ÐÓ°ÉÔ­´´

Take a good look at the issue of New ÐÓ°ÉÔ­´´ that you are holding
in your hand. Now put it on a table, close your eyes for ten seconds and
open them again. The chances are that the magazine will still be on the
table; but was it there when you were not looking?

If you have never encountered the strange world of quantum mechanics,
you will probably be thinking: ‘Of course the magazine was there – its behaviour
does not depend on whether I am observing it or not.’ But quantum mechanics
says that physical systems do behave differently when they are being observed
and when they are not. This theory, and what it implies about the way we
look at the Universe, has kept physicists and philosophers debating for
the past 60 years. According to quantum theory, we must remain outside a
physical system if we want to describe it because in measuring a system
we interact with it in a subtle way and therefore change its quantum mechanical
state in the process. How then can we describe the Universe in this way,
because we cannot step outside of it? Some physicists think the way to get
round these difficulties might lie in a process called decoherence. But
before we can look at decoherence, we need to say a bit more about the strangeness
which lurks in the quantum mechanical world.

To understand this strangeness, take a look at what happens when we
move from classical physics to quantum theory to describe a physical system.
Suppose a ball is thrown from location A at some instant of time and reaches
another location B 10 seconds later. In classical physics, using the laws
of Newtonian mechanics, if we know the forces which were acting on the ball,
then we can calculate the exact path taken by the ball in going from A to
B. We can even calculate the position and speed of the ball at any instant
while it was in flight.

The situation is very different in quantum theory, which is concerned
with the microscopic: with interpreting the behaviour of elementary particles
and atoms which do not obey Newtonian mechanics. And one of the fundamental
principles in quantum theory is that we cannot specify simultaneously both
the position and the speed of the particle. So, if our ‘ball’ is a subatomic
particle and, for example, we know the precise position of the particle
at any given instant of time, we are then completely ignorant of its speed
at that moment. So we will not know where the particle will be at the next
instant.

PROBABILITIES ARE PIVOTAL

Quantum mechanics, then, quite clearly rules out the possibility of
describing the motion of the particle in terms of a given path. So instead
of a single path connecting A and B, we now have to deal with all possible
paths connecting these two points. The particle that starts at A and ends
up at B could have followed any one of the paths connecting A and B. So
there is some chance that the particle has followed one particular path
among all the possible paths. Quantum mechanics assigns a number called
the ‘probability amplitude’ to each path and the rules for calculating this
amplitude can be found in the mathematical description of quantum mechanics
.

The description of the physical world in terms of probabilities is central
to quantum mechanics. The description appears in many different guises.
Another example is the spin state of an electron emitted by an electron
gun. Quantum mechanics tells us that the spin of an electron along any specified
direction, say the vertical one, can take the values +(1/2) for up or -(1/2)
for down. We have no way of knowing which of these two states the electron
will be in when it is emitted by the electron gun. All we can say is that
it has some chance of being ‘spin-up’ (denoted by the symbol up>) and some
chance of being ‘spin-down’ (denoted by the symbol down>). These two states
are allowed in the mathematical description of quantum mechanics, but they
are by no means the only states which are allowed. The equations of quantum
mechanics allow several combinations of these two basic quantum states –
the state up>+down>, for example, where we cannot attribute a definite spin
to the electron because there are contributions from both the spin-up and
spin-down states.

In 1922 the physicists Otto Stern and Walter Gerlach, working at the
University of Rostock, devised an experiment to measure the spin of the
electron. They, and others since, found that the result of the measurement
will always give the value +(1/2) if the electron is in the state up> and
a value -(1/2) if it is in the state down>. What happens if it is in a combined
state like (up>+down>)? Then sometimes the result is +(1/2) and sometimes
-(1/2). But what is really surprising, as physicists soon discovered, is
that if they measured the spin of an electron and found it was in the +(1/2)
state and then measured its spin again, they then found it only +(1/2) never
-(1/2). In other words, the first act of measurement somehow changed the
complicated original state of the electron to the state up>. The act of
observation or measurement has disturbed the quantum system in a very specific
way.

The situation for other quantum measurements is similar. Suppose an
electron has a choice of two routes, and we try to nail down the path that
the electron takes by setting up a complicated series of devices to determine
whether the electron went by one particular route or not. If we do that,
we discover that the electron will indeed simply go by one route or the
other – the behaviour of the electron depends on whether we are observing
it or not.

