IIE.  Many Possible Futures in Quantum Mechanics.

In (the mathematics of) classical physics, as we said, the future—including the thoughts we think and the actions we take—is completely determined.  This is not so in (the mathematics of) quantum mechanics, where there are many possible futures.  We will explain this profound difference here with a simple half-silvered mirror experiment and then in section IIF with the well-known Schrödinger’s cat experiment.

1. Visualization of Two Branches of the Wave Function.
Half-Silvered Mirror Experiment

In section IID, we visualized the electron as a cloud traveling through space.  When the wave function for light was split into two parts by a half-silvered mirror, we imagined in our mind’s eye two clouds in the same picture, one moving horizontally and one vertically (figure IID.2).  This, however, does not properly convey what the mathematics implies and it is therefore misleading—so misleading that we miss the most crucial aspect of quantum mechanics.

2. Picturing the Two-Branch Wave Function

To more accurately display the content of the two-branch wave function in the half-silvered mirror experiment, we will put a detector of light on the vertical path and another detector on the horizontal path.  If the vertical detector does not detect light, we denote this by [V, no]; and if it detects light, we denote this by [V, yes].  The same for the horizontal detector, with [H, no] and [H, yes].  We now send a single lightlike wave function through the half-silvered mirror, two-detector apparatus and draw the wave function just before its two parts hit the detectors.  We cannot do this properly with a single picture; instead we need two pictures.

Figure IIE.1.  A proper depiction of the two-branch half-silvered mirror wave function requires two diagrams, each outlined in gray, rather than the single diagram of figure IID.2.

The motions of the two parts of the photon wave function do indeed happen simultaneously (hence the + sign, meaning and).  But it is simply not a proper representation of the mathematics to depict them in the same drawing, as in figure IID.2. 

When the wave function in the top diagram hits the V detector, its reading is changed from no to yes, with a similar statement for the bottom diagram.  Thus after the two branches of the photon wave function hit their respective detectors (and are annihilated), the wave function of the apparatus is properly represented by figure IIE.2.

Figure IIE.2.  The two branches of the wave function of the apparatus, each outlined in gray, after the two branches of the wave function of the photon have hit their respective detectors.

Note that in the top diagram of figure IIE.2, it is as if an actual photon traveled on the vertical path and set off the V detector, and in the bottom diagram, it is as if an actual photon traveled on the horizontal path and set off the H detector.

3. Perception of Only One Branch

Of necesssity, in a book we have to draw the two possibilities in figure IIF.2 near each other.  But in reality (or more accurately, in the mathematics), these two possibilities exist in entirely different, totally separate universes.  We, as observers, are in one universe or the other.  If we are in the universe corresponding to the top diagram, we will perceive [V,yes] [H,no], but not [V,no] [H,yes], as indicated by the shading in figure IIE.3V.  But if we are in the universe corresponding to the bottom diagram, we will perceive [V,no] [H,yes], but not [V,yes] [H,no], as indicated by the shading in figure IIE.3H.

Figure IIE.3V.  In this diagram, the observer perceives only the [V,yes], [H,no] branch of the wave function, in black, even though the [V,no], [H,yes] branch, in gray, simultaneously exists.

Figure IIE.3H.  Here, the observer perceives only the [V,no], [H,yes] branch of the wave function, in black, even though the [V,yes], [H,no] branch, in gray, simultaneously exists.

That is, we perceive one and only one of the versions of reality ([V,yes], [H,no] or [V,no], [H,yes]) allowed by quantum mechanics.  We call this perception of just one branch only-one perception.  Perception of one and only one branch—only-one perception—also holds when more than two versions of reality are mathematically allowed by quantum mechanics, as happens in more complicated situations.

[Note: A beam of light consists of millions of photonlike wave functions traveling at the speed of light.  We are not aware of the only-one, either-or “quantum logic” of the beam with our naked eye (that is, without the detectors).  We are only aware that each of the two parts of the beam has half the intensity of the original beam (because half the wave functions are “detected” by our eye on each path).]

4. The Central Mystery of Quantum Mechanics

Figures IIE.3V and IIE.3H pictorially display the central mystery of quantum mechanics.  Why do we perceive one and only one version of reality when both are simultaneously unfolding in the wave function?  (Or more exactly, why do we perceive one particular version of reality; see below and section IIIC1.)

5. Which Outcome?

What determines which outcome—[V, yes], [H, no] or [V, no], [H, yes]—we will see when a single photonlike wave function goes through the apparatus?  Quantum mechanics does not.  In fact, it is not known what determines which outcome we will see.  But if the experiment is run many times, quantum mechanics can tell us the probability of seeing one result or the other (explained later in this section). 

6. Many Possible Futures

If we start from the time just before the wave function hits the half-silvered mirror, we can say that quantum mechanics allows two possible futures.  In one, [V, yes], [H, no] is perceived and in the other, [V, no], [H, yes] is perceived.  This is very different from classical physics where, once the system was started out, the mathematics allowed only one possible future.  It means that—in contrast to classical physics—the future is not set by the mathematics of quantum mechanics; many futures are allowed.

7. No Objective Reality in Quantum Mechanics

We naturally tend to think that there is an actual world “out there.”  That is, we tend to think there is one and only one version of reality, an objective world that “actually exists.”  But that is not true in the mathematics of quantum mechanics.  Instead there are many versions of the world; the detectors read [V,yes][H,no] and the detectors read [V,no][H,yes], or Schrödinger’s cat is dead and Schrödinger’s cat is alive. 

One possible way to understand this is to suppose that quantum mechanics is simply describing—in its own peculiar wave function language—the behavior an actually existing, objective, single-version reality.  That is, there actually is a photon that takes one path or the other.  We will show in section IIIC, however, that that is almost certainly not true.  What physically exists is the wave function alone, with all its branches, all its possible futures.  This lack of an objective reality is a most profound change from the classical view—or indeed practically any view!