Discover Spacetime in 1+1 Dimensions

Discover Spacetime in 1+1 Dimensions: one dimension of space, and one of time. Accurate, animated diagrams reveal its profound concepts. This series presumes no more than an education level of a university matriculation examination, as Einstein wrote of his own book on relativity. The focus is on seeing the concepts accurately, and on the physics, not on the algebra: the math is there, as geometry. And we build spacetime first on Newton's physics, where it is easier to see. The course has four modules: Introduction: velocity, on the diagrams we know from school. Galilean spacetime: Newton's space and time, studied with the tools of relativity. Minkowski spacetime: discover special relativity, and why the twin who accelerates comes back younger. Schwarzschild spacetime: Einstein's gravity, and why Newton, sitting under his tree, was accelerating in spacetime, and the falling apple was not. Chapters 0:00 Welcome 1:31 1 Introduction 8:34 2 Galilean spacetime 16:04 Spacetime velocity and our first metric! 27:04 3 Minkowski spacetime 39:06 Study the effects of relativity 48:09 Apparent paradoxes explained 55:19 Ride an accelerated worldline 1:06:51 4 Schwarzschild spacetime 1:22:50 Closing words References, numbered as on each slide 0.01 Outline 1. A. Einstein, Über die spezielle und die allgemeine Relativitätstheorie, Vieweg (1917); transl. R. W. Lawson (1920) 2.02 The Galilean transformation 1. P. Frank, Sitzungsber. Akad. Wiss. Wien IIa 118, 373 (1909) 2. G. Galilei, Dialogo sopra i due massimi sistemi del mondo (1632) 3. I. Newton, Philosophiae Naturalis Principia Mathematica (1687) 2.06 The Galilean transformation 1. H. Minkowski, Phys. Z. 10, 104 (1909) 3.01 The speed of light 1. J. C. Maxwell, Phil. Trans. R. Soc. Lond. 155, 459 (1865) 2. A. A. Michelson, E. W. Morley, Am. J. Sci. 34, 333 (1887) 3. H. A. Lorentz, Proc. KNAW 6, 809 (1904) 4. H. Poincaré, C. R. Acad. Sci. Paris 140, 1504 (1905) 5. A. Einstein, Ann. Phys. 17, 891 (1905) 6. H. Minkowski, Phys. Z. 10, 104 (1909) 3.04 The Lorentz factor 1. H. A. Lorentz, Proc. KNAW 6, 809 (1904) 2. A. A. Michelson, E. W. Morley, Am. J. Sci. 34, 333 (1887) 3.06 The Minkowski metric 1. H. A. Lorentz, Proc. KNAW 6, 809 (1904) 2. H. Poincaré, C. R. Acad. Sci. Paris 140, 1504 (1905) 3. H. Minkowski, Phys. Z. 10, 104 (1909) 3.10 Simultaneity at work 1. B. Rossi, D. B. Hall, Phys. Rev. 59, 223 (1941) 2. D. H. Frisch, J. H. Smith, Am. J. Phys. 31, 342 (1963) 3.11 The twin paradox 1. P. Langevin, Scientia 10, 31 (1911) 4.01 Einstein's gravity 1. A. Einstein, Jahrb. Radioakt. Elektron. 4, 411 (1907) 2. A. Einstein, manuscript (c. 1920), Collected Papers Vol. 7, Doc. 31 3. A. Einstein, Sitzungsber. Preuss. Akad. Wiss., 844 (1915) 4. K. Schwarzschild, Sitzungsber. Preuss. Akad. Wiss., 189 (1916) 4.02 The Schwarzschild metric 1. K. Schwarzschild, Sitzungsber. Preuss. Akad. Wiss., 189 (1916) 4.04 Parallel transport 1. T. Levi-Civita, Rend. Circ. Mat. Palermo 42, 173 (1917) 2. Compare Schild's ladder, in C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, Freeman (1973) 4.05 Geodesics in spacetime 1. E. F. Taylor, J. A. Wheeler, Spacetime Physics, 2nd ed., W. H. Freeman (1992) 4.06 Newton's apple 1. A. Einstein, Jahrb. Radioakt. Elektron. 4, 411 (1907) 2. A. Einstein, manuscript (c. 1920), Collected Papers Vol. 7, Doc. 31