green grass, and the same events happening in the external world. How is this agreement possible if everything is only happening in each of their minds? Why would these events be correlated at all?

As we have seen, Wigner tried to resolve this issue (in his papers in the 1960s) by suggesting that the encounter of the object with any conscious observer would change the quantum wave function in some way, while, in a sense, preserving the actual collapse of the wave function for the scenario when the

necessary information concerning the object actually reaches “my consciousness.” Evidently, Wigner, in his later years, became unhappy with even this form of solipsism. In his own words, at a talk given in German, he made the remark that “as I talk to you I’m sure you exist and are listening to me.”

The main thing that probably disturbed Wigner about solipsism, in his later life, is that it implied the absence of a real world beyond the content of our consciousness. At the end of a paper published in 1977, Wigner expressed the hope that perhaps a deeper theory of physics would solve this problem and, in

his own words, “that quantum mechanics will also turn out to be a limiting case, limiting in more than one regard, and that the philosophy which an even deeper theory of physics will support will give a more concrete meaning to the word ‘reality’, will not embrace solipsism, much truth as this may contain, and will let us admit that the world really exists.”

The problem here is that, within the philosophical framework of a mind-matter duality, there seems to be little choice other than to gravitate towards either materialism or solipsism. The vast majority of physicists prefer materialism, but that would necessitate the exclusion of consciousness as a factor,

which is extremely problematic since the very formulation of quantum mechanics pivots around the observer. Solipsism, however, appears to be equally problematic as Wigner’s eventual dissatisfaction with it demonstrates.

What we need to realize is that both materialism and solipsism are actually viewpoints that arise from the acceptance that there is an actual mind-matter duality in the first place. This means that the mind-matter duality may, in fact, be the crucial problem hindering the proper interpretation of quantum mechanics.

We already see this problem of the mind-matter dichotomy arising in the writings, on quantum mechanics, by Werner Heisenberg, Erwin Schrodinger, John von Neumann, Eugene Wigner, and many others; and this problem of the mind-matter duality continues to this day. As an example, here is a passage from philosopher, David Chalmers:

… in some interpretations of the quantum formalism, consciousness itself plays a vital causal role, being required to bring about the so-called “collapse of the wave-function.” This collapse is supposed to occur upon any act of measurement; and in one interpretation, the only way to distinguish a measurement from a nonmeasurement is via the presence of consciousness. This theory is certainly not universally accepted (for a start, it presupposes that consciousness is not itself physical, surely contrary to the views of most physicists), and I do not accept it myself …

As another example of the impact of this mind-matter duality on the contemporary view on quantum physics, here is a passage by physicist, Alistair Rae, from his recent book “Quantum Physics: Illusion or Reality?”:

Philosophers have long had difficulty proving that there is an objective real world ‘out there’ rather than that everything is just my sense impressions. However, the aim of science has always been to seek an objective description of the physical universe that can be consistently believed in if we so choose.

To suggest that consciousness must fill an essential role in our understanding of the quantum world would run directly against this trend. It may be that a theory based on consciousness and subjectivism could be consistent with the observed facts, but I find its implications—such as the nonexistence of a

physical universe until a mind evolved (from what?) to observe it—quite unacceptable. I would prefer to believe almost any theory that preserved some form of objectivity.

It should be evident that the issue of a mind-matter duality presents problems in the interpretation of quantum mechanics. Neither materialism nor solipsism offers an adequate solution to the mystery of quantum physics, and this problem persists to the present day.

Ironically, two of the founders of quantum mechanics, towards the later part of their lives, had, in fact, reached what may turn out to be the correct approach to the mystery of quantum physics. Here, Werner Heisenberg writes about a consensus he had reached with Wolfgang Pauli:

Wolfgang Pauli

The physicist Wolfgang Pauli once spoke of two limiting conceptions, both of which have been extraordinary fruitful in the history of human thought, although no genuine reality corresponds to them. At one extreme is the idea of an objective world, pursuing its regular course in space and time,

independently of any kind of observing subject; this has been the guiding image of modern science. At the other extreme is the idea of a subject, mystically experiencing the unity of the world and no longer confronted by an object or by any objective world; this has been the guiding image of Asian

mysticism. Our thinking moves somewhere in the middle, between these two limiting conceptions; we should maintain the tension resulting from these two opposites.

Heisenberg has, in fact, agreed with Pauli, that the ideal approach lies somewhere between the extremes of materialism and solipsism. In other words, they are agreeing that the appropriate approach is to take the middle way between these extremes.

We are not sure which form of Asian mysticism Heisenberg was referring to in the quote, but it appears that he was, unfortunately, unaware of the important Eastern philosophy whose name can literally be translated as the “Middle Way”—namely, Madhyamika philosophy.

5.1 TheExperiential Event as the Primary Reality

We have already learned, from the theory of relativity, that our science is actually a science of our experience, and not a science of a universe “out there” that exists independent of us as conscious observers. So, as our science is actually a science of our experience, let us now apply this consideration to quantum mechanics in order to learn what it actually tells us about the nature of our experienced reality.

Here, we will work on the premise that the mathematical formulation of quantum mechanics directly represents our experiential reality. We will remove all ad hoc hypothetical additions, as well as extraneous philosophical extrapolations, if they do not concur with either the mathematical formulation of

quantum mechanics or our direct experience of the universe (which, of course, has to be part of our experienced reality). This is what we mean by a direct experiential interpretation of quantum mechanics.

The main philosophical idea we will be removing is this notion that there is a mind-matter dichotomy. This is because it is not represented at all in the formulation of quantum mechanics and neither does it enter into our direct experience of the universe. Removal of this mind-matter dichotomy actually solves a lot of the interpretational problems of quantum mechanics.

