To that end, it will be better to imagine Born rigid motion as a state achieved by something like a flotilla of Rather than the detailed material properties or other factors that would be needed to implement it in practice. Of a “perfectly rigid body” that responds to a push at one end with the far end moving instantly inĮxactly the manner needed to maintain the object’s shape becomes even more absurd in special relativity, which imposes a limit of the speed of light on the rate at which any such influence can propagate.īut our discussion here will be focused on the geometry of rigid motion in special relativity, The idealisation, often used in Newtonian physics, Happen automatically by virtue of its material properties. Order to maintain this state of rigid motion, or that the required distribution of forces across the object would Note, however, that we are not saying that no forces would need to be applied to the object in This means that any two observers fixed to neighbouring points on the object would measure their mutual separation as unchanging, and they could hold the two ends of a spring without it being stretched or squeezed as they moved. Object, and in the limit of the two points being infinitesimally close, we say the object is undergoingīorn rigid motion if the orthogonal distance between all such pairs of world lines is constant over time. We examine the world lines of any pair of points belonging to the In 1909, the German physicist Max Born suggested the following definition for rigid relativistic motion. Rotating or accelerating, observers attached to different points on the object might suffer the same kind of Necessarily just defer to the idea of an observer travelling with the object itself, because if the object is The object (the totality of the world lines of its constituent particles) in different ways. To ascribe different shapes to the same object, because those slices will cut through the world-tube of If you and I are in relative motion, our different ideas of “space”Īt some moment – the 3-dimensional slice through spacetime that lies orthogonal to our world lines – can lead us In the spacetime of special relativity, this issue becomes more subtle, since there is no universal way to slice Then we say that the object is undergoing rigid motion. Of each point in the object to its present location x i( t): x i( t) = E( t) x i(0) If we have a continuous 1-parameter family of such maps, E( t), that take the initial location x i(0) That preserves distances and angles is called a Euclidean isometry. In Newtonian physics, space obeys Euclidean geometry,Īnd the set of points that an object occupies at any given time is an unambiguous Moving through space without changing its shape. In everyday life, we’re familiar with the idea of a three-dimensional object Back to home page | Site Map | Side-bar Site Map.Symmetries and the 24-cell | Average Shadows | Ball Bearings in a Hypersphere | Black Hole Passing | Born Rigid Motion | Catacaustics | Resonant Modes of a Conical Cavity | The Doppler Shift Triangle Law | Conic Section Orbits | Double-Crossing Orbits | Dihedral Angles | The Ellipse and the Atom | Find The Fake Coin | The Finite Fall | General Relativity in 2+1 dimensions | Howell’s Moving Orbits | Klein's Quartic Curve | Paparazzo vs Bodyguards | Light Mill applet | Littlewood applet | LRL made easy | The Mermin-Peres Magic Square Game | There Are No Corkscrew Orbits | Peeling the Octonions | Ordered Sums | Optimised Origami | Weak-field GR near a planar mass | Polar Orbits Around Binary Stars | The Rindler Horizon | Rotating Elastic Rings, Disks and Hoops | Constant Weight Rollercoasters | Steffen’s Polyhedron | Superpermutations | Symmetric Waves | Symplectic applet | The Tell-Tale Board | Exact values of regular 10j symbols.If you link to this page, please use this URL:.Born Rigid Motion - Greg Egan Born Rigid Motion by Greg Egan
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