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 10⁷⁰ strokes in order to expect one success. The universe is thought to be around 15 billion years old (equal to 5 x 10¹⁷ seconds) and therefore, swinging at the rate of one stroke each 5 seconds, this would require about 10⁵³ 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 10⁷⁰ strokes added to his score by taking the one stroke penalty and dropping within two club lengths of the present ball position.

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