special relativity · 2020-01-09 · special relativity presentation to uct summer school jan 2020...
TRANSCRIPT
![Page 2: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/2.jpg)
Test your understanding of simultaneity
Jan is a railway worker working for South African Railways. He has ingeniously synchronised the clocks on all South Africa’s railway stations. Motsi is on a high-speed train travelling from Cape Town to Johannesburg. As the train passes De Aar at full speed, all the clocks strike noon
According to Motsi when the Cape Town clock strikes noon, what time is it in Johannesburg? (a) noon? (b) before noon? (c) after noon?
2
![Page 3: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/3.jpg)
Test your understanding of Einstein’s second postulate
Asaveryhigh-speedrocketshipfliespastyouitfiresaflashlightthatshineslightinalldirectionsAnobserveraboardthespaceshipobservesawavefrontthatspreadsawayfromthespaceshipatspeedc inalldirectionsWhatistheshapeofthewavefrontthatanearthobservermeasuresa)spherical,b)ellipsoidalwiththelongestsideoftheellipsoidalongthedirectionofthespaceship'smovementc)ellipsoidalwiththeshortestsideoftheellipsoidalongthedirectionofthespaceship’smovementd)neitherofthese?Isthewavefrontcenteredonthespaceship?
![Page 4: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/4.jpg)
Time Dilation and Lorentz gamma (𝛾)
4
![Page 5: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/5.jpg)
5
Inordertogainabetterunderstandingofwhatishappening,weclearlyneedtoderiveaquantitativerelationshipthatallowsustocomparetimeintervalsindifferentframesofreference
ThiswillbedoneusinganotherthoughtexperimentThiswillbedoneusinganotherthoughtexperimentAgainwewillusetrainmovingclosetothespeedoflightMavis,sittinginamovingtrainisinreferenceframeS’StanleyisstationaryonthegroundinreferenceframeSReferenceframeS’movesatconstantvelocityu,relativetoreferenceframeS,alongthecommonx– x’axisMavis,ridinginframeS’measuresthetimeintervalbetween
![Page 6: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/6.jpg)
6
Inordertogainabetterunderstandingofwhatishappening,weclearlyneedtoderiveaquantitativerelationshipthatallowsustocomparetimeintervalsindifferentframesofreference
Thiswillbedoneusinganotherthoughtexperiment
![Page 7: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/7.jpg)
Time Dilation Thought Experiment
Theobjectiveoftheexperimentistodemonstrate:
Thatobserversmeasureanyclocktorunslowifitmovesrelativetothemandastherelativespeedapproachesthespeedoflight,themovingclock’schangeintimetendstozero
7
![Page 8: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/8.jpg)
8
ImaginewehaveatrainmovingclosetothespeedoflightalongastraightstretchofrailwaytrackMavis,sittinginamovingtrainisinreferenceframeS’StanleyisstationaryonthegroundinreferenceframeSReferenceframeS’movesatconstantvelocityu,relativetoreferenceframeS,alongthecommonx– x’axisMavis,ridinginframeS’measuresthetimeintervalbetweentwoeventsthatoccuratthesamepointinspace(a)
![Page 9: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/9.jpg)
9
Imaginewehaveatrainmovingclosetothespeedoflightalongastraightstretchofrailwaytrack
Sarah,sittinginacoach,isridinginframeS’whereshemeasuresthetimeintervalbetweentwoeventsthatoccuratthesamepointinspace(a)onher‘lightclock’betweentwoeventsthatoccuratthesamepointinspace(a)
![Page 10: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/10.jpg)
10
Peter
SarahSarah
Referenceframe S’
![Page 11: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/11.jpg)
11
SarahMirror
Lightsource
d
S’
O’(Event1occurshere)
![Page 12: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/12.jpg)
12
SarahMirror
Lightsource
d
S’
O’(Event2alsooccurshere)
![Page 13: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/13.jpg)
13
SarahMirror
Lightsource
d
S’
Sarahmeasuresaroundtriptimeof∆t0 forthelightbeam
O’(Events1and2occurhere)
![Page 14: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/14.jpg)
14
Thelightbeamtravelsatotaldistanceof2dinatimeof∆t0 andsincethespeedoflight=c,d=c∆t0/2
SarahMirror
Lightsource
d
O’(Events1and2occurhere)
S’
Sarahmeasuresaroundtriptimeof∆t0 forthelightbeam
![Page 15: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/15.jpg)
15
Sarah
Sourcemovesfromheretohere
Event1occurshere
Peterwhoisstationaryobservesthesamelightpulsefollowingadiagonalpath
![Page 16: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/16.jpg)
16
Sarah
Sourcemovesfromheretohere
Event1occurshere
Event2occurshere
![Page 17: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/17.jpg)
17
Petermeasurestheround-triptimetobe∆t
Sarah
Sourcemovesfromheretohere
Event1occurshere
Event2occurshere
![Page 18: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/18.jpg)
18
Petermeasurestheround-triptimetobe∆t
