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Wigner's Friend
Eugene Wigner made quantum physics even more subjective than had John von Neumann or even Erwin Schrödinger with his famous Cat Paradox. Wigner claimed that a quantum measurement requires a conscious observer, without which nothing ever happens in the universe.

In 1961 he complicated the problem of the von Neumann or Heisenberg"Schnitt" (or the "shifty split" of John Bell) that forms the dividing line between the quantum world and the classical measurement apparatus. Wigner moved it farther into the conscious mind of the observer.

Wigner is often said to have extended the problem of Schrödinger's Cat, by adding a second observer inside the laboratory who is commonly known as Wigner's Friend. Popular treatments of Wigner's Friend usually describe it in terms of a live and dead cat. Actually, Wigner's example was a photon and whether its wave function collapsed to cause a flash on a screen or not. Wigner's goal was to show that only consciousness can collapse a wave function.

The cat example is more vivid. You can see it on Wigner's page. Here we give Wigner's original photon example

The physicist friend inside the lab either sees a photon flash or not. (In a footnote Wigner notes that the human eye can perceive as few as three quanta.) But Wigner is outside the lab and does not know the outcome. Wigner says that without human consciousness, this leaves the world in a superposition of states."

Wigner says that any inanimate material measuring device will leave both himself and his friend in a superposition of states. The only thing he sees that could change this is human consciousness, He resolves the paradox by saying that his friend's consciousness collapses the wave function inside the laboratory.

Here is Wigner's complete argument:

Given any object, all the possible knowledge concerning that object can be given as its wave function. This is a mathematical concept the exact nature of which need not concern us here—it is composed of a (countable) infinity of numbers. If one knows these numbers, one can foresee the behavior of the object as far as it can be foreseen. More precisely, the wave function permits one to foretell with what probabilities the object will make one or another impression on us if we let it interact with us either directly, or indirectly. The object may be a radiation field, and its wave function will tell us with what probability we shall see a flash if we put our eyes at certain points, with what probability it will leave a dark spot on a photographic plate if this is placed at certain positions. In many cases the probability for one definite sensation will be so high that it amounts to a certainty—this is always so if classical mechanics provides a close enough approximation to the quantum laws. The information given by the wave function is communicable. If someone else somehow determines the wave function of a system, he can tell me about it and, according to the theory, the probabilities for the possible different impressions (or "sensations") will be equally large, no matter whether he or I interact with the system in a given fashion. In this sense, the wave function "exists."

It has been mentioned before that even the complete knowledge of the wave function does not permit one always to foresee with certainty the sensations one may receive by interacting with a system. In some cases, one event (seeing a flash) is just as likely as another (not seeing a flash). However, in most cases the impression (e.g., the knowledge of having or not having seen a flash) obtained in this way permits one to foresee later impressions with an increased certainty. Thus, one may be sure that, if one does not see a flash if one looks in one direction, one surely does see a flash if one subsequently looks in another direction. The property of observations to increase our ability for foreseeing the future follows from the fact that all knowledge of wave functions is based, in the last analysis, on the "impressions" we receive. In fact, the wave function is only a suitable language for describing the body of knowledge—gained by observations—which is relevant for predicting the future behaviour of the system. For this reason, the interactions which may create one or another sensation in us are also called observations, or measurements. One realises that all the information which the laws of physics provide consists of probability connections between subsequent impressions that a system makes on one if one interacts with it repeatedly, i.e., if one makes repeated measurements on it. The wave function is a convenient summary of that part of the past impressions which remains relevant for the probabilities of receiving the different possible impressions when interacting with the system at later times.

