Tag Archives: Schrödinger

CHAPTER 6. NINE LIVES OF SCHRÖDINGER’S CAT

Many of the founders of quantum physics found its strange implications difficult to accept. Schrödinger himself expressed his doubts about the interpretation of quantum mechanics in terms of probability waves in a paradox now known as Schrödinger’s Cat.

Suppose we put a cat in a cage with a radioactive atom and a Geiger counter. A radioactive atom will decay in accordance with the laws of probability. If the atom decays, the Geiger counter will go off and turn on the hammer, the hammer will break the bottle of poison, and the poison will kill the cat. Let’s say that the probability that this will happen within an hour is 50% (Fig. 21).

Img. 21.
Schrödinger’s cat paradox

Then how does quantum mechanics describe the state of a cat after an hour? Of course, if we look, we will find that the cat is either alive or dead. What if we don’t look? There is a 50% chance that the cat is dead. The probability that the cat is alive is also 50%.

If we think classically, as required by material realism, and are guided by the principles of determinism and causal continuity, then we could draw a mental analogy with a situation in which someone tossed a coin and then covered it with his palm. We don’t know whether it came up heads or tails, but of course it came up as one or the other. The cat is either alive or dead, with a 50% probability of each outcome. We simply do not know which outcome actually materialized. This is not the scenario suggested by the mathematics of quantum mechanics. Quantum mechanics approaches probabilities very differently. She describes the cat’s state at the end of the hour as half dead, half alive. Inside the box there is quite literally a “coherent superposition of a half-living and half-dead cat,” as it sounds in the technical jargon of quantum physics. The paradox of a cat being alive and dead at the same time is a consequence of how calculations are done in quantum mechanics. No matter how strange the consequences of this mathematics may be, we must take it seriously, since the same mathematics gives us the wonders of transistors and lasers.

This absurd situation is summed up by the following parody from T. S. Eliot’s Old Possum’s Book of Practical Cats:
Schrödinger’s cat is a mysterious cat,
it illustrates the laws;
the complicated things she does have no
apparent reason;
she confuses determinists
and drives them to despair,
because when they try to catch her,
there is no trace of the quantum cat!

The parody is, of course, true – no one has seen a quantum cat, or a coherent superposition, in fact, not even quantum physicists. In fact, if we look into the box, we see either a living or a dead cat. The inevitable question arises: what is so special about our act of observation that it can solve the cat’s devilish dilemma?

It’s one thing to plausibly talk about an electron passing through two slits at the same time, but when we talk about a cat being half alive and half dead, the absurdity of quantum coherent superposition becomes self-evident.

One way out is to insist that the mathematical prediction of coherent superposition should not be taken literally. Instead, following the interpretation in terms of ensemble statistics favored by some materialists, one can convince oneself that quantum mechanics makes predictions only about experiments with very large numbers of objects. If there were ten billion cats in exactly the same boxes, quantum mechanics would tell us that after an hour, half of them would be dead – and surely observation would confirm the truth of this statement. Perhaps for one cat the theory simply does not apply. A similar argument was made for electrons in the previous chapter. However, in fact, interpretation in terms of ensembles faces difficulties even when explaining the interference pattern in a simple double-slit experiment.

Moreover, interpretation in terms of ensembles is tantamount to abandoning quantum mechanics as a physical theory for describing a single object or single event. Since single events do occur (and even single electrons have been isolated), we should be able to talk about single quantum objects. In fact, quantum mechanics was formulated in relation to single objects, despite the paradoxes that this raises. We must be prepared for Schrödinger’s paradox and look for a way to resolve it. The alternative is to have no physics at all for single objects – and this is completely unacceptable.

Today, many physicists, when dealing with Schrödinger’s cat paradox, prefer to hide behind the anti-metaphysical philosophy of logical positivism. This philosophy grew out of the work of the Viennese philosopher Ludwig Wittgenstein, Tractatus Logico-Philosophicus, where he expressed his famous judgment: “What cannot be spoken about, one should remain silent about.” Following this rule, such physicists—we might call them the neo-Copenhagen School—claim that we should limit our discussion of reality to what is visible, rather than trying to assert the reality of something that cannot be observed. For them, the main argument is that we never see a coherent superposition. Is the unobserved cat half alive or half dead? They would say that such a question cannot be asked because it cannot be answered. Of course, this is sophistry. A question that cannot be answered directly can nevertheless be approached indirectly and the answer can be calculated based on consistency with what we can know directly. Moreover, complete avoidance of metaphysical questions is incompatible with the spirit of the original Copenhagen interpretation and with the views held by Bohr and Heisenberg.

According to Bohr, the Copenhagen Interpretation reduces the absurdity of the half-dead, half-alive cat through the principle of complementarity: coherent superposition is an abstraction; in the abstract, a cat can exist both alive and dead. This description is in addition to the description we give of a dead or living cat when we see it. According to Heisenberg, the coherent superposition—the half-living, half-dead cat—exists in transcendental potency. It is our observation that “collapses” the dual state of the cat into a single one.

