In this accessible narrative essay, we take a journey with 20th century physicists beyond the limits of old world views to explore the fascinating world of quantum mechanics and its profound philosophical implications. The world described by quantum mechanics is strange and counter-intuitive, undermining the notions of materialism, determinism, and separation. We also explore the measurement problem in quantum mechanics and examine arguments why consciousness is needed to fully resolve the problem. Such resolutions, however, force us to radical alterations in our understanding of both the world and consciousness.
In 1492 Columbus set sail on a journey to unknown lands, pushing the limits of human experience and knowledge. It was the beginning of the Renaissance, and the beginning of a revolution in thought that would give birth to modern science, a vessel that would carry Newton beyond the earth itself.
Four hundred years later the earth was mapped, lands were colonized and Columbus was a legend. The earthly realm was no longer a mystery. But by this time science had gone far ahead. It had mapped the planets, stars, and galaxies. It had revealed the laws of nature—both on earth and beyond. And people had put the knowledge into practice, transforming the lives of everyone it touched. The universe was no longer a mystery, but an intricate lawful machine.
Yet, at the dawn of the 20th century, while civilization was transforming under the influence of this Newtonian vision, a few adventurous souls were being guided by another vision which would take them to an unknown frontier, beyond the limits of Newton's universe. These would be the future pioneers of a strange new world, a wonderland that defied common sense. But no one could then imagine what profound implications this revolution would have. Not even the pioneers themselves could foresee the depth of mystery before them as they took the first few steps on the journey through the quantum realm.
Werner Heisenberg, the first revolutionary physicist to abandon the classical Newtonian universe and break trail into the quantum realm, compared his journey with that of Columbus. The greatest achievement in his discovery of America was not the idea to sail around the world or his careful preparation for the trip. No, Heisenberg says, "his most remarkable feat was the decision to leave the known regions of the world and to sail westward, far beyond the point from which his provisions could have got him back home again." And so it is with science, Heisenberg continues, "it is impossible to open up new territory unless one is prepared to leave the safe anchorage of established doctrine and run the risk of a hazardous leap forward."
Young and daring, Heisenberg took the first quantum leap with his abstract matrix mechanics in 1925. These strange laws formed the first consistent theory of the atoms whose behavior defied explanation within Newton's universe. Like Columbus, Heisenberg had discovered a new world. But he hadn't found it alone. . .
Only a few months after young Heisenberg had set foot on the new land, an older fellow appeared on the horizon, having found the same frontier by a different route. It was Erwin Schrödinger, who had found his way to the quantum realm with a theory of wave mechanics. Being the older of the two, Schrödinger had traveled with more caution and vision.
Both had dared. And both survived the dangers, discovering by two different paths the same new frontier of scientific exploration.
Neither Heisenberg nor Schrödinger could fully anticipate in those early days just how much their discoveries would change the Newtonian world back home. The wonders that this quantum realm revealed would soon challenge the materialism that had been the basis for the Newtonian universe. As one crossed the border into the quantum realm, materialism seemed to evaporate. Thus, just as the pioneers of Columbus' time could return home with word that the world was not flat, our quantum pioneers would bring us word that the world is not ultimately comprehensible in terms of material objects. Regarding the assumption of materialism, Schrödinger comments, "anyone who wants to make it can do so; it is convenient, if somewhat naive. He will be missing a great deal if he does." Or, as Heisenberg put it, "materialism rested upon the illusion that the kind of existence, the direct "actuality" of the world around us, can be extrapolated into the atomic range." And he adds a warning that "the naive materialistic way of thinking is an obstacle to understanding the quantum concept of reality."
Despite the profound discoveries of Heisenberg and Schrödinger over sixty years ago, most of us today still think we live in the naive materialistic world. Like the ancient Greek philosopher Democritus, we think that the fundamental substance of the universe is composed of indivisible and indestructible atoms which move in empty space. From the complex arrangements and motions of these basic particles of matter, all other things are derived. As Democritus put it, "A thing merely appears to have color, it merely appears to be sweet or bitter. Only atoms and empty space have a real existence." This ancient seed of materialism came to dominate the modern Western worldview.
In the 1680s Isaac Newton formulated his mathematical laws of universal motion, throwing the scientific revolution into full swing. Newton's laws united the motion of objects in heaven and earth—both the moon and an apple moved according to the same laws he discovered. With their mathematical precision, it seemed that nothing could not be described by these universal laws. Thus the conception grew that the universe was made of material objects which moved in space according to these laws of Newton, like a big cosmic clockwork. So, in this grand vision, everything could be reduced to the lawful motion of material bodies. And since these laws made predictions with mathematical certainty, the cosmic machine was totally determined—there was no freedom. Furthermore, this world existed objectively, independent of our observation. Thus, in addition to materialism, the world view of classical physics was characterized by determinism and objectivity.
This classical mechanism was the old universe which Heisenberg and Schrödinger would abandon in search of a new frontier. But what prompted them to leave? The powerful laws of Newton had explained everything from the motion of the planets to the motion of baseballs. It had given people incredible machines and engines, tools and instruments. But as the 20th century drew closer, and classical physics extended its investigations into the small world of those fundamental atoms, nature began to defy Newtonian explanation. Experimental results no longer agreed with the predictions of Newton's theory.