Sarah
Sourcemovesfromheretohere
(Distancetravelled)
Event1occurshere
Event2occurshere
![Page 19: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/19.jpg)
19
Petermeasurestheround-triptimetobe∆t
Sarah
Sourcemovesfromheretohere
(Distancetravelled)
Theround-tripdistanceforthelightbeaminreferenceframeS is2ℓ
Event1occurshere
Event2occurshere
![Page 20: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/20.jpg)
Pythagorean theorem
20
ThePythagoreantheoremstatesthatforaright-angletriangle,thesquareofthehypotenuse(c)isequaltothesumofthesquaresoftheremainingtwoshorterperpendicularsides(a &b)
a
b
c
Thusc2 =a2 +b2
∴ c= 𝑎$ + 𝑏$
![Page 21: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/21.jpg)
d
21
Peter
Sarah
![Page 22: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/22.jpg)
u∆t/2
d
22
Peter
Sarah
![Page 23: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/23.jpg)
Using the Pythagorean theorem we can calculate ℓ
ℓ = 𝑑$ + (𝑢∆t/2)$
The speed of light is the same for both observers, so theround-trip time measured in S is
∆t = 2ℓ/c = 2/c 𝑑$ + (𝑢∆t/2)$
23
![Page 24: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/24.jpg)
Using the Pythagorean theorem we can calculate ℓ
ℓ = 𝑑$ + (𝑢∆t/2)$
The speed of light is the same for both observers, so theround-trip time measured in S is ∆twhere
∆t = 2ℓ/c
24
![Page 25: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/25.jpg)
Using the Pythagorean theorem we can calculate ℓ
ℓ = 𝑑$ + (𝑢∆t/2)$
The speed of light is the same for both observers so theround-trip time measured in S is ∆twhere
∆t = 2ℓ/c = 2/c 𝑑$ + (𝑢∆t/2)$
25
![Page 26: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/26.jpg)
We would like to have a relationship between ∆t and ∆t0 thatis independent of d (but is dependent on u and c)
By substitution we get
∆t = 2/c (𝑐∆t0/2)$+(𝑢∆t/2)$
Squaring this equation and solving for ∆t we get
∆t = ∆t0 / 1 − 𝑢$/𝑐2
26
![Page 27: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/27.jpg)
We would like to have a relationship between ∆t and ∆t0 thatis independent of d (but is dependent on u and c)
Remembering that d = 𝑐∆t0/2, then by substitution we get
∆t = 2/c (𝑐∆t0/2)$+(𝑢∆t/2)$
Squaring this equation and solving for ∆t we get
∆t = ∆t0 / 1 − 𝑢$/𝑐2)
27
![Page 28: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/28.jpg)
We would like to have a relationship between ∆t and ∆t0 thatis independent of d (but is dependent on u and c)
Remembering that d = 𝑐∆t0/2, then by substitution we get
∆t = 2/c (𝑐∆t0/2)$+(𝑢∆t/2)$
Squaring this equation and then solving for ∆t we finally get
∆t = ∆t0 / 1 − 𝑢$/𝑐2
28
![Page 29: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/29.jpg)
Sincethequantity 1 − 𝑢$/𝑐2 islessthan1,∆tisalwaysgreaterthan∆t0
ThusStanleymeasuresalongerround-triptimeforthelightpulsethandoesMavis
Thequantity𝟏/ 𝟏 − 𝒖𝟐/𝒄2appearssoofteninrelativitythatithasitsownsymbol andisreferredtoasLorentzgamma
𝛾 =𝟏/ 𝟏 − 𝒖𝟐/𝒄2Lorentzgammadefinition29
![Page 30: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/30.jpg)
Sincethequantity 1 − 𝑢$/𝑐2 islessthan1,∆tisalwaysgreaterthan∆t0
ThusPetermeasuresalongerround-triptimeforthelightpulsethandoesSarah
Thequantity𝟏/ 𝟏 − 𝒖𝟐/𝒄2appearssoofteninrelativitythatithasitsownsymbol andisreferredtoasLorentzgamma
𝛾 =𝟏/ 𝟏 − 𝒖𝟐/𝒄2Lorentzgammadefinition30
![Page 31: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/31.jpg)
Sincethequantity 1 − 𝑢$/𝑐2 islessthan1,∆tisalwaysgreaterthan∆t0
ThusPetermeasuresalongerround-triptimeforthelightpulsethandoesSarah
Thequantity1/ 1 − 𝑢$/𝑐2appearssoofteninrelativitythatithasitsownsymbol 𝛾 andisreferredtoasLorentzgamma
𝛾 =𝟏/ 𝟏 − 𝒖𝟐/𝒄2Lorentzgammadefinition31
![Page 32: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/32.jpg)
Sincethequantity 1 − 𝑢$/𝑐2 islessthan1,∆tisalwaysgreaterthan∆t0
ThusPetermeasuresalongerround-triptimeforthelightpulsethandoesSarah
Thequantity1/ 1 − 𝑢$/𝑐2appearssoofteninrelativitythatithasitsownsymbol 𝛾 andisreferredtoasLorentzgamma
𝛾 =1/ 1 − 𝑢$/𝑐2Lorentzgammafactor32
![Page 33: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/33.jpg)
Notethat𝛾 isalways≥1and1/𝛾 isalways≤1!
If𝛾 appearsinthenumeratorofanyrelativisticequation,itwilltendtowardsinfinityasvelocityapproachesc
Converselyif𝛾 appearsinthedenominatorofanyrelativisticequation,itwilltendtowardszeroasvelocityapproachesc
33
![Page 34: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/34.jpg)
Notethat𝛾 isalways≥1and1/𝛾 isalways≤1!
If𝛾 appearsinthenumeratorofanyrelativisticequation,itwilltendtowardsinfinityasvelocity,u approachesc
Converselyif𝛾 appearsinthedenominatorofanyrelativisticequation,itwilltendtowardszeroasvelocityapproachesc
34
![Page 35: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/35.jpg)
Notethat𝛾 isalways≥1and1/𝛾 isalways≤1!
