What is the wavefunction of the observer himself?
Solution 1
I have just found this interesting paper by Thomas Breuer from 1995:
https://homepages.fhv.at/tb/cms/?download=tbPHILSC.pdf
The paper seems to prove that for a system that includes observer himself there are quantum states which are indistinguishable by the observer however technical means he employs, while he can measure any such states in the brains of other people.
The paper claims this proves that not only quantum mecanics is not universal theory that is applicable to all objects in the universe, but that no such universal theory can exist.
It also follows that in the world that the observer himself observes there is hidden information in his brain which cannot be extracted and read by any means even with help of other people (while the same information can be easily extracted from the brains of other people).
I do not know however how to interpret it regarding the wavefunction. Does it mean the observer's wavefunction indeterminate, singular or inexistent?
UPDATE.
And this this paper says it all. There will be subjective decoherence once the observer wants to measure himself. So he will see himself in a mixed state while others in the same situation will be observed as if they were in coherent state.
Note that this position is often taken for quantum mechanics. According to many interpretations, as for example the one of Bohr, or the one of London and Bauer (1939) and Wigner (1961, 1963), or even perhaps19 the one of von Neumann (1932), the “true” observer (or his mind) cannot be described by quantum mechanics. These authors say that if quantum mechanics is universally valid at all, then it is so only in the relative sense that every observer can perhaps apply it to any selected part of the world, except himself. It supposedly applies to Schroedinger’s cat, Wigner’s friend and Wigner himself under the condition that they lose their status of observer and are observed by something or somebody else.
Solution 2
You might want to look at Tegmark's recent paper at http://arxiv.org/abs/1108.3080 . In it, he proposes a variant interpretation of quantum mechanics based upon a tripartite division of the universe into a system, observer and environment. As in decoherence, a partial trace is taken over the environment, but a relative state is taken over the observer. The observer part is tied in with the anthropic principle cosmologically, and conditioning upon observers, i.e. taking the relative state lowers the entropy of the system.
Another point about observers has been brought up by Zurek. He noticed the fundamental difference between an observer and an apparatus is that an observer as an apparatus with access to its memory states, and memories are records which survive over time. Observers can introspect.
Solution 3
A measurement is a type of entanglement. If you measure a photon at the opening of a slit in a double slit experiment then you can think of there being a spin state at this opening. If the photon passes through it the spin changes direction. So the wave function for the photon in the double slit experiment is $$ \psi(x)\rangle~=~C(e^{ikx}1\rangle~+~e^{ik(x’)}2\rangle) $$ where the x and x’ denote the different paths through the two slits. If you compute the modulus squared you get $$ \langle\psi\psi\rangle~=~C^2(2~+~e^{ik(x’x)}\langle 12\rangle~+~ e^{ik(x'x)}\langle 21\rangle) $$ The exponential terms give the interference between the superposed states $1\rangle$ $2\rangle$ which have a nonzero overlap $\langle 12\rangle~\ne~0$. We now consider the coupling of a spin to this $$ \psi(x)\rangle~\rightarrow~C(e^{ikx}1\rangle+\rangle~+~e^{ik(x’)}2\rangle\rangle) $$ which serves as the detector. Since $\langle +\rangle~=~0$ if you compute $\langle\psi\psi\rangle$ the interference term is gone. This gives a reason for why one can’t measure which slit the particle travels through. We have replaced a superposition of states type of nonlocality with an entanglement. Now in doing this we have not addressed the question of how one actually observes the spin. One might presume we entangle some other states and do so up some “chain.” This of course leads to the Schrodinger cat problem. A cat or a human being, our brains and the like are not described well as single quantum systems. In fact they are messy thermal systems with high entropy. This is one problem with the whole idea of quantum consciousness, which never got out of the starting gates as a serious physical problem.
Solution 4
Hugh Everett is often misunderstood. His interpretation of quantum mechanics is taken by most physicists today to mean a many worlds interpretation with splittings. His interpretation was actually something else, the relative state interpretation. Most physicists narrowed in on the the part of his thesis where he gave a reduced density matrix analysis, but his real interpretation lies in the concept of a relative state. Decompose the universe into the observer and everything else. The internal states of the observer are entangled with the rest of the universe. Relative to a choice of a classical internal state of the observer, the term in the entanglement expansion given by the tensor product of this internal state with the wave function of the rest of the universe is the relative state.
Let me give you a consistent histories overview for more precision. An Information Gathering and Utilization System, or IGUS in short, is some cybernetic system taking in information from the outside world through its senses, processing them internally, storing some information as memories, and as a result of all the processing, it decides how to act in or manipulate the external world. An IGUS may be an animal, human, robot, computer or whatnot. In a succession of moments in time, the IGUS makes consecutive measurements of its environment and also its internal states through its senses and introspection. This can be modeled as coarse grained measurements in consistent histories. The end result stored in the memory banks of the IGUS is not a simple transcript of all of these measurements but the result of a classical computational processing of these measurements. It is undoubtedly classical because scientists have successfully simulated the brains of worms, or cortical columns of a rat using classical simulations and nothing else. Consistent histories can be adapted so that the choice of successive measurements by the senses is dependent upon the outcomes of earlier measurements, and a further coarse graining of these measurements by combining collections of histories into a further coarse grained history reflecting the actual memory contents of the IGUS after elaborate processing. The wave function of the universe is an entanglement between the memory contents of the IGUS and the rest of the universe. The memories are encoded in synaptic connections, magnetic disks, solid state drives, or what not, with all the attendant coarse grained fuzziness.