Just as circumnavigation established the reality of a globe behind the illusion of a flat earth, the discovery of quantum mechanics revealed a strange new reality beneath the illusion of material objects. While it may be convenient to assume a flat or material world, were we to expand our range of experience, we would find limits to these notions. Similarly, beyond the physics of Newton we find that reality is not a big machine after all, even though it seems to be. The door has been opened to a new frontier.
What has the quantum realm revealed beneath the illusion of Newton's universe?
As strange as this new quantum world may seem, it is not off in some far land—it is here and now, hidden beneath the veil of materialism. And one does not need a particle accelerator to get to the quantum realm any more than one needs a boat to get to a round earth—it is already here, the true nature of this apparently flat world. We already live in this quantum wonderland. So let us take a look at our true home.
The first piece of the Newtonian mechanism to crumble was materialism: the immutable atoms were not so immutable after all. Soon after the discovery of radioactivity in 1896 it was found that atoms sometimes transmute into other atoms, just as the alchemists had dreamed. Next, the electron was discovered in 1897, a particle much smaller than any of the supposedly fundamental atoms. Thus, the atoms forming the substantial basis for all existence in the material world view were not the firm foundation they were taken to be. But this discovery in itself only pushed materialism down one step in scale, to the smaller sub-atomic particles which made up the atoms. While the substantial foundation of matter had shifted, it was still just as firm. . .or so they thought.
Thus, at the dawn of the 20th century, the physicists of a new generation were faced with a new realm to explore. Since atoms were no longer fundamental entities, it was now the task of these 20th century physicists to discover the true elementary particles, how they combine to form the atoms, and the laws governing those atomic systems. It was at this point, however, that Newton's classical laws began to fail. Attempts to explain the structure and behavior of atoms using the classical laws simply gave the wrong answers. For example, in 1911 Rutherford in England proposed a planetary model of the atom, in which a collection of negatively charged electrons orbited a positively charged nucleus, just as planets orbit the sun. But the known laws predicted that any electronic charge moving in an orbit must radiate energy. Consequently, as they lost energy to radiation, the orbiting electrons would spiral into the nucleus, in much the same way that a satellite falls out of orbit, losing energy due to its drag in the earth's atmosphere. In the case of the electrons in an atom, however, they would fall out of orbit very quickly, resulting in an almost instant collapse of the whole atomic structure—catastrophe. But the plain fact was that the atomic orbits were stable, and classical physics simply could not explain this fact.
To add to the troubles, Max Planck proposed in 1900 that atoms absorbed and radiated energy only in specific discrete quantities. According to Newton's laws, atoms could exchange energy in arbitrary amounts. But this did not explain the observed spectrum of radiation from atoms. To produce the observed spectrum, Planck proposed that energy in atoms was like quantities of money: instead of coming in any amount, it must always come in collections of a smallest quantity, called quanta. The quantum of money in the U.S., for example, is the cent. And the quantum of action in the universe is now called Planck's constant. When he made his hypothesis, there was no explanation for this strange quantization of atoms, and yet there was no way around it. This quantum, which Planck called "the mysterious ambassador from the real world," was then revealing the first of many paradoxes of the quantum world.
To help remedy the situation, a young Danish student of Rutherford made a quite radical proposal. His name was Niels Bohr, and he was to become the father of the quantum revolution. Bohr used Planck's strange quantum idea and proposed a bold model of the atom which explicitly denied the validity of the old classical laws. Without explaining why, Bohr simply assumed that there were only certain stable electron orbits, so that the electrons could orbit at some distances but not at any others. In addition, when electrons "jump" from one orbit to another, a quantum of light is emitted. From this simple model, Bohr was then able to predict the observed atomic spectra, and offer a reason why only certain wavelengths of light were emitted from atoms. But while Bohr broke away from the classical laws of Newton, he did not find any new fundamental laws to replace them. The physicists still could not explain why Bohr's orbits were stable, or what the electrons did during their jumps.
Before Heisenberg and Schrödinger could solve this atomic puzzle and reveal the strange laws of the quantum, one last piece was needed. One day, a French physicist named Louis de Broglie was thinking about Einstein's paradoxical proposal that light was composed of particles, despite the fact that it was known to be a wave. Somehow, light had both a wave aspect and a particle aspect. De Broglie then had a brilliant insight that connected this paradox with Bohr's atomic model in a new way: If light waves can have particle properties, de Broglie thought, then material particles ought to have wave properties. The particle-wave duality should hold for matter and light alike. Using this hypothesis, de Broglie explained why there were only certain stable orbits in Bohr's model: If the electron is not just a particle but also a wave, then only certain standing waves would be allowed around the nucleus. Just as a plucked string on a stringed instrument plays a specific fundamental tone and specific overtones, the standing wave of the electron can only vibrate at certain frequencies. These frequencies of the electron wave, de Broglie proposed, correspond to Bohr's stable orbits, with higher tones being higher energy orbits. It was a brilliant proposal. Yet, what does it mean to say that matter is a wave? Here we have our first hint that the solid particles of Newton's universe were to quickly dissolve.
Inspired by de Broglie's vision of matter waves, Schrödinger set out to discover their laws. Just as light waves obey an equation, these matter waves should have their own wave equation, too. In 1925 he began to search, to find a path into the quantum realm. After hitting a blind alley and struggling for months, Schrödinger finally broke through, discovering the now-famous Schrödinger wave equation. Solving this equation for the case of the atom, Schrödinger derived wave functions which corresponded to Bohr's electronic orbital waves, thus placing atomic stability on the solid basis of mathematical law. With this wave mechanics, he had set a firm foot into the strange land of the quantum.
