Dierck-Ekkehard Liebscher

Relativity, geometry, and cosmology in pictures


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Abstandsmessung
Distance measurments



Spiegelung
Reflection



Perspektive
Perpective



Projektive Geometrie
Projective geometry



Kegelschnitte
Conics in particular



Minkowski geometry
Minkowski geometry



Lobachevski geometry
Lobachevski geometry



Aberration


Michelson


Raum-Zeit
Space-time



SRT Basis
SRT Basics



SRT zum Selbermachen
Do it yourself SRT



Stoßgesetze
Collisions



Krümmung
Curvature



Gravitation
Gravitation



Kosmologie
Cosmology



Kosmische Elementsynthese
Cosmic nucleosynthesis



Kosmische Strukturbildung
Cosmic structure



Kosmischer Hintergrund
Cosmic back-ground



Nagelpunkte
Cosmic pinpoints



Zeit und Entropie
Time and entropy



Quantenphysik
Quantum hysics



Supplements
 


Geometry of distances in pictures


moving scales around

Jakobsstab

Quadrant

Abplattung

Parallaxe

Sternstrom

Winkelgröße

Helligkeit

Hertzsprung-R.

Rotverschiebung

Entfernung

Doppelstern mit weißem Zwerg

Milchhstraße: Spiralstruktur


Verkehrsradar

Milchstraße

Struktur der Milchstraße

Struktur der Milchstraße

Scanning slow

Scanning fast

Reflections


Rakotz-Brücke

Badspiegel

Winkelspiegel

Mirror pair

Ping-Pong

Tennis

relative mass

equal masses

Geometry of reflections


static mirror

explorion in a moving mirror

explosion in head wind

reflection of a wave

galilean reflection

galilean movie

full stop

Lichteck

Lichtspuren haben Länge Null

wave reflection

wave reflection

Gal. mirror

Gal. kinetics

wave reflection

Geometry by reflection (Bachmann)


Incidence

Point

Pole

Points

Incidence

fourth ray<

second line

connecting to a distant point

orthocenter

circumcenter

polarity by three poles

the polarity is projective

orthogonal set

the fourth pole

the polar

euclidean symmetry

minkowski symmetry

general reflection


Perspective


Krummin

Coming home

Khufu

Giotto

battisterio di FI

Brunelleschi

Dürer

Perspectivity
Mercure
Reconstruction

Projective geometry


Desargues

quadratic tiling

cross ratio

cross ratio 1

cross ratio 2

cross ratio 3

cross ratio 4

quadrangle and quadrilateral

quadrangle

completing a quadrangle 1

completing a quadrangle 2

completing a quadrangle 3

completing a quadrangle 4

completing a quadrangle 5

complete quadrangle

quadrilateral

quadrilateral

harmonic reflection

harmonic reflection

harmonic bisection

harm. Bisection

harmonic continuation

reflection on a line

Cross ratio permanence

Coordinates

Coordinates

Pappos

Polarity


The polar

The pole

polar triangles

polarity and orthogonality

construction of tangents

polarity

thick lenses

Line orthocenter

polarity and bisection

The polar triangl

Conics


Slices of a cone

X-ray telescope

elliptic gears

Pascal

Brianchon

Brianchon 2

Euclidean focus

Circles 1

Circles 2

5-point conic

5-point conic

Circles 3

Six foci

Mink. foci

deSitter circles

deSitter conics

Six foci 1

Six foci 2

Six foci 3

Neville's problem

Neville set

Directrices

Neville proof

Neville hyperbolae

Neville Lobachevski

Neville Lobachevski

Adjoint foci

Focus-sharing hyperbolae

Asymptote-sharing conics


Minkowski geometry (pseudoeuclidean geometry)


Applet

eucl. circle

eucl. circle

mink. circle

mink. circle

Mink. circle

Galilei-Kreis

symmetry of dilation

circumcenter

circumcenter

orthocenter

orthocenter

Eucl. Pythagoras

Eucl. Pythagoras

Right angles

Mink. Pythagoras

Mink. Pythagoras

Mink. Pythagoras

eucl. tesselation

Mink. tesselation

eucl. Feuerbach

Mink. Feuerbach

Mink. Feuerbach

eukl. trisection

Mink. trisection

Paradoxes


Length congruency

length contraction

length contraction paradox

long jump distance

time dilation

Twin paradox 1

Twin paradox 2

Twin paradox 3

Twin paradox 4

Twin paradox 5

Rotating disk 1

Rotating disk 2

Rotating disk 3

Rotating disk 4


Non-euclidean (Lobachevski) geometry


Beyond infinity

2 Parallelen

Reflection 1

Reflection 2

Reflection 3

Reflection 4

Reflection 5

Reflection 6.

Zero angles

Infinity

Simple reflection

Zero distances

Zero distances

Twin paradox

Tesselattin

right-angle Pentagram

Bisector pair

Four circumcircles

collision characteristic

forward scattering

curved velocity space

bilance of angles

antminkowski Feuerbach

Interval bisectors

non-euclidean Feuerbach

Minkowski Feuerbach

Beyond infinity

Curvature


external curvature

minimal surface

Milne universe

internal curvature 1

internal curvature 2

internal curvature 3

internal curvature4.

