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Christoph Schiller

MOTION MOUNTAIN – .

www.motionmountain.net

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Christoph SchillerTranslated by Megumi Hirooka

M M

e Adventure of PhysicsVolume II

Relativity

Edition . , available as free pdf with lms at www.motionmountain.net

http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/


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Editio vicesima septima.

Proprietas scriptoris © Chrestophori Schillertertio anno Olympiadis trigesimae.

Omnia proprietatis iura reservantur et vindicantur.Imitatio prohibita sine auctoris permissione.Non licet pecuniam expetere pro aliqua, quae

partem horum verborum continet; liberpro omnibus semper gratuitus erat et manet.

Twenty-seventh edition.

Copyright © – by Christoph Schiller,the third year of the th Olympiad.

is pdf le is licensed under the Creative CommonsAttribution-Noncommercial-No Derivative Works . Germany Licence, whose full text can be found on the websitecreativecommons.org/licenses/by-nc-nd/ . /de,with the additional restriction that reproduction, distribution and use,in whole or in part, in any product or service, be itcommercial or not, is not allowed without the written consent of the copyright owner. e pdf le was and remains free for everybody to read, store and print for personal use, and to distributeelectronically, but only in unmodied form and at no charge.

http://localhost/var/www/apps/conversion/tmp/scratch_7/creativecommons.org/licenses/by-nc-nd/3.0/dehttp://localhost/var/www/apps/conversion/tmp/scratch_7/creativecommons.org/licenses/by-nc-nd/3.0/dehttp://localhost/var/www/apps/conversion/tmp/scratch_7/creativecommons.org/licenses/by-nc-nd/3.0/de


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To Britta, Esther and Justus Aaron

τῷ ἐµοὶ δαὶµονι


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Die Menschen stärken, die Sachen klären.


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“Primum movere, deinde docere.*

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M o t i onM o un t ai n–Th eA d v en t ur e of Ph y si c s

c o p yri gh t © Ch ri s t o ph S ch i l l er J un e1 9 9 0 –M a y2 0 1 6 f r e e p d f l e a v ai l a b l e a t w w w.m o t i onm o un t ai n.n e t

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Galilean physics, heat and electricity The world of everyday motion : human scale, slow and weak.Adventures: sport, music, sailing, cooking, describingbeauty and understanding its origin (vol. I);using electricity, light and computers,understanding the brain and people (vol. III).

Special relativityAdventures: light,magnetism, lengthcontraction, time

dilation andE0 = mc 2(vol. II).

Quantum theoryAdventures: biology,birth, love, death,chemistry, evolution,

enjoying colours, art,paradoxes, medicineand high-tech business(vol. IVand vol. V).

Quantumtheory with gravity

Adventures: bouncingneutrons, understanding tree

growth (vol. V).

Final, unified description of motionAdventures: describing all motion , understanding

the origin of colours, space -time and particles, enjoyingextreme thinking, calculating masses and couplings,catching a further, tiny glimpse of bliss (vol. VI).

G c h, e, k

PHYSICS:Describing motionwith the least action principle.

Quantum field theory

Adventures: buildingaccelerators, under-standing quarks, stars,bombs and the basis of life, matter & radiation(vol. V).

P o w e r f u l m o t i o n T i

n y m o t

i o n

General relativity

Adventures: thenight sky, measu-ring curved andwobbling space,exploring blackholes and theuniverse, spaceand time (vol. II).

Classical gravityAdventures:climbing, skiing,space travel,

the wonders ofastronomy andgeology (vol. I). F

a s t m

o t i o n

F I G U R E 1 c, G, h, k e.

Munich, May .



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F I G U R E 2 , .

Earth (firstmeasurement)

Jupiter and Io(first measurement)

Earth (secondmeasurement)

Jupiter and Io(second measurement)

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(Galileo) . * , Ref. 3 (Ole

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rain light

light's perspective wind’s perspectiverain's perspective

human perspectivewalker’s perspective

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windsurfer’s perspective

F I G U R E 4

= 2π / = 29.7km

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, (Hippolyte Fizeau) (b. ,d. ) .

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lightsource

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20/335

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. , , ,. ‐ (Albert

Einstein) , . .

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21/335

F I G U R E 9 (1879–1955).

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22/335

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23/335

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24/335

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, . ( . )Challenge 15 s ,

, ,2 . ,Challenge 16 s

= +− or

= 2

−12

+1 . ( )


25/335

second

observeror clock

firstobserver

or clock

light flash

light flash

1 = (2+1) /2 2 = 2

FIGURE 10 ,

two fixed watches

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FIGURE 11 . , ,.