An Example

It may be worthwhile to illustrate the point of the preceding section on a schematic example. Suppose that all our interactions with the system consist in looking at a certain point in a certain direction at times t0, t0 + 1, t0 + 2, ... , and our possible sensations are seeing or not seeing a flash. The relevant law of nature could then be of the form: "If you see a flash at time t, you will see a flash at time t + 1 with a probability 1/4, no flash with a probability 3/4; if you see no flash, then the next observation will give a flash with the probability 3/4, no flash with a probability 1/4; there are no further probability connections." Clearly, this law can be verified or refuted with arbitrary accuracy by a sufficiently long series of observations. The wave function in such a case depends only on the last observation and may be Ψ1 if a flash has been seen at the last interaction, Ψ2 if no flash was noted. In the former case, that is for Ψ1, a calculation of the probabilities of flash and no flash after unit time interval gives the values 1/4 and 3/4; for Ψ2 these probabilities must turn out to be 3/4 and1/4. This agreement of the predictions of the law in quotation marks with the law obtained through the use of the wave function is not surprising. One can either say that the wave function was invented to yield the proper probabilities, or that the law given in quotation marks has been obtained by having carried out a calculation with the wave functions, the use of which we have learned from Schrödinger.

The communicability of the information means, in the present example, that if someone else looks at time t, and tells us whether he saw a flash, we can look at timet + 1 and observe a flash with the same probabilities as if we had seen or not seen the flash at time t ourselves. In other words, he can tell us what the wave function is: Ψ1 if he did, Ψ2 if he did not see a flash.

The preceding example is a very simple one. In general, there are many types of interactions into which one can enter with the system, leading to different types of observations or measurements. Also, the probabilities of the various possible impressions gained at the next interaction may depend not only on the last, but on the results of many prior observations. The important point is that the impression which one gains at an interaction may, and in general does, modify the probabilities with which one gains the various possible impressions at later interactions. In other words, the impression which one gains at an interaction, called also the result of an observation, modifies the wave function of the system. The modified wave function is, furthermore, in general unpredictable before the impression gained at the interaction has entered our consciousness: it is the entering of an impression into our consciousness which alters the wave function because it modifies our appraisal of the probabilities for different impressions which we expect to receive in the future. It is at this point that the consciousness enters the theory unavoidably and unalterably. If one speaks in terms of the wave function, its changes are coupled with the entering of impressions into our consciousness. If one formulates the laws of quantum mechanics in terms of probabilities of impressions, these are ipso facto the primary concepts with which one deals.

It is natural to inquire about the situation if one does not make the observation oneself but lets someone else carry it out. What is the wave function if my friend looked at the place where the flash might show at time t? The answer is that the information available about the object cannot be described by a wave function. One could attribute a wave function to the joint system: friend plus object, and this joint system would have a wave function also after the interaction, that is, after my friend has looked. I can then enter into interaction with this joint system by asking my friend whether he saw a flash. If his answer gives me the impression that he did, the joint wave function of friend + object will change into one in which they even have separate wave functions (the total wave function is a product) and the wave function of the object is Ψ1. If he says no, the wave function of the object is Ψ2, i.e., the object behaves from then on as if I had observed it and had seen no flash. However, even in this case, in which the observation was carried out by someone else, the typical change in the wave function occurred only when some information (the yes or no of my friend) entered my consciousness. It follows that the quantum description of objects is influenced by impressions entering my consciousness. Solipsism may be logically consistent with present quantum mechanics, monism in the sense of materialism is not. The case against solipsism was given at the end of the first section.

The Reasons for Materialism

The principal argument against materialism is not that illustrated in the last two sections: that it is incompatible with quantum theory. The principal argument is that thought processes and consciousness are the primary concepts, that our knowledge of the external world is the content of our consciousness and that the consciousness, therefore, cannot be denied. On the contrary, logically, the external world could be denied—though it is not very practical to do so. In the words of Niels Bohr,