Although both Heisenberg and Schrödinger embarked on their historic journeys at about the same time, Heisenberg took a short-cut, and arrived earlier. Instead of using de Broglie's wave-pictures of the atomic orbits, he made a youthful plunge from Bohr's model straight into the quantum realm. Heisenberg put all the possible electron jumps of the atom into a big table, called a matrix. He was then able to discover the proper laws for these matrices, and directly set foot into the quantum realm with this matrix mechanics. And it was not long before Schrödinger proved that they had both indeed arrived at the same discovery: the wave mechanics and the matrix mechanics were mathematical variations of the same quantum mechanics. It was 1926, and the new territory was opened up.
Although quantum mechanics gave all the correct predictions, no one yet really understood what it meant. While Heisenberg and Schrödinger deserve the credit for giving quantum mechanics a consistent mathematical basis, it was Niels Bohr who was to tackle the conceptual problems of this new theory. Just what were the "matter waves" described by the wave functions, anyhow? Were material particles just "the foam on a wave of radiation" as Schrödinger said? Or did matter rest on nothing but the probabilities in Heisenberg's matrices? Bohr's answer turned out to be a strange combination of both: in a sense, the world is particles and in a sense, the world is waves. The two views are complementary, neither one by itself telling the whole story.
These waves of matter were not ordinary waves, however. Waves of water or sound are vibrations of an underlying physical medium. The quantum waves, however, are not vibrations of anything physical. Matter had dissolved into a nonmaterial wave of probability, describing not the actual physical properties of the particles, but only their probable, or potential properties. So an atomic orbit is not an actual path followed by a material particle, but rather a wave of possibility for the particle to be found in different locations. And rather than describing the movement of actual particles as Newton's laws did, the quantum laws describe the movement of these waves potentiality. The actual particles are gone—only their possibilities remain. Thus the solid substance of materialism had evaporated into wave functions, describing only the probabilities for particles to appear.
And so it happened that the journey into the quantum realm revealed that the apparent world of hard matter rested not on solid material particles as Democritus envisioned, but on the airy cloud of non-material probabilities. Materialism was just a castle in the clouds, no less an illusion than the flat earth.
The overthrow of the material basis for the world was to be only the beginning of the quantum revolution. Basing physical reality on waves of potentiality was to undermine other assumptions of the Newtonian universe as well, and determinism was to be the next pillar of classical physics to fall. The universal machine was no longer predictable with absolute certainty. Now it had spontaneity.
In both quantum and classical physics, we begin by choosing an isolated system to study. For example, we might study the solar system, or a single atom, or perhaps two billiard balls. By restricting our study to a specific system like this, we define and simplify the problem, for it would be just too complicated to consider the whole universe at once.
In the case of classical physics, it was found that when the systems got very small—about the size of an atom—then the strict deterministic laws of Newton did not work anymore. So, the domain of classical physics was found to be limited to large systems, just as the domain of "flat earth" geometry is limited to small areas. And just as "round earth" geometry can explain everything that "flat earth" geometry explains and more, the quantum physics, too, applies to both the large systems and small atomic systems. It is more general and more comprehensive than classical physics alone.
After choosing a system to study, the next step in describing the world with physics is to determine the state of the system. In the case of classical physics, the state is quite simple: the state at any given moment is the set of positions and velocities of the objects in the system. If we are considering the solar system, for example, then the state would be given by the positions and velocities of all the planets in their orbits. Likewise, the state of a system of two billiard balls would be given by the position and velocity of each ball. So for any given system, it can exist in many different possible states: the two balls can be close together and at rest, they can be far away and moving quickly, one can be moving and the other at rest, and so on. If, for the sake of simplicity, we consider just their positions in one dimension, then every possible state of the two billiard balls can be represented as a point in a two-dimensional graph, plotting the position of one ball on the x-axis and the position of the other ball on the y-axis. So by just specifying a point on this graph, we know the state of our system. We can call this the "state-point."
y | | | * | | |____________x y=position of ball 1 x=position of ball 2
Given any initial state, the classical laws will then tell us how the two balls will move in the future. Thus, the state-point will move around on the plane of the graph, following a curve corresponding to the state-points at each instant in time. There are two important features of this movement: First, the movement of the state-point is smooth and continuous: neither of the balls suddenly "jumps" from one place to another, causing a break in the curve. This means that once any state-point is known, the whole curve of future and past state-points is totally determined. If we know where the balls are now, we can predict with certainty where they were or will be. Second, the state-point represents the actual state of the system, the state that we would observe were we to look. So when we observe the two balls, we can directly observe the state, and this does not change it at all. For example, if you were to look at the two billiard balls, this observation would not change their locations. In other words, the state accurately represents the two balls both when they are observed as well as unobserved.
Now if our system is very small, this method of classical physics no longer works and we must use the methods of quantum mechanics. Let us take the example of an atom. As we discussed earlier, it was found that the electrons have only certain stable orbits, which are described by standing waves of potentiality and not actual paths through space. So, instead of describing the orbital state by the electron's position, each of these orbits is represented by a wave function, which is the mathematical description of the electron's possible positions when measured. Thus, since the electron has no actual position, but only a potential position, we cannot use the classical method of "state- points" to describe its state. We must find another way.