How should we understand this concept of a half-living, half-dead cat existing in potency? The answer, which sounds like science fiction, was proposed by physicists Hugh Everett and John Wheeler. According to Everett and Wheeler, both possibilities are realized—a living cat and a dead cat—but they occur in different realities, or parallel universes. For every living cat we find in a box, our counterpart in a parallel universe opens our box’s counterpart to discover our cat’s dead counterpart. Observing the dual state of a cat causes the universe itself to split into parallel branches. It’s an intriguing idea, and one that some science fiction writers (notably Philip K. Dick) have capitalized on. Unfortunately, this is also an expensive idea. According to it, the amount of matter and energy would double every time an observation causes the universe to split apart. This offends our penchant for parsimony, which may be a prejudice but nevertheless serves as the cornerstone of scientific reasoning. Moreover, since parallel universes do not interact, this interpretation is difficult to test experimentally and is therefore scientifically useless. (In fiction, things are simpler. In Philip K. Dick’s novel The Man in the High Castle, parallel universes interact. Otherwise, how could there be a plot?)

Fortunately, there is a possible idealistic solution. Since our observation magically resolves the cat’s dichotomy, it must be us—our consciousness—that causes the collapse of the cat’s wave function. Material realists don’t like this idea because it makes consciousness an independent causal entity; to admit this would be to hammer nails into the coffin of material realism. Contrary to materialism, such famous scientists as John von Neumann, Fritz London, Edmond Bauer and Eugene Wigner agreed with this solution to the paradox.

Idealistic solution

According to the idealist solution, it is the observation of the conscious mind that puts an end to the live-or-dead cat dichotomy. Like Plato’s archetypes, coherent superpositions exist in a fairyland of transcendental order until we collapse them and bring them into the world of manifestation by our act of observation. In this case, we select one aspect from two, or many, resolved by the Schrödinger equation; Of course, it is a limited choice, subject to the general probability constraint of quantum mathematics, but it is a choice nonetheless.

Even if material realism is wrong, should we be quick to abandon scientific objectivity and invite consciousness into our science? One of the pioneers of quantum physics, Paul Dirac, once said that great breakthroughs in physics always involve the abandonment of some great prejudice. Perhaps it is time to abandon the bias of strict objectivity. Bernard D’España considers the objectivity allowed by quantum mechanics to be weak objectivity. Instead of the independence of events from the observer that strict objectivity requires, quantum mechanics allows for some intervention by the observer—but in such a way that the interpretation of events does not depend on any individual observer. This weak objectivity represents the invariance of events with respect to the observer: whoever the observer is, the event remains the same. Because individual measurements involve subjective choice, this principle is clearly a statistical one, and observer invariance only holds for large numbers of observations—which is nothing new. Having long ago accepted the probabilistic interpretation of quantum mechanics, we are now obliged to accept the statistical nature of some of our scientific principles – for example, the principle of causality. As cognitive psychology regularly demonstrates, we can certainly do science with weak objectivity defined in this way. We don’t really need strict objectivity.

The solution to Schrödinger’s paradox by the intervention of consciousness is the simplest – so simple that it is sometimes called the naive solution. However, many questions have been asked about this decision, and only by answering these questions can we overcome the charge of naivety.

Questions about the idealistic solution

One question you may still be asking is how can a cat be half alive and half dead? It can’t – if you think in terms of material realism. Material realism suggests that the state of a cat at any given time must be causally continuous in being either one or the other, or alive or dead. However, materialistic thinking is a consequence of assumptions of causal continuity and either/or descriptions of events. These assumptions are not necessarily true, especially when tested by quantum mechanics experiments.

The idealistic philosopher is not particularly concerned about the paradox of a cat being both alive and dead. In one story, a Zen master was shown a so-called dead man who was about to be buried. When asked whether a person was alive or dead, the Zen master replied, “I can’t tell.” How could he? According to idealism, the essence of man – consciousness – never dies. Therefore, it would be wrong to directly say that a person is dead. However, when a person’s body is being prepared for burial, it would be absurd to say that he is alive.

Is the cat alive or dead? When the Zen master Zeshu was asked, “Does a dog have Buddha nature?” he answered “mu.” Here again, to answer “no” would be wrong, since, according to the teachings of the Buddha, all beings have Buddha nature. Answering “yes” would also be risky, since Buddha nature must be realized and lived, not intellectually understood. Therefore, the master answered “mu” – neither yes nor no.

Apparently, when quantum mechanics states that at the end of an hour, Schrödinger’s cat is half alive and half dead, it assumes an idealistic philosophy similar to that of the Zen masters. How can it be? How can consciousness play a decisive role in shaping the reality of the physical world? Doesn’t this presuppose the supremacy of consciousness over matter?

If before we look inside the box Schrödinger’s cat is both alive and dead, but after we look inside it is in a single state (alive or dead), then simply by looking we must do something . How can a fleeting glance affect a cat’s physical condition? Realists ask these questions in an attempt to refute the idea that consciousness causes the collapse of a coherent superposition.

Yes, the idealistic solution does imply the action of consciousness on matter. However, this impact only poses a problem for material realism. In this philosophy, consciousness is considered an epiphenomenon of matter, and it seems impossible that an epiphenomenon of matter could affect the very tissue from which it is formed—essentially causing itself. This causal paradox is avoided by monistic idealism, in which consciousness is primary. In consciousness, coherent superpositions represent transcendental objects. They become immanent only when consciousness, through a process of observation, selects one of the many aspects of a coherent superposition, although its choice is limited by the probabilities that the quantum calculus allows. (Consciousness is law-abiding. The creativity of the cosmos comes from the creativity of its quantum laws, and not from arbitrary lawlessness.)