The key to a direct experiential interpretation of quantum mechanics is to work on the premise that the mathematical formulation actually represents our reality directly. The eigenvalues and their corresponding eigenstates thus represent our direct experience of the object involved in our measurement. Let

us call what is represented in quantum mechanics, in the act of measurement, an experiential event. According to the mode of thinking in terms of a mind-matter duality, this experiential event would be called “the encounter between a conscious observer and the object under measurement.”

The difference now is that we no longer consider the mind as a separately existing entity, and we also no longer consider the object as a separately existing entity. We are to consider the experiential event itself as the real entity that the mathematical formulation of quantum mechanics actually deals

with. Our justification for this approach is that neither the mind, as a separate entity, nor the object, as a separate entity, is actually represented in the mathematical formulation of quantum mechanics. What is represented, in terms of the eigenstates and their corresponding eigenvalues are, in fact, the experiential events of the conscious observer experiencing the object.

This view of reality is actually not as strange or as revolutionary as it may seem. It is not even a new viewpoint that I am inventing or introducing, because it is a view of reality that corresponds to the Madhyamika philosophy of Buddhism, which has been extant for more than a thousand years. What this

means is that the perspective of reality according to Madhyamika philosophy actually corresponds very closely to what is being represented by the mathematical formulation of quantum mechanics!

In Madhyamika philosophy, particles do not inherently exist on their own right. Particles arise only in dependence upon causes and conditions, in dependence upon their parts, and in dependence upon the mind that apprehends them. This would correspond very well with the mathematical formulation of quantum mechanics. The quantum wave function of a particle would correspond to the “causes and conditions” aspect, and the eigenstate and its corresponding

eigenvalue would correspond to the experiential event of the mind experiencing the particle. Neither the separate inherently-existing particle, nor the separate inherently-existing mind appears in the mathematical formulation. What does appear is the experiential event, where the conscious experience and the particle appear as a combined reality. These experiential events are what actually make up our reality.

Note that we have dispensed with the idea of a mind-matter duality, and in the process, dispensed with the need to gravitate to either materialism or solipsism in our interpretation of quantum mechanics. The justification for this is actually obvious. Neither the mind-matter duality, nor materialism, nor

solipsism, is represented in the formulation of quantum mechanics. All these concepts were actually added onto the formulation arbitrarily because they happen to be part of the prevailing Western philosophical framework concerning our reality. They are therefore not inherently part of the formulation of quantum mechanics. And since, these arbitrary concepts lead to problems in interpreting quantum mechanics—problems that still remain unresolved to this day—it is probably wise that we remove them from our direct experiential interpretation of quantum mechanics.

5.2 Madhyamika Philosophy

It is important to realize that Madhyamika philosophy is a philosophy that is based on profound logical analyses, analyses that are often backed by deep meditational insight by the Madhyamaka masters. Madhyamika philosophy is not based on blind faith. This is clearly evident because many Madhyamaka texts are in the form of philosophical discourses grounded on logical reasoning that is very precise.

There is even a historically recorded philosophical dispute on the finer points of the philosophy, that was debated on logical grounds, by different Madhyamaka masters. This led to two versions of Madhyamika philosophy, known as the Svantantrika Madhyamaka and the Prasangika Madhyamaka.

Here, we shall be looking at the Prasangika version of Madhyamika philosophy, which is considered to be the ultimate truth, and which forms the cornerstone of much of Tibetan Buddhism. The Prasangika version of Madhyamika philosophy is based on the philosophical texts of Nagarjuna, Aryadeva, Buddhapalita, Chandrakirti, Shantideva, Lama Tsongkhapa, and others.

The key principle of Prasangika Madhyamaka is the principle that all things are empty of inherent existence. What this means requires considerable explanation, but it must be understood, right at the beginning that Madhyamika philosophy is not a nihilistic philosophy. This is extremely important.

There are warnings, even by Nagarjuna, about presenting the teachings of emptiness to people who are unprepared for it. These warnings are given because of this very danger of misunderstanding Madhyamika philosophy as a doctrine of nihilism, a misunderstanding that can be very harmful.

So if any reader thinks that Madhyamika philosophy points towards nihilism, please realize that there is an error somewhere in the reasoning process that would lead to such a wrong conclusion. In other words, please realize that you are making a serious mistake if you think that Madhyamika philosophy suggests nihilism. It is extremely important to keep this in mind. Madhyamika philosophy is not about nihilism.

Madhyamika philosophy is also known as the Middle Way philosophy because it takes the middle path between these two extremes: the nihilistic extreme that things are totally non-existent, and the objectivist extreme that things exist inherently and independently, on their own right.

The key principle of Madhyamika philosophy—that all things are empty of inherent existence—actually means that all things are only dependently arisen. The very existence of any entity depends on causes and conditions, depends on its parts, and depends on the mind that apprehends it. Without this dependence on

these other factors, the entity cannot exist at all. In other words, it cannot exist concretely and independently, on its own right, free of these dependencies. There is no such inherently existing entity.

Therefore, when Madhyamika philosophy states that all things are empty of inherent existence, it does not mean that all things are non-existent. It actually means that our reality is “like an illusion.” In the words of Shantideva:

That which is seen and that which is touched are of a dream-like and illusion-like nature.

While being “empty of inherent existence” means that our reality is like an illusion, it does not mean, however, that our reality is an illusion. It only means that our reality is not composed of things that inherently exist, independently and on their own right. So while all things are empty of inherent existence, there is, nonetheless, an actual reality.