If𝛾 appearsinthenumeratorofanyrelativisticequation,itwilltendtowardsinfinityasvelocity,approachesc
Converselyif𝛾 appearsinthedenominatorofanyrelativisticequation,itwilltendtowardszeroasvelocity,u approachesc
35
![Page 36: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/36.jpg)
∆t0 iscalledthepropertimeandisequaltothetimeintervalbetweentwoeventsthatoccuratthesameposition
Onlyoneinertialframe(S’)measuresthepropertimeanditdoessowithasingleclockthatispresentatbothevents
Aninertialreferenceframemovingwithvelocityurelativetothepropertimeframemustusetwoclockstomeasurethetimeinterval:Oneatthepositionofthefirsteventandoneatthepositionofthesecondevent
Byrearrangingourearlierequations,thetimeintervalintheframewheretwoclocksarerequiredisasfollows
36
![Page 37: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/37.jpg)
∆t0 iscalledthepropertimeandisequaltothetimeintervalbetweentwoeventsthatoccuratthesameposition
Onlyoneinertialframe(S’)measuresthepropertimeanditdoessowithasingleclockthatispresentatbothevents
Aninertialreferenceframemovingwithvelocityurelativetothepropertimeframemustusetwoclockstomeasurethetimeinterval:Oneatthepositionofthefirsteventandoneatthepositionofthesecondevent
Byrearrangingourearlierequations,thetimeintervalintheframewheretwoclocksarerequiredisasfollows
37
![Page 38: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/38.jpg)
∆t0 iscalledthepropertimeandisequaltothetimeintervalbetweentwoeventsthatoccuratthesameposition
Onlyoneinertialframe(S’)measuresthepropertimeanditdoessowithasingleclockthatispresentatbothevents
Aninertialreferenceframemovingwithvelocityu relativetothepropertimeframemustusetwoclockstomeasurethetimeinterval:Oneatthepositionofthefirsteventandoneatthepositionofthesecondevent
Byrearrangingourearlierequations,thetimeintervalintheframewheretwoclocksarerequiredisasfollows
38
![Page 39: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/39.jpg)
∆t0 iscalledthepropertimeandisequaltothetimeintervalbetweentwoeventsthatoccuratthesameposition
Onlyoneinertialframe(S’)measuresthepropertimeanditdoessowithasingleclockthatispresentatbothevents
Aninertialreferenceframemovingwithvelocityurelativetothepropertimeframemustusetwoclockstomeasurethetimeinterval:Oneatthepositionofthefirsteventandoneatthepositionofthesecondevent
Byrearrangingourearlierequations,thetimeintervalintheframewheretwoclocksarerequiredisasfollows
39
![Page 40: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/40.jpg)
∆t=∆t0 / 1 − 𝑢$/𝑐2 =𝛾 ∆t0 andthus∆t≥ ∆t0
ThestretchingoutoftimeofthetimeintervaliscalledtimedilationTheequationAbovetellstwothings:Firstly,ifitwerepossibletotravelfasterthanthespeedoflightthen1– u2/c2 wouldbenegativeand 1 − 𝑢$/𝑐2wouldbeanimaginarynumber.Wedon’thaveimaginarytime!Secondly,atimedilationplotof∆t/∆t0asafunctionofrelativevelocity,uwilltendtoinfinityasu approachesc (orinotherwordsasu/capproachesone)Thisisillustratedgraphicallyinthefollowingslide 40
![Page 41: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/41.jpg)
∆t=∆t0 / 1 − 𝑢$/𝑐2 =𝛾 ∆t0 andthus∆t≥ ∆t0
ThestretchingoutoftimeofthetimeintervaliscalledtimedilationTheequationAbovetellsustwothings:Firstly,ifitwerepossibletotravelfasterthanthespeedoflightthen1– u2/c2 wouldbenegativeand 1 − 𝑢$/𝑐2wouldbeanimaginarynumber.Wedon’thaveimaginarytime!Secondly,atimedilationplotof∆t/∆t0asafunctionofrelativevelocity,uwilltendtoinfinityasu approachesc (orinotherwordsasu/capproachesone)Thisisillustratedgraphicallyinthefollowingslide 41
![Page 42: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/42.jpg)
∆t=∆t0 / 1 − 𝑢$/𝑐2 =𝛾 ∆t0 andthus∆t≥ ∆t0
ThestretchingoutoftimeofthetimeintervaliscalledtimedilationTheequationAbovetellstwothings:Firstly,ifitwerepossibletotravelfasterthanthespeedoflightthen1– u2/c2 wouldbenegativeand 1 − 𝑢$/𝑐2wouldbeanimaginarynumber.Wedon’thaveimaginarytime!Secondly,atimedilationplotof∆t/∆t0asafunctionofrelativevelocity, willtendtoinfinityasu approachesc (orinotherwordsasu/capproachesone)Thisisillustratedgraphicallyinthefollowingslide 42
![Page 43: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/43.jpg)
0
1
2
3
4
5
6
7
8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
∆t/∆t 0=𝜸=1/√(1−u2/c
2 )
Speedu relativetothespeedoflight(u/c)
Time dilation
Asu approachesc,𝜸 approachesinfinity
∆t/∆t0=𝛾
43
![Page 44: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/44.jpg)
Timedilationissometimesdescribedbysayingthatmovingclocksrunslow.Thismustbeinterpretedcarefully
Thewholepointofrelativityisthatallinertialframesareequallyvalidsothereisnoabsolutesenseinwhichaclockismovingoratrest
44
![Page 45: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/45.jpg)
Timedilationissometimesdescribedbysayingthatmovingclocksrunslow.Thismustbeinterpretedcarefully
Thewholepointofrelativityisthatallinertialframesareequallyvalidsothereisnoabsolutesenseinwhichaclockismovingoratrest
45
![Page 46: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/46.jpg)
46
Toillustratethispoint,thisimageshowstwofirecrackerexplosionsi.e.twoeventsthatoccuratdifferentpositionsinthegroundframeAssistantsonthegroundneedtwoclockstomeasurethetimeinterval∆tInthetrainreferenceframehoweverasingleclockispresentatbothevents,hencethetimeintervalmeasuredinthetrainreferenceisthepropertime∆t0
![Page 47: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/47.jpg)
47
Toillustratethispoint,thisimageshowstwofirecrackerexplosionsi.e.twoeventsthatoccuratdifferentpositionsinthegroundframeAssistantsonthegroundneedtwoclockstomeasurethetimeinterval∆tInthetrainreferenceframehoweverasingleclockispresentatbothevents,hencethetimeintervalmeasuredinthetrainreferenceisthepropertime∆t0
![Page 48: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/48.jpg)
48
Toillustratethispoint,thisimageshowstwofirecrackerexplosionsi.e.twoeventsthatoccuratdifferentpositionsinthegroundframeAssistantsonthegroundneedtwoclockstomeasurethetimeinterval∆tInthetrainreferenceframehoweverasingleclockispresentatbothevents,hencethetimeintervalmeasuredinthetrainreferenceisthepropertime∆t0
![Page 49: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/49.jpg)
49
Inthissensethemovingclock(theonethatispresentatbothevents)‘runsslower’thanthetheclocksthatarestationarywithrespecttobothevents
Moregenerally,thetimeintervalbetweentwoeventsissmallestinthereferenceframeinwhichthetwoeventsoccuratthesameposition
![Page 50: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/50.jpg)
50
Inthissensethemovingclock(theonethatispresentatbothevents)‘runsslower’thanthetheclocksthatarestationarywithrespecttobothevents
Moregenerally,thetimeintervalbetweentwoeventsissmallestinthereferenceframeinwhichthetwoeventsoccuratthesameposition
![Page 51: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/51.jpg)
In deriving the time dilation equation we made use of a lightclock which made our analysis clear and easy
The conclusion is about time itself
Any clock, regardless of how it operates (e.g. a grandfatherclock, a wind-up wristwatch, alarm clock or supper accuratequartz clock (as used in GPS satellites)) behave the same!