According to monistic idealism, objects are already in consciousness as incipient, transcendent, archetypal forms of possibility. Collapse does not consist of doing something to objects by measuring, but of choosing and recognizing the result of that choice. Take another look at the earlier illustration of the gestalt “My wife and mother-in-law” (Fig. 12). This illustration contains an overlay of images. When we see a wife (or mother-in-law), we do nothing with the picture. We simply choose and acknowledge our choice. The process of consciousness collapsing a wave function is something like this.

However, there are dualists who try to explain the action of consciousness in Schrödinger’s paradox, finding evidence of psychokinesis – the ability to move matter through the action of the mind. Eugene Wigner argues that if a quantum object can influence our consciousness, then consciousness must be able to influence a quantum object. However, the evidence for psychokinesis is insufficient and questionable. In addition, consideration of another paradox—the “paradox of Wigner’s friend”—essentially excludes a dualistic interpretation.

Wigner’s friend paradox

Suppose two people open the box containing Schrödinger’s cat at the same time. If the outcome of collapse is chosen by the observer, as the idealistic solution implies, then what if the two observers make different choices—wouldn’t that create a problem? If we say no, then only one of the observers can make the choice, and supporters of realism rightly consider this decision unsatisfactory.

In Wigner’s friend paradox, formulated by physicist Eugene Wigner, what happens is that instead of observing the cat himself, Wigner asks his friend to do so. His friend opens the box, sees the cat and then reports the results of his observation to Wigner. At this stage we can say that Wigner has just actualized a reality that includes his friend and the cat. There is a paradox here: was the cat alive or dead when Wigner’s friend observed it, but before he reported the result of the observation? To say that when Wigner’s friend observed the cat, its state did not collapse is to say that his friend was unconscious until Wigner asked him – that his friend’s consciousness could not decide whether the cat was alive or dead without prompting from Wigner. This is quite similar to solipsism, a philosophy that believes you are the only conscious being and everything else is a figment of your imagination. Why should Wigner be the privileged agent who is allowed to cause the cat’s state function to collapse?

Suppose we instead say that the collapse of the superposition causes the consciousness of Wigner’s friend. Doesn’t this open Pandora’s box? If Wigner and his friend look at a cat at the same time, whose choice will matter? What if two observers make different choices? If individual people determined the behavior of the objective world by their choices, then life would turn into absolute hell, since, as we know, subjective impressions are often contradictory. In such a case, the situation would be similar to that in which motorists moving from different directions would choose the color of the traffic light (red or green) at will. This argument is often considered the death blow to the solution of Schrödinger’s paradox by conscious intervention. However, it is only fatal to the dualistic interpretation. To understand why this is so, let’s look at Wigner’s paradox in more detail.

Wigner compared his paradoxical situation to one in which an inanimate device is used to make observations. When a mechanism is used, there is no paradox. There is nothing paradoxical or frustrating about a machine being in a state of uncertainty for any length of time, but experience tells us that the observation of a conscious being is crucial. Once a conscious being makes an observation, material reality becomes manifest in a single state. According to Wigner:

Therefore, a conscious being must have a different role in quantum mechanics than an inanimate measuring device… This argument assumes that “my friend” has the same kinds of impressions and sensations as I do – in particular, that after interacting with an object he is not in an unconscious state… It is not necessary to see a contradiction here from the point of view of orthodox quantum mechanics, and there is none if we believe that the alternative is meaningless – does my friend’s consciousness contain… the impression of what he saw [either a dead or a living cat]. However, to deny the existence of a friend’s consciousness to such an extent is undoubtedly an unnatural position, approaching solipsism, and few people in their hearts will agree with it.

It’s an insidious paradox, but Wigner is right. We need not say that as long as Wigner does not manifest his friend, the friend is in an unconscious state. Equally, we need not resort to solipsism. There is another alternative.

Wigner’s paradox arises only when he makes the unfounded dualistic assumption that his consciousness exists separately from the consciousness of his friend. The paradox disappears if there is only one subject, rather than separate subjects as we usually understand them. The alternative to solipsism is a single subject-consciousness.

When I observe, I see the whole world of manifestation, but this is not solipsism, since there is no individual seeing self as opposed to other selves. Erwin Schrödinger was right when he said: “Consciousness is the only thing for which there is no plural.” Etymology and spelling have preserved the uniqueness of consciousness. However, the existence of terms such as “I” and “mine” in language leads us into a dualistic trap. We consider ourselves separate because we talk about ourselves in this way.

In the same way, people get used to thinking about having consciousness, as in the question: “Does a cat have consciousness?” Only in material realism does consciousness represent something that can simply be possessed. Such a consciousness would be deterministic, not free, and would not be worth having.

The watched pot still boils

Let’s look at another complication in Schrödinger’s paradox. Let us assume that Schrödinger’s cat is itself a conscious being. The situation becomes even more critical if we assume that there is a person in the box with a radioactive atom, a bottle of poison and everything else. Then suppose that after an hour we open the box, and if he is still alive, we ask him whether he experienced the half-dead, half-alive state? He will answer – of course not! Think a little. What if we asked him if he felt alive the whole time? If this person is thoughtful enough, after some thought he will probably say no. You see, we are not aware of our body all the time. In fact, under ordinary circumstances, a person is very little aware of his body. Therefore, from the point of view of an idealistic interpretation, what happens can be described as follows. Over the course of an hour, the man became aware from time to time that he was alive. In other words, he observed himself. At these moments, his wave function collapsed, and, fortunately, each time the choice was the living state. Between these moments of wave collapse, its wave function expanded and became a coherent superposition of the dead and living states in a transcendental realm beyond experience.