This result may appear strange and counterintuitive, but it has been
routinely verified in numerous experiments carried out by researchers during
the 1970s and 1980s. While these experiments show that the evolution of
the system does depend on whether it is being observed or not, they raise
a deep philosophical problem: how can we make sense of the fact that the
system being observed must be regarded as separate from the apparatus doing
the detecting? At a fundamental level, both are subject to the same laws
of physics. But several theoretical difficulties arise if we artificially
separate the physical system into a part which is being observed and the
instrument which is observing. A good example to illustrate these difficulties
is one known as ‘Schrodinger’s cat’.

One version of this example runs like this: think of a completely sealed
room, inside which we place a cat and a device containing a poisonous gas.
The device is set to be triggered by an event such as the decay of a radioactive
atom, which involves physical interactions on a microscopic scale. When
the decay occurs, the device is triggered, releasing the poisonous gas which
will instantaneously kill the cat.

We set up this system at some given time and ask, at some later time,
‘Is the cat now dead or alive?’ This is equivalent to asking whether the
radioactive atom has ‘decayed’ or not, which is a quantum mechanical question.
Let 0> and 1> denote the quantum states in which the atom has ‘decayed’
and ‘not-decayed’ respectively. These are similar to the states up> and
down> for the electron spin discussed earlier. But just as for the electron
spin, the system need not exist in either of these simple states. In fact,
there is some chance for the atom to have decayed and some chance for the
atom not to have decayed, in other words the quantum state of the system
will be a combination of 0> and 1>. The same goes for the cat too. It is
both dead and alive, existing in a mixed state obtained by ‘linear superposition’
of two intuitively obvious states – in this case the ‘dead state’ and the
‘live state’.

COLLAPSE OF THE QUANTUM STATE

But have you seen a cat in such a state? No, when it comes to large
systems such as cats, we almost never see them in such weird superposed
states. Consider another example. Quantum mechanics allows a billiard ball
to be at a position A (state A>) or at another location B (state B>). But
it also allows the billiard ball to exist in a state in which it is both
here and there (A>+B>). The trouble is that, for macroscopic objects, such
states are almost never seen in the real world, even though they are perfectly
legitimate in quantum theory. But why don’t we observe them?

The conventional interpretation of quantum mechanics does not offer
much of an explanation. This interpretation relies on a hypothesis called
‘collapse of the quantum state’. The central idea is that the act of measurement
makes the system ‘jump into’ one of the states selected by the measuring
instruments. For example, the billiard ball could be in the state A>+B>
as long as it is not observed. But the moment we try to measure its position,
the state will change into either A> or B>. In other words, we have a 50/50
chance of finding the billiard ball at position A or position B, and no
observation will catch it in the mixed state. The same goes for the cat
in the sealed box. When we open the box and peep inside, that act of observation
will make the state become either ‘dead’ or ‘alive’.

Such an interpretation depends crucially on the existence of an external
apparatus being used to make the measurements. And because we always attribute
a definiteness to the result of a measurement, such definiteness can exist
only if the measuring apparatus obeys the classical laws of physics and
deals with the system at the macroscopic level. The ultimate classical
apparatus is the human brain, which comes into play in any sequence of recording
process which ends in analysis. This artificial division of a physical system
into a classical observer and a quantum mechanical subject has always been
the most unsatisfactory feature of the above interpretation. Even in the
early days of quantum theory in the 1930s, people like Niels Bohr, Werner
Heisenberg, Max Born and Albert Einstein debated it, and came to no satisfactory
conclusion.

UNIVERSAL DILEMMA

But in most cases, working physicists did not worry too much about these
‘philosophical’ issues. The reason was quite simple. Though these issues
are important at a fundamental level, they did not affect the results of
any computations. The practical application of quantum mechanics to physical
systems did not suffer as a result of the lack of answers to these questions
. . . until physicists started to develop a quantum theory of the Universe.

The most remarkable feature of our Universe is that it is expanding.
Astronomical observations show that distant galaxies are flying away from
us and from each other with speeds which increase as they get farther apart.
It is possible to construct a mathematical model for such a universe, the
Friedmann model, which accounts for the expansion of the Universe and agrees
very well with several observational tests.

The fact that the Universe is expanding today, however, implies that
it must have been smaller, denser and hotter in the past. Using the Friedmann
model we can work back from the present behaviour of our Universe to its
past. This works fairly well up to a point, but when we take the Universe
back in time, we have to deal with a Universe in which the scales become
smaller and smaller. But Friedmann’s model is based on Einstein’s theory
of relativity, a classical theory which does not take into account any quantum
mechanical effects. When the size of the Universe becomes truly microscopic,
quantum mechanical effects become important and Einstein’s equations cease
to be valid. If we carry on extrapolating Einstein’s equations beyond this
point, we end up with mathematical absurdities known as ‘singularities’.
At a mathematical singularity, physical parameters such as density and temperature
become infinitely large and the size of the Universe becomes infinitesimally
small – the event more familiarly known as the ‘big bang’. To understand
the behaviour of the Universe when it is very small, we need a cosmological
model which incorporates the principles of quantum theory.