Now choose a classical configuration for the memories. The relative state of the universe with respect to this classical configuration is what we want. A particular history. It contains limited information about the universe out there and most of the world out there remains in a macroscopic superposition.
You might ask, why classical memories? Can quantum IGUSes exist? Suppose for the sake of argument that there are quantum memory registers. Because of no cloning, either the register is representing classical information of the external world in some basis, it does not represent anything out there, or it is the incorporation of some quantum information which once existed out there but now only exists inside the register. In the latter case, such quantum information can only be useful with respect to the goal of successful action if it is entangled with something out there. The information must have its coherence preserved right until the decision to determine which action. Because most actions decohere, this has to be an essentially classical command and we can fix the classical information stored in the memories right before it was used to determine the action in the appropriate basis. Unless the action is some communication over a quantum channel. In that case, it's pretty safe to say the IGUS was never conscious of the quantum information passing through it because of no cloning. Unconscious processing.
In string theory, the universe is in a superposition of multiverses, and the relative state picks out multiverses hospitable to IGUSes. The classical memories manifest the right anthropic laws and the right environment in the past.
This is an epistemic interpretation, more or less, with radical epistemological uncertainty. The central concept is the internal consistency and coherence of the story the contents of the memory tell. What sort of branches in the world out there correspond to the relative state of the classical memories? For very high internal story consistency, a good contribution comes from an external world which more or less match the contents of the story at a coarse grained level. But the contributions coming from being in a realistic computer simulation are also high... For slightly less internal consistency, it could be from something which more or less matches but with inaccurate recall/perception and distortions along the way, or maybe the IGUS had been systematically deceived. For even less consistency, it could be fiction or a not so naturalistic computer simulation or a brain in a vat. For very low consistencies like near randomness, the most likely contribution to the relative state comes from Boltzmann type statistical fluctuations conspiring together. There is no objective reality in quantum mechanics. This is what the math tells us.
How is the IGUS selected if there are many IGUSes? Pool the memory contents of many IGUSes together to form a supraIGUS. The individual IGUSes are like drops of water and the supraIGUS the ocean, and the drops of water merge into the collective consciousness of the ocean.
Let me tell you the meaning of consistent histories. Consistent histories are about what an observer external to our universe in some higher plane can measure and record externally in some Akashic records about our universe without being detected from the inside. The selection of framework is now transparently what the external observer chooses to measure. Why should the external observer select quasiclassical histories? Because that tells him a coherent meaningful story. Why should the external observer select the memories of IGUSes? Because that gives him a predigested condensed high information coarse grained meaningful description of the universe.
Solution 5
Think in terms of the anthropic principle. In the universal wave function of the universe, the probability for the existence of observers is exponentially small. The probability is definitely smaller than the finetuning in the cosmological constant, $10^{123}$, most likely much much smaller than that. Anthropic selection effects.
Ask yourself, what is the Shannon entropy of consciousness? What is your naive estimate of the Shannon entropy of human consciousness as encoded within neuronal firing and encoding patterns within the brain? The capacity of working memory is $7 \pm 2$, and the logarithm of the number of possible neural network symbols parseable by working memory is relatively small. Is the product of this with $7\pm 2$ still less than the log of $10^{123}$? If so, statistically speaking, will Boltzmann brain fluctuations predominate over evolved life?
Something isn't quite right here. Should we add short term memory into the contents of consciousness, and not just working memory? Maybe consciousness isn't what we think it is?
Why digital encoding in terms of discrete symbols for working memory? Why not analog encoding? Surely the particular form of the encoding of the symbols within the neural network ought to be irrelevant to consciousness? Or not?
What physical process searches through the haystack of the universal wave function looking for needles looking like the "conscious states" of observers encoded in a messy form of neural networks anyway so that it can attach "consciousness" to those states?
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Anixx
Updated on January 16, 2022Comments

