IIID.  Summary.

1. What Follows from Quantum Mechanics. 

There is a great deal that follows strictly from the mathematics of noncollapse quantum mechanics, by itself:

Y1. The particlelike properties of mass, energy, momentum, spin and charge are properties of the wave function.  (IIIA2)

Y2. Even though many versions of reality are simultaneously present in quantum mechanics, it is, in effect, not possible for an observer to physically perceive more than one of them.  And observers cannot disagree on which version they perceive.  (IIIA3)

Y3. The photoelectric and Compton effects can be explained without the presumed existence of particulate photons or electrons.  (IIIA4)

Y4.  Localization and particlelike trajectories can be explained without the presumed existence of particles.  (IIIA5)

Y5.  The discrete nature of matter can be explained without the presumed existence of particles.  (IIIA6)

It is remarkable that a wave-based theory leads to all these particlelike properties.

Y6.  More generally, the wave function (state vector) always includes an exact description of what we perceive (among its many potential versions of reality). (IIIB3)

2. What Cannot Be Explained by Quantum Mechanics. 

N1. The mathematics cannot tell us why one particular version of the brain corresponds to our conscious perceptions while the others do not.  (IIIA3)

N2. There is no understanding of why the probability law holds.

3. Possible Explanations or Interpretations.

I1.  Objective Reality.  There is presumed to be an objective reality, perhaps made up of particles, underlying quantum mechanics.  The Bohm model (IIIB2) appears to be a correct interpretation of this sort, but, upon close examination it is found to be wanting.  Further, it is shown in section IIIB3 that (1) there is no experimental evidence for an objective reality, (2) the existence of an objective reality does not appear to solve the problem of perception of one particular branch after all, and (3) it is a near certainty that no theory of objective reality can be grafted onto the mathematics of quantum mechanics.

I2. Mathematical Collapse. (IIIB4).  The GRW-Pearle model of collapse appears to give an explanation of N1 and N2.  But it has so many questionable assumptions built into it that it is not currently acceptable; and it does not seem possible to satisfactorily amend it.

I3. Collapse by Conscious Perception. (IIIB5).  The primary objection here is that the equations of quantum mechanics must be turned off upon some signal from our conscious perceptions.  There is also no explanation of the probability law. These shortcomings do not seem acceptable.

I4. The Everett Many-Worlds Model. (IIC).  This model, which purports to derive the probability law from the other laws of quantum mechanics, makes an unacceptable assumption and is therefore not valid.  (But Everett reaches the same noncollapsed-wave-function-only conclusion that we do.)

I5. Decoherence.  (IIB4).  It cannot achieve its goal of showing collapse within quantum mechanics.

I6. The Copenhagen Interpretation. (IIIB3).  Assumes only an objective macroscopic world.  Critical of the attempt to interpret on the atomic level.  This pessimism is not justified.

I7. Conscious Perception within Quantum Mechanics. (IIIB5).  It is not possible to account for conscious perception of one particular branch within quantum mechanics.

4. Conclusion.

Our criticisms of collapse and objective reality theories do not constitute an airtight proof that only the noncollapsed wave function exists.  But at this present point in time—with no experimental evidence for either collapse or an objective reality, and with no realistic prospects for constructing a viable theory of collapse or objective reality—the most reasonable conclusion by far (in my opinion) is that only the noncollapsed wave function physically exists.  Note that this conclusion can be experimentally tested by the method of section IIIE, subsections 7 and 8.

We consider an interpretation in which only the noncollapsed wave function physically exists in section IIIE.