51
![Page 52: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/52.jpg)
In deriving the time dilation equation we made use of a lightclock which made our analysis clear and easy
The conclusion is about time itself
Any clock, regardless of how it operates (e.g. a grandfatherclock, a wind-up wristwatch, alarm clock or supper accuratequartz clock (as used in GPS satellites)) behave the same!
52
![Page 53: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/53.jpg)
In deriving the time dilation equation we made use of a lightclock which made our analysis clear and easy
The conclusion is about time itself
Any clock, regardless of how it operates (e.g. a grandfatherclock, a wind-up wristwatch, digital watch, alarm clock or asuper accurate quartz clock) behaves in the same way!
53
![Page 54: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/54.jpg)
![Page 55: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/55.jpg)
![Page 56: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/56.jpg)
0
1
2
3
4
5
6
7
8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
∆t/∆t 0=𝜸=1/√(1−u2/c
2 )
Speedu relativetothespeedoflight(u/c)
Time dilation
Asu approachesc,𝜸 approachesinfinity
∆t/∆t0=𝛾
56
![Page 57: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/57.jpg)
For𝛥t/𝛥t0 =7,u/c=0.990
For𝛥t/𝛥t0=8,u/c=0.992
![Page 58: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/58.jpg)
Faster than the speed of light?
![Page 59: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/59.jpg)
Spaceisexpandingfasterthanthespeedoflight.Thisisbecausespacetimeitselfisexpandingandisdenyingustheopportunitytoseefurtherthan14billionlightyearsInwater,muonscantravelfasterthenthespeedoflight.ThisisknownasCherenkovlightwhichhasadistinctbluehue.Itcanbeobservedinnuclearreactors.AlthoughthisistruenothingcantravelfasterthanthespeedoflightinavacuumNeutrinosfromsupernovaexplosionsarriveatearthbeforephotonsdo.Thisisbecausethephotonstakeasignificantamountoftimetoescapefromtheexplodingstarwhileneutrinos(withnearzeromass)escapeunhinderedWeareconstantlymovingthroughspacetimeatthespeedoflightinavacuum.Weeitherexperiencespaceortimeoramixtureofboth
59
![Page 60: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/60.jpg)
Hubbleultradeepfieldimage
Galaxiesasoldas13billionyearsarevisible
60
![Page 61: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/61.jpg)
Spaceisexpandingfasterthanthespeedoflight.Thisisbecausespacetimeitselfisexpandingandisdenyingustheopportunitytoseefurtherthan14billionlightyearsInwater,muonscantravelfasterthanthespeedoflight.ThisisknownasCherenkovlightwhichhasadistinctbluehue.Itcanbeobservedinnuclearreactors.Althoughthisistrue,nothingcantravelfasterthanthespeedoflightinavacuumNeutrinosfromsupernovaexplosionsarriveatearthbeforephotonsdo.Thisisbecausethephotonstakeasignificantamountoftimetoescapefromtheexplodingstarwhileneutrinos(withnearzeromass)escapeunhinderedWeareconstantlymovingthroughspacetimeatthespeedoflightinavacuum.Weeitherexperiencespaceortimeoramixtureofboth
61
![Page 62: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/62.jpg)
62
AnexampleofCherenkovradiationinsideanuclearreactorwheremuons(heavyelectrons)travelfasterthanphotonsoflightinwater
![Page 63: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/63.jpg)
Spaceisexpandingfasterthanthespeedoflight.Thisisbecausespacetimeitselfisexpandingandisdenyingustheopportunitytoseefurtherthan14billionlightyearsInwater,muonscantravelfasterthanthespeedoflight.ThisisknownasCherenkovlightwhichhasadistinctbluehue.Itcanbeobservedinnuclearreactors.Althoughthisistrue,nothingcantravelfasterthanthespeedoflightinavacuumNeutrinosfromsupernovaexplosionsarriveatearthbeforephotonsdo.Thisisbecausethephotonstakeasignificantamountoftimetoescapefromtheexplodingstarwhileneutrinos(withnearzeromass)escapeunhinderedWeareconstantlymovingthroughspacetimeatthespeedoflightinavacuum.Weeitherexperiencespaceortimeoramixtureofboth
63
![Page 64: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/64.jpg)
Spaceisexpandingfasterthanthespeedoflight.Thisisbecausespacetimeitselfisexpandingandisdenyingustheopportunitytoseefurtherthan14billionlightyearsInwater,muonscantravelfasterthanthespeedoflight.ThisisknownasCherenkovlightwhichhasadistinctbluehue.Itcanbeobservedinnuclearreactors.Althoughthisistrue,nothingcantravelfasterthanthespeedoflightinavacuumNeutrinosfromsupernovaexplosionsarriveatearthbeforephotonsdo.Thisisbecausethephotonstakeasignificantamountoftimetoescapefromtheexplodingstarwhileneutrinos(withnearzeromass)escapeunhinderedWeareconstantlymovingthroughspacetimeatthespeedoflightinavacuum.Weeitherexperiencespaceortimeoramixtureofboth
64
![Page 65: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/65.jpg)
Time Dilation in nature
65
![Page 66: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/66.jpg)
66
Imageofanexplodingsupernovainadistantgalaxy.Itsbrightnessdecaysatacertainratebutbecauseitismovingawayfromusatasubstantialfractionofthespeedoflight,itdecaysmoreslowlyasseenfromearth.Thesupernovaisa‘movingclockthatrunsslow.’
