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CAUGHT ALIVE AND DEAD

By Vijesh Kamath
The Deccan Herald
Wednesday, September 30, 1998  

Hey Jerry! how about checking if I am alive? VIJESH KAMATH throws
insights into the famous Schrodinger cat paradox in quantum physics
dealing with simultaneous dual existence of a system.

ONE of the founders of quantum theory, Erwin Schrodinger published the
''cat paradox`` in 1935 to bring out the absurdity in the
probabilistic interpretation of his famous wave equation. Since then,
there been a debate among physicists whether one could conduct a real
experiment on similar lines as the 'thought experiment` proposed by
Schrodinger.

Recently, physicists at the National Institute of Science and
Technology in the United States have indeed succeeded in conducting
such an experiment. A team lead by C Monroe conducted an experiment
wherein a Beryllium ion was made to oscillate in the quantum level
corresponding to the zero-point energy of a harmonic oscillator
resulting in 'Schrodinger cat`- like states. The team has published
the results of the experiment in the journal Physical Review.

What is the Schrodinger cat paradox? 

Before we try to understand the paradox, it is necessary to understand
the contrasting features of classical and quantum mechanics.

Classical Newtonian mechanics is deterministic. By giving the state of
the system at an initial time, the evolution of a system can be
predicted once the solution of the equation of motion is fixed.
Ideally, a classical system can be observed without disturbing the
state of the system. In contrast, to these properties of classical
systems the time evolution of quantum systems is given by the
solutions of the Schrodinger equation. The solutions of the equation,
when used to solve a particular system are called 'wave functions`.
They can be expanded in terms of superposition of observable states
called the 'eigen states`. According to quantum theory, the act of
observing a quantum system disturbs the system and the solutions of
the Schrodinger equations can only predict the probabilities that can
be associated for finding the system in different eigen states.

This probabilistic notion was brought out in a series of 'thought
experiments` proposed by Albert Einstein and Niels Bohr during the
development of the quantum theory. A thought experiment consists of
description of an experiment that can be done in principle and that
which brings out the difference between the way the state of a system
is given in classical and quantum theory.

Schodinger visualised a cat placed in a closed chamber in which a
radioactive atom is used to trigger a device that will release poison
inside the chamber. To make his arguments simple, he suggested that an
atom which has equal probability of emitting an electron in one hour
and of remaining undecayed be placed inside the chamber with the cat.
The emitted electron as it carries an electric charge is planned to
trigger a Geiger Mueller counter which can give a surge of voltage
which in turn opens a phial containing poison.

The cat and the atom are placed in the chamber for one hour. It is
obvious that only two things can happen - if the atom has decayed
during the hour the cat would have died due to the release of poison
from the phial. If the atom has remained undecayed the cat would be
found alive when the box is opened. The probability of finding the cat
alive or dead on opening the box after one hour is half.

The paradox arises only when we consider the quantum theory. According
to quantum theory, the cat is neither dead nor alive before the
chamber is opened, but in a state which is a superposition of both the
states that is alive + dead. It is not until a measurement is made
which in this case is by opening the chamber and looking at the cat
that the wave function that describes the cat changes from 'half dead
- half alive` to either the wave function of alive cat or the wave
function of a dead cat. This sudden change in the state of a system
when a measurement is performed is described as collapse of the wave
function. This state is known as the 'Schrodinger cat state`. 

Therefore, according to quantum theory one knows whether the the cat
is dead or alive only when one opens the chamber and not by knowing
whether the atom has decayed or not as in the classical case.

Many theories have been put forth to get over the paradox. Most
physicists believe that these considerations do not affect the
measurements on theory they use on atomic size systems and hope that
somewhere between atoms and cats quantum physics turns into classical
physics. 

Some other popular theories are: 1) Mind over Matter: An
interpretation which supposes that wave function changes involves the
conscious mind that behaves differently from other objects in the
universe. 2) Many Worlds: Interprets that when the cat is observed the
universe splits into two, one in which the cat is alive and one in
which the cat is dead. In this view there would be countless parallel
universes that result from splitting of all the measurements that have
occured in the course of time!

Now, coming back to the experiment of Moroe and his team, they used a
Beryllium neutral atom to drift in an electromagenetic trap and one of
its electrons was stripped off to confine the ionised atom
electromagnetically by a harmonic force.

They then laser cooled the ion and made it oscillate in the quantum
level corresponding to the zero-point energy of a harmonic oscillator.
In this situation they found that the ion settled virtually motionless
at the centre of the trap. The ion can exist in two hyperfine ground
states. The two states which may be called spin up and spin down were
found separated in frequency by 1.25 GHz. Quantum theory tells us that
at any instant the ion has an equal probability of being in any one of
the two states. Now, they pushed apart the ion in the two states by
applying a pair of laser beams which drive the harmonic oscillator at
the natural vibrational frequency of the trap.

The team found that each force sets the ion in motion with the spin-up
and spin-down state respectively. The result was that two wave packets
which are tied up to one or the other hyperfine internal states of the
ion begin to oscillate with a constant phase difference. Although
there are two localised wave packets, there is only one atom. The
Schrodinger cat like states has been achieved experimentally.

Einstein did not like the probabilistic nature of the quantum theory.
He once said ''God does not play dice with the universe``, but quantum
theory correctly describes results of real experiments.

Source - http://www.deccanherald.com/deccanherald/sept30/jerry.htm

Jai Maharaj
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