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.1

2 = 11− 22 = ( ) . ( ) , . ,

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26/335

FIGURE 12 . ( ) ( ) , . (© Max Planck

Gesellschaft TSR relativity team)

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. , = 2 . . ( ) ( ) , . ,

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⊳ , ,


27/335

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. , .


28/335

Leo

Aquarius

almost static reference:Vegav = 13.6 km/s at 27 al

redshift

quasar 3C273 in Virgov = 44 Mm/s at 2 Gal

quasar APM 08279-5255in Lynxv = 276 Mm/s at 12 Gal

redshift

Redshifts of quasar spectra

redshift

Lyman α Hγ Hβ Hα

FIGURE 14 : . : ( ) (

) . , (© Maurice Gavin, NASA) .

, ,, ( ) .

, , . ,Vol. III, page ?? , , , .

, , , , . ,

.Challenge 19 e

r

s

= 11−2

/2

(1− cos r

) = (1− cos r

) . ( )


29/335

If this red text appears blue,you are too fast.

FIGURE 15 , ,,

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, , . ,

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30/335

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= Δ = SR −1 = +− −1 . ( )

* ?Challenge 21 s


31/335

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32/335

FIGURE 17

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, , . . ,, km -

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.Page 63 ,

* ‘ . ’


33/335

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2

= = 1− 2 / 2 = 12 2

= 2

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., ,

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, sci.physics.relativity newsgroup.Ref. 38 . , www.crank.net , Crackpots

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.

http://www.crank.net/http://www.crank.net/


34/335

secondobserver(e.g. train)

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space

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35/335

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, , , , . ,. , (Pieter Zeeman) ,

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(Wilhelm Röntgen) , (Alexander Eichenwald) ,

(François Arago) , (Augustin Fresnel) ,


36/335

mirror

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intereferencedetector

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FIGURE 20 . , 1881 .

. (© Astrophysikalisches Institut Potsdam, Stephan Schiller) .

, , , ,. (Albert Michelson)

, (Stephan Schiller)Figure . , ,

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., .

* , .

(Hippolyte Fizeau) , (Martin Hoek) , (Harold Wilso n) ,(Albert Michelson) ,Ref. 44 ( ,

) (Edward Morley) , (Oliver Lodge) ,(John Strutt Rayleigh) , , ,

(Georges Sagnac) (Willem de Sitter) .* . , ,

.Vol. I, page ?? , , , .

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37/335

⊳ ( ) ,. , , : il moto [ ...] nienteopera ed come s’ e’ non fusse. [ ...] ,

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.Ref. 20*Challenge 34 s ?** ‘xi’ , ‘upsilon’, ‘zeta’ ‘tau’ . , ,

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38/335

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= 0 = const

FIGURE 21 . .

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, ,

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,

(d

)2

−(d

)2

= (d

)2

−(d

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d = d1−2/2 = d . ( ).

. ,

, , , ,


39/335

, . , . , . ,

,

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2 ⋅ 105 ,

1012 . ?Challenge 38 s

, , , , . , ., . ,

. , L. , ., = (− ) . ( )

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= (− /2) . ( ). (Henri Poincar) ,

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, Challenge 40 s ., , ,

. ,

* For information about (Hendrik Antoon Loren tz), page .

** , (Woldemar Voigt) (b. , d. ) .

. , , (George Fitzgerald) (b.

, d. ) .


40/335

.Page 46, ,

.Ref. 47 . , , .

, .

“Von Stund’ an sollen Raum f ür sich und Zeitf ür sich völlig zu Schatten herabsinken und nurnoch eine Art Union der beiden sollSelbstsändigkeit bewahren.*

”(Hermann

Minkowski) .

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? )Challenge 41 s , . , . .

, , , .

, . ,Ref. 48

d 2= 2d 2−d 2−d 2−d 2= 2d 2 1− 22 , ( )d ( ) ,

, . , (Hermann Minkowski) ***, ,

(Albert Einstein) , , , ,. ,

. , .

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. , Gesellscha f ür Naturforscher und Ärzte .

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41/335

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42/335

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FIGURE 23 O T , 1 2 . . , .

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. , . ?Challenge 43 s

, , . ,, ( )

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43/335

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= 1−2/2 . ( ).