What “illusion-like” means is that our reality is what would be suggested by the phrase “an interplay between the elements,” only that we need to also remove the term “the elements” from the phrase. In other words, there is just the “interplay” without any inherently existing elements. To most people,

this would be a revolutionary way of thinking, but Madhyamika philosophy is meant to revolutionise our way of thinking, in the same way that quantum mechanics also requires a revolution in our way of thinking.

We normally think of “an interplay” as being an interaction between inherently existing entities, but in Madhyamika philosophy, these interacting entities themselves are also empty of inherent existence. There is thus just the interplay between elements that are themselves also not existing on their own right. That is one sense of the phrase “like an illusion.” It is important to understand Madhyamika philosophy in this manner.

So it is not a case of pure idealism or solipsism. There truly is this reality, only we need to realize that this reality is like an illusion. It also means that it is not a case of pure objectivism or materialism, since things do not exist inherently and independently, on their own right. That is why Madhyamika philosophy is known as the Middle Way philosophy, and why it fits perfectly as the approach that both Werner Heisenberg and Wolfgang Pauli realised would be the appropriate one to use in interpreting quantum mechanics.

5.3 Madhyamika Philosophy and Quantum Mechanics

It must be realized that, even without the findings of quantum mechanics, the correctness of the Prasangika Madhyamaka view has already been established through profound logical analysis. It is a logical analysis that is also backed by deep meditational insight. Let us look, now, at how well a direct experiential interpretation of quantum mechanics fits the Prasangika version of Madhyamika philosophy.

In a direct experiential interpretation of quantum mechanics, the reality of what observers perceive are the results of measurements. These are represented by the eigenvalues of the eigenstates that the collapse of the wave function transforms the quantum wave function into. Quantum mechanics thus tells us

directly that the eigenvalues of the corresponding eigenstates constitute our reality. If we are to interpret the meaning of quantum mechanics directly, without further ad hoc hypothetical additions to the formulation, that is what we have to accept. The formulation is directly telling us that.

The eigenvalues are our experienced reality, and this reality occurs upon the act of observation that triggers off the collapse of the wave function. Prior to that experiential event, the object involved cannot even be said to manifest as an actual object, since we only have the uncollapsed quantum wave

function which only provides us with a probability distribution of the possible results of measurement if and only if we actually make a measurement. Thus, as Heisenberg pointed out, between any two measurements, we cannot even conceive of a possible path for the object. The object essentially has not even manifested. As Heisenberg puts it, only upon an actual measurement, does the object make the transition from the ‘possible’ to the ‘actual.’

This fits perfectly with Madhyamika philosophy. According to Madhyamika philosophy, objects only exist in dependence upon causes and conditions, and in dependence upon the mind that apprehends it. This means that until the collapse of the wave function, and the selection of one of the possible eigenstates,

with its corresponding eigenvalue, the object has not even manifested. And when it does manifest, it does so as an experiential event, which means that it is dependent upon the mind of the observer that apprehends it. The process of the collapse of the wave function is therefore the process of dependent origination.

That is why, in Madhyamika philosophy, we say that this object is empty of inherent existence—its very existence depends on causes and conditions (represented by the quantum wave function) and depends upon the mind that apprehends it (which is the experiential event that occurs in the act of observation). There is no such object without this dependent origination via these factors.

This is what a direct experiential interpretation of quantum mechanics tells us. This fits perfectly with the Madhyamaka principle that all things are empty of inherent existence because they are dependently originated. There is no object that is not dependently originated. That is why, without an actual

act of measurement there is no collapse of the wave function, and all we have is a probability distribution of possibilities. Only upon the apprehension by a conscious mind, does the object actually manifest—what Heisenberg calls the transition from the ‘possible’ to the ‘actual.’

What we see now is that the findings of quantum mechanics not only fit in with the Prasangika Madhyamaka view but also reinforces it. The reason that quantum mechanics reinforces the Madhyamaka view is simply the fact that alternative views, like a mind-matter duality, or either the extremes of materialism or solipsism, actually lead to serious interpretation problems.

These problems have, in turn, led to all sorts of ad hoc additions (inserted by hand) to the formulation of quantum mechanics, in attempts to produce a consistent interpretation that is free of contradictions. However, even with all these hypothetical ad hoc additions, the problem of interpreting quantum mechanics has yet to be solved after more than a century.

The Prasangika Madhyamaka view, on the other hand, provides an interpretation of quantum mechanics that fits perfectly and directly, without the need for any further ad hoc hypothetical additions to the formulation. In other words, a direct experiential interpretation of quantum mechanics actually provides further evidence that, truly, all things are empty of inherent existence because they are dependently originated.

5.4 The Case Against Materialism

The case against pure materialism, and against the claim that consciousness must be derived from matter, is actually very strong. In the first place, there is no actual scientific evidence that consciousness arises from matter. All we have is evidence that the content of consciousness is linked in some way to

the functioning of the physical brain, but that hardly amounts to concrete scientific evidence that the material brain must be the source of consciousness. A link between two things does not necessarily imply that one created the other.

Such a rash conclusion would perhaps be akin to the thinking of a primitive man should he stumble upon a modern television set. This primitive man, who has never encountered a television set before, notices that the picture on the monitor is linked to the control panel on the television. When he fiddles with

this control panel, the picture on the screen changes, in the same way that we notice our consciousness being affected by any change or damage to our physical brain. However, if we then insist that this is proof that consciousness must be derived from the physical brain, that would be akin to the

primitive man insisting that the picture on the monitor must be derived from the physical parts of the control panel itself. That would be totally illogical and unscientific. That is why we actually have no concrete scientific evidence that consciousness is derived from matter.

