The
mystery
Spontaneous
radioactive decay
The double slit experiment
Quantum entanglement
What does it mean?
A
few additional web links
The
Mystery
Some time after Einstein's General Theory of Relativity was published,
Arthur Eddington is said to have been asked if it was true that
only three people in the world understood the theory. Sir Eddington
thought for a moment and said: "Who would that third person
be?"

For
Physics World by John Richardson

The situation is even worse with regard to Quantum Mechanics. Richard
Feynman, who received the Nobel prize in 1965 "for his fundamental
work in quantum electrodynamics, with deepploughing consequences
for the physics of elementary particles" had this to say: "I
think that I can safely say that nobody understands quantum
mechanics."
The basic theory was developed in the late 1920s. It was subsequently
refined to the point where it is now the most successful, thoroughly
tested, and precise theory we have ever had with which to explain
and predict physical phenomena. It is routinely used by thousands
of scientists and engineers on a daily basis and has found widespread
practical use.  Yet even after two thirds of a century, its concepts
and predictions are so baffling and at odds with our intuition and
common sense, that a hot debate is still raging over what it really
means.
Can something be said to exist if it cannot be observed even in
principle? Can a physical object be in several places at once?
Can there be an effect without a cause? Can measurements on a physical
system influence a physical system that is far removed from the
first system instantaneously (not at the speed of light 
instantaneously!)?
Let us consider three puzzling phenomena: spontaneous radioactive
decay, the double slit experiment, and quantum entanglement.
Spontaneous
radioactive decay
More than a hundred years after Becquerel discovered radioactivity
in uranium crystals, we still are unable to predict when an individual
radioactive atom will decay. Most
isotopes of the 92 basic elements in nature (and all manmade elements
with higher atomic numbers) spontaneously decay into other elements.
This occurs with a halflife (i. e. the time it takes for half of
the original sample to decay) that varies widely between different
isotopes, but is quite welldefined for each particular isotope.
 Carbon 14, commonly used in the dating of human
remains and artefacts, has a halflife of 5730 years. Iodine 131
has 8 days, Uranium 238 well over 4 billion years, Polonium 212
just 300 nanoseconds.
This decay occurs according to a stringent physical law: an exponential
decrease of the original sample at a rate that is specific to each
isotope. It is not affected, as far as we know, by the external
environment (temperature, pressure etc). But it is a statistical
law. We can make no prediction concerning an individual atom, just
determine the probability that it will decay during a given time
interval.
Two different explanations have been given for our inability to
predict the fate of the individual atom:
 We simply do not know enough about the inner workings of the
atom. The atoms of a particular isotope may not be identical to
each other. Perhaps there is an interior structure, of which we
have no knowledge, that determines how stable the individual atom
is.
This is the "hiddenparameter" scenario. It comes
in two flavors: a) We may in time come to develop our understanding
to the point where we can make predictions, at least in principle,
for the decay of individual atoms. b) There is an inner structure
that differentiates one atom from the next and determines exactly
when it will decay, but it will remain hidden from us forever
because of fundamental limits to observability.
 Each atom of the same isotope is identical. Its structure determines
its halftime, which can be measured and may be accessible to
calculation. The decay of the individual atom, on the other hand,
is an intrinsically random event governed by its probability,
and there is no additional law to discover.
The second standpoint has been the prevailing view among leading
scientists for the better part of a century; with some notable exceptions,
including Einstein. ("I cannot believe that the good Lord
is playing dice with the universe.") But even Einstein
admitted that a probabilistic universe was not a logical
impossibility.
Intuitively, it seems hard to accept, though. "How does an
atom know when to decay?" After all, probability theory
has been developed as a discipline to describe deterministic phenomena
that are too complex to analyse in detail (the toss of dice, morbidity,
atmospheric turbulence...). It seems quite a stretch to believe
that the universe is intrinsically probabilistic. And if
an atom can undergo a transition without any external triggering
event, what about the universe itself?
On the other hand, suppose that all atoms of a certain isotope
really are identical (except for external attributes such
as position), then, in a deterministic universe, we would expect
them all to exhibit the same behavior. If their stability (or lack
thereof) is such that it corresponds to a median life of 5730 years,
we would expect them all to decay simultaneously after an
interval of that order of magnitude. Poff!  Such a scenario seems
just as difficult to envision. Yet, after a century of increasingly
refined measurements, including the discovery of many subatomic
particles and the modelling of quarks, no evidence has ever been
found for any kind of individuality at the atomic level.
The
double slit experiment
Nature
and Nature's laws lay hid in night: God said, "Let Newton
be!" and all was light.  Alexander Pope