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, . , , , . . ( .Page 46,

= = 1−2/2 = . ( ), , . ,

, . ,


44/335

Earthtime time

comparisonandchange ofrocket

firsttwin

firsttwin

trip ofsecond twin

FIGURE 24

. *

–

, . , ,

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, , .Ref. 51 , Ref. 52 ,

. 900 km/h , , 100ns. . ,. = . ( )

. , , , . ,

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* , w a = a v a w b = b v b ( ) ,,Challenge 51 es‖ = a b(a +b‖) and s⊥ = b⊥ , ( ). ,

‖⊥

, , v a . ,Ref. 50 .


45/335

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decays

FIGURE 25 , .

. , , .Ref. 53 , ,

?Challenge 52 s , , . ,

(Sergei

Krikalyov) , , , ., .

, , , . ,

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. , .Vol. V, page ?? ( )

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660m) . ,

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* (Nahin) .Ref. 54 , . ,

,

.


46/335

. , ,

0.62 µs .

, . , , .

, , , . .Challenge 54 s , . , .Ref. 56, ,

, , . , ,

, = . , , . , , , .Ref. 16

, , , , , .

, .Ref. 57 ,

. , , , . , , ,

., . ,

. . , ,

10m

/s2 ,

, , 10m/s2 , , , , , , , , . . 22000, , 44000. , , , 2 ⋅ 1019 , .Challenge 55 e . .Ref. 58

, .

. ?Challenge 56 s . , ,

. , , . , .

. . , , , .Challenge 57 e

300km

/h

,,

83m

/s

0.15 pm .


47/335

observationsby the farmer

observationsby the pilot

pilottime

farmertime

barn endsplane ends

FIGURE 26

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FIGURE 27 ( ) ( ) ( )

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) , . , ,

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48/335

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, , . ? )Challenge 61 s

, , (Harald van Lintel) (Christian Gruber)

.Ref. 60 . , .

, ,.

, ,

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. ., , ,

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, . ,

?Challenge 63 s ( , , ,

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. ) ., , , Figure ,

, . = 0, , . , , .

, ,

= /1−2

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. , . , ,


49/335

FIGURE 30 Daniel Weiskopf 0.9. , , .

(© Daniel Weiskopf) .

, ,.Challenge 64 s

, , .Ref. 64 , , , ,

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. , , . , , , .

, , , ?Challenge 65 s , , ?Challenge 66 s

, , ., . images.

–

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, . , . * , Figure .

, , .

* , Anthony Searle www.anu.edu.au/Physics/Searle Craig Savage www.anu.edu.au/Physics/vrproject

. realtimerelativity.org , . Daniel Weiskopf www.tat.physik.uni-tuebingen.

de/~weiskopf/gallery/index.html, Norbert Dragon Nicolai Mokros www.itp.uni-hannover.de/~dragon/stonehenge/stone .htm, , Hanns Ruder Ute Kraus www.

tempolimit-lichtgeschwindigkeit.de .

http://www.anu.edu.au/Physics/Searlehttp://www.anu.edu.au/Physics/Searlehttp://www.anu.edu.au/Physics/vrprojecthttp://localhost/var/www/apps/conversion/tmp/scratch_7/realtimerelativity.orghttp://www.tat.physik.uni-tuebingen.de/~weiskopf/gallery/index.htmlhttp://www.tat.physik.uni-tuebingen.de/~weiskopf/gallery/index.htmlhttp://www.tat.physik.uni-tuebingen.de/~weiskopf/gallery/index.htmlhttp://www.itp.uni-hannover.de/~dragon/stonehenge/stone1.htmhttp://www.itp.uni-hannover.de/~dragon/stonehenge/stone1.htmhttp://www.itp.uni-hannover.de/~dragon/stonehenge/stone1.htmhttp://www.tempolimit-lichtgeschwindigkeit.de/http://www.tempolimit-lichtgeschwindigkeit.de/http://www.tempolimit-lichtgeschwindigkeit.de/http://www.tempolimit-lichtgeschwindigkeit.de/http://www.itp.uni-hannover.de/~dragon/stonehenge/stone1.htmhttp://www.itp.uni-hannover.de/~dragon/stonehenge/stone1.htmhttp://www.tat.physik.uni-tuebingen.de/~weiskopf/gallery/index.htmlhttp://www.tat.physik.uni-tuebingen.de/~weiskopf/gallery/index.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_7/realtimerelativity.orghttp://www.anu.edu.au/Physics/vrprojecthttp://www.anu.edu.au/Physics/Searlehttp://www.anu.edu.au/Physics/Searle


50/335

maximum speed, observers at rest and

Views for an observer at rest

Views for an observer at relativistic speed

FIGURE 31 Nicolai Mokros Norbert Dragon 0.912 ( 2 ) .

(© Nicolai Mokros) .