With quantum mechanics we represent the state of a system by the wave function. Let us illustrate with a simple example how this wave function represents the potential properties of the electron. Suppose our electron can potentially exist in only two places: inside a box or outside a box. Now before we look, the electron's state is described as not actually in the box or actually out of the box, but only potentially in either position. Now we can imagine that there might be a large possibility for the electron to be in the box and only a small possibility for the electron to be out of the box, or vice versa, or perhaps the possibilities are about equal. If we imagine a two-dimensional graph with the "inside box" possibility on one axis and the "outside box" possibility on the other axis, then the state can be represented as an arrow pointing either more toward one axis or the other, depending on which position is more probable. Thus our quantum state can be thought of as an arrow, or vector, living in a possibility space. In addition, this state-vector, as it is called, points in a direction which determines the relative potentialities of the system.
y | | . | / | / | / |/___________x y=probability electron is inside box x=probability electron is outside box
Now since the state-vector does not necessarily point entirely along one axis but can have components along both axes, the electron is not actually in the box or actually out of the box. Rather, the electron is just potentially in or out of the box, but not actually either. So the state vector, or wave function, represents only a potentiality for something to exist in a definite place.
We noticed earlier that Newton's equations moved the state- point of the billiard balls around continuously in its actual space. In a similar way, Schrödinger's equation moves this state-vector around continuously in the possibility space. So as time passes, the direction of the arrow may change, meaning that the electron's potential for being in or out of the box will also change. And, just as with the classical state-point, this state-vector will continuously move around in a completely determined way. But there is a radical difference between what happens to the quantum state-vectors and the classical state-points when we make a measurement. In the classical case, we could directly measure the state of the billiard balls without changing anything. But in that case the state was not a mere potentiality: it already represented something actual.
In quantum mechanics the state-vector represents a potential for something actual, rather than simply something actual. But we cannot observe a merely potential position, for when we measure position, we only measure an actual position in the box or out of the box—never potentially both in and out of the box at the same time. In quantum mechanics, when a system is measured, the state changes from being a potential for several things to actually being one thing. This means that when the system is measured, the state vector must suddenly jump so that it is pointing along just one axis or another, and not somewhere in between. It is as if we could only see the shadow of the potential state, as it is projected onto an axis of actuality. Thus, the transition from potential to actual is often called a projection.
One of the most remarkable features of this projection is that the actual event which manifests in any given case is determined only by probability. When the state becomes actual, there is a sudden, discontinuous jump in the state that has an element of true spontaneity to it. Although deterministic laws still apply to the unobserved potentials, when a measurement is made, and the electron manifests either in the box or out of it, the result is unpredictable. It is not determined by the particular circumstances surrounding the event but is truly spontaneous. Which of the possibilities manifests upon measurement is not determined—even in principle.
Thus, in the quantum realm, the deterministic machine of Newton has cracked open. No longer is the universe a giant cosmic machine. While there is a deterministic law in the quantum realm, it applies only to the possibilities while the system is unobserved. When a measurement is made, however, the potential is made actual, breaking deterministic law and introducing spontaneity into the world. There is no predicting which state will become actual—only the probabilities are determined. And so one more premise of the Newtonian mechanism has been undermined. The cosmic machine is falling apart, its matter dissolving into potentiality, its determinism making room for freedom.
In Newton's mechanistic universe, not only was reality made of matter which followed strict deterministic law, but it was thought to be composed of many separate, independent material particles. So far on our journey into the quantum realm, the materialistic and deterministic assumptions have been undermined. First, we found that the particles were not substantial bits of solid matter but rather waves of potentiality. Then we found that, while these waves of potentiality themselves are determined, their projection into actuality exhibits spontaneity. Next, we will investigate whether this quantum world, like the classical world, is really composed of separate, independently existing entities. In other words, is this new world of potentiality a "Many" or a "One"?
Let us, for the sake of simplicity, consider a system of just two particles which have interacted with each other at some point in the past. Suppose we have a box as before and each particle can be either in the box or out of the box. Now when we look, we will find one of four actual states: 1) both in the box, 2) both out of the box, 3) one in the box and the other out of it, and 4) vice versa. So our possibility space for the system will have four directions, and the state of this two-particle system will be represented by a single state vector pointing in some combination of the four directions. For example, if the vector has a large component in the direction where both particles are in the box, then the probability of finding the particles in that actual state will be large. But, so long as the vector has components in the other directions as well, there is a possibility of finding one of several actual states when we look. Thus, the state vector represents a potential for the particles to be found in any of the four possible states we can actually observe.
Now it is important to notice that the one state vector describes the potentialities of both particles. So if one of the particles is measured, the state vector for the whole system will be projected. Thus, by measuring one of the particles, the state of both is affected.
What is amazing about this is that the state of the other particle changes instantly—even if it is in another galaxy. One might think at first that some strange faster-than-light communication passes between the two particles when one is measured. But such strange mechanisms are not at all necessary when we remember that the two particles were not really separate in the first place—the one state vector described the potentiality for them both. Thus, in the world of potentiality, there were not two particles at all, but just one potentiality which contained the possibilities for measurements of them both. And, since the potentiality exists in a possibility space rather than a physical space, the "physical" distance between the particles is irrelevant. Although they are separated in spacetime, in the potential world they are united as one. Thus, the complementary wave-particle aspects of matter are accompanied by their respective nonlocal-local aspects.