The very insistence that consciousness is derived from matter is, in fact, a curiosity in itself. This is because we have no conceivable idea how such a thing can be possible. In most cases of scientific ignorance concerning the cause of a phenomenon, what we do not know is which one of a whole range of

possible causes is the correct one. This is definitely not the case with regards to how consciousness may be derived from matter. Here, we do not know of even a single mechanism how consciousness can possibly arise from matter! That is why philosopher David Chalmers calls this problem the “hard problem.” This fact alone makes it curious why so many scientists dogmatically insist that consciousness must, somehow or other, be derived from matter!

Now we have yet another strong reason to doubt this dogmatic claim that consciousness must be derived from matter, and that comes from the very formulation of quantum mechanics. Right from the onset we can see that quantum mechanics pivots around the observer. The formulation provides rules for what the conscious observer finds and not rules for the behaviour of matter directly.

A direct experiential interpretation of quantum mechanics, without ad hoc additions, inserted by hand, tells us that, in fact, particles are dependently originated. Crucially, this dependent arising of the object requires the act of measurement or observation by the conscious observer. Using Heisenberg’s

terminology, we can say that physical particles only make the transition from the ‘possible’ to the ‘actual’ upon the act of measurement by the observer. How then can the reverse also be possible? In other words, how then can physical particles also be considered to be the cause of the mind of the observer?

It would be like claiming that we can lift ourselves up from the ground by pulling on our own bootstraps. This is the fundamental incompatibility, and it needs to be recognized.

In other words, mind and consciousness cannot be derived purely from matter. It is quantum mechanics that tells us that this is impossible, since there is no inherently existing elementary particle that is not dependently arisen. And given that one of the factors required for its dependent arising as an

actual particle is the mind that apprehends it, how can this entity, or collection of such entities, be what the mind is purely derived from, in the first place? That would be totally illogical.

It is the denial of this fact that consciousness cannot be purely derived from matter—a fact that is inherent in the very formulation of quantum mechanics—that has led to all sorts of ad hoc additions, inserted by hand, in order to try to make the original formulation somehow fit into some hypothetical scheme

that negates the observer. The large number of repeated attempts at reaching a logically consistent interpretation of quantum mechanics, through ad hoc additions—like infinite parallel universes, hidden variables, spontaneous wave function collapses, collapses due to consistent histories, and so on—are

essentially attempts at salvaging the idea of materialism. The fact that all these attempts have still not succeeded, after more than a century of persistent attempts at getting rid of the observer, is very telling!

Should physicists continue with this endeavour to remove the observer from quantum mechanics? Apart from not adopting the principle of Occam’s razor, there is, of course, no problem with trying, if one so wishes. Still, it is perhaps time to recognize that such attempts may be futile. This is because the very formulation of quantum mechanics revolves around the observer.

As mentioned, quantum mechanics does not directly provide rules for the behaviour of particles per se. Quantum mechanics, instead, only provides rules for the results of measurements by the observer. So all these persistent attempts at trying to get rid of the conscious observer, from quantum mechanics, may

be destined to fail, simply because the observer is an intrinsic part of the quantum mechanics formulation. There is no point in denying this fact just to cling on to materialism. In other words, quantum mechanics is directly pointing to the fact that materialism is probably an incorrect idea.

Given that the theory of relativity is also telling us that our science is actually a science of our experience, and not a science of the material world “out there” independent of us as observers, it is surely reasonable now to end our dogmatic insistence that consciousness is derived from matter. At the very least, as scientists, we need to admit that we actually do not know that consciousness is derived purely from matter.

5.5 The Case Concerning Solipsism

In spite of the strong case against materialism and against the claim that consciousness must be derived from matter, this materialistic dogma will probably persist if the only alternative is solipsism. This is because the idea that the external world lacks reality is simply not acceptable to most people. Fortunately, there is no reason why a role for consciousness in quantum physics must mean solipsism.

The direct experiential interpretation of quantum mechanics only tells us that particles are empty of inherent existence, and that they only manifest in an experiential event that is the act of observation or measurement. In other words, it tells us that the experiential event is, in fact, the process of dependent origination for the particle.

This direct experiential interpretation of quantum mechanics, however, does not tell us that the external world lacks reality because the quantum wave function does exist, even without the experiential event of an observation. What this means is that the causes and conditions for the manifestation of the particle is still present in the absence of an actual measurement. That is the nature of our reality, which is nonetheless real.

This fits in perfectly with Madhyamika philosophy and the idea that our reality is, in the words of Shantideva, “like an illusion.” Note that the words are “like an illusion” and not that it is an illusion. The central principle of Madhyamika philosophy—that all things are empty of inherent existence—does not

imply nihilism. It is called the Middle Way philosophy because it avoids both the extremes of inherent existence as well as that of nonexistence. Madhyamika philosophy is not a nihilistic philosophy; nor is it a teaching of solipsism.

Thus, the problem, in solipsism, of why different minds observe the same external reality, does not arise if we do not posit a mind-matter duality. Any mind that makes an observation would cause a collapse of the wave function, and this collapse would alter the quantum wave function. Since we do not

consider the external reality as non-existent, there is no problem in acknowledging that the quantum wave function in the “external world” has been changed upon the observation by any mind. In other words, the causes and conditions in the “external world” changes upon the observation by any mind.

This problem, in solipsism—of why different minds observe the same external reality—is only a problem if we need to assign a reality to the mind while having to negate the reality of the external world. A direct experiential interpretation of quantum mechanics, however, tells us that, since both mind and matter are empty of inherent existence, both mind and matter have the same ontological status. There is thus no need to reify one while negating the other.