You know how we see movies. Our brain-mind is not capable of distinguishing between individual still pictures running before our eyes at a speed of twenty-four frames per second. Likewise, what appears to be continuity to one observing oneself is in fact a mirage consisting of many discrete collapses.

This last argument also means that we could not save Schrödinger’s cat from the cruel outcome of radioactive decay by constantly looking at it, and thus continuously collapsing its wave function and keeping it alive. This is a noble impulse, but it is doomed to fail – for the same reason that a pot that is watched boils, although the proverb suggests otherwise. It’s good that the pot is being watched, because if we could prevent change by simply looking at an object, the world would be full of narcissists trying to avoid old age and death by meditating on themselves.

Erwin Schrödinger’s reminder should be taken into account: “Observations should be considered individual discrete events. There are gaps between them that we cannot fill.”

The solution to Schrödinger’s cat paradox tells us a lot about the nature of consciousness. By manifesting material reality, it makes a choice between alternatives; it is transcendental and one; and his actions elude our normal everyday perception. Of course, from a common sense perspective, none of these aspects of consciousness seem self-evident. Try to curb your disbelief and remember what Robert Oppenheimer once said: “Science is an extraordinary sense.”

Quantum collapse is a process of selection and recognition by a conscious observer; ultimately there is only one observer. This means we need to resolve another classic paradox.

When does the measurement end?

According to some realists, a measurement is complete when a classical measuring device, like the Geiger counter in Schrödinger’s cat cage, measures a quantum object; it completes when the counter clicks. Note that if we make this decision, then the paradox of the dual state of the cat does not arise.

This reminds me of a story. Two elderly gentlemen were talking, and one of them complained of chronic gout. Another said with some pride: “I don’t have to worry about gout; I take a cold shower every morning.” The gentleman with gout looked at him mockingly and replied, “So you get chronic cold showers instead!”

These realists try to replace the dichotomy of Schrödinger’s cat with the dichotomy of the quantum and classical levels. They divide the world into quantum objects and classical measuring instruments. However, such a dichotomy is untenable and completely unnecessary. We can state that all objects are subject to quantum physics (the unity of physics!), and at the same time satisfactorily answer the question: “When does measurement end?”

What is the definition of measurement? To put it slightly differently, when can we say that quantum measurement is finished? You can approach the answer historically.

Werner Heisenberg, who proposed the uncertainty principle, formulated a thought experiment that Bohr further refined. David Bohm recently described an experiment that I will use here. Let us assume that the particle is at rest in the plane of the microscope target and we analyze its observation from the position of classical physics. To observe a target particle, we point another particle at it (using a microscope), which is deflected by the target particle onto a photographic plate, leaving a mark on it. Based on the study of the trace and our knowledge of how the microscope works, we can, in accordance with classical physics, determine both the position of the target particle and the momentum imparted to it at the moment of deflection. Specific experimental conditions do not affect the final result.

In quantum mechanics, all this changes. If the target particle is an atom and if we look at it with an electron microscope in which an electron is deflected by the atom onto a photographic plate (Fig. 22), the following four considerations arise:

1. The deflected electron should be described both as a wave (while it moves from the object O to the image P) and as a particle (when it reaches P and leaves a trace T).

2. Due to this wave aspect of the electron, the image P gives us only the probability distribution of the position of the object O. In other words, the position is determined only within the limits of some uncertainty ∆x.

3. In the same way, Heisenberg argued, the direction of the trace T gives us only the probability distribution of the impulse O and, thus, determines the impulse only within the limits of uncertainty ∆p. Using simple mathematics, Heisenberg was able to show that the product of two uncertainties is greater than or equal to Planck’s constant. This is the Heisenberg uncertainty principle.

4. In a more detailed mathematical description, Bohr showed that the wave function of an observed atom cannot be determined separately from the wave function of the electron used to observe it. In reality, Bohr said, the wave function of the electron cannot be separated from the wave function of the photographic emulsion. And so on. It is impossible to draw an unambiguous dividing line in this chain.

Img. 22.
Bohr-Heisenberg microscope</strong”>

Despite the uncertainty in drawing the dividing line, Bohr felt that we must draw it due to the “necessary use of classical concepts in the interpretation of all correct measurements.” Bohr was reluctant to admit that the experimental setting should be described in purely classical language. It must be assumed that the dichotomy of quantum waves ends in the measuring device. However, as the philosopher John Schumacher has convincingly shown, all actual experiments contain a second built-in Heisenberg microscope: the process of seeing a trace in an emulsion involves the same kind of consideration as what led Heisenberg to the uncertainty principle (Fig. 23). Photons from the emulsion are amplified by the experimenter’s own visual apparatus. Can we ignore the quantum mechanics of our own vision? If not, then aren’t our brain-mind-consciousness inextricably linked to the process of measurement?

Img. 23.
Mechanics of vision. Another Heisenberg microscope in action?

Does a cat belong to the quantum or classical world?

When we think about it, it becomes clear that Bohr was replacing one dichotomy with another – the dichotomy of the cat with the dichotomy of a world divided into quantum and classical systems. According to Bohr, we cannot separate the wave function of an atom from everything else in the cell (various measuring instruments for determining the decay of an atom, such as a Geiger counter, a bottle of poison, and even a cat), and therefore the line we draw between the microworld and the macrocosm turns out to be completely arbitrary. Unfortunately, Bohr also talked about the need to recognize that measurement with a mechanism—a measuring device—resolves the dichotomy of the quantum wave function.