It
did not last: the Devil howling "Ho! Let Einstein be!" restored
the status quo.  J.C. Squire


For centuries, there were divided opinions on the nature of light.
Around 1700, Huygens held that light was a wave phenomenon, while
Newton thought that light consisted of tiny corpuscles. A hundred
years later, the wave theory got the upper hand, when interference
was discovered, and the double slit experiment (see below) was first
performed (in another
form) by Thomas Young. Later in the 19th century, visible light
was identified as electromagnetic radiation within a certain wavelength
band, and was shown to be governed by Maxwell's equations. The case
seemed settled.
Ironically,
it was Einstein who unwittingly opened the door to quantum mechanics
and all its paradoxes by proposing that light itself was quantized
into what came to be known as "photons". This explained
the photoelectric effect and won him the physics Nobel prize in
1921 (thereby letting the Swedish Academy of Sciences off the hook
of having to take a stand on the still controversial Theory of Relativity).
However, Einstein's discovery raised as many questions as it answered.
In particular, the double slit experiment needed to be revisited.

In this experiment, coherent
light (coming from above in the illustration at right) illuminates
two parallel narrow slits (having a width on the order of the wavelength
of the light). Each of the slits will then act as a light source,
and the screen at the bottom will exhibit an interference pattern
with alternating lighter and darker bands.  This effect is strikingly
similar to the pattern we would get if we threw two stones of similar
size into a pond, with the two systems of waves alternately reinforcing
and cancelling out each other in different spots. It clearly demonstrates
the wave nature of light. It also seems to disprove the theory of
light as small corpuscles travelling in straight lines. But the
quantization of light had by now (in the 1920s) been firmly established.
Somehow light seemed to exhibit some of the characteristics of both
waves and particles. Scientists started to talk about "wave
packets".
As early as 1909 it was discovered
that the interference pattern in the double slit experiment persisted
even when the intensity of the light source was drastically reduced.
This later led to Dirac's famous exclamation: "The photon
interferes with itself!"  Around 1930 it was shown through
experiments involving diffraction off crystals that electrons,
too, exhibit wavelike characteristics. (Double
slit experiments with single electrons were not actually performed
until the 1960s. They confirmed that electrons behave exactly in
accordance with quantum theory, as expected).
The baffling fact, which had been firmly established around 1930,
was this: If electrons were sprayed at the two slits in the diagram,
an interference pattern similar to the one for light would occur
on the screen at the bottom. This was absolutely in contradiction
to classical physics, where the electrons would be expected to be
grouped behind the slits without any interference fringes. Moreover,
this interference pattern could be observed even if the electrons
were fired one at a time, but only if no attempt was made to
measure which slit the electron was passing through. This meant
that each electron was indeed interfering with itself! Somehow
each electron was simultaneously passing through both slits! But
if measurements were made to determine the path taken by the electron,
the interference pattern vanished! So the electron went through
both slits at the same time only if no one was looking!

Cartoon
by Nick Kim.