In this quantum world, things are interconnected beyond the limits of space and time. Behind the classical world of separate material particles lies a world that is nonseparable. In essence, a system of two particles is not really two separate particles at all, but one nonseparable potential which contains the possibilities for the two particles. Similarly, a system of many particles is also united in the same way. Thus, the whole universe is united in one cosmic wave of potentiality living in a vast space of unimaginable possibility. While the world appears to be a Many, quantum mechanics demonstrates that it is fundamentally a One.
As we explore further into the quantum realm, things only get stranger. With the evaporation of matter, determinism, and finally separability, our hero Schrödinger began to get a bit worried, for as he looked further into the unexplored territory, he saw some very odd things, indeed. What was most disturbing to Schrödinger was the fact that when an atom was not observed it could be in a potential state and then—just by merely measuring it— we somehow trigger the projection of the potential to the actual. To illustrate just how odd this situation is, Schrödinger imagined performing the following experiment with a cat.
He envisioned a single radioactive atom which can spontaneously decay, transforming into a different element. So whenever we measure this atom, it will be in one of two mutually exclusive actual states: decayed or not decayed. (This is entirely analogous to the electron being actually in or out of the box.) But if we do not measure the atom, then its state vector can be potentially in both states, pointing partly in the decayed direction and partly in the not-decayed direction. Initially, of course, the atom was in the not- decayed state, so the state vector pointed along the not- decayed axis. But as Schrödinger waits, there is a larger probability that he could find the atom decayed, so as time passes the vector has a smaller component along the not- decayed axis and a larger component on the decayed axis. But the main point is that, so long as Schrödinger does not measure it, the atom is not actually in one or the other states, but only potentially decayed or not-decayed.
Now Schrödinger imagines putting the radioactive atom, a detector, a hammer, a poison bottle into a cage with a cat in it. Schrödinger arranges it all so that when the atom decays, the detector will be triggered, causing the hammer to break the poison bottle, releasing the poison and killing the cat. Schrödinger closes the cage and waits a few minutes. Now since the state of the cat is directly dependent on the state of the bottle, which in turn is dependent on the state of the atom, when Schrödinger opens the cage to observe the state, he will see an actual live cat, if the atom is not decayed, or an actual dead cat, if the atom is decayed.
But what is the state of the cat while the cage is closed? In this case, we are forced to say that the cat is in a state similar to that of the atom: it is not actually dead or actually alive, but just in a state of being potentially both dead and alive. While it may not seem so strange to think of tiny atoms as having no actual state, it seems ridiculous to think of a cat in this way. Can it be true that in the quantum realm even cats can be in potential states? And can it be that just because Schrödinger opens the cage, the potential state of the cat suddenly becomes actual?
A classical physicist, not having ventured into the strange quantum realm, would consider such ideas as nonsense: "It is impossible for a cat to be in such a state!" But this reaction is like a land-locked sailor considering a round earth as nonsense: "It is impossible for my lake to be round." Indeed, the roundness is very difficult to detect on such a small scale. But a sailor with expanded horizons would recognize the fact that the lake, like the earth upon which it lies, must be slightly round. Similarly, while it is for all practical purposes impossible to detect the strange quantum effects for large objects such as cats, were we to expand our classical horizons into the quantum realm, we would recognize the fact that cats, like the atoms of which they are composed, can be in potential states. Like it or not, this is how the world really works beneath the illusion of classical mechanism, beneath the illusion of a world actually "out there," independent of measurement.
This brings us to the second, more mysterious question: What exactly transforms the cat from a potential state to an actual state? What projects the state-vector onto just one or the other of the axis states? A classical physicist, in an attempt to retain the actual world of large objects, might propose that the projection takes place when the system "gets large," and can then be treated with the old classical physics. But just how large? Two atoms, ten atoms, a thousand? Making size determine projection is very arbitrary. Moreover, this solution does not even make sense, for if one or two atoms can be in a potential state, then so can three or four, or fifty or five thousand—size is a matter of degree, while actuality is not. Claiming that the world suddenly becomes actual when the system gets "big enough" is like our land-locked sailor claiming that when a lake gets small enough, then suddenly it really becomes perfectly flat. What he ought to say is that when the lake gets small enough, it is as if it were really flat, while in reality it is still slightly round. Similarly, when our system gets big enough, it is as if it were really in an actual state, while in reality it is still in a potential state. We must be careful not to drag classical illusions into the quantum reality.
So potential states do not suddenly, of themselves, become actual when a system gets "large enough." But when do they become actual? We still have not answered this difficult question. In an attempt to solve this problem, Eugene Wigner, one of the many physicists to explore the newly discovered quantum realm, made a radical proposal.
Wigner began by taking the paradox of Schrödinger's cat one step further. What would happen, he wondered, if he put another cage around both Schrödinger and the first cage? Now Schrödinger is in a new cage, and since Schrödinger's state is dependent on what he sees when he looks at the cat, he is ultimately dependent on the atom's state now as well. So as long as Wigner does not open the big cage, Schrödinger will be in a potential state just like the cat! The state vector will be in a possibility space with the two directions: 1) "Schrödinger seeing a live cat" and 2) "Schrödinger seeing a dead cat", leaving poor Schrödinger suspended in potentia until Wigner decides to open the larger cage. But now we can ask, What stops us from putting Wigner and his cage in another, even bigger, cage? After all, Wigner is made of atoms, too, just like Schrödinger and the cat. So Wigner would then be in a potential state too. By extension, we can see that, because there is noone outside the universe to observe it, the whole world will be forever in a potential state with nothing to project it into an actual state. Is there a way to avoid such absurdity?