However, any macroscopic body is ultimately a quantum object; there is no such thing as a classical object unless we are willing to accept the vicious quantum/classical dichotomy in physics. It is true that in most situations the behavior of a macroscopic body can be predicted based on the rules of classical mechanics. (In such cases, quantum mechanics makes the same mathematical predictions as classical mechanics—this is the correspondence principle that Bohr himself discovered.) For this reason, we often roughly consider macroscopic bodies to be classical. However, the measurement process is not such a case, and the correspondence principle does not apply to it. Of course, Bohr knew this. In his famous debates with Einstein, Bohr often invoked quantum mechanics to describe macroscopic bodies in measurement to counter Einstein’s pointed objections to probability waves and the uncertainty principle.

As an example of the dispute between Bohr and Einstein, consider the situation of the double-slit experiment, but with one additional aspect. Let’s assume that before hitting the double slit, the electrons pass through a single slit in the diaphragm – its purpose is to accurately determine the initial position of the electrons. Einstein proposed installing this first slot on extremely sensitive springs (Fig. 24). He argued that if the first slit deflects an electron to the upper of the two slits, then, due to the principle of conservation of momentum, the first diaphragm will move down, and if the electron is deflected down to the lower of the slits, then the opposite will happen. Thus, measuring the recoil of the diaphragm will tell us which slit the electron actually passes through—information that is impossible from the point of view of quantum mechanics. If the first diaphragm had truly been classical, then Einstein would have been right. In defending quantum mechanics, Bohr pointed out that, ultimately, this diaphragm is also subject to quantum uncertainty. Therefore, when measuring its momentum, its position becomes uncertain. Bohr was able to demonstrate that this widening of the first slit effectively eliminated the interference pattern.

Img. 24.
Einstein’s idea: an initial slit on springs for a double-slit experiment. If, before passing through a partition with two slits (not shown), electrons pass through a slit in a diaphragm mounted on springs, is it possible to determine which slit the electron passes through without destroying the interference pattern?

However, let us further assume that the principle of complementarity operates and that sometimes a macroscopic device does acquire a quantum dichotomy (as the Bohr-Einstein controversy shows), but that at other times this does not happen – as in the case of a measuring device. This original idea, called macrorealism, comes from the brilliant physicist Tony Leggett, whose work led to the creation of a magnificent experimental device called SQUID (Superconducting Quantum Interference Detector).

Ordinary conductors conduct electricity, but always offer some resistance to the passage of electric current, which results in the loss of electrical energy in the form of heat. In contrast, superconductors allow current to flow without resistance. If you create an electric current in a superconducting circuit, then this current will flow almost forever – even without a source of energy. Superconductivity is due to a special correlation between electrons that spreads throughout the superconductor. Electrons require energy to escape from this correlated state, making the state relatively immune to the random thermal motion present in a normal conductor.

A SQUID is a piece of superconductor with two holes that almost touch at a point called the “weak link” (Figure 25). Let’s say we create a current in a loop around one of the holes. Current creates a magnetic field, just like any electromagnet, and magnetic field lines passing through a hole are also a common occurrence. In the case of a superconductor, what is unusual is that the magnetic flux—the number of field lines per unit area—is quantized; the magnetic flux passing through the hole is discrete. This gave Leggett his key idea.

Img. 25.
Will the flux line split between the two holes, showing quantum interference at the macroscopic level?

Let us assume that we create such a small current that there is only one flux quantum. Then we created a double-slit interference situation. If there is only one hole, then it is obvious that the quantum can be anywhere in it. If the link between two holes is too thick, the flow will be confined to only one hole. Is it possible, with a suitable size of the weak link, to create quantum interference so that the flux quantum is non-localized, being in both holes at the same time? If so, then quantum coherent superpositions clearly persist even at the level of macroscopic bodies. If no such delocalization is observed, then we can conclude that macroscopic bodies are indeed classical and do not admit coherent superpositions as their allowed states.

There is still no evidence of a violation of quantum mechanics in the case of SQUID, but Leggett stubbornly expects the collapse of quantum theory. At a recent conference, he said: “But at times, when the full moon shines brightly, I do what in the physics community may be the intellectual equivalent of becoming a werewolf: I wonder whether quantum mechanics is the complete and final truth about the physical universe… I am inclined to believe that somewhere between the atom and the human brain it [quantum mechanics] not only can, but must fail.”

He spoke like a true material realist!

Many physicists feel inclined to ask the same questions that inspire Leggett, so SQUID research continues. I suspect that one day they will provide evidence for quantum mechanics and show that quantum coherent superpositions are clearly present even in macroscopic bodies.

If we do not deny that ultimately all objects acquire a quantum dichotomy, then, as von Neumann first argued, if a chain of material mechanisms measures a quantum object in a state of coherent superposition, they all acquire the object dichotomy in turn, ad infinitum (Fig. 26). How to get out of the deadlock created by the von Neumann chain? The answer is amazing: jumping out of the system, out of the material order of reality.

Img. 26.
Von Neumann chain. According to von Neumann’s proof, even our brain-mind becomes infected with the cat dichotomy, so how does the chain end?