These and other observations led to the formulation of quantum
theory through legendary scientists such as Planck, Bohr, Schrödinger,
Heisenberg, Dirac, de Broglie, Pauli and others. At its heart is
the concept of uncertainty. It is fundamentally impossible to
simultaneously measure the exact position and the exact momentum
of a particle. The same goes for its exact energy at an exact
point in time.
These limits to observations are due to the fact that all observations
involve a disturbance of the observed entity of at least one quantum
of energy. In the microscopic world this is enough to influence
the observed system, so that it is fundamentally impossible to disentangle
the observer from the observed object.
Mathematically, particles are described by a wave function denoted
with the greek letter psi. This is a highly abstract entity.
In the opinion of many scientists it is devoid of physical meaning,
but it allows the calculation of physically relevant parameters.
For instance, the square of the absolute value of psi at
a certain point in space is proportional to the probability of detecting
the particle at that point, if a measurement is made. Particles
such as electrons or photons are envisioned as tiny smearedout
clouds, where the central parts correspond to their most probable
locations.
In the double slit experiment, when a particle is fired, there
is a 50 percent chance that it will pass through the left slit,
and an equal probability that it will pass through the right slit,
assuming symmetry. This is reflected in the psi function which becomes
a superposition of the two states corresponding to passage
through one slit or the other. When the particle hits the screen
at the far side, the psi function will predict bands of probability
for the postion of the particle that correspond exactly to the fringes
observed. If a measurement is made to determine through which slit
the particle actually passes, the wave function "collapses"
and is no longer a superposition of two states, and the interference
fringes vanish.
In the more than seventy years since quantum mechanics was invented
(or discovered, take your pick), it has withstood every test. Its
predictions of the outcome of experiments are invariably exactly
fulfilled. But it still leaves open the question: What does it really
mean?
According to Niels Bohr, physical reality is that which can be
observed. Atoms and particles are real, but the psi function has
only symbolic meaning and does not represent anything real. It is
not only pointless but also meaningless to speculate about the reality
of things we cannot observe. Such speculations lie outside the realm
of science, for they cannot be put to the test of experiments. 
This has come to be known as the Copenhagen
interpretation and has dominated thinking among scientists since
it was put forward.
Einstein is said to have countered: "Do you really think
the moon isn't there if you aren't looking at it?" Not only
Einstein, but also such a central figure as Schrödinger, who
formulated the fundamental equation for describing quantum mechanical
behavior, was uncomfortable with the role accorded to the observer
in the Copenhagen interpretation of the theory.
Schrödinger devised a thought experiment intended
to show that the analysis of the role of observation in quantum
mechanics was incomplete. A cat is placed in a sealed box for an
hour together with a radioactive substance with the characteristic
that there is exactly a 50 percent chance that an atom will decay
during that hour. If an atom decays, it triggers the release of
poison gas, killing "Schrödinger's
cat". Now, according to quantum mechancis, in the absence
of an observation, the cat exists as a superposition of two states
just before we open the box: dead and alive. Only when we open the
box and make the observation, the wave function "collapses"
and the fate of the cat is decided. But this is manifestly absurd.
The cat must be either alive or dead whether we are looking or not.
If it turns out to be dead when we open the box, we can easily establish
how long it has been dead.
Quantum
entanglement
If you find it surprising that a particle can simultaneously pass
through two slits, just wait: it gets weirder. According to quantum
theory, two particles that interact become entangled from that point
on. They are both described by a single combined wave function.
If a measurement is made on one particle, it instantly influences
the state of the other particle no matter how far the two particles
are separated from each other.
Nearly all the giants of physics were present
at a series of conferences arranged by the Belgian industrialist
Ernest Solvay, the very same Solvay who financed the Solvay
hut on the Matterhorn!


Solvay conference 1911. I am particularly
fond of this picture, as I have spent many hours staring at
it in the main conference room at the Joint Research Centre
in Ispra, Italy.

Click
to enlarge and access mouseover links.


Solvay conference 1927. Its theme was "Photons
and electrons". This meeting came at a key moment in
the development of quantum theory.

Click
to enlarge and access mouseover links.

