Ok, going to get into math below but not tough math and it is necessary to show the paradox of having a human observer in quantum.
Let’s first, though, look at von Neumann’s seminal book on Quantum, in which he explicitly brings in the subjective observer into quantum.
" Let us now compare these circumstances with those which actually exist in nature, or in its observation. First, it is inherently correct that measurement or the related process of subjective perception is a new entity relative to the physical environment, and is not reducible to the latter. Indeed subjective perception leads us into the intellectual inner life of the individual, which is extra-observational by its very nature, since it must be taken for granted by any conceivable observation or experiment. (See the discussion above.) Nevertheless, it is a fundamental requirement of the scientific viewpoint–the so-called principle of psycho-physical parallelism–that it must be possible so to describe the extra-physical process of subjective perception as if it were in the reality of the physical world; i.e., to assign to its parts equivalent physical processes in the objective environment, in ordinary space. (Of course, in this correlating procedure there arises the frequent necessity of localizing some of these processes at points which lie within the portion of space occupied by our own bodies. But this does not alter the fact of their belonging to ‘the world about us,’ the objective environment referred to above.) In a simple example, these concepts might be applied as follows: We wish to measure the temperature. If we want, we can proceed numerically by looking to the mercury column in a thermometer, and then say: ‘This is the temperature as measured by the thermometer.’ But we can carry the process further, and from the properties of mercury (which can be explained in kinetic and molecular terms) we can calculate its heating, expansion, and the resultant length of the mercury column, and then say: ‘This length is seen by the observer.’ Going still further, and taking the light source into consideration, we could find out the reflection of the light quanta on the opaque mercury column and the path taken by the reflected light quanta into the eye of the observer, their refraction in the eye lens, and the formation of an image on the retina, and then we would say: ‘This image is registered by the retina of the observer.’ And were our physiological knowledge greater than it is today, we could go still further, tracing the chemical reactions which produce the impression of this image on the retina, and in the optic nerve and in the brain, and then in the end say; ‘These chemical changes of his brain cells are perceived by the observer.’ But in any case, no matter how far we proceed–from the thermometer scale, to the mercury, to the retina, or into the brain–at some point we must say: ‘And this is perceived by the observer.’ That is, we are obliged always to divide the world into two parts, the one being the observed system, the other the observer. In the former we can follow all physical processes (in principle at least) arbitrarily precisely. In the latter, this is meaningless. The boundary between the two is arbitrary to a very large extent. In particular, we saw in the four different possibilities considered in the preceding example that the ‘observer’–in this sense–need not be identified with the body of the actual observer: in one instance we included even the thermometer in it, while in another instance even the eyes and optic nerve were not included. That this boundary can be pushed arbitrarily far into the interior of the body of the actual observer is the content of the principle of psycho-physical parallelism. But this does not change the fact that in every account the boundary must be put somewhere if the principle is not to be rendered vacuous; i.e., if a comparison with experience is to be possible. Indeed, experience only makes statements of this type: ‘An observer has made a certain (subjective) observation,’ and never any like this: ‘A physical quantity has a certain value.’ " John Von Newumann, Mathematical Foundations of Quantum Mechanics: New Edition (Princeton: Princeton University Press, 2018), p. 272-273
To prove that it is widely believed that there are interpretations of quantum which incorporate consciousness, I would present how Zvi Schrieber’s veiw of von Neumann’s position. In his thesis, Schrieber entitles a chapter, Mind causes collapse and says
"It is therefore possible to assume that the unitary mechanics applies to the entire physical universe and that wave function collapse occurs at the last possible moment, in the mind itself. This, of course, assumes a non-physical mind.