In the words of Nagarjuna [from “The Fundamental Wisdom of the Middle Way” (Mulamadhyamakakarika)]:

Without detachment from vision there is no seer.

Nor is there a seer detached from it.

If there is no seer

How can there be seeing or the seen?

What Nagarjuna is saying, here, is that the observer, the object seen, as well as the act of seeing, are all empty of inherent existence, since all of these entities are dependently arisen.

In summary, both mind and matter are empty of inherent existence because it is actually the experiential events—that involve both mind and matter—that make up the primary reality. The experiential event, which occurs during a collapse of the wave function, is actually the process of dependent arising. And

since both the mind and matter are dependently arisen in an experiential event, they are both empty of inherent existence, and have the same ontological status. There is thus no need to assign an inherent reality to either mind or matter, while having to negate the reality of the other.

5.6 Emptiness of Mind in Quantum Mechanics

Let us now take a closer look at this emptiness of the mind that is suggested by the formulation of quantum mechanics. We must realize, however, that quantum mechanics only involves one of the two possible kinds of mental experience. These two kinds of mental experience are the perceptual and the

conceptual. A perceptual mental experience is an experience in which the mind accesses its object directly and involves the senses. A conceptual mental experience does not require the mind to access its object directly through the senses.

The experiential events that quantum mechanics deal with are only those that involve the perceptual kind of mental experience. Clearly, quantum mechanics does not deal directly with our conceptual mental experiences. The reason for this is evident. Quantum mechanics is a formalism that is designed to

correlate with the results of our experimental measurements. Since our scientific equipment cannot measure or directly involve our conceptual thoughts, the formalism of quantum mechanics does not deal with our conceptual mental experiences. Conceptual mental experiences are nonetheless real, only they are not accounted for in the formulation of quantum mechanics. Let us now look at what quantum mechanics tell us about our perceptual mental experiences.

What quantum mechanics tells us is that the experiential events, represented by the eigenstates and their corresponding eigenvalues, actually constitute our primary reality. So if an object is dependently originated in an experiential event, so is the perceptual mental experience. This mind, in the

experiential event, arises in dependence upon causes and conditions, and in dependence upon the object that it perceives. In this sense, the mind is also dependently originated and hence is also empty of inherent existence.

Thus, in Madhyamika philosophy, both the mind and the so-called “external world” are dependently originated and both are empty of inherent existence. This means that we do not have the situation of solipsism where only the external world is empty of inherent existence. If both the mind and the “external world” are empty of inherent existence, we cannot say that one is real while the other is not.

That is why Madhyamika philosophy is the “middle way” philosophy that steers clear of both materialism and solipsism. All things are empty of inherent existence, but there is still a reality. Our reality is like an illusion, but there is nonetheless a reality. Both Madhyamika philosophy and the direct experiential interpretation of quantum mechanics are telling us that this is the case.

Unfortunately, quantum mechanics cannot provide any information about conceptual mental experiences, since our scientific equipment have no access to this aspect of the mind. And because quantum mechanics is specifically formulated to fit the data from our scientific equipment, quantum mechanics can only

provide information on the perceptual mental experiences, and not the conceptual ones. In order to investigate the conceptual mental experiences, we need

make use of the mind itself as a direct probe. There is no other way to access this part of our reality but to train the mind itself for this purpose. That is actually a key purpose of training the mind in deep meditation—it is to examine the very nature of the mind itself.

Backed by this deep meditational insight, the Madhyamaka masters also reach the same conclusion that the mind—as well as this notion of the “self”—is empty of inherent existence. That this is true can fortunately also be proven intellectually by very precise logical analysis. Some prominent examples of the

deep logical analyses, used by the Madhyamaka masters, are the seven-point analysis, the diamond slivers or refuting the four possibilities of production, and, of course, the analysis based on dependent origination (which is the analysis that we have been discussing).

The logical analysis concerning why mind is empty of inherent existence is, of course, beyond the scope of this paper. Our aim here is to demonstrate that Madhyamika philosophy fits perfectly with a direct experiential interpretation of quantum mechanics while steering free from the extremes of materialism and solipsism, both of which are beset with problems.

We now turn to exploring the nature of the quantum wave function itself and what it actually represents in a direct experiential interpretation of quantum mechanics.

6.1 The Delayed Choice Quantum Eraser and Quantum Entanglement

An innovative experimental set-up for the double-slit experiment, that is particularly appropriate for exploring the nature of the quantum wave function, is an intriguing version of the experiment known as the delayed choice quantum eraser.

Recall that, in the basic double-slit experiment, a particle like a photon would pass through both slits if no measurement is made to ascertain which slit the particle went through. This is because, without a measurement being made, the quantum wave function would not collapse, and the particle actually does

not manifest as a single particle at a single position. The quantum wave function would continue uncollapsed and represent merely a probability distribution of possible measurement findings if and only if we make an actual measurement. Effectively, we can say that the particle is behaving like a wave and passing through both slits simultaneously, and would form an interference pattern on the screen, as a wave would do.

It is only the act of measurement—to ascertain which slit the particle passes through—that would cause the collapse of the wave function and force the particle to manifest at one or other slit. If the particle did that, there would then not be an interference pattern on the screen.

Now suppose we do the measurement of which slit the particle passes through in an unusual and indirect way. First we can delay the choice of whether or not we make an actual measurement—that tells us which slit the particle passes through—until after the original particle actually hits the screen. This can actually be done, and is what the phrase “delayed choice” refers to.

