1. Collapse by Conscious Perception.

In this interpretation, one branch is consciously perceived, presumably by an aspect of the observer that is outside of physical reality, that is, outside the laws of quantum mechanics (see below and section IIIE).  This is presumed to cause the collapse of the nonperceived branches.  For example, perceiving the Schrödinger’s-cat-alive branch of the wave function forces the collapse of the “dead” branch of the wave function.  There is presumably no mathematical mechanism associated with the collapse. 

As another simple example, consider the half-silvered mirror experiment of section IIE.  If we include the wave function of the neurons of the observer, the total wave function after a single run of the experiment is

[V,1][H,0][observer’s neurons correspond to [V,1][H,0]]

and

[V,0][H,1][observer’s neurons correspond to [V,0][H,1]]

There are two versions of the brain, and quantum mechanics cannot say which one will correspond to our actual, conscious perceptions.  Nevertheless, “conscious perception” of  one branch is presumed to collapse the other branch.

For a more complicated example, suppose the half-silvered mirror experiment is run 6 times.  When we take into account the different possible orderings of V’s and H’s, there are a total of 2⁶=64 different end states (or branches, or versions of reality).  Suppose there is a dial that records only the total number of V states and suppose that dial is consciously perceived as reading 3.  Then whatever it is that causes collapse must not collapse all 20 states that have 3 V’s, but it must collapse the 64 – 20=44 remaining states.

2. There Can Be No Conscious Perception within Quantum Mechanics. 

Note: This argument is done in a better way in section IIIC.

When we think of conscious perception of one branch, we think that the observer looks at the results and perceives one or the other of the possibilities.  The observer sees the cat alive or the observer sees the cat dead.  But it isn’t that simple.  If we look at the cat-observer system, the wave function after perception is

                                [cat alive][observer’s neurons “see” the cat alive]

(IIIB5-1)                                                        +                                                                      

                                [cat dead][observer’s neurons “see” the cat dead]

There are two versions of the observer’s brain.  If we are to have conscious perception, then one and only one version must be conscious.  However we can show that, if we stay within quantum mechanics, that cannot be. That is,

Theorem: If everything in existence obeys the linear, noncollapse laws of quantum mechanics, there can be no conscious perception of one and only one branch.

Proof: To show this, we suppose the contrary.  Then one of the versions of the observer in Eq. (IIC5-1), say the cat alive version, must correspond to conscious perception and the other must not.  This implies that there must be something about the wave function of one version of the brain—perhaps some peculiarity in the wave function of the prefrontal lobe—that confers consciousness, while the other version must be missing that consciousness designator.

At a time before the perception of the state of the cat, the wave function is

                             [cat alive][observer’s neurons not yet perceive the cat]   

(IIIB5-2)                                                        +                                                                                                  

                                       [cat dead][observer’s neurons not yet perceive the cat]

Now according to the rules of quantum mechanics, each branch will evolve entirely independently of the other (section IIIA3, subsection 5); there can be no coordination between the two time evolutions.  Thus whatever the time evolution (from state (2) to state (1)) is that confers consciousness, it will occur or it will not occur independently on the two branches.  This implies one cannot guarantee that precisely one branch has the peculiarity in the brain wave function which corresponds to conscious perception.  It could just as well be no branches, or two branches, both of which are forbidden.  We conclude that conscious perception of a single branch cannot occur within quantum mechanics.

3. Problems with Collapse by Conscious Perception. 

• As in the proposed mathematical collapse schemes, there is no evidence, experimental or otherwise, for collapse.
• The highly tested equations of quantum mechanics (the Schroedinger time-evolution equations) are made invalid at some instant.  This is a very high price to pay.
• There is no description of how the “consciousness principle” causes the collapse of the unobserved branches of the wave function.
• One must invoke a “consciousness principle” outside quantum mechanics for conscious perception (point 2 above).  One then requires that this “nonphysical” agent interfere with the physical.
• This interference by the nonphysical aspect with the laws of the physical universe seems like a throwback to Cartesian attempts to introduce free will into Newtonian physics.Why is collapse by conscious perception better than a mathematical model of collapse?
• If there is no mathematical model associated with collapse by conscious perception, why does the probability law hold?

The details of collapse by conscious perception are not clear.  At what stage in the perceptual process—visual area 17? 18? 19? comparison to memory?—does the perception become conscious?  Our minds have a great range of intensity of consciousness perception (and memory of what we perceived).  What is a sufficient intensity of consciousness to alter (collapse) the wave function?  What if the light level in the room is too low to accurately perceive the readings of the dials on the meters?  What if one is presented with a large amount of data (from a quantum experiment) that one lightly peruses?  Does that count as conscious perception and thereby lock the variables in to the values on the sheet?  What counts as a conscious perceiver?  Cat?  Ant?  Amoeba?  

• Since noncollapse quantum mechanics by itself implies perception of one and only one branch (IIB3), and since one must invoke a “consciousness principle” outside quantum mechanics for conscious perception (point 2 above), it seems that it is not necessary to have the “consciousness principle” collapse the wave function.  One can get away with the scheme of IIIE, in which the “consciousness principle” merely concentrates its awareness on just one branch (but does not collapse the wave function).

Conclusion.  Without a more specific model of conscious perception and collapse, I do not think collapse by conscious perception can be counted as a valid interpretation of quantum mechanics. 

Reference.

See Quantum Enigma (Oxford University Press, Oxford, 2006) by Bruce Rosenblum and Fred Kuttner for extensive use of the idea of conscious perception of only one branch.