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Prelude: GR for the Common Man

Prelude: GR for the Common Man. Intro Cosmology Short Course Lecture 1 Paul Stankus, ORNL. Same path through space-time. Same subjective elapsed time. What is Calvin & Hobbes’ primary misconception?.

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Prelude: GR for the Common Man

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  1. Prelude: GR for the Common Man Intro Cosmology Short Course Lecture 1 Paul Stankus, ORNL

  2. Same path through space-time Same subjective elapsed time What is Calvin & Hobbes’ primary misconception? Subjective time -- “proper time” -- is a fundamental physical observable, independent of coordinates

  3. Newtonian: Most general: (dt, dx) x t gmn Metric Tensor B. RiemannGerman Formalized non-Euclidean geometry (1854)

  4. Assuming Newton found parking…. t for all paths Car You Me x Bank News Stand Galilean/ Newtonian

  5. t Down-going muon decays Down-going photon Lab Stopped muon decays 2.2 msec Down Up Basement x Basement detector Cosmic ray lab Down-going muons v < c Lifetime of down-going muons > 2.2msec We observe:

  6. Rest frame of lab-stopped muon Rest frame of down-going muon t t’ Curve of constant Dt=2.2 msec x x’ H. Minkowski German “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (1907)

  7. The Twin “Paradox” made easy t Castor inbound DT Pollux at rest Castor outbound It’s just that simple! x DX

  8. New, generalized laws of motion B t 1. In getting from A to B, all free-falling objects will follow the path of maximal proper time (“geodesic”). A x 2. Photons follow “null” paths of zero proper time.

  9. Recovering Newton’s First Law t t B B T T A A x x e X X An object at rest tending to remain at rest

  10. Gravitational Red Shift t Photon period DtUpstairs DtUpstairs Photon period DtDownstairs DtDownstairs Up Down x Detector Upstairs Source Downstairs Non-inertial frame -- curved space!

  11. Motion in curved 1+1D space t B T T A x h Conservative (Newtonian) Potential!

  12. Albert Einstein German General Theory of Relativity (1915) Force law: action at a distance Isaac Newton British Universal Theory of Gravitation (1687) Metric: a local property

  13. Points to take home • Subjective/proper time as the fundamental observable • Central role of the metric • Free-fall paths maximize subjective time • Minkowski metric for empty space recovers Newton’s 1st law • Slightly curved space reproduces Newtonian gravitation

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