Lorentz contraction, Bell's spaceships and rigid body motion in special relativity

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. 1 “Lorentz contraction ” in special relativity We have put the term “Lorentz contraction ” in quotes, because, as we will explain, Lorentz contraction is not what actually occurs for a moving object in special relativity (SR). This is well known to most physicists, but too often “Lorentz contraction ” is given a spurious physical reality. Lorentz contraction is so called because H. A. Lorentz proposed an actual physical contraction of a moving object as an explanation of the null result of the Michaelson-Morley experiment, thus preserving the aether[1]. Lorentz’s equation for the length L ′ of a rod moving at velocity v was 1 L ′ = L/γ, with γ = 1 √ , (1) 1 − v2 where L is the length the rod would have at rest. The same equation with similar motivation had been suggested previously by G. F. Fitzgerald[2], and the effect is often called “Lorentz-Fitzgerald contraction”. Lorentz and Fitzgerald attributed this physical contraction to new electromagnetic molecular forces within a moving rod with concomitant stresses and strains. Although there is an equation identical to Eq. (1) in special relativity, ∗ Internet address: