Special Relativity in Week One: 1) The Principle of ... - Loreto-Unican

went up in the air over Boston, the Earth turned for threehours under the plane, and then the plane came back down inSan Francisco. It was the Earth that moved, not the plane.Definition of the principle of relativityThe stage is now set for a more precise definition of theprinciple of relativity. Imagine that you are in a capsule andyou may have any equipment you want inside the capsule. Theprinciple of relativity states that:There is no experiment that you can performthat will allow you to determine that thecapsule is moving with uniform motion.We point out that our classroom is such a capsule. Due tothe rotation of the Earth, the motion of the Earth about theSun, the fact that the Sun is carried around by rotation ofthe Milky Way galaxy, and then there is the expansion of theuniverse, all these contribute to the motion of our classroom.But only the rotation of the Earth, which carries us aroundin a circle every 24 hours, has been directly observed. Whenyou are moving in a circle, you are not moving in a straightline. This slight deviation from uniform motion can bedetected with a Foucault pendulum.Speed of wavesThere is one experiment that was expected to allow us todetect uniform motion. That experiment involved the measurementof the speed of a light wave.To illustrate why such an experiment might be important,we start with an analogous experiment that is easier to observe.It is the measurement of the speed of a compressionalpulse on a stretched Slinky. Figure 2 is a photograph of astretched Slinky suspended from a steel pipe. There is a supportingthread from the pipe down to every fourth coil of theSlinky.If you pull back on one end of the Slinky and let go, you geta compressional pulse like the one shown in Fig. 3, that travelsdown the Slinky, reflects at the far end, and returns. Althoughwe had demonstrated these Slinky pulses for many years, onlyrecently did we do a careful analysis of the speed v pulse of acompressional pulse. The result was v pulse= KL / µ , where Kis the Hooke’s law spring constant, L the length of the Slinky,and m its mass per unit length. 3,4A phenomenon observed by David Keeports 5 is that thetime it takes for the pulse to travel down the spring and comeback does not depend on how much you stretch the spring. Tosee why, write the mass per unit length as m = m/L, where m isthe mass of the spring. Then our formula for v pulse becomes2vpulse = KL = KL = LK .m / L m mThe time T it takes the pulse to go down and back, a distance2L, is T = 2L/v pulse . The factors of L cancel, with the resultthat T should not depend on L. Figure 4 shows our test of thisfeature of the pulse speed formula. We tripled the length ofthe Slinky from 83 cm to 260 cm, and the time the pulse tookto go down and back changed by only one video frame, 2.83 sto 2.87 s.The point of our Slinky experiment is that we have a formulafor the speed of the Slinky wave pulse, and that we canuse a video camera and simple algebra to precisely test thatformula.Relative motionThe next experiments are where we study my motion relativeto the Slinky. As shown in Fig. 5(a), I hold a meterstickSunSunFig. 2. Slinky suspended by threads from a pipe.supersonic jetsupersonic jetBostonSanFranciscoSanFranciscoBostonFig. 3. Compressional pulse.rotatingEarthrotatingEarthFig. 1. A hypothetical trip from Boston to San Francisco.Fig. 4. We tripled the length of the Slinky and the pulse tookone more video frame to go down and back.The Physics Teacher ◆ Vol. 49, March 2011 149