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The meaning of Lorentz contraction in special relativity and its connection with Bell's spaceships parable is discussed. The motion of Bell's spaceships is then compared with the accelerated motion of a rigid body. We have tried to write this in a simple form that could be used to correct students' misconceptions due to conflicting earlier treatments. * Internet address: Jerry.F@TEMPLE.EDU 1 We are using units with c = 1.

Motivated by recent work involving the graviton-graviton tree scattering amplitude, and its twin descriptions as the square of the Bel-Robinson tensor, B µναβ , and as the "current-current interaction" square of gravitational energy pseudo-tensors t αβ , we find an exact tensor-square root equality B µναβ = ∂ 2 µν t αβ , for a combination of Einstein and Landau-Lifschitz t αβ , in Riemann normal coordinates. In the process, we relate, on-shell, the usual superpotential basis for classifying pseudo-tensors with one spanned by polynomials in the curvature.

We consider the one-dimensional motion of a particle randomly accelerated by Gaussian white noise on the line segment 0ϽxϽ1. The reflections of the particle from the boundaries at xϭ0,1 are inelastic. The velocities just before and after reflection are related by v f ϭϪrv i , where r is the coefficient of restitution. Cornell, Swift, and Bray ͓Phys. Rev. Lett. 81, 1142 ͑1998͔͒ have argued that there is an inelastic collapse transition in this system. For rϾr c ϭe Ϫ/ͱ3 the particle moves throughout the interval 0ϽxϽ1, while for rϽr c the particle is localized at xϭ0 or xϭ1. In this paper the equilibrium distribution function P(x,v) is analyzed for rϾr c by solving the steady-state Fokker-Planck equation, and the results are compared with numerical simulations.

Baryon magnetic moments and beta decay ratios (G A /G V ) are calculated in a phenomenological quark model. Non-static effects of pion exchange and orbital excitation are included. Good agreement with experiment is found for a combined fit to all measured baryon magnetic moments and beta decay ratios. The model predicts an antiquark content for the proton that is consistent with the Gottfried sum rule.

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Relations between baryon magnetic moments are derived which are independent of orbital corrections, relativistic corrections, and two-body exchange corrections (and generally any two-body correction) in the quark model, provided that the wave-function contributions leading to these corrections are SZ7^-symmetric. Among the relations derived are M(S~)+3/I(S°) = 6/X(A)+2JU(S + )-3fi(p)-/*(») (independent of quark moments) and ju (S°) -M (E~) = M (p)+2/x (n) (if Mf l > = -2/*^).