![Page 67: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/67.jpg)
HighenergycosmicrayprotonsenteringourupperatmosphereinteractwiththenucleiofN2andO2 generatingpionswhichthendecayintomuons(heavyelectrons)whichmoveoffataspeedof0.994c
Thehalflifeofamuonis2.2microseconds.
After660metershalfthemuonswouldhavedecayedbutataspeedof0.994cthehalflifeis20microseconds.
About25%ofthemuonscreatedreachtheground.
Iftherewasnotimedilationonly1/220muonswouldreachtheearth
67
![Page 68: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/68.jpg)
HighenergycosmicrayprotonsenteringourupperatmosphereinteractwiththenucleiofN2andO2 generatingpionswhichthendecayintomuons(heavyelectrons)whichmoveoffataspeedof0.994c.
Thehalflifeofamuonis2.2microseconds
After660metershalfthemuonswouldhavedecayedbutataspeedof0.994cthehalflifeis20microseconds.
About25%ofthemuonscreatedreachtheground.
Iftherewasnotimedilationonly1/220muonswouldreachtheearth
68
![Page 69: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/69.jpg)
HighenergycosmicrayprotonsenteringourupperatmosphereinteractwiththenucleiofN2andO2 generatingpionswhichthendecayintomuons(heavyelectrons)whichmoveoffataspeedof0.994c.
Thehalflifeofamuonis2.2microseconds.
After660metershalfthemuonswouldhavedecayedbutataspeedof0.994c thehalflifeis20microseconds
About25%ofthemuonscreatedreachtheground.
Iftherewasnotimedilationonly1/220muonswouldreachtheearth
69
![Page 70: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/70.jpg)
HighenergycosmicrayprotonsenteringourupperatmosphereinteractwiththenucleiofN2andO2 generatingpionswhichthendecayintomuons(heavyelectrons)whichmoveoffataspeedof0.994c.
Thehalflifeofamuonis2.2microseconds.
After660metershalfthemuonswouldhavedecayedbutataspeedof0.994cthehalflifeis20microseconds.
About25%ofthemuonscreatedreachtheground
Iftherewasnotimedilationonly1/220muonswouldreachtheearth
70
![Page 71: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/71.jpg)
HighenergycosmicrayprotonsenteringourupperatmosphereinteractwiththenucleiofN2andO2 generatingpionswhichthendecayintomuons(heavyelectrons)whichmoveoffataspeedof0.994c
Thehalflifeofamuonis2.2microseconds
After660metershalfthemuonswouldhavedecayedbutataspeedof0.994cthehalflifeis20microseconds
About25%ofthemuonscreatedreachtheground
Iftherewasnotimedilationonly1/220muonswouldreachtheearth
71
![Page 72: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/72.jpg)
Youcanbuildyourownmuondetector!
Allyouneedisamobilephonewithacamera+astripofblackinsulationtape
ForaniPhonedownloadtheappfromcosmicrayapp.com.Forotherphonesthereareequivalentapps
Tapeupthecameralensandyouarereadytogo
Justfollowtheapp’sinstructions
![Page 73: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/73.jpg)
Why don’t we experience time dilation in our everyday lives?
73
![Page 74: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/74.jpg)
Thesunwiththeearthintowistravellingaroundthecentreofthemilkywayataspeedofapproximately220000m/s
Atthisspeed𝜸 fortheearthisonly1.00000027aroundthecentreofourgalaxy
Atsuchalowvalueof𝜸, thesurfaceoftheearthistoallintentsandpurposesaninertialreferenceframe
Ahighvelocityriflebullethasa𝜸 ofonly1.000000000001
Itisnotsurprisingthatwedon’texperiencerelativityIoureverydaylives! 74
![Page 75: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/75.jpg)
Thesunwiththeearthintowistravellingaroundthemilkywayataspeedof217261m/s
Atthisspeed𝜸 fortheearthisonly1.0000003asitmovesaroundthecentreofourgalaxy
Atsuchalowvalueof𝜸, thesurfaceoftheearthistoallintentsandpurposesaninertialreferenceframe
Ahighvelocityriflebullethasa𝜸 ofonly1.000000000001
Itisnotsurprisingthatwedon’texperiencerelativityIoureverydaylives! 75
![Page 76: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/76.jpg)
Thesunwiththeearthintowistravellingaroundthemilkywayataspeedof217261m/s
Atthisspeed𝜸 fortheearthisonly1.0000003asitmovesaroundthecentreofourgalaxy
Atsuchalowvalueof𝜸, thesurfaceoftheearthistoallintentsandpurposesaninertialreferenceframe
Ahighvelocityriflebullethasa𝜸 ofonly1.000000000001
Itisnotsurprisingthatwedon’texperiencerelativityIoureverydaylives! 76
![Page 77: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/77.jpg)
Thesunwiththeearthintowistravellingaroundthemilkywayataspeedof217261m/s
Atthisspeed𝜸 fortheearthisonly1.0000003asitmovesaroundthecentreofourgalaxy
Atsuchalowvalueof𝜸, thesurfaceoftheearthistoallintentsandpurposesaninertialreferenceframe
Ahighvelocityriflebullethasa𝜸 ofonly1.000000000001
Itisnotsurprisingthatwedon’texperiencerelativityIoureverydaylives! 77
![Page 78: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/78.jpg)
Thesunwiththeearthintowistravellingaroundthemilkywayataspeedof217261m/s
Atthisspeed𝜸 fortheearthisonly1.0000003asitmovesaroundthecentreofourgalaxy
Atsuchalowvalueof𝜸, thesurfaceoftheearthistoallintentsandpurposesaninertialreferenceframe
Ahighvelocityriflebullethasa𝜸 ofonly1.000000000001
Whenbloodhoundfinallyreachesitstargetspeedof1000mph,its𝜸 willonlybe1.0000000000006 78
![Page 79: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/79.jpg)
Time Dilation in Practice
79
![Page 80: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/80.jpg)
80
Cathoderaytubeinwhichelectronsreach30%ofthespeedoflight
![Page 81: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/81.jpg)
81
![Page 82: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/82.jpg)
Length contraction
![Page 83: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/83.jpg)
Relativity of length
83
Wealsoneedtoderiveaquantitativerelationshipbetweenlengthsindifferentcoordinatesystems(i.e.differentreferenceframes)usinganotherthoughtexperiment
Onceagain,wehaveatraintravellingneartothespeedoflightalongastretchofstraightrailwaytrack
SarahistravellinginthecarriageinreferenceframeS’
Nexttoherontheseatisaruler,alightsourceandamirrorasillustrated
![Page 84: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/84.jpg)
Relativity of length
84
Wealsoneedtoderiveaquantitativerelationshipbetweenlengthsindifferentcoordinatesystems(i.e.differentreferenceframes)usinganotherthoughtexperiment
Onceagain,wehaveatraintravellingneartothespeedoflightalongastretchofstraightrailwaytrackSarahistravellinginthecarriageinreferenceframeS’