Anixx over 1 year
I am aware about different interpretations of quantum mechanics out there but would mostly like to see an answer from the perspective of Copenhagen interpretation (or relative quantum mechanics if you wish).
Let an observer being a man with brain consisting of molecules and atoms. According the basic principles of quantum mechanics each of these particles has a wave function.
The question is: is there a combined wave function of all those particles which constitute the observer? Can such wavefunction be (in theory) determined by the observer himself?
Since the observer cannot isolate himself from his own brain, this would mean that the wave function, at least the part which determines his thoughts is permanently collapsed (i.e. the measurement happens instantly once the state changes). Does this "permanently collapsed" wave function imply special physical properties of the observer's own brain?
Does knowing his own thoughts constitute a measurement? Which moment should be counted as the moment of the collapse of wave function when making measurements on own brain?
Pretend an observer tries to measure the wave function of his own brain by a means of an Xray apparatus or other machinery and read his own thoughts. Would not his own knowledge of that measurement or its results invalidate the results thus making the whole measurement impossible?
Does the behavior of particles which constitute the observer's brain differ statistically (acoording his measurements) from the behavior of particles which constitute the brains of other people?
Is there a connection with quantum immortality here?

gigacyan over 12 yearsI guess that you have read "Quarantine" by Greg Egan, am I right?

Anixx over 12 yearsNo, and according to what is in the Wikipedia's article, the plot is a fantasy far from any understanding of quantum mechanics. The point is the brain can appear as having special physical/statistical properties only to its possessor, the brains of other people/animals would appear as conventional substances, having normal wavefunction.

gigacyan over 12 yearsyes, it is SciFi, and the plot is based exactly on your question, that is why I thought that you read it and wanted to know if described effect is possible or not.

yatima2975 about 12 yearsFor what it's worth, Egan winces at the scientific flaws of the novel and discusses in great detail where he departs from reality here: gregegan.customer.netspace.net.au/QUARANTINE/QM/QM.html

Ron Maimon over 11 yearsThe question has one major intrinsic flaw the electrons and nuclei do not each have a wavefunction, the wavefunction is a global construction for the combined position of all the electrons and nuclei. This is the source of entanglement and exponential growth in QM, and if it weren't so, the interpretation of QM wouldn't be thorny. The other flaw is the notion that the wavefunction of a single system can be uniquely determined two wavefunctions with 99% overlap will behave exactly identically 99% of the time, only 1% of the time will they be different.