"The word consciousness, applied to ourselves as well as to others, is indispensable when dealing with the human situation."
In view of all this, one may well wonder how materialism, the doctrine that "life could be explained by sophisticated combinations of physical and chemical laws," could so long be accepted by the majority of scientists. The reason is probably that it is an emotional necessity to exalt the problem to which one wants to devote a lifetime. If one admitted anything like the statement that the laws we study in physics and chemistry are limiting laws, similar to the laws of mechanics which exclude the consideration of electric phenomena, or the laws of macroscopic physics which exclude the consideration of "atoms," we could not devote ourselves to our study as wholeheartedly as we have to in order to recognise any new regularity in nature. The regularity which we are trying to track down must appear as the all-important regularity—if we are to pursue it with sufficient devotion to be successful. Atoms were also considered to be an unnecessary figment before macroscopic physics was essentially complete—and one can well imagine a master, even a great master, of mechanics to say: "Light may exist but I do not need it in order to explain the phenomena in which I am interested." The present biologist uses the same words about mind and consciousness; he uses them as an expression of his disbelief in these concepts. Philosophers do not need these illusions and show much more clarity on the subject. The same is true of most truly great natural scientists, at least in their years of maturity. It is now true of almost all physicists—possibly, but not surely, because of the lesson we learned from quantum mechanics. It is also possible that we learned that the principal problem is no longer the fight with the adversities of nature but the difficulty of understanding ourselves if we want to survive.

Simplest Answer to the Mind-Body Question

Let us first specify the question which is outside the province of physics and chemistry but is an obviously meaningful (because operationally defined) question: Given the most complete description of my body (admitting that the concepts used in this description change as physics develops), what are my sensations? Or, perhaps, with what probability will I have one of the several possible sensations? This is clearly a valid and important question which refers to a concept—sensations—which does not exist in present-day physics or chemistry. Whether the question will eventually become a problem of physics or psychology, or another science, will depend on the development of these disciplines.

Naturally, I have direct knowledge only of my own sensations and there is no strict logical reason to believe that others have similar experiences. However, everybody believes that the phenomenon of sensations is widely shared by organisms which we consider to be living. It is very likely that, if certain physico-chemical conditions are satisfied, a consciousness, that is, the property of having sensations, arises. This statement will be referred to as our first thesis. The sensations will be simple and undifferentiated if the physico-chemical substrate is simple; it will have the miraculous variety and colour which the poets try to describe if the substrate is as complex and well organized as a human body.

The physico-chemical conditions and properties of the substrate not only create the consciousness, they also influence its sensations most profoundly. Does, conversely, the consciousness influence the physicochemical conditions? In other words, does the human body deviate from the laws of physics, as gleaned from the study of inanimate nature? The traditional answer to this question is, "No": the body influences the mind but the mind does not influence the body. Yet at least two reasons can be given to support the opposite thesis, which will be referred to as the second thesis.

The first and, to this writer, less cogent reason is founded on the quantum theory of measurements, described earlier in sections 2 and 3. In order to present this argument, it is necessary to follow my description of the observation of a "friend" in somewhat more detail than was done in the example discussed before. Let us assume again that the object has only two states, Ψ1 and Ψ2. If the state is, originally, Ψ1, the state of object plus observer will be, after the interaction, Ψ1 x Χ1; if the state of the object is Ψ2, the state of object plus observer will be Ψ2 x Χ2 after the interaction. The wave functions Χ1 and Χ2 glve the state of the observer; in the first case he is in a state which responds to the question "Have you seen a flash?" with "Yes"; in the second state, with "No." There is nothing absurd in this so far.

Let us consider now an initial state of the object which is a linear combination
α Ψ1 + β Ψ2 of the two states Ψ1 and Ψ2. It then follows from the linear nature of the quantum mechanical equations of motion that the state of object plus observer is, after the interaction, α (Ψ1 x Χ1 ) + β (Ψ2 x Χ2). If I now ask the observer whether he saw a flash, he will with a probability |α|2 say that he did, and in this case the object will also give to me the responses as if it were in the state Ψ1. If the observer answers "No"—the probability for this is |β|2 —the object's responses from then on will correspond to a wave function Ψ2. The probability is zero that the observer will say "Yes," but the object gives the response which Ψ2 would give because the wave function α Ψ1 + β Ψ2 of the joint system has no
(Ψ2 x Χ1) component. Similarly, if the observer denies having seen a flash, the behavior of the object cannot correspond to Χ1 because the joint wave function has no (Ψ1 x Χ2) component. All this is quite satisfactory: the theory of measurement, direct or indirect, is logically consistent so long as I maintain my privileged position as ultimate observer.