Early attempts in the 1960s to develop a quantum theory of the Universe,
notably by John Wheeler of Joseph Henry Laboratories at Princeton, Bryce
DeWitt of the University of Austin, Texas, and Charles Misner of the University
of Maryland, produced an unexpected dilemma. The conventional interpretation
of quantum mechanics relies on having an observer who is external to the
system being observed. The normal rules of quantum mechanics make sense
only in this context. But how in this case can we study an all-encompassing
quantum universe which by definition has nothing external to itself? What
is more, we need to study it when it is so small that not even atomic structures
(let alone living systems with consciousness) could have existed. To make
sense of a quantum universe, we need to reformulate quantum theory so that
we can do without the notion of external observers. The philosophical issue
has now become a practical necessity.

Remarkably enough, this can be achieved. Several researchers – Dieter
Zeh and Ernest Joos of the University of Heidelberg, Claus Keifer of Zurich
Institute for Theoretical Physics, Jonathan Halliwell of MIT, Wojciech Zurek
of Los Alamos National Laboratory and myself – realised in the 1980s that
there is a physical process, now known as decoherence, which can make macroscopic
systems behave classically: that is, to behave in the way we expect them
to behave from experience. Decoherence explains why the bizarre features
of quantum theory disappear when we are dealing with large systems.

To see how this process works, let us go back to Schrodinger’s cat.
Why is it that cats are never seen in a state which is a superposition of
the live and dead states? And, why do we never see billiard balls in states
with no definite location in space? To understand this we have to look deeper
into what we mean by a state. The state of a truly quantum mechanical object
– an electron in a hydrogen atom, say – can be specified by very few parameters
called ‘degrees of freedom’. In fact, you need only three of these to specify
the state of an electron in a hydrogen atom, if we ignore the spins. (This
is similar to describing the position of a particle in space by specifying
three coordinates.)

For a hydrogen molecule made up of two hydrogen atoms we would require
more parameters: three each to specify the states of the electron in each
atom and a few more to describe the mutual interaction of the atoms. In
general, the larger the system, the more parameters needed to specify its
quantum mechanical state. Generally, a system of N particles needs about
3N numbers to specify its state. So for a cat weighing 1 kilogram with 1026
atoms in its body you would need about 3 x 1026 independent parameters to
specify the state of the cat completely. Such a description will be purely
quantum mechanical and will tell you everything about the cat. But to attempt
this would be crazy. When you think of a cat sitting in the corner of a
room, you specify far fewer parameters than this in describing the cat.
In other words, there are several possible quantum states of a cat which
will be acceptable to us as a fair description of the situation ‘there is
a cat sitting in the corner of this room’.

This fact – that in practice we can work with far less information than
is needed to specify a quantum mechanical system – changes the situation
drastically. Suppose we first develop a full quantum theory of a cat and
then ignore all the parameters or degrees of freedom we have not bothered
to measure. This can, in principle, be done mathematically by using a device
called a ‘density matrix’ developed by Eugene Wigner and others in the 1930s.
Such a computation shows that the effect of unobserved degrees of freedom
is to make the system behave as though it is classical, that is as we expect
it to behave.

So there is no fundamental difference between a classical system and
a quantum mechanical system. A system appears to behave more and more classically
as we start ignoring large numbers of internal parameters of the system.
This theory suggests that if we could devise an experiment to measure all
the parameters specifying a cat, we would find that the cat behaves as quantum
mechanically as an electron, and could exist in a combined state in which
it is both dead and alive.

MEASURING THE CAT’S TAIL

In the case of the cat, we divided the full set of parameters into two
parts: those which we observe and those which we don’t. This division is
quite arbitrary and only depends on what we are measuring. We might choose
to measure the length of the cat’s tail, for example, or we might ignore
it. Theoretical physicists call the unobserved degrees of freedom – such
as an unmeasured tail – the ‘environment’. Sometimes, a system we are studying
cannot be considered to be really isolated because it has a weak interaction,
or coupling, with its surroundings. The tail of the cat, for example, does
interact with the cat to some extent. In such a case, we cannot provide
a complete description of the system without taking into account what happens
to the environment. But very often we cannot observe and specify the quantum
state of the environment completely. This means that we have to ignore several
parameters which are, strictly speaking, part of the description of the
system.