You might say: "Big deal! If someone puts a black marble in
one box and a white marble in another box behind my back and sends
one of the boxes to Mars, I can determine the color of that marble
just by opening the box left behind. That does not mean that my
'measurement' influences the color of the marble on Mars."
But this is not what the theory says. It actually states that
the measurement of one entangled particle instantaneously
affects the state of the other particle, and this has been experimentally
verified. Moreover, it is close to being exploited in practical
applications such as quantum computers and quantum cryptography.
"But I thought that no signal can travel faster than light",
you might say. The answer to that, according to quantum theory,
is that this "communication" between the particles does
not involve any signal in the conventional sense and cannot be used
to transmit information from one observer to another. But even if
we accept this, it implies that to some observers the state of the
second particle will be found to have been influenced by the measurement
on the first particle before it occurred, according to the
special theory of relativity!
Einstein was the first to point out that this nonlocality was
required by quantum theory. In a seminal paper
in 1935, he and his students Rosen and Podolsky concluded that either
quantum mechanics was incomplete and particles must have definite
states even when they were not measured (hidden parameters), or
action at a distance was necessary, which meant that in some frames
of reference an effect could precede its cause. They argued that
a particle must have a definite state even in the absence of an
observer. Einstein rejected what he called "spooky action
at a distance". (See also this web article.)
Three years earlier, the eminent mathematician John von Neumann
had shown that hiddenparameter theories could not be consistent
with observed reality. His proof ultimately turned out to be flawed,
but for some time it seemed very persuasive. In 1952, David Bohm
succeeded in doing "the impossible" (John Bell). He devised
a consistent theory of quantum mechanics allowing "hidden parameters",
i. e. a deterministic description where the observer lost his key
role in defining reality (in the Copenhagen interpretation). The
theory, which built on a similar model from the 1920s by Louis de
Broglie, involved the concept of pilot waves guiding particles
in such a manner that all the manifestations of wavelike and particlelike
behavior were respected, while restoring the reality of particle
trajectories between observations. The theory was shown to be mathematically
equivalent to the standard theory of quantum mechanics.  Bohm's
theory was widely criticized for violating Occam's
razor by adding assumptions beyond what was necessary to explain
observations, however. To some it was reminiscent of Ptolemy's invention
of epicircles to predict planetary motion, when a simpler model
(Kepler's laws) did a better job. Some scientists felt that Bohm's
theory was an excursion into metaphysics.  It certainly was not
part of the curriculum (textbook by F. Mandl.) when I studied quantum
mechanics in the early 1960s.
Then in 1964, John Bell published his famous theorem,
which in essence states: No physical theory of local hidden variables
can ever reproduce all of the predictions of quantum mechanics.
This seemed to strengthen the Copenhagen interpretation: the
world is probabilistic. What was widely overlooked was the word
"local". A deterministic universe was still possible,
but then "spooky action at a distance" had to be accepted.
In 1982, experiments
seemed to demonstrate conclusively that the predictions of quantum
mechanics concerning entanglement are correct, while the predictions
of "objective local" theory are wrong. Subsequent experiments
have confirmed this result, except for a few cases where it is believed
that errors were introduced in the experiment setup. More recently,
quantum entanglement has been demonstrated
at separation distances of greater
than 10 km. Other effects dependent on quantum entanglement,
such as quantum
teleportation and quantum
cryptography, have been demonstrated in the laboratory. Here
is an article
from 2001; and here is a news
item from December 2005, reporting that six Beryllium ions have
been coaxed into spinning in opposite directions at the same time.
At this point my head is in a (classical) spin. It is time to disentangle
myself before quantum collapse occurs, so I refer to another
source for recent developments in quantum entanglement, which
I anyway am too lazy to try to understand :). And here
is a fairly recent article from New Scientist.
What
does it mean?
Our present standard theory of quantum mechanics has been extremely
successful in modelling physical reality. All attempts to "falsify"
it, i. e. to make observations which contradict theory, have failed.
Thus, any future theory attempting to replace present theory will
have to make the same predictions concerning the outcome of previously
conducted experiments within the present accuracy of our measurements
(just as the predictions of the special theory of relativity become
indistinguishable from those of newtonian mechanics at low speeds).
This means that "spooky" effects such as those described
