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The mind's 'projection' & the position observable:

  1. May 5, 2004 #1
    The Law of Projection:
    "No matter where a particular sensory pathway is stimulated along its course to the cortex, the conscious sensation produced is referred to the location of the receptor."
    ('Review of Medical Physiology', 6th Edition, W.F. Ganong, p. 63)

    OK, the term 'projection' might be out-of-use at this stage for all I know, but you get the point. That's the best description I could find for the phenomenon. To give a specific exmample of the phenomenon: a particular area of a subject's somatosensory cortex is stimulated, and the sensation is 'projected' to his left hand. To quote from (the same page of) the afore-mentioned book again: "the patient reports sensation in his left hand, not in his head."

    Here's my proposition:
    'Projection' occurs when the wavefunction for the position observable of the quantum entity being observed collapses.

    Do you find this notion plausible? Isn't it a fundamental postulate of quantum mechanics that: once an eigenvalue for a particular observable has been obtained, the wavefunction collapses to the eigenstate which corresponds to that eigenvalue during the measurement.

    I am unaware of any other explanation for the phenomenon of projection, and it just occurred to me that this might be a canditate. I suspect the proposition isn't new at all, and that it has been investigated before. Can anyone refer me to such research & literature? I have searched, albeit not very hard, I confess. Or, can anyone, on the other hand, refer to alternative explanations for the phenomenon.

    Thanks!

    P.S. Please respond in a manner as simple as possible. I am completely new to quantum mechanics (currently struggling with merely the 4th Chapter of Sam Treiman's 'The Odd Quantum', which I read when I have the time)
     
  2. jcsd
  3. May 5, 2004 #2
    SamLuc:
    I don't think it would be helpful to draw a parallel between the meaning of projection from neurology to that in quantum mechanics. More useful would be to look at it's meaning in geometry. If you have two vectors (arrows) with a common origin and different direction, then the projecttion of one on the other is the "shadow" of the first on the second with the "light" illuminating perpendicularly to the second. Or, in other term, you draw a perpendicular from the tip of the first, perpendicular to the second and the projecttion is the line segment from the origin to the intersection of the perpendicular with the second line.
    Now, think about the following:
    (I'll be sloppy, avoid subtleties and just try to give you an intuitive "picture" of the mathematical concepts. I use the term "mixture" loosely and avoid talking about complex numbers, and use the term Hilbert space for discreete spaces)
    1) A quantum state can be considered to be a superposition (sum or mixture) of certain other base states (could be different wave functions)
    2) If these base states fill certain conditions (orthogonality) they can be represented by a vector space where each dimension (perpendicular axis) in this space represents each of the base states. This space is called a Hilbert space.
    3) A quantum state can be represented by a vector in Hilbert space.
    4) Like a vector in three dimensional physical space, the state vector equals the sum of it's projections on each of the axis of Hilbert space. These projections tell you how much of each base state is in the mixture (superposition).
    5) The length of the vectors are related to the probability of finding that state when you measure.
    6) You can design an experiment so that when you measure, you get one of the base vectors (you don't know which beforehand). The probability of getting that base will be related to the length of the projection of the state vector in that direction. Every time you repeat the experiment with the compound state prepared identically, you may get a different result (base vector) but you'll get more often those with a longer projection.
    7) In the previous point, once you measure, you changed the state, so to analyze the state, you have to prepare many copies of the same state, measure them and discard them. This way you get the probabilities of getting the different possible results (base states)
    So you can see that to a certain point you could say that the projection is related to the measurement process. But there is a problem. Once you measure, you get that state (the result of your measurement) and now the probabilities change. You know now that you got that result, so the probability becomes 100%. The projection gives you the base state, and the probability before measuring, but not the probability after (100%)
    In order to understand all this, I guess youll have to read it many times and from different books/sources. Don't expect to understand it the first time. I have studied quantum mechanics for one year and still there are a lot of things you could consider basic that I don't understand.
    I could have explained this better if I had given you a concrete example, but I was feeling my post was getting a little long. A good simple example is the 1/2h spin of an atom or electron where you have a two-dimensional space (spin up and spin down represented by perpendicular axes)
    Good luck,
    --Alex--
     
  4. May 6, 2004 #3
    Thanks for the taking the time to explain Alex; much obliged. You're right: I will have to read this (and other explanations) a number of times before I grasp it. As for my proposition above, well, I mentioned it partly in the hope that it has been suggested by others (who are far more qualified in these areas than myself) before.
    Anyway, in the meantime, I'll be trying to educate myself.
     
