**Quantum Golf**

(C)1994, 1995 *Institute For Ordinary Research*

Rob Peterson, Director

**Recently, an unusual request was received
by the Institute. Local golfers are increasingly stymied
by trees on fairway edges. Question: can
the quantum mechanical "tunneling" effect
be of any help? Tunneling describes the fact
that an object which has insufficient energy
to pass through a barrier (at least according
to the classical laws of physics before the
discovery of quantum mechanics in the first
part of this century) does indeed have a
non-zero probability of surmounting that
barrier. The golfers wonder if it would be
worth the extra strokes to simply try to
hit the ball through the obstructing tree
and let the tunneling effect produce some
successes. The radiation of alpha particles
from some atomic nuclei is one example of
tunneling: the particles are strongly attracted
by the nucleus but because of the immense
number of times per second that each particle
attempts the escape (and due to the large
number of atoms contained in any small sample
of the material), a measurable number of
successes can occur each second. The scanning-tunneling
microscope seen in recent science reports
is another example of this process at work.
**

**In response to this clear need, a staff scientist
was assigned to calculate the probability
that a standard 45.6 gram golf ball, accelerated
to a typical velocity of 40 m/s, will penetrate
a 30 cm - diameter tree of average strength
(data for a healthy Spruce were used). Since
the Institute is dedicated to ordinary (non-advanced)
research, several approximations were used
to get 10^{-70} as the desired probability (that's 0.00000...[69
zeros in front of the one]....00001). The
most useful interpretation of this result
is that the golfer must make 10^{70} strokes in order to expect one success.
The universe is thought to be around 15 billion
years old (equal to 5 x 10^{17} seconds) and therefore, swinging at the
rate of one stroke each 5 seconds, this would
require about 10^{53} times the age of the universe to accomplish.
The Institute therefore recommends that tunneling is not
a viable solution to the golfing dilemma.
In addition to the benefit of being home
on time for dinner, the golfer can avoid
the extra 10^{70} strokes added to his score by taking the
one stroke penalty and dropping within two
club lengths of the present ball position.**

{IFOR-101}