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Spacetime Diagram Explorer

Spacetime Diagram Explorer
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2014-09-26 19:15
VectorTrigonometryCoordinate GeometryCalculusGeometric Construction
This example demonstrates how to construct spacetime diagrams, light cones, and causality concepts. It involves core mathematics like spacetime coordinates, Lorentz transformations, and geometric representations of light cones. Constructed using GeoGebra commands like Point, Rotate, Angle, Line, Ray, Intersect, Segment, Polygon, Mirror, and objects such as β, A, B, θ, O, etc. Suitable for high school students and enthusiasts in physics or mathematics for exploring relativistic concepts.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Rotate(B, θ, O) → B'
  4. Angle(B, O, B') → α
  5. Rotate(A, (-θ), O) → A'
  6. Angle(A', O, A) → γ
  7. Line(O, A') → CtPrime
  8. Line(O, B') → XPrime
  9. Rotate(B, 45*°, O) → B'_1
  10. Angle(B, O, B'_1) → δ
  11. Ray(O, B'_1) → FortyfiveDegreeLine
  12. Line(O, A) → Ct
  13. Line(O, B) → X
  14. Line(Event1, XPrime) → E1CtPrimeProjection
  15. Intersect(E1CtPrimeProjection, CtPrime) → C
  16. Segment(Event1, C) → b
  17. Line(Event1, CtPrime) → E1XPrimeProjection
  18. Intersect(E1XPrimeProjection, XPrime) → D
  19. Segment(Event1, D) → c
  20. Line(Event1, X) → E1CtProjection
  21. Intersect(E1CtProjection, Ct) → E
  22. Segment(Event1, E) → d
  23. Line(Event1, Ct) → E1XProjection
  24. Intersect(E1XProjection, X) → F
  25. Segment(Event1, F) → f
  26. Line(Event2, XPrime) → E2CtPrimeProjection
  27. Intersect(E2CtPrimeProjection, CtPrime) → K
  28. Segment(Event2, K) → e
  29. Line(Event2, CtPrime) → E2XPrimeProjection
  30. Intersect(E2XPrimeProjection, XPrime) → L
  31. Segment(Event2, L) → h
  32. Line(Event2, X) → E2CtProjection
  33. Intersect(E2CtProjection, Ct) → M
  34. Segment(Event2, M) → g
  35. Line(Event2, Ct) → E2XProjection
  36. Intersect(E2XProjection, X) → N
  37. Segment(Event2, N) → a
  38. Polygon(Event1, P, Q) → poly1, q, event1, p
  39. Mirror(Event1, E1CtProjection) → Event1'
  40. Mirror(P, E1CtProjection) → P'
  41. Mirror(Q, E1CtProjection) → Q'
  42. Polygon(Event1', P', Q') → poly1', q', event1', p'
  43. Polygon(Event2, R, S) → poly2, s, event2, r
  44. Mirror(Event2, g) → Event2'
  45. Mirror(R, E2CtProjection) → R'
  46. Mirror(S, E2CtProjection) → S'
  47. Polygon(Event2', R', S') → poly2', s', event2', r'

AI Drawing Prompt Reference

Draw a spacetime diagram with two events Event1 and Event2, and their projections on the X axis, X' axis, Ct axis, and Ct' axis. Rotate points B and A using angle β to construct light cones and causality. Draw lines and rays, and use intersection and reflection operations to show the projections of events in different coordinate systems.
The prompt above was compiled from the original drawing commands and is for reference only.