    Last edited: May 6, 2004
  5. May 6, 2004 #4
    I am glad to help. I would like to hear from you again once you get a better grasp of the projection operation, and tell me how you see it. I am myself trying to understand better the meaning of operators in quantum mechanics. (I have that question posted on this forum).
    Good Luck,
    Alex
     
  6. May 7, 2004 #5
    No probs...but just to let you know, it could be a while before that happens
     
  7. May 7, 2004 #6
    I think (not sure) Von Newman was the guy who came up with the concept of projection in relation to a measurement. The problem is that all Von Newman has written is very mathematical. He used to talk about two different processes: process 1 and process 2. If I recall correctly, process 2, represented the unitary time evolution of the state vector as given by the Schrodinger equation. Process 1 represented the sudden jump that occurs during measurement. I think he explained process 1 in terms of a projection.
    (The projection postulate?) <<Look it up in Google
    So your idea is I think partially correct, but it has been in the literature since Von Newman's time.
    As you probably know, the "meassurement problem" has been (and still is) a controversial issue in quantum mechanics and it is connected with many paradoxes.
    --Alex--
     
    Last edited: May 7, 2004
  8. May 7, 2004 #7
    Yeah, I'd searched for info on Von Neumann's views on the observer-quantum system relationship before, but, as you said, descriptions of most of his work is bound to be very mathematical. I'll try again though.

    I was, in one way, shooting myself in the foot by using cortical stimulation as an example in my first post, so let me elaborate on my above proposition, this time using external stimulation of sensory receptors as an example:

    (i) The observables of the quantum entities in our environment exist in a superposition of states before causing an action potential in our sensory receptors (a large assumption?)
    (ii) registration in the cortex of information collected at the sensory receptors constitutes a 'measurement' of the observable (again, an assumption - as you said Alex, the 'measurement' problem is a controversial issue)
    (iii) the observable collapses into the eigenstate corresponding to the eigenvalue obtained in the 'measurement'
    (iv) in the case of the position observable, the eigenvalue obtained will, in most cases (phantom limb sensations a possible exception? - forgive the wild nature of my propositions) correspond to the position of the sensory receptor which has been stimulated
    (v) the quantum entity will therefore, at the moment the measurement is carried out, be at the sensory receptor
    (in the case of the tactile and chemical senses anyway).

    I used the position observable as an example because its common to all the senses (even hearing), to a greater or lesser extent.
    Consider these propositions to be merely 'thinking aloud' on my part, and, accordingly, go easy with your criticisms (if you bother to offer them).

    P.S. Alex, your above explanation is beginning to become clearer in my mind.
     
    Last edited: May 8, 2004
  9. May 10, 2004 #8
    There has been a lot of argument as to the exact point at which the wavefunction collapses, with some people postulating that consciousness is what collapses the wave function. Penrose has also speculated about quantum processes in microtubules of the neurones.
    I think present thought is that collapse happens way before you perceive the outcome of the experiment. It is considered that due to the phenomenom of environment-induced decoherence, as soon as information is leaked to the macroscopic medium around the system in a state of superposition, the wavefunction collapses. After that point, you cannot see interference anymore.
    In the many-worlds interpretation, it could be argued that even after decoherence there is no more interference, you could still have the different outcomes of the experiment coexisting but in different branches of the universe.
    When they talk about an observer in quantum mechanics, it doesn't need to be a human observer. It can be just a measurement apparatus that due to its macroscopic size is considered as a classical divice.
    If I were you, I would look into "Interpretations of quantum mechanics" and specially the "many worlds interpretation" which in my view is more satisfactory than the Copenhagen interpretation. You should also look into Scrodinger's cat and the EPR experiment with entangled spins. I don't think the paradoxes of quantum mechanics can be explained from a neural-sensory point of view, although perhaps in the future what we learn from quantum mechanics could have some application in understanding consciousness.
    --Alex--
     
  10. Jun 5, 2004 #9
    For the record, 'projection' in neural-sensory terms is in no way a mysterious phenomenon. An event in the brain is experienced in, say, the left hand because that is where the event is attributed in the brain's sensory map of the body. All sensation events, whether they have origins in the body or not, occur in the brain. There is no need for each point on the body to have separate processing of sense information, or for sense signals to return to their origin after reaching the brain.
     
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