IIIA3. Perceptions of Only One Version of Reality

 1. Introduction.

Perhaps the most striking characteristic of quantum mechanics is that the wave function gives many versions of reality.  In the Schrödinger’s cat experiment, for example, the cat is both dead and alive at the same time.  As we obviously know, however, we are aware of only one of these possibilities, and we all agree on what we see.  The question is: Is quantum mechanics alone—without the existence of actual electrons, protons, atoms and so on, and without the collapse of the wave function down to just one version of reality—capable of  explaining this apparently objective (that is, single-valued) existence?  Yes it is, if a reasonable “communicability” criterion is agreed upon.  This is most clearly shown using a specific example, which we choose as the Schrödinger’s cat experiment of section IIF.

2. Schrödinger’s Cat. 

As in section IIF, a cat and a vial of cyanide are put in a box.  The cyanide is electronically hooked up to the half-silvered mirror experiment.  If the detector on the vertical path registers the passage of the wave function, nothing happens.  But if the detector on the horizontal path registers the passage of the wave function, the vial of cyanide is broken and the cat dies.  So quantum mechanics presents us with two entirely different versions of reality, one with a live cat and one with a dead cat.  If, as in section IIF, we include an observer in the experiment, the wave function, schematically, is

[V,yes][H,no][cat alive][observer’s brain perceives cat alive]

and

[V,no][H,yes][cat dead][observer’s brain perceives cat dead]

where [observer’s brain perceives cat alive] means the neurons of the brain fire in a pattern corresponding to perceiving a live cat.  Thus at the end of the experiment and for all time after that, there is not, in quantum mechanics, a single, objective version of  the cat in a definite state (either alive or dead); instead there are, existing simultaneously, two versions of the cat.  And there are two simultaneously existing versions of the observer.

3. Branches of the Wave Function. 

Each of the potentially perceived versions of reality present in the wave function will be called a branch of the wave function (because the wave function branches into two or more parts).  Experientially, we know that we perceive only one of these branches—either an alive cat or a dead cat.  This holds true in general; one and only one branch of the wave function is perceived.  The question is whether this only-one perception is implied by quantum mechanics or whether one must postulate an underlying objective existence (an objectively existing cat) to explain it.  “Objective existence” in this context means an existence in which there is only one version of reality, in contrast to the many versions of reality in the wave function.  (In noncollapse quantum mechanics, we think of each branch of the wave function as “existing.”  It is just that we perceive only one branch.)

4. Definition of Branches. 

When do two parts of the wave function qualify as distinct branches?  For the purposes of this argument, they are branches if they are macroscopically distinguishable, that is, if they can be distinguished by the minimally aided human senses—live versus dead cats, different readings on measuring instruments, unexposed versus exposed film grains; a technically sophisticated definition is not needed here.  Note that each branch corresponds to a “classical” version of matter that is consistent with our everyday experience.

5. Each Branch Corresponds to a
Separate, Isolated Universe. 

An important property of branches is that they each constitute an isolated, independent universe.  (This has nothing to do with the “many universes” of cosmology.)  To show this, assume a macroscopic number of “particles” have macroscopically different locations—the pointer on a dial may point in different directions for the two branches, for example, so the atoms of the pointer are in different locations on the two branches—and consider the equation

(IIIA3-1)                                

where H is the wave-function-independent Hamiltonian (which we presume cannot change the macroscopic state of a detecting instrument, or the cat, or the brain once the experiment in question is finished).   Assume  are all different from zero and  are all zero when  is near .  Then for that region of ,the  terms drop out of equation (1).  Similarly when  is near .   This shows that the two wave functions satisfy separate time-evolution equations,

(IIIA3-2.1)  

(IIIA3-2.2)   ,

(with H, as we said, independent of the wave function).  Now imagine that a light ray could be sent from state 1 to state 2.  Then what happens in state 1—sending the light ray—influences what happens in state 2, which receives the light ray.  But this would contradict the condition of Eq. (IIIA3-2.2), which says that state 2 evolves independently of what happens in state 1.  More generally, no signal, no information, can be passed from one branch to the other. 

This implies that each branch is, in effect, a separate universe that will never have knowledge of or be affected by the events on any other branch. 

6. Communicability Criterion for Perception. 

We need a criterion for deciding whether or not quantum mechanics alone can account for our perception of only one classical (that is, dead or alive, not some mixture) branch.  In our ordinary experience, when we are aware of something, we can communicate that awareness.  So our criterion will be

Communicability Criterion: If quantum mechanics does not allow an observer to communicate that she is aware of anything other than one classical branch,  then quantum mechanics, by itself, accounts for our perception of only one classical branch.

I emphasize that this simple criterion agrees with our conscious experience; any perceptual fact that we are aware of can be communicated.  So if quantum mechanics prohibits an observer from communicating that she is aware of more than one branch, we take this as proof that quantum mechanics prohibits the awareness of more than one branch from entering her conscious physical perception.