51/335

FIGURE 32 ( ) (© Daniel Weiskopf)

, , .

, . Figure . ,

, . , .

. , , .

.Ref. 65 , .

, , . , , . Figure . .

.Page 15 , . . ,

, , .. ,

, , . ,

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,


52/335

FIGURE 33 ( ) ,

. ,

. (Mpglm © Ute Kraus at www.tempolimit-lichtgeschwindigkeit.de)

?Challenge 68 r

, .Ref. 63 , , ,

,

= 0

. ( . )

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f = b . , ,Challenge 69 eb

= Δ /2

+f , ( )

. , , . , ,

., , . , ,

, . , .

, , , ?Challenge 70 s

,

http://www.tempolimit-lichtgeschwindigkeit.de/http://www.tempolimit-lichtgeschwindigkeit.de/http://www.tempolimit-lichtgeschwindigkeit.de/http://www.tempolimit-lichtgeschwindigkeit.de/http://www.tempolimit-lichtgeschwindigkeit.de/http://www.tempolimit-lichtgeschwindigkeit.de/


53/335

light signal

spacespace

timetime

moving judge

average athletespeed:

average athletespeed:

J

J

light signal

moving judge

feet ofathletefeeofathlete

/2 /3

FIGURE 34 , , , .

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, . ., .Page 43

. ( ? )Challenge 71 s , ,.

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, .


54/335

X

FIGURE 35

J.S. Bach

J.S. Bach

J.S. Bach

FIGURE 36

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. .

, . ?Challenge 72 s

, . . ,

. , .

, , , , . ,, . , .

.Challenge 73 s, , , . , , ,

. .Vol. III, page ?? , ,, .

, . , . , , ,

. , , , . = /− / . ( )

. appr

appr

= = − , ( )


55/335

space

time

tachyon

observer

light cone

emitted or reflected light

FIGURE 37

, /2 . , , (quasi-stellar object

) . , , ,

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.Ref. 67, ,

leav = + , ( ), /2 . , .

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Challenge 74 e , .


56/335

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FIGURE 38 O R , R G , O G .

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57/335

, .

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58/335

,

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FIGURE 39

,

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, , ,, = 299782458m/s . , , , , , , , , ,

. , .





59/335

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, . , . .

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Ref. 75

= const ( )

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60/335

Observer A

Observer B

before:

after:

before:

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FIGURE 40 2 2

(A) , = + = . (B) , .Challenge 78 e , = 21+2/2 . ( ). ,

= 11−

2

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. ( )

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61/335

A B

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after

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Figure .

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62/335

target detectorsaccelerator beam

relativistic pool rule: + < 90°

FIGURE 42 ,. , CERN HARP . (© CERN)

FIGURE 43 ‘Big European Bubble Chamber’ . . (© CERN)

,Challenge 82 s / = 2(1+) > 2 . ( ). , , 2 . , .

∑ .

, .





63/335

, =

2

= 2

1−2

/2

, ( )

, , , . , 2 . ,

, (

. ) , 0 ,0

= 2 . ( )

. , ,

2

2 .

, . 2 . . 2. = 2 , . , , , .

.

⊳ ., . ,. ,

, . .

, . , . , , ,

, . , ,, ,

, , .

2 .

1kg

. , , .

2 ,

.

⊳ . ,

. , , , ,

. , . , , , ,

, .





64/335

, . , ( ) = 2 −2 = 122+ 1 ⋅ 32 ⋅ 4

4

2 + 1 ⋅ 3 ⋅ 52 ⋅ 4 ⋅ 66

4 +... ( ).Challenge 83 e , , Galilean = 12 2 .- = 2 , . , ,

, . , . , . -

. ., .

. , , . , , ,

.Challenge 84 e- , ,

. , , ,

, , .

.- = 2 SF . - . , ,

. ,. , .

. ( )

, .

1nJ

/m3 . .Page 205

, , .

- = 2 ,, 90kJ, 210 kcal . , , , ,

. , , . , 2 , . ,

1aJ (

6eV) , , ,





65/335

, . , , .

-

= 2 ,

. , . ,

. , – .

, . , ,

. (Da vid Pritchard) , , .

, ,

Δ0

= 2

Δ .Ref. 77 , ,

. , ,

., –

. , , . , .

, . , . , ,

, .

,

1+ /1− /,

, .

/22Challenge 85 e , . . , , = − /2= (− /2) . , /2. , ., ,

0

0 = 2 . ( ). .

, .

. ( ) ( ) . ,

Challenge 86 e4 2= 2−2 2 ( )

. , . ,

= 2 , ( )



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