We can also do something even more unusual. Not only can we delay the choice of whether or not we actually make the measurement till after the original particle hits the screen, we can also delay the “choice” of whether or not the experimental set-up provides us, the observers, with the actual information

of which slit the particle passed through. And this choice can also be made after the original particle has already hit the screen. This is the so-called “quantum eraser” part of the experiment, since the experimental set-up can act as though the “which-slit” information has been erased and cannot reach the observer.

The “delayed choice” and the “quantum eraser” aspects of the experiment can be achieved through the use of quantum entanglement; in this case, through the use of entangled pairs of photons. Entangled photons have properties that are correlated in such a way that the quantum wave function of each of the

photons cannot be described independently of each other. Essentially they become one system. Because of this, a measurement of certain properties of one photon would provide information about the other photon.

In the delayed choice quantum eraser experiment, one of the photons in an entangled pair is called the signal photon and the other is called the idler photon. The basic strategy is to allow the signal photon to travel to the screen while directing its corresponding idler photon onto a different path.

Then, only after the signal photon has already hit the screen, do we make a measurement on its corresponding idler photon in order to determine which slit the signal photon emerged from. That is how the delayed choice aspect of the experiment can be implemented.

We can also arrange the experimental set-up such that some of the idler photons would encounter devices designed to “scramble” the information that it carries concerning which slit its corresponding signal photon emerged from. After this information has been scrambled, the observer can no longer obtain the “which slit” information from measurements made on the idler photon. This is the quantum eraser part of the experiment.

This delayed choice quantum eraser experiment also illustrates the peculiar quality of quantum entanglement, whereby the measurement of one of the entangled pair of photons actually appears to affect the other photon, as though a “message” has been sent between them, a “message” that is faster than

the speed of light. In other words, the measurement made on one of the entangled pair of photons—in this case, the idler photon—appears to result in a “message” from the idler photon telling the signal photon that it has to now “decide” which slit it had passed through.

Here, the apparent “message” being sent to the signal photon, by having a measurement made on the idler photon, is even more dramatic than being faster than the speed of light. The “message” appears to have been sent backwards in time! This is because we have already allowed the signal photon to hit the screen before a measurement is made on the idler photon. That, in the first place, is why it is called a “delayed choice” experiment.

The measurement made on the idler photons, nonetheless, still appears to affect the pattern the signal photons leave on the screen, even though the measurement on each idler photon was made, every time, after the corresponding signal photon had already hit the screen. So if we consider that a message has been sent by the idler photon to its corresponding signal photon, it could only have been sent backwards in time!

6.2 The Original Delayed Choice Quantum Eraser Experiment

A delayed choice quantum eraser experiment was first performed by Yoon-Ho Kim, R. Yu, S. P. Kulik, Y. H. Shih and Marlan O. Scully, around 1999. There have been other versions of this experiment since, but we shall look more closely at the original experiment of this kind. The experimental set-up is as shown in Figure 4.

Figure 4. Diagram illustrating the Delayed Choice Quantum Eraser experiment by Y-H Kim et al. (picture credit: Patrick Edwin Moran) In the diagram, the paths taken by the entangled photons that emerge from the upper slit A are in red and the paths taken by the entangled photons that emerge from the lower slit B are in blue. The signal photons are those heading upwards towards the screen represented by detector D0, while the idler photons are those diverted downwards, away from detector D0.

Let us look at the part of the experimental set-up that would encounter the idler photons. There are three beam splitters in this part of the experimental set-up—BSa, BSb, and BSc. The beam splitters function in this way: If an idler photon encounters a beam splitter, it has a 50% chance of passing straight through and a 50% chance of being reflected. Ma and Mb are plain mirrors.

The beam splitters and the mirrors direct the idler photons towards the detectors D1, D2, D3 and D4. If we look at the possible paths taken by the idler photons, we can conclude the following:

If an idler photon is recorded at detector D3, it can only have come from slit B.

If an idler photon is recorded at detector D4, it can only have come from slit A.

If an idler photon is detected at detector D1 or D2, it might have come from slit A or slit B.

This means that if D3 or D4 detects an idler photon, we know that its corresponding signal photon must have emerged from slit B and slit A respectively. If D1 or D2 detects an idler photon, we would still not know which slit its corresponding signal photon emerged from.

The experimental set-up is such that detectors D1, D2, D3 and D4 would only detect an idler photon after the signal photon has already hit the screen. Hence we have a “delayed choice” in getting the “which slit” information.

Beam splitter BSc acts as a scrambler of the “which slit” information carried by the idler photon, since an encounter with this beam splitter would render the observer unable to deduce which slit this idler photon emerged from. This beam splitter represents the “quantum eraser” part of the experiment.

The results of the experiment show that whenever the “which slit” information was available to the observer, we do not obtain an interference pattern at the screen (detector D0). Whenever this “which slit” information was not available to the observer, an interference pattern would form.

6.3 The Two “Weird” Things About the Double-Slit Experiment A simple way to obtain an overview of the delayed choice quantum eraser version of the double-slit experiment is to look at the two “weird” things that would arise if we were thinking along the lines of a mind-matter duality—i.e., where the object (the photon) is distinct from the mind (the observer).

It is important to realize that there are actually two things that are “weird” about this experiment. One weird thing is that, although the photon displays the properties of a wave (like producing an interference pattern), we only see a photon as a particle whenever we make an actual observation. This, as we

know, is the collapse of the wave function. To reiterate, before the observation, the quantum wave function provides us with a probability distribution of where the photon may be found if and only if we make an actual observation. When we actually make an observation, however, the photon is only found in one place. This is one of the two weird things about the double-slit experiment.