However, if after having completed the whole experiment I ask my friend, "What did you feel about the flash before I asked you?" he will answer, "I told you already, I did [did not] see a flash," as the case may be. In other words, the question whether he did or did not see the flash was already decided in his mind, before I asked him. If we accept this, we are driven to the conclusion that the proper wave function immediately after the interaction of friend and object was already either Ψ1 x Χ1 or Ψ1 x Χ2 and not the linear combination α (Ψ1 x Χ1 ) + β (Ψ2 x Χ2). This is a contradiction, because the state described by the wave function α (Ψ1 x Χ1 ) + β (Ψ2 x Χ2) describes a state that has properties which neither Ψ1 x Χ1 nor Ψ2 x Χ2 has. If we substitute for "friend" some simple physical apparatus, such as an atom which may or may not be excited by the light-flash, this difference has observable effects and there is no doubt that
α (Ψ1 x Χ1 ) + β (Ψ2 x Χ2) describes the properties of the joint system correctly, the assumption that the wave function is either Ψ1 x Χ1 or Ψ2 x Χ2 does not
. If the atom is replaced by a conscious being, the wave function
α (Ψ1 x Χ1 ) + β (Ψ2 x Χ2) (which also follows from the linearity of the equations) appears absurd because it implies that my friend was in a state of suspended animation before he answered my question.

It follows that the being with a consciousness must have a different role in quantum mechanics than the inanimate measuring device: the atom considered above. In particular, the quantum mechanical equations of motion cannot be linear if the preceding argument is accepted. This argument implies that "my friend" has the same types of impressions and sensations as I—in particular, that, after interacting with the object, he is not in that state of suspended animation which corresponds to the wave function α (Ψ1 x Χ1 ) + β (Ψ2 x Χ2). 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, whether my friend's consciousness contains either the impression of having seen a flash or of not having seen a flash. However, to deny the existence of the consciousness of a friend to this extent is surely an unnatural attitude, approaching solipsism, and few people, in their hearts, will go along with it.

The preceding argument for the difference in the roles of inanimate observation tools and observers with a consciousness—hence for a violation of physical laws where consciousness plays a role—is entirely cogent as long as one accepts the tenets of orthodox quantum mechanics in all their consequences.

The information interpretation of quantum mechanics helps to resolve this paradox as follows,

  • If the physicist friend inside the lab clearly looks for the flash and is seen to record the result in a notebook, we can safely conclude that the superposition of states has "collapsed" (been projected) into either the flash or no flash state.

  • New information has been created in the universe. Entropy has been radiated away, so the change is irreversible.

  • We can assume that an observation has been made, recorded as a measurement, and, to satisfy Wigner, von Neumann, Wheeler, Bell. and others, the measurement has entered the mind of the "conscious observer," though our information interpretation does not require this step.The wave-function collapse occurs with the creation of new information, without the need for observations or measurements.

  • Since Wigner does not know the actual outcome, he only knows the possibilities and can estimate ordinary probabilities, for example, that there is a 75% chance of a flash and 25% probability of no flash.

  • But here is the resolution of Wigner's paradox. These probabilities are no longer about superposed quantum states interfering with one another. They are no longer quantum probabilities. The flash either occurred and was recorded or not! The chances are no longer ontological. They are epistemic, just human ignorance.

  • So Wigner is wrong to conclude that without consciousness the quantum superposition would remain.

  • When we were doing calculations for probabilities of flash or no flash, we used the quantum superposition as our best estimates. And it was important to include the possible interference effects while the wave function is still coherent. But once we get information about the flash/no flash, the wave function decoheres and we must switch to "classical" probabilities.

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