Sample Problem and Lorentz Transformations A target of interest lies at a spacelike spacetime interval of 21 light-years from the Earth. A rocket travels to the target at velocity = 21/29, so that in the Earth rest frame 29 years pass on Earth v/c while the rocket travels to the target. Upon reaching the target, the rocket immediately rotates so as to return to Earth. During the return journey, 29 years are observed to pass on Earth as the rocket crosses a spacelike spacetime interval of 21 light-years. Figure 1 depicts this rocket journey from the Earth to the target and back as observed in the Earth rest frame in a standard spacetime diagram. All general relativistic, Hubble expansion, and other corrections have been ignored so that calculations can be kept strictly special relativistic. The origin has been placed at the rocket arrival at target event to facilitate comparisons between different reference frames and enhance visualization of the effects of Lorentz transformation. Figure 2 illustrates the results of the Lorentz transformation between the Earth rest frame event spacetime coordinates and a frame at rest with the first half of the rocket motion, the outbound rocket. Figure 3 shows the results of the Lorentz transformation between the Earth rest frame event spacetime coordinates and a frame at rest with the second half of the rocket motion, the return rocket. Figure 4 depicts the standard spacetime diagram of the rocket journey in the rest frame of the rocket. This involves a spacetime rotation about the rocket when it arrives at the target, which is the origin in all four figures. In particular, both coordinates of the Earth, i.e., space and time, change signs due to this rotation. All event spacetime coordinates
Sample Problem and Lorentz Transformations A target of interest lies at a spacelike spacetime interval of 21 light-years from the Earth. A rocket travels to the target at velocity v/c = 21/29, so that in the Earth rest frame 29 years pass on Earth while the rocket travels to the target. Upon reaching the target, the rocket immediately rotates so as to return to Earth. During the return journey, 29 years are observed to pass on Earth as the rocket crosses a spacelike spacetime interval of 21 light-years. Figure 1 depicts this rocket journey from the Earth to the target and back as observed in the Earth rest frame in a standard spacetime diagram. All general relativistic, Hubble expansion, and other corrections have been ignored so that calculations can be kept strictly special relativistic. The origin has been placed at the rocket arrival at target event to facilitate comparisons between different reference frames and enhance visualization of the effects of Lorentz transformation. Figure 2 illustrates the results of the Lorentz transformation between the Earth rest frame event spacetime coordinates and a frame at rest with the first half of the rocket motion, the outbound rocket. Figure 3 shows the results of the Lorentz transformation between the Earth rest frame event spacetime coordinates and a frame at rest with the second half of the rocket motion, the return rocket. Figure 4 depicts the standard spacetime diagram of the rocket journey in the rest frame of the rocket. This involves a spacetime rotation about the rocket when it arrives at the target, which is the origin in all four figures. In particular, both coordinates of the Earth, i.e., space and time, change signs due to this rotation. All event spacetime coordinates
AAPT%20Poster_stephen_rodrique.docx