No abstract

We present the problem of relativistic torques with particular reference to the right-angle lever problem and outline a simple solution. The important elements of our solution are, first, a reexamination of the classical relation between torque and angular momentum and, second, the consequent realization that in relativistic analysis there exists a net internal torque which exactly cancels the net external torque experienced by an extended body in dynamic equilibrium. We find that the lever has constant angular momentum according to all Lorentz inertial reference systems and that this is consistent with the relativistic relationship between torque and angular momentum. Our solution is not restricted to relativity. It is valid for a wider class of theoretical frameworks.

In a previous paper, it was proposed that the cosmological term in Einstein's field equations be huge. This proposal heuristically followed from the combination of Leibniz' principle, Einstein's general relativity, and the observational dominance of Euclidean geometry. This paper presents preliminary results of a treatment of the large A field equations which holds promise of yielding quantum wave mechanics with no additional assumptions.

Cerium hexaboride is an antiferromagnetic metal with a Néel temperature of 3°K. The high-temperature inverse susceptibility of this material is observed to decrease with decreasing temperature more rapidly than would be expected from a Curie-Weiss law. Since the temperature at which this deviation appears is much higher than the eventual ordering temperature, short-range ordering effects should be negligible. Also, it can be shown that crystal-field effects alone cannot produce such a decrease in χ−1. In this paper we offer a possible mechanism which explains this behavior. Basically, we assume that the Ce–Ce exchange arises through an indirect exchange involving the conduction electrons. We visualize the conduction electrons as moving in the spaces between the boron complexes so that the magnitude of the s-f exchange will be different for the different crystal-field states of cerium. In a cubic field the 2F5/2 state of Ce3+ splits into a Γ7 and a Γ8. Low-temperature measurements of the saturation moment indicate that the Γ7 state lies lowest. Therefore, as the temperature decreases, the Γ8 state, which protrudes into the space between the borons and, hence, contributes strongly to the s-f exchange, is frozen out, leaving only the weakly coupled Γ7 state.

A division algebra of highest possible dimension is the eight-dimensional Cayley algebra. This remarkable property of mathematics suggests an intimate fundamental connection between Cayley algebras and descriptions of the physical universe. On this basis, it is suggested that Einstein's field equations with the huge A proposed by this author elsewhere be factored by use of such an algebra. This factorization promises to yield Diraclike spinor quantum wave equations.