Nexttoherontheseatisaruler,alightsourceandamirrorasillustrated
![Page 85: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/85.jpg)
Relativity of length
85
Wealsoneedtoderiveaquantitativerelationshipbetweenlengthsindifferentcoordinatesystems(i.e.differentreferenceframes)usinganotherthoughtexperiment
Onceagain,wehaveatraintravellingneartothespeedoflightalongastretchofstraightrailwaytrack
SarahistravellinginthecarriageinreferenceframeS’
Nexttoherontheseatisaruler,alightsourceandamirrorasillustrated
![Page 86: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/86.jpg)
Relativity of length
86
Wealsoneedtoderiveaquantitativerelationshipbetweenlengthsindifferentcoordinatesystems(i.e.differentreferenceframes)usinganotherthoughtexperiment
Onceagain,wehaveatraintravellingneartothespeedoflightalongastretchofstraightrailwaytrack
SarahistravellinginthecarriageinreferenceframeS’
Nexttoherontheseatisaruler,alightsourceandamirrorasillustrated
![Page 87: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/87.jpg)
87
Sarah
![Page 88: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/88.jpg)
88
Sarah
Peter
![Page 89: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/89.jpg)
By using logic like the derivation of time dilation we get
In special relativity a length ℓ0 measured in the frame inwhich the body is at rest is called a proper length
Lengths measured perpendicular to the direction of travel arenot contracted (the velocity in the y and z direction is zero)
89
ℓ =ℓ0/𝛾 Lengthcontractionformula
![Page 90: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/90.jpg)
By using logic like the derivation of time dilation we get
In special relativity a length ℓ0 measured in the frame inwhich the body is at rest is called a proper length
Lengths measured perpendicular to the direction of travel arenot contracted (the velocity in the y and z direction is zero)
90
ℓ =ℓ0/𝛾 Lengthcontractionformula
![Page 91: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/91.jpg)
By using logic like the derivation of time dilation we get
In special relativity a length ℓ0 measured in the frame inwhich the body is at rest is called a proper length
Lengths measured perpendicular to the direction of travel arenot contracted (the velocity in the y and z direction is zero)
91
ℓ =ℓ0/𝛾 Lengthcontractionformula
![Page 92: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/92.jpg)
Rearranging the previous equation we get
What this tells us is that observers measure any ruler tocontract in length if it moves relative to them
To the traveler her ruler will continue to show the properlength ℓ0 as she is at rest in her reference frame
What the equation also tells us is that as a travelerapproaches the speed of light her ruler will contract to zeroas observed by a stationary observer as shown in the nextslide 92
ℓ/ℓ0 = 1/𝛾
![Page 93: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/93.jpg)
Rearranging the previous equation we get
What this tells us is that observers measure any ruler tocontract in length if it moves relative to them
To the traveler her ruler will continue to show the properlength ℓ0 as she is at rest in her reference frame
What the equation also tells us is that as a travelerapproaches the speed of light her ruler will contract to zeroas observed by a stationary observer as shown in the nextslide 93
ℓ/ℓ0 = 1/𝛾
![Page 94: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/94.jpg)
Rearranging the previous equation we get
What this tells us is that observers measure any ruler tocontract in length if it moves relative to them
To the traveler her ruler will continue to show the properlength ℓ0 as she is at rest in her reference frame
What the equation also tells us is that as a travelerapproaches the speed of light her ruler will contract to zeroas observed by a stationary observer as shown in the nextslide 94
ℓ/ℓ0 = 1/𝛾
![Page 95: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/95.jpg)
Rearranging the previous equation we get
What this tells us is that observers measure any ruler tocontract in length if it moves relative to them
To the traveler her ruler will continue to show the properlength ℓ0 as she is at rest in her reference frame
What the equation also tells us is that as a travelerapproaches the speed of light her ruler will contract to zeroas observed by a stationary observer as shown in the nextslide 95
ℓ/ℓ0 = 1/𝛾
![Page 96: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/96.jpg)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
𝓵 /𝓵 0=1/𝛄=√(1−u2/c
2 )
Speedurelativetothespeedoflightc(u/c)
Length contraction
Asu approachesc,1/𝛄 approacheszero
ℓ/ℓ0 =1/𝛾
96
![Page 97: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/97.jpg)
Tarringroadsreducesthedistance!AnadvertseeninJohannesburginternationalairport
Ausefulrelationshiptoremember:
∆t0/∆t=l/l0 = 1/𝛾
![Page 98: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/98.jpg)
Tarringroadsreducesthedistance!AnadvertseeninJohannesburginternationalairport
Ausefulrelationshiptoremember:
∆t0/∆t=ℓ/ℓ0 = 1/𝛾
![Page 99: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/99.jpg)
Length contraction of a cube as it would appear at various relative velocitiesMeasuredlengthVisualAppearance
0.0c
00.5 c 0.99c
MeasuredlengthVisualAppearanceMeasuredlengthVisualAppearance
![Page 100: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/100.jpg)
Length contraction of a cube as it would appear at various relative velocitiesMeasuredlengthVisualAppearance
0.0c
00.5 c 0.99c
MeasuredlengthVisualAppearanceMeasuredlengthVisualAppearance
![Page 101: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/101.jpg)
Length contraction of a cube as it would appear at various relative velocitiesMeasuredlengthVisualAppearance
0.0c
00.5 c 0.99c
MeasuredlengthVisualAppearanceMeasuredlengthVisualAppearance
![Page 102: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/102.jpg)
Length Contraction in Practice
102
![Page 103: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/103.jpg)
103
Electronsreachaspeedofjust1cm/slessthancinthe3kmbeamlineoftheSLACnationalacceleratorAsmeasuredbytheelectronthebeamlinewhichstretchesfromthetoptowardsthebottomofthephotoisonly15cmlong!