“This interpretation was hinted at by Von Neumann [Neu55,§VI.1] and later advocated in [LB39, §11], [Wig67]. It was at one time known as the standard interpretation” Zvi Schreiber, The Nine Lives of Schrodinger’s Cat, master’s Thesis, University of London, Oct 1994 p. 46, https://arxiv.org/pdf/quant-ph/9501014.pdf
The rules of quantum mechanics are correct but there is only one system which may be treated with quantum mechanics, namely the entire material world. There exist external observers which cannot be treated within quantum mechanics, namely human (and perhaps animal) minds, which perform measurements on the brain causing wave function collapse." Zvi Schrieber, "The Nine Lives of Schrodinger’s Cat, University of London: MS Thesis, Oct 1994, p. 46 https://arxiv.org/pdf/quant-ph/9501014v5.pdf
It is interesting that Schrieber understands that there are formulations of quantum involving the immaterial soul, namely the late great John von Neumann’s who was a better mathematician/physicist than anyone on this list. Mind and consciousness are synonyms for the same thing.
Ok, let’s get mathematical Sorry everyone else, I think this is necessary but I will try to go slow and explain things. This is taken from Squires’ book Conscious Mind in the Physical Universe pages 184-191. It is simplified a bit to the relevant parts of the equations so that it is easier to follow by those with no experience with this notation.
Lets consider the spin of an electron. It is measured in a Stern-Gerlach device and one spin will be deflected upward, and the other spin deflected downward. We will call the upward spin + and the downward spin -. Since I can’t use greek letters here or don’t know how to, I will use English letters. Wavefunctions are described by | …> and attributes are put inside where the … is. A particle with an upward spin would be | + > and a particle with a negative spin would be | - >
Before we observe the spin the electron is in the state:
|Psi>=a| + > +b | - >
In words, Psi is the wave function and is it is a mixture of + and - states. a and b are coefficients that for our purposes we don’t need to worry about.
One must understand that in quantum, whenever something that is subject to the laws of quantum interacts with an object, it goes into superposition with that object. So, when we add a pointer to the apparatus, which would point up or down in the direction the electron went , prior to observation of the apparatus, the quantum state of the electron AND the pointer would be:
|Psi>=a| +, up > +b | -,down >
The added up and down refer to the direction of the pointer. Before observation, the pointer and the electron are both in mixed states of superposition. In other words, it is in both states at once. This is why one hears that in quantum all possible answers exist at the same time in the wavefunction.
This addition to the chain of objects in superposition can go on forever. Kuttner and Rosenblum describe this von Neumann chain as it is known, because John von Neumann was the first to describe it.
" In his rigourous 1932 treatment, The Mathematical Foundations of Quantum Mechannics, John von Neumann showed that quantum theory makes physics’ encounter with consciousness inevitable. He considered a measuring apparatus, a Geiger counter, for example. It is isolated from the rest of the world but makes contact with a quantum system, say, an atom simultaneously in two boxes. This Geiger counter is set to fire if the atom is in the top box and to remain unfired if the atom is in the bottom box. Von Neumann showed that if the Geiger counter is a physical system governed by quantum mechanics, it would enter a superposition state with the atom and be, simultaneously, in a fired and an un fired state. (We saw this situation in the case of Schrodinger’s cat.)"
"Should a second isolated measuring apparatus come into contact with the Geiger counter-for example, an electronic device recording whether the Geiger counter has fired-it joins the superposition state and records both situations existing simultaneously. This so-called "von Neumann chain" can continue indefinitely. Von Neumann showed that no physical system obeying the laws of physics (i.e., quantum theory) could collapse a superposition state wavefunction to yield a particular result."
"However, when we look at the Geiger counter, we will always see a particular result, not a superposition. Von Neumann concluded that only a conscious observer doing something that is not presently encompassed by physics can collapse a wavefunction. Though for all practical purposes one can consider the wavefunction collapsed at any macroscopic stage of the von Neumann chain, von Neumann concluded that only a conscious observer can actually make an observation." Bruce Rosenblum and Fred Kuttner, Quantum Enigma, (Oxford: Oxford University Press, 2006), p. 184
It is also interesting that Rosenblum and Kuttner interpret von Neumann the same as Schrieber does and apparently differently than does Mitch.
