Letter to the Editor
The Crunch Is On, Maybe!
From: PSCF 46 (December 1994): 283-284.
I was amazed to read Crenshaw's demonstration that scientists do not know what they are talking about (Perspectives, June 1994, p. 148). His claim struck me as something that belonged rather in the National Enquirer. One gross error he makes is the assumption that scientists give real definitions, whereas they only give instrumental descriptions. His demand for a proof of the "force of gravity" requires science to deal with essences. It can't.
An equally grave error assumes that a field erases a force. But the incorporation of three of the four fundamental forces (strong, weak and electromagnetic, but not gravitational) into a single unified field theory has not disposed of them. Even realization of the theorists' hope of including gravity in a grand unified theory will not eliminate any of these forces. In addition, in direct contradiction to Crenshaw's argument, Einstein's General Theory of Relativity does not alter the range of gravity.
A more subtle error is Crenshaw's unrecognized assumption that the universe is Euclidean. He seems totally unaware of the assertion, fundamental to both Newtonian and Einsteinian physics, that the path of a beam of light is a straight lineˇEuclidean for Newton, Riemannian for Einstein. A finite Euclidean geometry must have boundaries. A Riemannian may be finite and unbounded, which is the way Einstein's theory describes the universe. Neither Euclidean not Lobachevskian geometries can have this characteristic.
The simplest possible Riemannian geometry can be mapped onto the surface of a Euclidean sphere. Riemannian straight lines, in this mapping, are great circles, like the equator or the meridians of longitude of the earth. Just as one cannot reach the edge of the earth and fall off, so one cannot reach the edge of the Riemannian plane, even though it is finite. This variety of geometry, in four dimensions with some incredibly complex characteristics, underlies Jeans' reference, which Crenshaw cites. It precludes "bending space-time in numerous other║ directions."
It appears that Crenshaw has read some science popularizations, misunderstood them, added his own presuppositions, and produced nonsense. He violates a rule of thumb generally applicable to academic disciplines: If it sounds stupid, you've misunderstood it. A technical statement may be wrong, but it is not silly. No scientist, let alone an entire discipline, would have missed such obvious corrections, were they germane. Predictions of a "Big Crunch" must be decided by empirical measurements of the total amount of matter in the universe. The difficulties inherent in the determination leave the question open at present.
David F. Siemens, Jr., Ph.D.
2703 E. Kenwood St.
Mesa, AZ 85213-2384