![Page 104: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/104.jpg)
104
Electronsreachaspeedofjust1cm/slessthancinthe3kmbeamlineoftheSLACnationalacceleratorAsmeasuredbytheelectronthebeamlinewhichstretchesfromthetoptowardsthebottomofthephotoisonly15cmlong!
![Page 105: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/105.jpg)
Experimental proof of time dilation and length contraction
![Page 106: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/106.jpg)
RicardFeynmanoncesaidthatnomatterhowbeautifulyourtheory,nomatterhowcleveryouareorwhatyournameis,ifitdisagreeswithexperiment,it’swrong!Let'sseeifthisappliestotimedilationandlengthcontractionAmuon(heavyelectron)hasahalflifeof2.2microsecondswhenatrestScientistshaveacceleratedabeamofmuonscirculatingarounda14mdiameterringto99.94%ofthespeedoflightattheAGSSynchrotroninNewYorkWithouttimedilationtheywouldonlylastfor15lapsoftheringTheylastfor400laps!aps
106
![Page 107: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/107.jpg)
RicardFeynmanoncesaidthatnomatterhowbeautifulyourtheory,nomatterhowcleveryouareorwhatyournameis,ifitdisagreeswithexperiment,it’swrong!Let'sseeifthisappliestotimedilationandlengthcontractionofamuon(heavyelectron)whichhasahalflifeof2.2microsecondswhenatrestScientistshaveacceleratedabeamofmuonscirculatingarounda14mdiameterringto99.94%ofthespeedoflightattheAGSSynchrotroninNewYorkWithouttimedilationtheywouldonlylastfor15lapsoftheringTheylastfor400laps! 107
![Page 108: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/108.jpg)
RicardFeynmanoncesaidthatnomatterhowbeautifulyourtheory,nomatterhowcleveryouareorwhatyournameis,ifitdisagreeswithexperiment,it’swrong!Let'sseeifthisappliestotimedilationandlengthcontractionAmuon(heavyelectron)hasahalflifeof2.2microsecondswhenatrestScientistshaveacceleratedabeamofmuonscirculatingarounda14mdiameterringto99.94%ofthespeedoflightattheAGSSynchrotroninNewYorkWithouttimedilationtheywouldonlylastfor15lapsoftheringTheylastfor400laps! 108
![Page 109: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/109.jpg)
RicardFeynmanoncesaidthatnomatterhowbeautifulyourtheory,nomatterhowcleveryouareorwhatyournameis,ifitdisagreeswithexperiment,it’swrong!Let'sseeifthisappliestotimedilationandlengthcontractionAmuon(heavyelectron)hasahalflifeof2.2microsecondswhenatrestScientistshaveacceleratedabeamofmuonscirculatingarounda14mdiameterringto99.94%ofthespeedoflightattheAGSSynchrotroninNewYorkWithouttimedilationthemuonswouldonlylastfor15lapsoftheringTheylastfor400laps! 109
![Page 110: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/110.jpg)
RicardFeynmanoncesaidthatnomatterhowbeautifulyourtheory,nomatterhowcleveryouareorwhatyournameis,ifitdisagreeswithexperiment,it’swrong!Let'sseeifthisappliestotimedilationandlengthcontractionAmuon(heavyelectron)hasahalflifeof2.2microsecondswhenatrestScientistshaveacceleratedabeamofmuonscirculatingarounda14mdiameterringto99.94%ofthespeedoflightattheAGSSynchrotroninNewYorkWithouttimedilationthemuonswouldonlylastfor15lapsoftheringInpracticetheylastedfor400laps! 110
![Page 111: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/111.jpg)
Thismeansthattheirlifetimehadbeenincreasedbyafactorof29tojustover60microseconds
Thisresultagreesexactlywiththeory(𝛾 =29)
Ifyoujoinedthemuonyouwouldofcoursecirculatethering400timesaswell
Theproblemhereisthatyourwatchwouldonlymeasure2.2microsecondsbecauseyouwouldbestandingstillinthemuonsreferenceframe
111
![Page 112: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/112.jpg)
Thismeansthattheirlifetimehadbeenincreasedbyafactorof29tojustover60microseconds
Thisresultagreesexactlywiththeory(𝛾 =29)Ifyoujoinedthemuonyouwouldofcoursecirculatethering400timesaswell
Theproblemhereisthatyourwatchwouldonlymeasure2.2microsecondsbecauseyouwouldbestandingstillinthemuonsreferenceframe
112
![Page 113: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/113.jpg)
Thismeansthattheirlifetimehadbeenincreasedbyafactorof29tojustover60microseconds
Thisresultagreesexactlywiththeory(𝛾 =29)
Ifyoujoinedthemuonyouwouldofcoursecirculatethering400timesaswell
Theproblemhereisthatyourwatchwouldonlymeasure2.2microsecondsbecauseyouwouldbestandingstillinthemuonsreferenceframe
113
![Page 114: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/114.jpg)
Thismeansthattheirlifetimehadbeenincreasedbyafactorof29tojustover60microseconds
Thisresultagreesexactlywiththeory(𝛾 =29)
Ifyoujoinedthemuonyouwouldofcoursecirculatethering400timesaswell
Theproblemhereisthatyourwatchwouldonlymeasure2.2microsecondsbecauseyouwouldbestandingstillinthemuon’sreferenceframe
114
![Page 115: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/115.jpg)
Youcouldnotcirculatethering400timesin2.2microseconds!