Loxodrome

eukl. dual curvature

Mink. dual curvature

Geodätenschar

Kegel 3:10

Kegel 7:10

Kalotte

The south-pointing chariot (Zhi nan che)


Zhi-nan Che 1

Zhi-nan Che 2

Zhi-nan Che 4

Zhi-nan Che 5

Zhi-nan Che 6

Zhi-nan Che on a table

Preparation of a ball

Zhi-nan Che on a ball

Curvature of space-time


Sphere

Pseudosphere

deSitter 1

deSitter 1 projected

deSitter 2

deSitter 2 projected

deSitter 3

deSitter 3 projected

Anti-deSitter

Anti-deSitter projected

Curvature of the universe: Mercator maps


Mercator earth

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Nordrichtung

comoving coordinates

Mercator map

Parallel transport 1

Parallel transport 2

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Aberration


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Anisotroy

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Huygens principle

Huygens' focus

Huygens' aberration

Umbrelles 1

Umbrelles 2

Umbrelles 3

Umbrelles 4

Umbrelles 5

Umbrelles 6

Regen

Regen in Fronten

gekippte Fronten

waves by green hat

waves by red hat

crest by green hat

crest by red hat

front aberration

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Mehrfachbild

Guthnick

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Quelle bewegt

Aberration of starlight

Planetar aberration

Penrose-Terrell

Two eyes

Two eyes

Tunnelfahrt

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northern hemisphere

Aberrationsjahr mit Lara

Aberrationsjahr mit Walzer

Regulusblick

Start to Regulus

The Michelson experiment


Michelson intro

6 Minuten Michelson 160 MB

1. Interferenz am Gerät 7 MB
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2. Ätherwinds 26 MB
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3. Fresnels Paradoxon 34 MB

4. Einsteins Schluss 26 MB

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mirror array

Michelson interference

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Isaak

Sensitivity of iinterference

double mirror

double slit

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Newtons Eimer

Sagnac

Haefele-Keating

Space-time in pictures


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Einstein train
Einstein train

Berlin-Ulm 1

Berlin-Ulm 2

Berlin-Ulm 3

Special relativity


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Doppler

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composition of velocities

composition of velocities

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Scattering

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Relativity: try it yourself


Lichteck

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Symmetry

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Time dilation

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Twin paradox

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Mechanics of collisions, mass, and energy


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relative mass

equal masses

Galileo invariance of collisions

Galileo-symmetric decay

equal masses

different masses

different masses

momenta vs velocities

definition of inertial mass

Compton effect

decay in different parts

photon emission

two-photon decay

mo2c2=m2c2-m2v2

mo2c2=m2c2-m2v2

E=mc2

E=mc2

E=mc2

E=mc2

E=mc2

E=mc2

Hebel 1

Hebel 2

vΔp=c2Δm

Tachyons

elastic tachyons

Gravitation


Kepler and Newton

Kepler laws

Retrogade motion

Kepler vs. Ptolmy

Planetarium applet.

retrograde motion and distance

Ecliptic page

Ecliptic solo

Central force from 2. Kepler law

Newton's laws

Conservation laws

Short and snappy

Einstein's lift

Lenses

folded cone page

folded cone

Lensing by droplets

light deflection on a string

Cosmology basics


Resumee

Wanderkarte

Cosmic loop

Cosmic loop

Olbers paradox

Fractal universe

Expansion

Expansion

Expansion

Caterpillar page

Caterpillar solo

Evolution

Expansion

Horizon problem

Horizon problem

Horizon problem

Field of view

Deuterum

Matter components

Friedman equations

Friedmann solutions

Friedmann solutions

Distances χ[z]

Ω-Λ-plane

age in Ω-Λ

horizon distance in Ω-Λ

fireball size in Ω-Λ

symmetry breakdown

Universe without bang

Split of light cones

Interacting strings

contracting dimensions

Cosmic nucleosynthesis

























Cosmic structure


Star of stars

structure formation

Zel'dovich start

Zel'dovich start

Voroni structure

Bubble structure

Bubble structure

Structure formation

Perturbation spectra and back-ground radiation


Linear amplification

Störungsspektrum

Störungsspektrum

Störungsspektrum

Störungsspektrum

Störungsspektrum

Störungsspektrum

Störungsspektrum

Störungsspektrum

Dependence on density

Dependence on inflation

Microwave background

Acoustic oszillations

Resumen

Resumen

Cosmic vacuum






Kepler disk

DM disk





Flow of energy 1

Flow of energy 2

Flow of energy 3

Flow of energy 4

Flow of energy 5

Flow of energy 6

density decay

density decay

density decay slow

Density decay

Density decay

Universe in T









Cosmic pinpoints












Entropie













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Time









Temperatures

best matching

best matching

Entropy

Entropy

Entropy applet

Time scale

Time scale

Three clocks applet

Conformal time

Three clocks movie

Three ages



Quantum physics


Photoeffekt





Photon rain

Wave packet

Wave packet

Antiparticles

Photon mass

periodic system

periodic system

Baryons

Resonances

Ω-

Ω-

Ω-

Ω-

Ω-

Ω-

Ω-

Bohr und Einstein


Strings

Standing wave

Classical string

Planck steps

Photon rain

Photo effect

Bohr's model

Bohr's model

Oszillations part 2

Dying out




Quantum vacuum


Supplements


Potentialstufe




Centers UIO

Polyhedra paper models