While it may be unusual for cats to be in potential states, Wigner considered it intolerable for humans to be in such a state. So to get out of this mess, Wigner proposed that the projection happens with the involvement of nonphysical consciousness. When Schrödinger opens the cage and looks at the cat, first his eye is in a potential state, "eye with image of live cat" and "eye with image of dead cat." Next, his brain is in a potential state, "experiencing seeing a dead cat" and "experiencing seeing a live cat." But it is at this point that we cannot go any further, Wigner argued, for Schrödinger is only ever conscious of one actual experience or another. And there should be no doubt about this for him: it is an undeniable fact that anything appearing in his consciousness is actually in one state or another. When he looks at a cat it is always actually dead or actually alive (or at least actually in some state or another). Never is he conscious of a cat in a potential combination of two mutually exclusive actual states. Thus, Wigner argued, the potential must become actual when it appears in Schrödinger's consciousness. Nothing physical—not the cat, not the eye, not the brain—can project the state vector. Only a nonphysical consciousness can do it. The buck stops with consciousness.
Incredibly, in order to account for the actual existence of any unique and definite measurement result, Wigner argues, we must recognize the existence of a nonphysical consciousness. The world cannot be just a bunch of inert matter, a collection of objects. There must also be a subject, a consciousness, apart from objects, which is aware of them. There is a similar argument in the context of classical physics. Just consider the simple question, "how is it that I am seeing anything at all?" Is there something like a little TV in your head? But then who is watching it? And then how is it that they see anything? By trying to account for the seeing of anything with a brain or a TV or any other material mechanism we are just adding more objects, and leaving the question unanswered: what sees any of these objects at all? One escape of this infinite regress is to recognize a subjective awareness apart from all objects. Similarly, to account for actual existence at all, we recognize a subject, or consciousness, which—by its very nature—is not another physical object in the system. So when any object is not in your conscious awareness—an atom, a bottle, a cat, your own body, a thought in your brain—it is (according to Wigner's interpretation of quantum mechanics) in a potential state.
What Wigner's interpretation proposes is that the human consciousness present in individuals is what projects the potential to the actual. Thus, not only can Wigner's consciousness project the cat's state, but Schrödinger or any other person can as well. This solution not only solves the problem of projection, but it also prevents Schrödinger from existing in a potential state—a proposition which Wigner just could not tolerate. But Wigner's restriction of this consciousness to human individuals has serious faults.
The first problem with Wigner's approach is that it gives an unexplained special status to human consciousness. Why is it that a human consciousness can make the cat actual but a monkey consciousness can not? And if we give consciousness to monkeys, then why not give it to cats? And then what about mice? How about insects? Where do we draw the line? And if we allow consciousness to go all the way down to the particles themselves, they would continually observe themselves, and never exist in potentia at all, contradicting experimental evidence. And even if we were able to draw a clear line somewhere between human consciousness and animal consciousness, at what age does a human suddenly have the ability to actualize cats? At ten? At two months? At birth? As a fetus? At conception? The development of an organism is a matter of degree, while the projection from potential to actual is not. This solution is thus very arbitrary, and is reminiscent of the idea that things become actual when they get big enough; only instead of size, Wigner has chosen "human consciousness" to be the property which determines when the world becomes actual. Considered as an observable property of biological organisms, the term "human consciousness" is both ambiguous and problematic. It is not surprising, then, that many physicists have rejected Wigner's proposal and looked for other explanations of the measurement problem. After decades, however, the problem still remains unsolved.
To illuminate the problems with Wigner's proposal, let us look at his argument for making human consciousness special. "O.K.", Wigner says, "suppose Schrödinger was in a potential state before I looked at him. Now, after I look at him I ask Schrödinger what he felt before I looked at him. Surely he will not say that he was in a potential state! Thus," Wigner concludes, "Schrödinger must have been in an actual state before I looked at him." As convincing as this may sound, Wigner's argument proves nothing. Suppose we replaced Schrödinger with a sophisticated robot. The robot would never say it was in a superposition either, for when Wigner looks at it, the robot will actualize into a state which had recorded either a live cat or a dead cat. Similarly, when Wigner looks at Schrödinger, Schrödinger will actualize into a state "Schrödinger with the memory of having seen a live cat" or "Schrödinger with the memory of having seen a dead cat." So there is no evidence that Schrödinger is any different than a robot or a cat. After all, as far as Wigner is concerned, Schrödinger's body and brain are made of atoms just like the radioactive atom, all of which will be in potential states until Wigner looks at them.
Wigner made the mistake of objectifying the subject: he gave a material object (Schrödinger's body) the property of a conscious subject. Wigner has no way of knowing for certain that Schrödinger is ever conscious of anything, and so he has no basis for the claim that Schrödinger or any other human is responsible for the projection from potentiality to actuality. Wigner's claim is just as arbitrary and unverifiable as the claim that big objects are responsible for the projection. This type of ambiguity is one reason many physicists object to bringing consciousness into physics as Wigner proposed.
