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Chapters II-V of Quantum Mechanics
Chapters II-V of Quantum Mechanics of
The Bible According to Einstein
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Copyright ©1999 by
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To Chapter I 
To Chapters VI-XIII 
212 The Bible According to Einstein
Chapter II: Paths
Ask among all paths, which is the good way?
And walk therein, for ye shall find there peace.
Now quantum mechanics
has two formulations. And the first is the
path integral. Now the position of a moving particle
as time evolves shall constitute the particle's trajectory. Thus
a trajectory shall be a curve through space and
time. And because it is a curve in space and time, it
shall also be a path. And a point on the path
at a particular time shall be the position of the particle.
The New Testament 213
And it is as though thou walkest along a wooded
valley trail between two mountains. And thou beginst
thy walk at the beginning of the trail. And thirty
minutes later, thou hast traversed one mile
of track. And one hour later, thou art two miles
from the start. And two hours later, thou finishest
thy walk. And since thou traverst the trail
in a steady manner, anyone knows where
thou art at any time. Thy motion is predictable. And
thy positions at various times constitute
a known trajectory. Thus in this example, the
trajectory is the trail itself.
Now in classical mechanics, there shall
be but one trajectory, or path. And this
path shall be computable from Newton's laws. And it
shall be called the classical trajectory. And
knowledge of this path shall provide knowledge
of the position of any object in the future, at
the present, or in the past.
In classical mechanics, it is as though thou
be infinitely lazy. And choosest thou the path
of least resistance. And avoidest thou
steep mountain slopes, so that thou walkest along
the center of the valley. And though thou
be tempted to take a short cut, it involves
climbing and descending. And thou mightest want to
pass along a longer, perhaps-more-scenic route, but
lazy as thou art, takest thou the easy path, the lazy path.
Only poets choose the path less travelled by.
And for thee, the classical trajectory shall be
the predictable, well-travelled trail. But in quantum
mechanics, thou shalt be free. Thou shalt be
allowed to walk along all paths.
Quantum mechanics -- it be
the democratization
of dictatorial classical-mechanics laws.
So in a quantum mechanical world, an object shall
transverse all paths. But some paths shall
be more preferable than others. And the
most preferred path of all shall be
the classical trajectory. And because all paths
are included, it shall be impossible to
predict with certainty where an
object be at a given moment. Thus uncertainty
shall be a property of quantum mechanics. And this
effect shall have a name -- the uncertainty principle
shall be its name.
And suppose thou livest in a quantum world and
thou beginst thy walk. Now in this quantum case, thou
dost not plan thy walk. And thou art only
somewhat lazy. So most of the time, movest thou
along the local trail of least resistance. But sometimes, decidest
thou to profit from a short cut. And sometimes, thou
decidest to ascend a little hill. And sometimes, thou
decidest to take a longer route. And these decisions
are made randomly but preferably, because
preferest thou the easy trails.
213 The Bible According to Einstein
And friends who are waiting for thee will
be frustrated and annoyed because they
do not know where thou be for sure. And
although it is most probable that thou art on or
near thy favorite well-travelled trail, thou perhaps
hast gone astray.
And this formulation of quantum mechanics shall be
called the path integral
because "integral" means "to include all."
Chapter III: Quantum Mechanics, Philosophers,
Scientists and God
And philosophers will
debate the meaning and implications of
quantum mechanics and be particularly concerned
about uncertainty. And many will be frustrated
and annoyed. But, as for the uncertainty principle, scientists
will understand it. And Nature simply shall obey it.
To decide and then revise. To
decide and then retreat.
Uncertainty will certainly confuse the wise.
And theorists using the rules of quantum mechanics
will carry out countless computations. And
the computations will all agree
with countless experiments performed
by experimentalists. And scientists will
develop a great trust in quantum-mechanical
dynamics. And for some scientists, the faith will
be as strong as a Christian's faith in God.
Now as a consequence of the uncertainty principle, it
shall be impossible to know simultaneously and
exactly the position and momentum of an
object.195 Thus position and
momentum in quantum mechanics shall
only probabilistically be known. And this
shall be completely different from the notion of
position and momentum in classical mechanics, where
they are known with certainty.
Chapter IV: The Planck Constant
and Quantum Hills
Now quantum mechanical behavior
and uncertainty shall be controlled by
a fundamental number. And this fundamental
parameter shall have a name -- Planck's constant shall
be called its name.
And theorists will pretend that they can
control Planck's constant. And if they play the
game of "god" and set the constant to zero, then
the classical and quantum worlds will coincide. And making
Planck's constant smaller shall be like making the slopes
of hills and mountains steeper. And so a somewhat
lazy walker will be forced to walk quite near
the trail of least resistance. And if the theorists
do play "god" and make the constant zero, then
they make the slopes of hills and mountains infinitely
steep -- with giant hands they fold together
mountains. And valleys turn into crevasses.
____________________
195 This effect
becomes particularly important for microscopic objects, such
as atoms and electons.
The New Testament 215
Walkers become completely trapped. And then even
the most energetic motivated hiker is compelled
to traverse the crack of least resistance. And since
this crack is the classical trajectory, the motion
shall be predictable and classical.
But in the real world, Planck's constant
is 6.6 x 10-34 Joule-seconds. Although
miniscule, it is nonetheless not
zero. And nobody, neither scientists, nor philosophers, nor
holy men, nor theorists can make the constant zero. Such
be written in firm stone. But since the constant
is so small, classical mechanics shall often
be a good approximation. And because the constant
is so small, quantum mechanical effects
shall only in the microscopic world
be manifest at all. Thus atoms, nuclei, nucleons, electrons, quarks
and other microscopic bodies shall feel
quantum effects, but living bodies, blocks and
balls shall not. And even in the microscopic
world, the hills and valleys shall be very small.
And ants may struggle to pass around a tiny pebble, rock
or clump of dirt, but elephants do not.
And quantum mechanics shall govern all --
All shall hearken to its song.
And quantum mechanics shall dominate the small.
Chapter V: Tunnelling
And quantum tunnelling
and barrier penetration shall be a consequence
of the uncertainty of paths. In the quantum
world, a marble in a coffee cup, in principle, may
suddenly jump out. A path exists which climbs the
cup and spout. And from the spout, quickly would the
marble fall. But for this path, the probability
is very very small. And during the lifetime
of the Universe, the marble will not jiggle its way out.
But in the subatomic world, a body has a
better chance to climb a wall. And sometimes, like
an army scout who leaves the troops and climbs a
little hill, a particle will jump and manage to
get out. How foreign from the world of man be the world
of the quantum and the small. And if a microscopic
particle should suddenly surmount a wall, one need
not shout nor be alarmed -- this is what barrier
penetration is about.
Now a process, which proceeds along a quantum path
through a classically forbidden region, shall by
definition be quantum tunnelling or barrier penetration. And
the decay of a radioactive nucleus shall take place
by means of quantum penetration. Such a nucleus
shall be like unto a marble in a cup.
Quantum mechanics shall be
full of fluctuations for objects of small size.
The quantum wings shall flap
like unto the wings of butterflies.
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To Chapters VI-XIII
Copyright ©1999 by
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