The second weird thing is this: If we now place a detector so that we can tell which slit the photon went through, the interference pattern disappears. It is as though, having a detector there, forces the photon to choose which slit it goes through. Now here’s the real peculiarity concerning this: we do not

actually have to make an observation for the interference pattern to disappear. Just having the detector there will cause the interference pattern to vanish. It is as though the photon knows that we can spy on it if we want to, and that is enough for it to stop performing the “interference pattern

trick.” All that is required is an experimental set-up that enables the observer to make an observation if he wants to, and the interference pattern disappears. No actual observation at the slits is required. Also, if we remove the detector at the slits, the interference pattern reappears. So it is the experimental set-up that determines the result.

To make this phenomenon even more intriguing, we have the delayed choice quantum eraser experiment, whereby the information on which slit the photon went through can only be obtained after the photon hits the screen (this is possible through the use of quantum entanglement). This does not seem to make any

difference to the result, i.e. as long as there is the ability to tell which slit the photon went through, no interference pattern occurs. It is as though the photon realizes that we can determine which slit it went through after it hits the screen, and that is already enough to stop it from performing the interference-pattern trick.

To make things still more intriguing, if we now insert another device (this is the eraser part) so that it now obscures the information concerning which slit the photon went through, the interference pattern reappears. Now, it is as though the photon has found out that the information from our detector

(that allows us to see which slit it went through) is now being scrambled by another device so that we can no longer obtain this information. That being the case, the photon is now happy to perform its interference-pattern trick again.

So what actually is going on? It almost appears like the photons know what we are able to do in terms of spying on them, and that these photons are conspiring to thwart us in our quest to determine how they are performing their tricks! Of course, no one actually thinks that the photons are sentient

beings involved in an elaborate conspiracy to trick us, but that really appears to be what is happening. This is the second weird thing about the double-slit experiment.

All this sounds extremely strange, and that has, in fact, been the central mystery of quantum mechanics for over a century now. However, remember that, here, we have considered the findings of the double-slit experiment in terms of a mind-matter duality. It is actually this mind-matter duality that led to these two so-called “weird” effects in the double-slit experiment.

Let us now, instead, consider the findings of the delayed choice quantum eraser version of the double-slit experiment in terms of a direct experiential interpretation of quantum mechanics.

6.4 The Nature of the Quantum Wave Function

Keep in mind that there are two key effects about the double-slit experiment that involve the observer:

The collapse of the wave function upon measurement by an observer.

Changes in the probability distribution of the measurement results that depend on whether or not the “which slit” information can reach an observer. Both these effects point to an observer effect in quantum physics. This means that any claim to a solution that negates the observer effect must account for both these effects.

The second effect, though, does not require an observer to be physically present and actually noting the results at the time of the experiment. What this tells us is this. If the experimental conditions enable us to tell which slit the signal photon passed through (if we wanted to find out), no interference

pattern would emerge on the screen. If the experimental conditions were such that we cannot tell which slit the signal photon passed through (even if we wanted to find out), then an interference pattern would emerge on the screen.

The key factor is whether or not the “which slit” information is available to the conscious observer. If the information is available, no interference pattern forms. If the information is not available, an interference pattern forms.

This result provides us with very important information concerning the nature of the quantum wave function. What it means is that the probability distribution for the measurement results changes upon altering the experimental conditions, even when the experiment is conducted without any conscious observer being present to note the results directly at that time. In other words, we can alter the quantum wave function just by altering the experimental set-up.

Note, however, that this does not mean that the collapse of the wave function can occur without the observer actually reading the results. All that has happened, without the observer present, is that the probability distribution of possible results has changed. No collapse of the wave function has occurred in this process.

In other words, while we know that there is a change in the probability distribution of the possible results—concerning where the set of photons end up on the screen—we still do not know where any one particular photon ends up. We still only have a probability distribution of possible results, and not the

actual results, if the observer does not make an actual observation of the results. In other words, the quantum wave function has changed but it has still not collapsed.

So what does this tell us about the quantum wave function? It tells us that the crucial factor in determining the form of the quantum wave function are the possible experiential events that the experimental set-up would allow the observer to have. In other words, the set of possible experiential events

determine the quantum wave function. If we change the set of possible experiential events by changing the experimental set-up, the quantum wave function would change accordingly to reflect this new set of possible experiential events that the observer could encounter.

Note that this mechanism is akin to a change in the preferred basis depending on what the observer chooses to measure. In other words, a change in the possible set of experiential events—which, of course, would change when a different property is being measured—would lead to the quantum wave function being altered to reflect this change in the set of possible experiential events.

All this means that it is the experiential events—that are the acts of observation involving both the particle and the conscious observer—that are the primary reality that the quantum wave function provides information on. A change in the possible set of experiential events changes the quantum wave

function, even without an observer being present at the time. Nonetheless, an actual act of measurement by a conscious observer is still required for the collapse of the wave function.

A direct experiential interpretation of quantum mechanics thus explains the two so-called “weird” effects of the double-slit experiment. These effects are actually only weird in terms of a mind-matter duality. If we adopt a middle way approach—as provided by Madhyamika philosophy—without positing a mind-

matter dichotomy, and consider instead that the experiential events are the primary reality that quantum mechanics deals with, we can arrive at a consistent interpretation of the double-slit experiment that is free of contradictions.

Note that if we consider the experiential events to be the primary reality, rather than the particles (in this case, the photons) themselves, it also explains the peculiar property of a “message” being sent faster than the speed of light—or in this case, even backwards in time—in cases involving quantum

entanglement. In other words, this idea of a message being sent, between an entangled pair of particles, only arises if we consider the particles to be inherently existing entities, that are independent of the conscious observer, in the first place.