7. Quantum Mechanics Alone Implies Perception of
Only One Version of Reality. 

Suppose now that an observer of the Schrödinger’s cat experiment writes down what she observes.  If she sees only a live cat, she writes alive on a piece of paper, if she sees only a dead cat, she writes dead,  and if she sees anything else—some mixture of a live cat and a dead cat, for example—she writes other.  The question is whether quantum mechanics allows her to write “other.”  To answer this, note that the mathematics of quantum mechanics implies that within each branch there will be agreement between the state of the cat, what the observer sees (equivalent here to what the neurons in the observer’s brain register), and what the observer writes; that is, each branch is consistent in the classical, everyday sense.  Thus the relevant two-branch wave function is

[live cat]

[the state of the observer’s neurons correspond to seeing a live cat]

[alive is written on the paper]

and

[dead cat]

[the state of the observer’s neurons correspond to seeing a dead cat]

[dead is written on the paper]

We see that quantum mechanics does not present an option in which the word other is written.  The observer must therefore either (because other was never written) write alive and thus perceive a live cat or write dead and thus perceive a dead cat; if her brain-body obeys the mathematics of quantum mechanics, she cannot write other.  Thus, under our communicability criterion, we see that the mathematics of quantum mechanics, by itself, with no underlying objective reality or collapse of the wave function, implies that the observer will be consciously aware of one and only one classically consistent branch of the wave function. 

We can arrive at this result in a different way.  The reason why she cannot be consciously, physically aware of both branches at the same time is that, since the two versions are in separate universes, neither version can be physically informed about what happens to the other version.  A version of an observer on one branch simply cannot interact in any way with a version on another branch.

8. The Preferred-Basis Problem. 

One might object that we used a “preferred basis” in deriving this result.  Instead of using the basis {[live], [dead]}, we could have used some linear combination such as {.707[live]+.707[dead],.707[live] – .707[dead]}.  But there are two arguments against this objection.  The first is that one still never gets other or disagree written.  And the second is that a “superselection” rule comes into play here.  Any linear combination of states is indeed allowed in quantum mechanics.  But there are some linear combinations that make no physical sense.  For example, one never considers a linear combination of states with charge 2 and charge 3.  Why?  Because these states remain orthogonal for all time so there can be no interaction between them.  Each continues on its own merry way, totally oblivious to what happens to the other.  Exactly the same superselection rule reasoning applies here.  A linear combination of states of an observer makes no sense because there can be no communication between the two parts.

9. Classical Consistency. 

Classical consistency means consistency in the ordinary, everyday sense.  It implies two properties.  First it implies that an observer will never see some linear combination of the cat alive and the cat dead, which we just showed.  And second, it implies that classical (that is, everyday) if-then logic holds.  For example, if the observer sees the detector on the vertical path registering yes, then the observer will also see the cat alive.  And a perception of the horizontal detector registering yes will always be paired with a dead cat (and a reading of no on the vertical detector).  Thus one might speculate that quantum mechanics is the “natural origin” of the concept of if-then logic.

10. Quantum Mechanics Alone Implies
Observers Cannot Disagree. 

We know experientially that if two observers look at the results in the Schrödinger=s cat experiment, they will agree on whether the cat is dead or alive.  Must one assume that there is an underlying objective reality or that the wave function for some reason collapses down to just one branch to guarantee this result?  No.  Ordinary noncollapse quantum mechanics, by itself, is sufficient to explain why observers must agree.  To see this, suppose there are two observers.  Then the laws of quantum mechanics imply that the total wave function has two simultaneously existing branches, each classically consistent.  They are

                  [(live cat)(obs. 1 sees a live cat)(obs. 2 sees a live cat)]

                                                         and                                                  

               [(dead cat)(obs. 1 sees a dead cat)(obs. 2 sees a dead cat)].

Now we ask obs. 2 to write down whether she agrees with obs. 1.  The two-branch wave function is then

[(live cat)(obs. 1 sees a live cat)(obs. 2 sees a live cat)(obs. 2 writes agree)]

and

[(dead cat)(obs. 1 sees a dead cat)(obs. 2 sees a dead cat)(obs. 2 writes agree)].

We see that disagree is never written.  Thus quantum mechanics prohibits two observers from disagreeing, in agreement with our everyday experience.

11. An Apparently Objective Universe. 

From the above results, we see that it is not necessary to postulate the existence of an actual objective world to explain why we see only one classically consistent version of reality and why we all agree on the version.  The total isolation of one branch of the wave function from another—without the existence of actual electrons, photons, atoms or any kind of objective world, and without collapse—is  sufficient to explain these observations.  That is, noncollapse quantum mechanics, with no particles, yields an effective objective reality, even though there are many branches of the wave function.

12. Which Branch Is Perceived? 
The Incompleteness of Quantum Mechanics. 

Quantum mechanics tells us that the observer will either write “alive” or she will write “dead.”  But it does not tell us which one she will perceive and write.  So, in this sense, quantum mechanics is an incomplete theory.  One potential way to complete it is to suppose there really are objectively existing particles, and their state determines which branch will be perceived.  But the bare fact that quantum mechanics is incomplete in this way is not sufficient to infer that objectively existing particles are the means by which it is completed.  Instead, one would need separate observations that positively confirm the existence of particles.  (And we show in section IIIA4 through IIIA6 that there are no observations which confirm the existence of particles.)

13. Quantum Mechanics and an Unstable Past. 

There is one other way in which quantum mechanics is insufficient.  Even if we were to agree that quantum mechanics limits our perception to only one branch, there is no guarantee that the reality we all perceive and agree on at one instant will be the same as the perceived reality at the next instant.  That is, at one instant we could be patting an alive cat, and at the next instant, we could be burying a dead cat—and we would never know about the shift because each branch comes as a complete unit, including the memory of what went before.  This is not an attractive feature; one hopes it will disappear when the mechanism that completes quantum mechanics is found.