Timothy over 4 yearsQuantum theory does not talk about consciousness at all and can't prove that a human with a normal brain is conscious. If you've never been in a narcotic state before and you feel like you will always be able to think clearly, that doesn't mean you really always will. You can also consistently drop the assumption of the laws of physics and instead assume your consciousness is going to go the way it seems. Under that assumption, your consciousness will never die. Indeed, one YouTube video said people couldn't prove the brain creates the consciousness. Under that assumption, you can prove that

Timothy over 4 yearsyour consciousness will never die and you will do different things than the laws of physics predict you will do but you can't prove or disprove under that assumption that what your consciousness will make you do in the near future turns out to be exactly the same as what the laws of physics will make you do. Your consciousness can't make the computations fast enough to predict what you will do a certain amount of time into the future before that time comes and make sure you do a different thing than you can be predicted to do.


Anixx over 12 yearsSo, what is in the outcome? You only say that "it is difficult" etc.

Anixx over 12 yearsYes. But when looking in the mirror one sees only the particles of skin, a tiny part of own wave function. My point was that there seems to be irreducible singularity somewhere inside the combined wave function of the observer. This is like looking at a rotating planet: one sees all the surface in motion, but the equations say that there is an axis along which all the points are static. This set of points may be different for different frames of reference and change with time, but does not disappear.

Anixx over 12 yearsSimilarly for any observer there is a "world axis"  the point which causes the wave function to collapse. Is is the top of the light cone of the observable events, the only point which can be measured at present: all other points in universe can me measured only in the past with a delay due to the speed of light. The closer to the present an observation of a point can be made, the closer it to the imaginable wave function singularity.

Vladimir Kalitvianski over 12 yearsThis axis is mathematical. It may well happen there is no physical particles in the axis. A pure wave function of a compound system is a product of a plane wave describing its center of mass motion and the wave function of relative (internal) motion. The latter may have so many close energy levels that it is practically impossible to keep this wave function intact  any small perturbation will lead to inelastic transitions. Elastic picture (wave function as a cloud) is quite different from inelastic one. Superconductors are described with wave functions though.

Anixx over 12 years"is practically impossible to keep this wave function intact"  yes, but my question is purely theoretical, does such wave function exist? Does it have singularity?

Anixx over 12 yearsThis is like a python who by making multiple practical experiments decided that he can eat anything. He even tried to eat the tip of his tail to find that he can eat it too. But does it mean that he can eat himself completely? Seems that there is some unedible point inside him, independent of how he is capable of eating other objects, he can eat his tail but cannot eat his head.

Vladimir Kalitvianski over 12 yearsNo, there is no special singularity in a wave function of a compound system.

Anixx over 12 years"a compound system" means any compound system outside the observer. My question was about the compound system which includes the observer himself.

Anixx over 12 yearsIt seems that you presume that physical properties of the observer as a system (or a quantum system that includes the observer) do not differ from physical properties of any other quantum system outside the observer, am I correct?

Vladimir Kalitvianski over 12 yearsYes, you are correct. Look, I am going to work and for some period I will be unavailable.

anna v over 12 yearsYes. Before all this entanglement language we used to speak of pure states and coherent versus incoherent ones. Coherent ones can be described with a mathematical wave functions consistent with quantum mechanics, a superposition of pure states where all the phases are known. Incoherent ones are described by a density matrix formalism. Super fluidity, lazing, super conductivity are macroscopic coherent phenomena that have a state function. Humans are an incoherent (phases lost) superposition of innumerable ( avogadro's number many) component state functions.

Lawrence B. Crowell over 12 yearsThe decoherence occurs with the loss of that overlap in the photon states at slit 1 and 2. The overlap is replaced with the entanglement. Now if you demolish the entanglement then you have decoherence. The demolition in the entanglement is similar to a coarse graining in statmech. As the superposition becomes entangled up with more and more degrees of freedom it is lost into the environment, So we just eliminate it and consider the diagonal elements of the density matrix. This is a nonunitary operation, whcih gets to the core of the whole measurement controversy in QM.

Vladimir Kalitvianski over 12 yearsDownvoters, don't be shy, tell me your truth.

Anixx over 12 yearsThank you for your answer. Is seems that you are the first answerer who understood the question. On the other hand, it would be interesting to know the answer from the pure Copenhagen point of view. I am sure that all interpretations of QM are complete and consistent so there should be a "copenhagen" answer. On the other hand, the decoherence/thermodynamic approach has its own disadvantages: by demoting the Observer they still have to explain why similar processes in a thermodynamically isolated space and in open space have different behavior.