The von Neumann chain is due to the fact that anything subject to the laws of quantum goes into superposition with what it interacts with. This is a problem. Bryce S. Dewitt talked about quantum putting the apparatus into a schizophrenic state in which it has two different answers at the same time. He says:
How can they prod the apparatus into making up its mind? "
"The usual suggestion is to introduce a second apparatus to get at the facts simply by looking at the first apparatus to see what it has recorded. But an analysis carried out along the above lines quickly shows that the second apparatus performs no better than the first. It too goes into a state of schizophrenia. The same thing happens with a third apparatus, and a fourth, and so on. This chain, known as “von Neumann’s catastrophe of infinite regression,” only makes the crisis worse . Bryce Dewitt,Quantum Mechanics and Reality, PHYSICS TODAY /SEPTEMBER 1970, p. 30- 31
This von Neumann chain can continue indefinitely by adding commas and attributes to the chain in between the | and the >. But we won’t go there. We will add a conscious observer in at this point and show why he can’t be subject to quantum laws.
Back to the math, Let’s add me as an observer to the apparatus with the pointer. IF my mind is subject to quantum laws, then I too, must go into superposition with the system. This is just like the pointer in our example or the counter and Geiger counter of Rosenblum and Kuttner’s example. In that case, the wave function would be:
|Psi>=a| +, up, Me+ > + b | -,down, Me- >
Where Me+ is the me who sees a positive spin and the Me- is the one who sees a negative spin.
" At this stage and only at this stage the wavefunction is apparently unacceptable, because it fails to describe my experience of one result ." Euan Squires, Consciousness Mind in the Physical World, (Adam Hilger, New York, 1990, p. 191
Quantum mechanics does not correctly predict my subjective mental state, which is that I am experiencing only one of the two possible realities.
Squires presented this argument in a paper "Quantum Theory and the Relation between Conscious Mind and the Physical World," Synthese, Vol. 97, No. 1 (Oct., 1993), pp. 109-123. His conclusion there is a bit more interesting:
" It is quite clear that we have made no progress. Indeed the problem might be considered to be even more acute: my brain is in a confused state containing some combination of both answers; I am, nevertheless, apparently convinced that I know one answer. " Euan Squires, "Quantum Theory and the Relation between Conscious Mind and the Physical World," Synthese, Vol. 97, No. 1 (Oct., 1993), p.111-112
If you assume that consciousness mind or soul is subject to the laws of quantum, quantum WILL describe any observer in a confused state seeing both possible outcomes. This is the fundamental problem of consciousness in quantum. I only see unmixed states, like:
|Psi>= | +, up, Me+ >
or |Psi>= b | -,down,Me- >
The thing I don’t see is the mixed state
|Psi>=a| +, up, Me+ > + b | -,down,Me- >
Now, Everett proposed the many worlds interpretation in 1957 and he would say that I have split into two different Me’s one seeing the up branch and one seeing the down branch. Such a situation is the draw of the many worlds view. But, unread by Mitch in our article are other reasons for rejecting the many worlds view.
Point is, this is the problem with consciousness in quantum. If my mind/consciousness/soul is subject to the laws of quantum, it creates a situation where reality (me seeing only one reality) is said to be false by the application of quantum rules.
Again, I affirm that many physicists have discussed the role of consciousness in quantum and the belief that observers external to the physical world is NOT a looney bin idea, but a great problem in the logical structure of quantum. Again, (one of those quotes Pevaquark but a repeat, lol)
"A careful analysis of the logical structure of quantum theory suggests that for quantum theory to make sense it has to posit the existence of observers who lie, at least in part, outside of the description provided by physics." Stephen M. Barr, Modern Physics and Ancient Faith, (Notre Dame: University of Notre Dame Press, 2003), p. 27-28