Review of Colin Bruce,
Schrödinger’s Rabbits:
The Many Worlds of Quantum
Joseph Henry Press (2004)
Herbert Gintis
In the nineteenth and early twentieth centuries, many natural philosophers believed that the laws
of the Universe could be derived from Reason. For instance, Galilean invariance gave us
Newton's Laws, and similar invariance conditions give rise to special and general relativity.
Quantum mechanics changed all that because many quantum mechanical phenomena violate one
or more 'reasonable' assumptions, such as the impossibility of action at a distance. This is really
why Einstein never accepted quantum mechanics as more than a provisional theory.
It is tempting to be dismissive of quantum mechanics because it only deals with phenomena at
extremely sub-microscopic dimensions, and classical mechanics and electrodynamics can get
along without it perfectly well at 'human' dimensions. Both reasons are faulty. First, quantum
mechanics explains quantum tunneling, which is central to solid state devices such as transistors,
and more generally, quantum effects can be amplified without difficulty to the human level (this
is the famous Schrödinger's Cat problem, to which the title of the book alludes. Second, there are
deep antinomies in classical electromagnetic theory, including the prediction that the energy in
blackbody radiation goes to infinity as the wavelength of the energy goes to zero.
There are many strange and beautiful quantum phenomena. Perhaps the two most famous are
wave/particle duality and entanglement. Wave-particle duality is well illustrated by the famous
two-slit experiment. Photons are directed towards an absorbing wall with two vertical slits some
macroscopic distant apart. The few photons that go through one of the slits hit a clear
photographic film that records the absorption of the photon by coloring the impact point black. If
photons are particles, there should be two widely separated masses of black dots whose location
can be calculated using simple geometry. If photons are waves (like waves in a pond), it is not
hard to show that there should be alternating bands of light and dark on the photographic plate,
corresponding the interference pattern of the two parts of the wave that pass through the distinct
slits. If you do this experiment, photons act wave-like. However, if you measure the passage of
the photon through a slit, you always find it went through either one or the other, but not partly
through both. This shows the photon is a particle. Moreover, if you can measure which slit the
photon went through, the interference patter on the plate disappears, and the photon leave a black
spot on the plate.
Early interpreters of this weir phenomenon argued that by measuring the photon, you interfered
with its normal path, as explained by classical signaling theory, so the phenomenon is just poor
experimental design. For a variety of reasons that you can read about, this explanation is faulty.
The widely accepted explanation (the so-called Copenhagen theory, named after Neils Bohr) is
that the photon is indeed a wave, as described by Schrödinger's famous equation or Planck's
relativistic version. These equations describe not where the photon is, but rather a probability
distribution over its possible locations. When observed, the wave 'collapses' to a particular
location, the location being proportion to its relative probability.
This experiment and its interpretation calls into question the nature of objectivity and
subjectivity in a highly radical form. What does it mean to be 'observed'? By whom? What if it is
'observed' by a machine and you do not have access to the machine's memory? The two-slit and
related experiments, as explained by the Copenhagen school, simply divides reality in to nature
plus observer, where observer means a human or an instrument that can be read and recorded,
accessible to a human. This is fine for all practical purposes, because that's how we humans do
science. But its ontological status is highly compromised.
A second weird phenomenon involves 'entanglement.' Electrons have 'spin,' which when
measured in any direction, is either 'up' or 'down.' When electrons are generated in pairs, they
may be entangled in the sense that after they are separated, if one measures 'up' in a particular
direction, the other must measure 'down.' However the state of spin is a probability distribution
that collapses to a particular up or down when you measure it. Suppose the entangled electrons
move apart until they are a light-second apart, and then the spin of one is measured in some
direction. Then immediately, not a second later, the other measures the opposite direction. This is
not a relativistic time effect, and it has been repeatedly verified in the laboratory. It is called a
violation of locality.
Einstein and his colleagues Podolsky and Rosen (1935) used a similar argument to show that
there must be something wrong with quantum mechanics, but it turns out that that is just the way
the world works, like it or not.
Most physicists do not care why quantum mechanics works the way it does, but some do, and
many of those think that there must be a better model that the Copenhagen collapse theory. One
is the Many Worlds Interpretation (MMI), which Bruce explains and defends in this book. The
MMI says that whenever there appears to be a collapse of the quantum wave, the Universe really
branches into a large number of alternative Universes, side-by-side, each of which captures one
of the possible states. So, for instance, if you set up an apparatus that kills you if a certain photon
is measured as having spin up, and does nothing if the spin is down. Then the whole Universe
splits into two Universes, in the first of which you are alive and the other of which you are dead.
This theory does explain most of the queerness of quantum mechanics, and it could be true. But
there is no evidence that it is true. Nor has anyone ever suggested an experiment that would
determine its truth value (Bruce suggests some possibilities, but they are far-fetched). Moreover,
the theory itself is completely outlandish, far weirder than the phenomenon it is supposed to
explain. The fact is that reading this and other attempts to explain quantum weirdness are fun and
challenging intellectually, but their real value is virtually zero. When someone tells me he
believes a version of the MWI, I treat the person the same as if they told me they believed in
transubstantiation or the tooth fairy.
Nevertheless, quantum mechanics is certainly not a "true" theory, if only because it makes no
room for gravity. The string and quantum gravity theorists attempt to repair this fault, but they
produce theories that are as yet untested, although possibly testable.
But I think there is a deeper problem. Quantum mechanics represents a particle (e.g., a photon)
as a point in Hilbert space, which is an infinite dimensional vector space. I don't believe there are
`real' infinities, and hence this representation must be an approximation of the true, finite, model.
We should be looking at finite or countable models of particle physics, not hugely overpopulated
continuous models. Richard Feynman registered his discomfort with nonconstructible,
continuous models, in the following words (quoted by Bruce, p. 242): "It always bothers me that,
according to the laws as we understand them today, it takes a computing machine an infinite
number of operations to figure out what goes on in no matter how tiny a region of space, and no
matter how tiny a region of time..." I have often make the hypothesis that ultimately physics will
not require a mathematical statement, that in the end the machinery will be revealed, and the
laws will turn out to be simple, like the checkerboard with all its apparent complexities."
I realize many readers will not share my skepticism concerning infinite models. But they should,
because it is the only reasonable position. Countable models are fine, because we can attain any
element of a countable model in finite time. But uncountable models are just a useful human
construct, probably not corresponding to anything real in the world. At any rate, reading Bruce's
book conjures up all sorts of cute ideas that are fun to think about while taking a break from the
real world.