Anixx over 12 yearsProbably they invent "external medium" or something alike (which is in fact another name for Observer) or postulate thermodynamic irreversibility. For the latter approach probably could be shown counterexamples with advance of quantum computers.

Anixx over 12 yearsOk. Just one наводящий вопрос. Imagine there is only a quantum computer in the universe and a black box, perfectly isolated from the external wold. You enter this box for a while. Do you expect all physical processes to continue as usual while you are inside, so after you exit the box you'll see no difference in the behavior of the quantum computer compared to its behavior when you are outside the box?

Vladimir Kalitvianski over 12 yearsAnnix, I do not know what a quantum computer is so I cannot answer your question.

Anixx almost 12 yearsPlease read this paper first: homepages.fhv.at/tb/cms/?download=tbDISS.pdf It is important before making judging

lurscher almost 12 yearscan you provide a summary of the reason why you can distinguish other people brain wavefunction, but not your own? what would happen if i apply the same hypothetical measurement apparatus i successfully use to measure others wavefunction to my own brain?

Anixx almost 12 yearsPlease read the papers, especially this one homepages.fhv.at/tb/cms/?download=tbDISS.pdf It says it all.

lurscher almost 12 yearsits a bit on the longish side, would appreciate your summary  i saved it on my folder of 'interesting papers to read'

Ron Maimon over 11 yearsScientists have not simulated the brain of anything, although there are oocasional claims, these are entirely fraudulent. they cannot even simulate the relevant computation in a single neuron, because we don't know exactly what it is, although it is still obviously classical. The "worm" is celegans, and it doesn't have a brain it only has a slightly bigger ganglion.

Anixx over 10 years@lurscher According to many interpretations, as for example the one of Bohr, or the one of London and Bauer and Wigner, or even perhaps the one of von Neumann, the “true” observer cannot be described by quantum mechanics. These authors say that if quantum mechanics is universally valid at all, then it is so only in the relative sense that every observer can perhaps apply it to any selected part of the world, except himself. It supposedly applies to Schrdinger’s cat, Wigner’s friend and Wigner himself under the condition that they lose their status of observer and are observed by somebody else.

Anixx over 10 years@lurscher this is a quote from the above paper.

lurscher over 10 yearswhat would be interesting is what would happen to an observer that can measure itself often enough to stop its natural spread (Quantum Zeno effect)

Anixx over 10 years@lurscher there is a newer paper (2011) by the same author: "A GoedelTuring Perspective on Quantum States Indistinguishable from Inside"

Anixx about 10 yearsBy the way, a quote. from Breuer. "Objective decoherence suggests a less radical solution to the problem of Wigner’s friend. It can explain why the magnitude of the interference terms decreases sharply as the size of the intermediate system increases. Therefore, objective decoherence explains why, after waiting suﬃciently long, the actual state s1 can only with great diﬃculty be distinguished from the state s2. But in the models usually considered the interference terms do not strictly vanish in ﬁnite time. (...)

Anixx about 10 years(...) Therefore objective decoherence cannot explain why the statistical state describing the observer’s impression in ﬁnite time actually is s2. The problem of Wigner’s friend being a matter of principle rather than a practical problem, the solution oﬀered by objective decoherence is not satisfying."

Timothy over 3 yearsI myself don't fully believe quantum theory itself. Maybe there's another theory that gives rise to the same observations. How do we know if we can't observe everything that's going on? However, I think something like the accepted quantum theory is more likely than the proposed one described in the article you linked. I think that according to the accepted quantum theory, a human being indeed is subject to quantum effects but a human being is also so large that they simulate classical physics really well and with the huge amount of information a brain can store combined with a brain being like

Timothy over 3 yearsa Conway's game of life, the brain ends up having actions corresponding to interpreting an observation and being aware of what it's observing.

Koantum over 1 yearIGUS, do you have any references for your obviously informed discussion?