Yet, despite this problem with Wigner's proposal, he can still be absolutely certain of one thing: While Wigner can never know if anyone else is conscious, he can be certain that he is. Strictly speaking, Wigner has absolute certainty regarding the existence of just one consciousness, namely, 'his' consciousness. For Wigner, the only time he can be absolutely sure that a potentiality has become an actuality is when a definite measurement result appears in his consciousness. But Wigner was repulsed by this denial of other people's existence, and understandably so: This all seems to imply solipsism, the view that he is the only subject, that he is the only conscious being and everyone else is just an object, like robots or machines, in his consciousness. Furthermore, this same argument would apply to each of us: The only conscious subject that you can be certain of is yourself. Your consciousness is responsible for the projection from potential to actual.
Thus, to correct Wigner's mistake of objectifying the subject, of arbitrarily granting consciousness to objects, we are apparently forced to accept solipsism: for you, there is no certainty that anything exists but yourself and your world. And for Wigner, the only certainty is himself and the existence of his world. So, are there millions of fragmented people experiencing their own personal worlds with no apparent connection between them? A world for you, a world for me, a world for Wigner? Yet the only world you can be certain of is your own.
The first problem that results from this situation is related to the identification of conscious subjects. In your world you will be claiming to be the true subject responsible for making the world actual, while other people will be arguing that, in fact, each of them is the observer of the world and you are just an object in their consciousness. Yet you know they are absolutely wrong. Thus we have a proliferation of conscious subjects, each of whom claims to be the one and only subject— hence the unresolvable arguments over who is responsible for whose existence.
The problem at the root of all this lies with the fact that solipsism does not completely eliminate the objectification of the subject. We get stuck in solipsism only because we are still making consciousness a property of our mind-body when, in fact, our own body, thoughts, and feelings are all objects appearing in consciousness. The conscious subject can not "belong" to any object, and that includes our thoughts and bodies as well as other humans such as Wigner and Schrödinger. Just as it is a mistake to attribute consciousness to objects such as Schrödinger and other people, it is also a mistake to attribute consciousness to the objects which comprise our own mind and body! All we can say for sure is that there is consciousness, and that the entire world of experience, including our own inner thoughts and feelings, appears in it.
Once this last objectification of the subject is recognized, we have solved the first problem, because we can no longer claim that other people are just objects in "our" personal consciousness. Now we are just an object in consciousness, too. And everyone will agree with us on this point. "Yes," they will each say, "there is a consciousness. This body and these thoughts are in it, and everyone else is in it, too." People can no longer argue, "you're just an object in my consciousness." Not because other people are not objects in consciousness, but because there is no "my" consciousness anymore.
At this point something amazing happens. What reason is there to think that the consciousness in which one person's world appears is different from the consciousness in which another person's world appears? Each unique person has a unique world that arises relative to their perspective. But the both the person and the world arise together to the subject, to consciousness itself. Is the subject to Wigner's world separate from the subject to Schrödinger's world? Consider what it would be like to switch places with a friend of yours, say Wigner. To just switch bodies, but not brains, would give you a good idea, but you would still not really know what it would be like to be Wigner unless you switched brains too. After all, even if you could be in his body, you still would not have his memories and skills that would allow you to truly experience what it is like to be Wigner in his essence. So you decide to switch places completely—body, brain, memories, everything. But to really know what it is like to be him, you must leave behind your own memories, for part of what makes Wigner unique is the fact that he does not have your memories. So you make this pure switch, and you live as Wigner for a day or two, then you switch back. But since none of the memories were switched, when you get back, it will be as if you had never switched at all! When you are Wigner, you would not know it and when you got back, you would not know you had been gone. So you could be switching back and forth all the time, repeatedly throughout the day, and your mind-body would never know it, "you" would never know it. But if that is the case, then what is the real difference between "your" consciousness and "Wigner's" consciousness? In your true essence, you are your friend. It is only one consciousness, one subject, that sees both worlds. Consciousness is not tied to any particular person or object whatsoever.
Therefore, the mistake that leads to solipsism is the objectification of the subject, or taking consciousness to be tied to a particular mind-body. In fact, the mind-body is a collection of objects in consciousness. The idea of separate conscious individuals is thus an illusion resulting from not recognizing this fact. As Schrödinger himself wrote, "the plurality that we perceive is only an appearance; it is not real." In fact, there is just one conscious subject, and you are that.
Although we have resolved the problem caused by the proliferation of subjects, we have still to solve another problem. This second problem is related to the fragmented worlds of which this subject is conscious. How are these separate experienced worlds integrated to give rise to a shared, objective world? In fact, we hardly need quantum mechanical paradoxes to see that this is a problem. After all, do not all individuals live in their own separate worlds, experiencing life from the particular point of view of one body, living in a certain culture during a certain time period? Certainly you see different things from Wigner, you experience different things from your friend. Even if you are both looking at the same object, you still see it from different angles and experience different reactions. Strictly speaking, no two people live in the same experiential world. Consequently, the notion of an objective world—that we actually experience the same world "out there"—becomes questionable. While we can say that it is as if there were an objective, shared world, in fact, we each experience our own personal world of phenomena. In this case, the whole quest of science to discover the laws of an objective world "out there" seems to be nothing more than a useful abstraction. All that is directly experienced are the various worlds of experience. And even if there is one subject common to the worlds, it still seems as if there are separate worlds, each centered around a particular mind-body. One world appears relative to your mind-body, while a totally different world appears relative to Wigner's mind-body. Thus, we still have a serious problem dealing with objectivity.