We know that observation by a conscious observer ends the dichotomy. It is therefore quite obvious that consciousness must act from outside the material world; in other words, consciousness must be transcendental—nonlocal.

Ramachandran’s paradox

If you are still concerned about the transcendence of consciousness, then you may enjoy considering the paradox that neuroscientist Ramachandran came up with.

Suppose that thanks to some super technology it is possible to record, using electrodes or something like that, everything that happens in the brain when external stimuli act on it. You can imagine that from these data and with the help of some super-mathematics you can obtain a complete and detailed description of the state of the brain in the situation of the action of a given stimulus.

Suppose the stimulus is a red flower; you show it to several people, collect the data, analyze it and get a set of brain states corresponding to the perception of a red flower. You would expect that, barring minor statistical variations, you would get essentially the same description of the state each time (something like there was a reaction in certain cells in a certain area of ​​the brain involved in color perception).

You might even imagine yourself using super technology to record and analyze your own brain data (while seeing a red flower). The brain state you find in yourself should not be any noticeably different from all others.

Consider this interesting twist to the experiment: You have no reason to suspect that the description of everyone else’s brain states is incomplete (especially if you fully believe in your superscience). And at the same time, in relation to your own brain state, you know that something is missing – namely, your role as an observer – your awareness of the experience corresponding to your brain state, the actual conscious perception of red. Your subjective experience cannot be part of the objective state of the brain, because in such a situation, who would observe the brain? A famous Canadian neurosurgeon was similarly puzzled when contemplating the prospect of operating on his own brain: “Where is the subject and where is the object if you operate on your own brain?”

There must be a difference between your brain as an observer and the brains of those you observe. The only alternative conclusion is that the brain states you construct, even with superscience, are incomplete. Since your brain state is incomplete, and other people’s brain states are identical to yours, then they must also be incomplete, because they do not take into account consciousness.

For material realists this is a paradox, since from their point of view none of the above solutions are desirable. The material realist will not be willing to give special privileges to the individual observer (which would be tantamount to solipsism), but will also be reluctant to admit that any achievable description of the state of the brain using materialist science would be ipso facto incomplete.

An important clue is provided by the neurosurgeon’s question – where is the subject and where is the object if you operate on your own brain? The essence of the problem is conveyed by the expression: “What we are looking for is what is looking for.” Consciousness presupposes paradoxical self-reference—the taken-for-granted ability to relate to ourselves separately from our surroundings.

Erwin Schrödinger said: “Unconsciously, and without being strictly consistent in this matter, we exclude the Subject of Knowledge from the sphere of nature that we are trying to understand.” A theory of quantum measurement that dares to invoke consciousness in matters of quantum objects must deal with the paradox of self-reference. Let’s clarify this concept.

When does the measurement end? (Summary)

A subtle criticism can be made from the statement that transcendental consciousness causes the collapse of the wave function of a quantum object: the consciousness causing the collapse of the wave function could be the consciousness of the eternal, omnipresent God, as in the following humorous passage:
There was once a man who said: “To God
It must seem exceedingly strange
If He discovers that this tree
continues to exist
when no one is around.”
Dear sir, your surprise is strange,
I am always nearby
and that is why the tree will continue to be,
as it is observed by I,
yours truly, God.

However, an omnipresent God causing the collapse of the wave function does not resolve the measurement paradox, since we can ask, “At what point is measurement finished if God is always looking?” The answer is crucial: measurement is not complete without the inclusion of immanent awareness. The most familiar example of immanent awareness is, of course, the awareness of the mind-brain of a human being.

When is the measurement completed? When transcendental consciousness causes the collapse of the wave function through the immanent mind-brain looking with awareness. This formulation is consistent with our ordinary observation that there is never an experience of a material object without an accompanying mental object, that is, the thought “I see this object,” or at least without awareness.

Note that a distinction must be made between consciousness with awareness and without awareness. Wave function collapse occurs in the first case, but not in the last. In psychological literature, consciousness without awareness is called unconscious.

Of course, in the idea that immanent awareness is required to complete a dimension, there is a certain causal circle, since without the completion of a dimension there can be no immanent awareness. Which comes first, awareness or measurement? What is the root cause? Are we facing an unanswerable “chicken or the egg” question?

One Sufi story has a similar connotation. One night, Mullah Nasreddin was walking along a deserted road when he noticed a group of horsemen approaching. Mulla got nervous and ran. The horsemen saw him running and galloped after him. Now the mullah was really scared. Having reached the walls of the cemetery and driven by fear, he jumped over the wall, found an empty grave and lay down in it. The horsemen saw him jump over the wall and followed him into the cemetery. After a little searching, they found the mullah, fearfully looking up at them.
“Something happened? – the horsemen asked the mullah. – Can we help you somehow? Why are you here?”
“Well, it’s a long story,” answered the mullah. “In short, I am here because of you, and I can see that you are here because of me.”

If only one order of reality is imposed on us – the physical order of things, then this is a genuine paradox for which there is no solution within the framework of material realism. John Wheeler called the circular nature of quantum measurement the “circle of meaning.” This is a very insightful description, but the real question is who is reading the meaning. There is no paradox here only for idealism, since consciousness acts from outside the system and completes the cycle of meaning.