In the Madhyamaka view of reality, these particles (the photons) do not inherently exist, independently, on their own right, or from their own side, but are only dependently arisen. Their very existence depends on causes and conditions, and on the mind of the observer that apprehends them. In other words, it is the experiential events that form our reality, and not the photons themselves, independent of the observer.

Now, if it is the experiential events that actually constitute our reality, we do not need to posit a “message” being sent between the idler photon and its corresponding signal photon. What we need to realize is that a measurement made on the idler photon changes the set of possible experiential events in the

experimental set-up, and this changes the quantum wave function accordingly. As already mentioned, this process is akin to a change in the preferred basis upon changing the observable we choose to measure.

Thus a direct experiential interpretation of quantum mechanics not only explains the two so-called “weird” effects of the double-slit experiment, it also explains why, in cases of quantum entanglement, apparent “messages” can be sent faster than the speed of light, or in our case, even backwards in time.

All these “weird” effects appear only because we have been inappropriately trying to fit the formulation of quantum mechanics into a philosophical framework that posits a mind-matter dichotomy. The problem of messages travelling faster than the speed of light, or even backwards in time, arises only if

we insist on forcing quantum mechanics into a framework of materialism, and trying to negate the critical role of consciousness in science and reality. This issue, however, is not a problem at all if we accept that the correct philosophical framework for quantum mechanics is that of Madhyamika philosophy, where all things are empty of inherent existence because they are dependently arisen.

7 Conclusion

A direct experiential interpretation of quantum mechanics is simply an acceptance of what the formulation of quantum mechanics is directly telling us about our experienced reality, coupled with the application of Occam’s razor.

In other words, in a direct experiential interpretation of quantum mechanics, we accept that the mathematical formulation actually represents our reality, without resorting to all sorts of additional hypothetical ad hoc conditions, inserted arbitrarily, just so that we can fit the formulation of quantum

mechanics into some preconceived and biased notion of what our reality should be like. Refusing to abide by the principle of Occam’s razor, and insisting on forcing the formulation of quantum mechanics into some preconceived notion of reality, is actually being illogical and unscientific. All such attempts, over the last century, to fit quantum mechanics into a predetermined view of reality, have, in fact, run into serious conceptual difficulties.

The preconceived notion, of what many scientists think our reality should be like, is this notion of a mind-matter dichotomy. And since most scientists choose to resolve this dichotomy by adopting the stance of materialism, the preconceived notion of reality that physicists have persistently tried to force

the formulation of quantum mechanics to fit into, is the idea of materialism—particularly the notion that consciousness must, somehow or other, be derived purely from matter.

It is crucial to realize, however, that these philosophical ideas are not at all suggested by the formulation of quantum mechanics. Quantum mechanics does not provide any indication of a mind-matter duality, and certainly does not suggest, in even the slightest way, that consciousness is derived from matter.

Quantum mechanics actually suggests the reverse: that both the idea of a mind-matter duality, and the assumption that consciousness is derived from matter, are, in fact, incorrect.

Coupled with the fact that the theory of relativity demonstrates that our science is actually a science of our experience—and not a science of a universe “out there” independent of us as conscious observers—it is time for us to acknowledge that consciousness is part of our primary reality. Consciousness is

not merely something derived from matter, and hence inconsequential or of secondary importance. The very formulation of quantum mechanics, as well as the theory of relativity, tells us that consciousness has, in fact, a crucial and primary role in our science and in our reality.

It is therefore time to acknowledge the central role played by consciousness, and learn directly what the formulation of quantum mechanics actually tells us about our experienced reality. This is what we mean by a direct experiential interpretation of quantum mechanics. And what this interpretation tells us

is that the eigenstates and their corresponding eigenvalues directly represent the experiential events that are our primary reality. These experiential events are made up of a combination of mind and matter, and since these experiential events constitute our primary reality, there is, in fact, no mind-matter dichotomy.

While this may seem to be an unusual view of reality, to those accustomed to thinking in terms of a mind-matter dichotomy, it is not a perspective that is, in any way, new since it is actually the viewpoint of Madhyamika philosophy that has been extant for more than a thousand years. It must be realized that

the Madhyamaka view is actually supported by extensive and very precise logical analysis, as well as backed by deep meditational insight. Thus we cannot ignore this understanding of our reality without being able to provide a logical argument to dispute the profound logical analysis that arrived at the crucial Madhyamaka conclusion that all things are empty of inherent existence because they are dependently arisen.

Furthermore, we can now see that this central point of Madhyamika philosophy agrees with the formulation of quantum mechanics. A direct experiential interpretation of quantum mechanics actually tells us that the collapse of the wave function that leads to the experiential event—represented by the

“chosen” eigenstate and its corresponding eigenvalue—is, in fact, the process of dependent origination. And since these experiential events are our primary reality, it tells us that both matter and mind are empty of inherent existence because they are only dependently arisen.

This direct experiential interpretation of quantum mechanics allows us to arrive at a consistent and direct interpretation of the formulation of quantum mechanics that is free of contradictions, and free of the need for further ad hoc hypothetical additions to the main formulation. In other words, an

acceptance of what the mathematical formulation of quantum mechanics directly means, leads us to the Madhyamaka view of reality. Thus, in addition to being supported by extremely precise logical analysis and deep meditational insight, there is now also concrete scientific evidence that Madhyamika philosophy is correct.

In actual fact, Madhyamika philosophy does not require quantum mechanics for its justification. Madhyamika philosophy, which has been extant for more than a millennium, is already established on the basis of extremely rigorous philosophical and logical analysis. The reverse, however, is more appropriate. It is the formulation of quantum mechanics that requires Madhyamika philosophy in order for it to make sense!