This page is a complement to the book:
Why has no one come
up with a time machine? Time travel has long excited man's imagination.
And, while it has been a long standing fantasy, the asymmetry of time
and our inability to move both forward and backward in time has long
been a nagging thorn in the side of theoretical physics. The problem is
that the microscopic constituents of matter behave symmetrically in
time. For every trajectory of a collection of elementary
particles that moves one-way into the future, there is a
corresponding trajectory that moves in precisely the opposite fashion
into the past; each trajectory is equally viable. Furthermore, there is
a one-to-one correspondence.
So why do we see only events that move into the future, things that
have never happened before, systems with ever increasing disorder? This
is the time-asymmetry paradox. The author "will resolve this paradox in
a simple, straightforward fashion. Fundamentally, it is a matter of
counting."
But there is more, a bonus: This book is also something of a science
memoir. Besides dealing with this paradox in time, the author takes a
Joycean romp through such diverse topics as: humor as an adaptive
trait, the conflict between determinism and free will, the ear as an
impedance-matching device, the biology of happiness, the rainbow
paradox, why we get energy from taking atoms apart (fission) and
putting them together (fusion), why flags flap, and why dogs wag their
tails.
There is time for whimsy and exploration in A Paradox in Time.
As an addendum to the book, there are a few interactive applications
that illustrate various topics. They are:
- The law of large numbers (actually a variant thereof) demonstrates
the fact that for systems with a large number of components, there is one
macrostate which is overwhelmingly more probable than any other at the
given energy, volume and particle numbers.
- Newton's reasoning that led him to his theory of gravity is
illustrated in this example linking the motion of a projectile here on
earth and the motion of the moon about the earth and the planets about
the sun.
- Temperature is defined as the reciprocal of the slope of the
entropy vs. energy curve. This application shows that that is not as ridiculous
a definition as it sounds.
- Time asymmetry paradox: This application demonstrates how a
system will behave asymmetrically in time even though it is composed of
elementary particles that behave symmetrically in time, .
- A rainbow paradox: The rainbow is caused by light from the sun
that is reflected from falling raindrops. But each drop reflects that sunlight
in exactly the same way. So, if the sky is uniformly filled with
reflecting raindrops, all of which are doing exactly the same thing, why
do we see that colored arch in the sky we call the rainbow, and why is
it at 42 degrees relative to the earth-sun line? Those of philosophical
inclination question whether there is a sound in the forest when a tree
falls, if there is no one there to hear it. (There is an acoustic vibration,
but this translates into the sound we hear only if there is an ear present.
Not a particularly cogent observation.) Much more appropriate is the question:
Does a rainbow exist if there is no one there to see it? The answer is
definitively, No. Why? Hint: Notice that the rainbow is always centered
on the observer. As the observer moves, the rainbow moves; hence the old
saw that you can never retrieve the pot of gold at the end of the rainbow.
These applications will be found in the two downloads, one for the Mac OS and one for the Windows
OS. They are each about 3.5 Megabytes.
This page last modified on: February 13, 2007.
If you have problems or comments, please e-mail Jim Hurley