This solution is similar to the solution to the so-called prisoner’s problem, an elementary game theory problem. You plan to escape from your prison cell through a tunnel dug with the help of your friend (Fig. 27). Obviously, your escape will be much easier if you and your friend are digging from opposite sides of the same camera corner; however, you cannot communicate and the cell has six angles from which to choose. The chances of escaping don’t look too good, do they? But think a little about the shape of your camera and you will realize that you will most likely decide to dig in corner number 3. Why? Because this is the only corner that looks different (concave) from the outside. So you would expect your friend to start digging here. Likewise, only corner number 3 is concave from the inside, so your friend will probably expect you to start digging there too.

Img. 27.
Prisoner’s dilemma: which angle to choose?

But what is your friend’s motivation for digging in this corner? It is you! He imagines you choosing this angle for the same reason you imagine him choosing it. Note that in this case we cannot establish any causal sequence and therefore no simple hierarchy of levels. Instead of a linear causal hierarchy, we have a circular causal hierarchy. Nobody chose the plan. Instead, the plan was a joint creation driven by a higher goal—the prisoner’s escape.

Douglas Hofstaedter called this type of situation a complex hierarchy—a hierarchy that is so intricate that it is impossible to distinguish higher and lower levels on the hierarchical totem pole. Hofstadter suggests that self-reference may arise from such a complex hierarchy. I suspect that in the brain-mind situation, in which consciousness causes the wave function to collapse, but only when awareness is present, our immanent self-reference comes from a complex hierarchy. The von Neumann chain ends precisely with the observation of a self-correlating system.

Irreversibility and the arrow of time

When does the measurement end? Idealism states that it ends only when self-referential observation has occurred. In contrast, some physicists argue that the measurement ends when the detector detects a quantum event. How does the detector differ from the previous measuring device? These physicists claim that detection by the detector is irreversible.

What is irreversibility? There are some processes in nature that can be called reversible, since observing these processes in reverse order, it is impossible to determine the direction of time. An example is the movement of a pendulum (at least for a short period of time): if you film its movement and then run it in the opposite direction, you will not find any visible difference. In contrast, filming an irreversible process cannot be replayed without revealing its secret. For example, suppose that while you are filming the movement of a pendulum on a table, you are also filming a cup that falls to the floor and breaks. When you rewind the movie, the pieces that fly up from the floor and become a whole cup again will reveal your secret – that you are rewinding the movie.

To understand the difference between a reversible meter and a detector, consider the following example. Photons have a characteristic called polarization, which can take two meanings: it is an axis directed (or polarized) in only one of two mutually perpendicular directions. Polarized sunglasses polarize normal non-polarized light. They transmit only those photons whose polarization axis is parallel to the polarization axis of the glasses. You can check this by placing two polarized glasses perpendicular to each other and looking through them. You will only see darkness. Why? Because one polarized glass polarizes photons, say, vertically, while another allows only horizontally polarized photons to pass through. In other words, both glasses together act as a double filter that blocks out all the light.

A photon polarized at 45° is a coherent superposition of half vertically and half horizontally polarized states. If such a photon passes through a polarization box with vertically and horizontally polarized channels, then it randomly appears in either the vertically polarized or horizontally polarized channel. This can be judged by the readings of detectors placed behind each of the channels (Fig. 28, a).

Now suppose that in the setup shown in Fig. 28, a, we will place a polarizer with a polarization angle of 45° between the polarizing box and the detectors (Fig. 28, b). It turns out that the photon restores its original state of polarization at an angle of 45° – a state of coherent superposition; he is reborn. Thus, a polaroid alone is not enough to measure photons – since the photons still retain their potential to become a coherent superposition. The measurement requires a detector in which irreversible processes occur, such as a fluorescent screen or photographic film.

Img. 28.
Experiments with photons polarized at an angle of 45°

If you think in terms of time reversal, then the motion of 45° polarized photons that pass through a polarization box and then again through a 45° polarizer is time reversible. However, if the photons are detected by some detector with an irreversible process, then by imagining this process in reverse, you are able to distinguish between forward and backward motion.

Remember the story about the scene filmed for silent films. The heroine was supposed to be tied to the tracks in front of an approaching train. According to the plot of the film, the heroine had to be saved – the train stopped at the last moment. Since the actress (for obvious reasons) did not want to risk her life, the director filmed the entire scene backwards – starting with the moment when the actress is tied to the rails, and the train stands motionless next to her. Then the train began to move backwards. But what do you think audiences saw when the film was played backwards? In those days, trains were driven by coal-fired steam locomotives. In the film, which was run in reverse, the smoke entered the locomotive’s chimney instead of coming out of it, thereby revealing the film’s secret. Smoke formation is an irreversible process.

Does this mean that the solution to the problem of quantum measurement is close – and without the assumption of the participation of consciousness? We only need to recognize the irreversibility of certain measuring instruments called detectors, and then perhaps we can break free of the von Neumann chain. Once the detectors have been triggered, the coherent superposition can no longer be reconstructed and can therefore be said to have truly ended.

But is this really so? Is the detector sufficient to complete the von Neumann chain? Von Neumann himself answers no. The detector must become a coherent superposition of the needle readings, for the simple reason that it also obeys quantum mechanics. The same is true for any subsequent measuring device – reversible or “irreversible”. The von Neumann chain continues.

The point is that the quantum Schrödinger equation is time reversible: it does not change when the sign of time changes. As the mathematician Jules Henri Poincaré showed, the behavior of any macroscopic body subject to a time-reversible equation cannot be truly irreversible. Therefore, a generally accepted point of view is emerging that absolute irreversibility is impossible; The apparent irreversibility that we observe in nature is due to the low probability of reversing the evolutionary path of a macroscopic body to the initial configuration, which has greater relative order.