While it may seem that objectivity is totally lost, it has only taken a new form. To understand what has happened to objectivity, it is useful to draw an analogy with Einstein's special theory of relativity. Einstein's theory showed two important things. First, all measurements of time and space are relative—they depend on the point of view, or reference frame, of the observer. Second, the laws of nature do not depend on the point of view—all worlds are governed by the same laws. Thus, while the way nature appears to each mind-body depends on its point of view, the laws of nature do not. Objectivity no longer applies to the separate worlds of appearances. It only applies to the common laws behind them.
Niels Bohr, the father of the quantum revolution, wrote that a study of these two revolutionary theories of the 20th century "reveals striking similarities as regards the renunciation of the absolute significance of conventional physical attributes of objects." So, he says, "[we must use the word] phenomena exclusively to refer to the observations obtained under specified circumstances." In other words, the phenomenal world that appears to each of us is not objective, or absolute, but relative. To talk of the "actual" state of an object without reference to an observer in quantum mechanics is meaningless, just as is talking about the "actual" length of a time interval without reference to an observer in relativity. The "actual" world you experience is just a particular projection of the world of potentiality, like shadows flickering on the walls of a cave. And the particular appearance of the shadows will depend on the position of the light, on your point of view.
In addition, just as there is no preferred reference frame in relativity, there is no point of view that is more special than any other. While the apparent world that manifests in your reference frame is a different world of appearance altogether from the world that manifests in the reference frame of your friend, both are fundamentally just as valid. While all points of view are created equal, they still are unique expressions of the world. Just as the shadow of an object cast by a light from one angle is no more true or false than a shadow cast by a light from another angle, no one person's point of view is ultimately any more true or false than another's.
But quantum mechanics differs from relativity in one important way: the objects casting the shadows are not actual but potential. There is an objective world, but it is not an actual world fixed in space and time. The objective reality described by quantum theory is a potential world of possibility, beyond this shadow-play of spatio-temporal appearances we call actual. Furthermore, that objective world of potentiality is nonseparable—even though it decoheres into apparently separate worlds, it is in a deeper sense a single object, just as we have found that there is just a single subject. But out of this pair are manifested many relative worlds appearing to different people in different places at different times. And from the different relative worlds, each mind-body never sees the whole potential reality but only a limited, actualized projection from one unique point of view. In Schrödinger's words, "this whole is not so constituted that it can be surveyed in one single glance." But behind this apparent proliferation of subjects and objects, all are united and intricately interconnected.
Thus, we have now revealed beneath the veil of Newton's universe a quantum realm of reality in which objects cannot exist alone, independent of a conscious subject. And while the one unitive subject is free of the limitations of any particular point of view, what becomes actual in each world depends on the observer at the center of that world, the individual mind-body who defines the reference point for that relative world. And there are as many relative worlds as reference points to be chosen. A world for you, a world for your friend, a world for every plant and every animal, and even a world for the stars and planets and every single atom. Yet, in a deep and profound sense, these worlds are merely different projections of a single potential reality common to them all, a nonseparable reality interweaving them all into a coherent whole and its archetypal Law, making objectivity and science possible. And at the center of each relative world is the one subject, uniting the worlds from the subjective side and making human relationships meaningful.
And so we lose our last remaining link to the old cosmic machine. We have pierced completely through the illusion of Newton's world and have discovered the strange and wonderful world of the quantum, a world that is right here and now, veiled beneath the apparent reality of matter, determinism, naive objectivity, and separation. The world is not made of hard matter. The world of appearance does not strictly follow deterministic laws. The world is not just a collection of separate parts. The properties of objects do not exist independent of observers. No, the world is not what we have thought it to be after all. Beneath this illusion lies a quantum realm where strange and wonderful things can happen. And this quantum wonderland is not some far off place, it is not some fiction. This is the world right here and now, a world that modern physics has lead us to.
Finally, we have found our way to the quantum realm, a world of possibility and spontaneity, a world of unbroken unity. This quantum reality we have found at the end of our journey is composed of a Subject and an Object. The Subject is the One source of conscious awareness which shines forth through the Many individuals. The Object is the One potential for the appearance of the Many phenomenal appearances in all the individual worlds.
Being such a profound change in our world view, what implications does this quantum reality hold for us? The most profound changes are not the changes to the world, but the changes in how we see the world. The discovery of quantum mechanics has opened up a vast new quantum world that can free us from an outdated world view and its illusions of separation and materialism. Going far beyond superficial technological changes, the quantum world has the potential to transform the basis of our individual and social actions. By recognizing the essential identity of oneself with other creatures, one acts from unity and compassion rather than separation and conflict. Kindness to others is kindness to oneself and cruelty to others is cruelty to oneself. In addition, by acknowledging the unity of all creatures, a common ground is established beneath the political, ideological, and cultural divisions at the root of so many world problems. In the quantum world, separateness is only half the story. Beneath all diversity is a unity.
So, let us follow the vision of these heroic adventurers to the quantum realm. The new world has been discovered. Now it awaits those who are called to leave the old lands and seek beyond. It awaits us.
It should be emphasized that the above exposition provides an interpretation of quantum mechanics, a way of understanding the world described by the mathematical formalism of the theory. There are other interpretations of quantum mechanics that also provide valid ways of understanding what kind of world the theory describes. Interpretations do not differ in their empirical content, and neither the theory nor experiment uniquely determine any one interpretation. We are free to choose. How we choose to understand the world, however, has consequences.