earlier are real, however much they may offend our intuition and
"common sense". The scientific debate is not about the
reality of these effects, but about their interpretation. Many scientists
feel uncomfortable with concepts such as indeterminacy, nonlocality,
and noncausality, and look for a more "rational" model
that would explain the observations.
I have seen at least six interpretations of quantum theory on the
Web, most of which attempt to replace the "positivistic"
Copenhagen interpretation with something considered to be more palatable
and/or understandable. Four of them appear to have the following
characteristics:
1. The
Copenhagen interpretation
Physical reality is by definition that which can be observed. To
speculate about what happens when "no one is looking"
is outside the realm of science. The
question of whether objects have reality when they cannot (even
in principle) be observed has no physical meaning.
Quantum mechanics is complete insofar as it can correctly predict
the outcome of all experiments to which it is subjected. There is
therefore (at present) no need for additional "laws" or
assumptions.
Physical reality is inherently probabilistic.
2. Bohm's
pilot wave interpretation
As mentioned above, this is mathematically identical to the standard
model, but makes the assumption of waves guiding particles so that
the latter exhibit wavelike behavior. It is deterministic (hidden
parameters) but nonlocal, so instantaneous action at a distance
is allowed.
3. The
ManyWorlds interpretation
Every probabilistic event spawns a separate universe for every
possible outcome of that event. Such problems as "How does
a radioactive atom know when to decay?" are addressed by proposing
that all possible outcomes are realized in a multitude of separate
universes. Our universe is no more real than all the others. There
are infinitely many alternative nonobservable universes.
This interpretation may perhaps offer some comfort
to those who have been the subject of an improbable accident: There
are many more universes, just as real, where the accident did not
happen!
4. Waves
travelling backward in time
This "transactional" interpretation by John Cramer builds
on ideas from Wheeler and Feynman on timesymmetric radiative processes
(if I have understood correctly). An emitter sends a wave forward
and backward in time. When the forward wave hits an absorber, a
new set of forward and backward waves is generated. "The emitter
can be considered to produce an 'offer' wave which travels to the
absorber. The absorber then returns a 'confirmation' wave [backward
through time] to the emitter and the transaction is completed with
an 'handshake' across spacetime." To an observer, a photon
has been emitted and absorbed, but the model can just as well be
interpreted to mean that a standing wave has been established between
emitter and absorber.
Mathematically, this is just another interpretation of the existing
formalism. It makes no predictions different from the Copenhagen
interpretation, but Cramer claims that it helps develop intuitions
and insights into quantum phenomena that up to now have remained
mysterious. (See also this
summary.)
All of these interpretations are equivalent, in the sense that
they assume, or can be shown to generate, the same governing equations
and predictions. They are all interpretations rather than
theories, as they make no additional predictions that would
make it possible to test their validity. In a sense, they are therefore
no more helpful than a claim that "the Universe was created
last Thursday with all its present features, including evidence
and memories of a much longer history", which also cannot be
disproved. But they may be of some value in helping scientists think
about quantum theory, and in suggesting avenues for research.
Personally, I find it quite remarkable that not only laymen, but
also philosophers and theologians, seem to take so little interest
in the amazing discoveries made during the past century about the
nature of physical reality. It appears that even educated people
often just have vague notions about clocks slowing down near the
speed of light, and about quantum uncertainty. It is common to hear
people ask: "But what happened before the Big Bang?" without
realizing that "before" has to do with time, and that
time is a feature of our physical universe.
Another thought is that the crucial role of the observer in defining
physical reality in the Copenhagen interpretation, which seems especially
hard to swallow to many physicists who believe in an "objective"
reality, perhaps should not be dismissed out of hand. Consider
a universe completely devoid of life and even of complex molecules,
from its Big Bang, expanding forever and ending up as a cold empty
void when the very last subatomic event has taken place after, say,
10^{100} years. What exactly do we mean when we say that
such a universe has an "objective" existence?
According to Albert Einstein: "The most incomprehensible thing
about the universe, is that it is comprehensible."  While
it does not appear all that comprehensible to me, it certainly seems
surprising that the laws of physics are as simple and straightforward
as they are, even when they are at odds with our intuition. When
you think about it: is it not surprising that there should be any
laws of physics?
A
few additional web links
