1 / 14

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?.

rolf
Download Presentation

Prelude: GR for the Common Man

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related