Accounting for irreversibility provides an important lesson. Although ultimately all objects are quantum objects, the apparent irreversibility of some macro objects allows us to make a rough distinction between the classical and the quantum. We can say that a quantum object is restored, while the restoration time of a classical object is extremely long. In other words, we can say that while quantum objects do not have a noticeable retention of their history – they do not have memory, classical objects – for example, detectors – have memory, in the sense that it takes a long time for the memory to be erased.

Another important question arises: if there is no absolute irreversibility in the movement of matter, then how does the idealistic interpretation cope with the idea of ​​unidirectional flow of time, the arrow of time? According to the idealist interpretation, in the transcendental realm time is a two-way street, showing signs of only approximate irreversibility for the movement of increasingly complex objects. When consciousness collapses the brain-mind wave function, it exhibits the unidirectional time we observe. Irreversibility and the arrow of time enter nature through the process of collapse itself—the quantum dimension—as physicist Leo Szilard suspected many years ago.

Apparently, the irreversibility of detectors does not solve the measurement problem. Such a solution can only be approached if we are willing to accept irreversibility in the form of disorder even more fundamental than quantum mechanics. There is a proposal to do just that.

Suppose that matter is fundamentally disordered and that the disordered behavior of the substrate of particles, through random fluctuations, gives rise to approximately ordered behavior, which we can call quantum. If this were true, then quantum mechanics itself would be an epiphenomenon—like all other ordered behavior. There is no experimental evidence to support this kind of theory, although if it could be proven it would be an ingenious solution to the measurement problem. However, some physicists still admit that there is a hidden underlying environment that causes randomness; They draw an analogy with the random movement of molecules that causes the random movement of pollen particles in water visible through a microscope (called Brownian motion). However, the assumption of an underlying environment is inconsistent with the Aspect experiment unless it involves nonlocality. And within the framework of material realism, it is difficult to accept non-local Brownian motion.

Nine Lives

Stephen Hawking says, “Whenever I hear about Schrödinger’s cat, I want to grab a gun.” Almost every physicist experiences a similar impulse. Everyone wants to kill the cat—that is, the cat paradox—but it apparently has nine lives.

In its first life, the cat is treated statistically, as part of an ensemble. The cat is offended (since this interpretation robs it of its distinctiveness), but is unharmed.

In its second life, philosophers of macrorealism saw the cat as an example of the quantum/classical dichotomy. The cat refuses to exchange its life/death dichotomy for yet another dichotomy.

In the third life, the cat is presented with irreversibility and randomness, but the cat says – prove it.

In the fourth life, the cat encounters hidden variables (the idea that its state never becomes dualistic, but is, in fact, entirely determined by hidden variables), and what happens remains hidden.

In the fifth life, representatives of the neo-Copenhagen school try to get rid of the cat using the philosophy of logical positivism. By most accounts, the cat remains unharmed.

In the sixth life, the cat encounters multiple worlds. Who knows, maybe she died in some universe, but as far as we can tell, not in this one.

In the seventh life, the cat encounters Bohr and his principle of complementarity, but is saved by the question: what constitutes a dimension?

In the eighth life, the cat comes face to face with consciousness (of the dualistic variety), but is saved by Wigner’s friend.

Finally, in the ninth life, the cat finds salvation in an idealistic interpretation. This ends the story of the nine lives of Schrödinger’s cat.

The book “The Self-Aware Universe. How consciousness creates the material world.” Amit Goswami

Contents

PREFACE
PART I. The Union of Science and Spirituality
CHAPTER 1. THE CHAPTER AND THE BRIDGE
CHAPTER 2. OLD PHYSICS AND ITS PHILOSOPHICAL HERITAGE
CHAPTER 3. QUANTUM PHYSICS AND THE DEATH OF MATERIAL REALISM
CHAPTER 4. THE PHILOSOPHY OF MONISTIC IDEALISM
PART II. IDEALISM AND THE RESOLUTION OF QUANTUM PARADOXES
CHAPTER 5. OBJECTS IN TWO PLACES AT THE SAME TIME AND EFFECTS THAT PRECEDE THEIR CAUSES
CHAPTER 6. THE NINE LIVES OF SCHRODINGER’S CAT
CHAPTER 7. I CHOOSE WITH THEREFORE, I AM
CHAPTER 8. THE EINSTEIN-PODOLSKY-ROSEN PARADOX
CHAPTER 9. RECONCILIATION OF REALISM AND IDEALISM
PART III. SELF-REFERENCE: HOW ONE BECOMES MANY
CHAPTER 10. EXPLORING THE MIND-BODY PROBLEM
CHAPTER 11. IN SEARCH OF THE QUANTUM MIND
CHAPTER 12. PARADOXES AND COMPLEX HIERARCHIES
CHAPTER 13. “I” OF CONSCIOUSNESS
CHAPTER 14. UNIFICATION OF PSYCHOLOGIES
PART IV . RETURN OF CHARM
CHAPTER 15. WAR AND PEACE
CHAPTER 16. EXTERNAL AND INTERNAL CREATIVITY
CHAPTER 17. THE AWAKENING OF BUDDHA
CHAPTER 18. IDEALISMAL THEORY OF ETHICS
CHAPTER 19. SPIRITUAL JOY
GLOBAR OF TERMS