This takes us back to our problem of how to observe the quantum universe.
The idea of unobserved degrees of freedom arises very naturally when we
attempt a quantum description of the Universe. We would require an incredible
amount of information to describe the quantum state of the Universe completely
– so much that it is not clear whether it is even possible in principle
to acquire and specify it. In practice, we have nowhere near enough information.
It is as though the quantum universe comes with its own environment which
is largely unobserved. The effect of ignoring these degrees of freedom is
make the system behave as though it is classical.

The existence of the unobserved degrees of freedom in the environment
suppresses the quantum mechanical interference and makes the Universe behave
classically. This is the process of decoherence. What is more, decoherence
is directly tied to the fact that classical systems are ‘large’. In fact,
the degree of classical behaviour exhibited by a system will be directly
related to the size of the system.

During the past four years, Murray Gell-Mann of California Institute
of Technology and James Hartle of the University of California have been
among the researchers trying to develop these ideas in order to understand
the evolution of our Universe. Their work suggests that decoherence plays
a crucial role in the observed classical nature of our Universe. In principle,
a quantum mechanical description of the Universe has to take into account
all possible past histories of the Universe. Gell-Mann and Hartle find that
only a fraction of these various histories will behave classically. The
process of decoherence seems to play a role in deciding how acceptable classical
histories can be singled out. Our Universe, it seems, behaves like a big
Schrodinger’s cat.

Thanu Padmanabhan is a member of the Astrophysics Faculty of Tata Institute
of Fundamental Research, Bombay. He is at present a visiting professor at
the Inter-University Centre for Astronomy and Astrophysics, Pune. Further
reading: In Search of Schrodinger’s Cat by John Gribbin (Black Swan, 1984).
The Emperor’s New Mind by Roger Penrose (Oxford UP, 1991).

* * *

Interference and decoherence

A general feature of quantum mechanics is that physical systems behave
differently when they are being measured by a classical device. The physicist
Richard Feynman illustrated it like this. He imagined an electron gun emitting
a stream of electrons, with two screens placed in front of it (see Figure).

Any electrons that pass through the slits A and B can be detected at
the screen XY. If we blocked slit B we would find that most of the electrons
appear in the top half of the screen (curve 1); if we blocked slit A they
would appear in the bottom half (curve 2). If both slits are open, we might
expect the electrons to be distributed as in curve 3 – the sum of those
arriving through A and B. In fact, what we see is a wavy pattern something
like curve 4.

If we look more closely, we find that this means some parts of the screen
receive fewer electrons with both slits open than with just one open. This
does not fit in with our assumption that each electron goes through either
A or B.

According to quantum theory there is a probability amplitude – let’s
call it x – for an electron passing through slit A, and y for the same electron
to go through slit B. The total probability amplitude for an electron to
reach the screen, somewhere, with both slits open is then (x+y). According
to the rules of quantum theory, the number of electrons that will reach
any point is proportional to the square of the amplitude, that is, (x+y)
², which is equal to x ² + y ² +2xy.

But just adding together the probability amplitudes that tell us how
many electrons arrive when only one of the slits is open only gives us x
² + y ². Where does the extra 2xy come from? This
term is the interference between the amplitudes x and y and it is a purely
quantum mechanical effect.

If we then make our experiment more sophisticated, by tracking the path
of each electron to try to determine which slit each one went through, we
no longer see the wavy pattern, but curve 3. If we watch the electrons,
each one goes by a ‘classical’ path. The behaviour of the system depends
on whether we are observing it or not. The act of observing the system destroys
the interference and – mathematically speaking – suppresses the term 2xy.
We conclude that it must be the classical apparatus doing the observing,
or making the measurement, that is responsible (see ‘Quantum rules, OK’,
Inside Science No 25, New ÐÓ°ÉÔ­´´, 1989).

This fact – that systems behave differently where they are coupled to
a classical measuring device – can be understood in terms of a process called
decoherence. When a classical measuring device is linked to a quantum mechanical
object, the physical system that incorporates both of them has several independent
parameters or degrees of freedom – that is, the total energy of the system
can be distributed in several different ways.

But we only ever use a small number of these degrees of freedom to describe
the outcome of any measurement that we make. Ignoring large numbers of degrees
of freedom leads to the phenomenon known as decoherence, which essentially
suppresses the quantum interference between these different alternatives.