Thecircumferenceoftheringmusthaveshrunkfromtheviewpointofthemuon
Thelengthoftheoftheringasdeterminedbythemuonmustshrinkbythesameamountthatthemuon’slifeincreases(29times)
Bothspaceandtimehavebecomemalleable!
Theeffectsarereal! 115
![Page 116: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/116.jpg)
Youcouldnotcirculatethering400timesin2.2microseconds!
Thecircumferenceoftheringmusthaveshrunkfromtheviewpointofthemuon
Thelengthoftheoftheringasdeterminedbythemuonmustshrinkbythesameamountthatthemuon’slifeincreases(29times)
Bothspaceandtimehavebecomemalleable!
Theeffectsarereal! 116
![Page 117: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/117.jpg)
Youcouldnotcirculatethering400timesin2.2microseconds!
Thecircumferenceoftheringmusthaveshrunkfromtheviewpointofthemuon
Infact,thelengthoftheoftheringasdeterminedbythemuonshrinksbythesameamountthatthemuon’slifeincreases(29times)
Bothspaceandtimehavebecomemalleable!
Theeffectsarereal! 117
![Page 118: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/118.jpg)
Youcouldnotcirculatethering400timesin2.2microseconds!
Thecircumferenceoftheringmusthaveshrunkfromtheviewpointofthemuon
Thelengthoftheoftheringasdeterminedbythemuonshrinksbythesameamountthatthemuon’slifeincreases(29times)
Bothspaceandtimehavebecomemalleable
Theeffectsarereal! 118
![Page 119: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/119.jpg)
Youcouldnotcirculatethering400timesin2.2microseconds!
Thecircumferenceoftheringmusthaveshrunkfromtheviewpointofthemuon
Thelengthoftheoftheringasdeterminedbythemuonshrinksbythesameamountthatthemuon’slifeincreases(29times)
Bothspaceandtimehavebecomemalleable!
Theeffectsarereal! 119
![Page 120: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/120.jpg)
Relativistic paradoxes
![Page 121: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/121.jpg)
Givenapairoftwinswhereonetravelsintospaceatnearthespeedoflightforsaytenyears,whenthetravellingtwinreturnscantheystillbethesameage?
121
![Page 122: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/122.jpg)
Givenapairoftwinswhereonetravelsintospaceatnearthespeedoflightforsaytenyears,whenthetravellingtwinreturnscantheystillbethesameage?Atraintravellingnearthespeedoflightapproachesatunnelwhichmeasures80%ofitslengthwhentheyarestationeryrelativetoeachother.Canthetrainfitintothetunnel?
122
![Page 123: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/123.jpg)
Givenapairoftwinswhereonetravelsintospaceatnearthespeedoflightforsaytenyears,whenthetravellingtwinreturnscantheystillbethesameage?Atraintravellingnearthespeedoflightapproachesatunnelwhichmeasures80%ofitslengthwhentheyarestationeryrelativetoeachother.Canthetrainfitintothetunnel?ToanswerthesequestionsweneedtousetwoimportantrelativisticequationscalledtheLorentztransformsnamedaftertheDutchphysicistHendrikLorentzwhodevelopedthemandfromwhichEinsteinbenefitted!
123
![Page 124: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/124.jpg)
Givenapairoftwinswhereonetravelsintospaceatnearthespeedoflightforsaytenyears,whenthetravellingtwinreturnscantheystillbethesameage?Atraintravellingnearthespeedoflightapproachesatunnelwhichmeasures80%ofitslengthwhentheyarestationeryrelativetoeachother.Canthetrainfitintothetunnel?ToanswerthesequestionsweneedtousetwoimportantrelativisticequationscalledtheLorentztransformsnamedaftertheDutchphysicistHendrikLorentzwhodevelopedthemTheLorentztransformsarealsorequiredtoresolvesimultaneityissuesandarethemostusefulsetofequationsusedinrelativisticproblemsolving
124
![Page 125: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/125.jpg)
Lorentz coordinate transformations
![Page 126: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/126.jpg)
Whenaneventoccursatpoint(x,y,z)attime tasobservedinaframeofreferenceS,whatarethecoordinates(x’,y’,z’)andtimet’oftheeventasobservedinasecondframeS’movingrelativetoSwithavelocityofu inthe+xdirection?
126
![Page 127: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/127.jpg)
Withoutperformingadetailedderivation,thetransformationofaneventwithspacetimecoordinatesx,y,zand tinframeSandx’,y’,z’andt’inframeS’isdonebyviathefollowingLorentzcoordinatetransformations
x’=𝛾 (x-ut)Lorentzcoordinatetransformations
t’=𝛾 (t-ux/c2)
Whereu isvelocityofS’relativetoS inthepositivex– x’axisc isthespeedoflight and𝛾 istheLorentzfactorrelatingframesS andS’y’=yand z’=zsincetheyareperpendiculartox
127
![Page 128: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/128.jpg)
Withoutperformingadetailedderivation,thetransformationofaneventwithspacetimecoordinatesx,y,zand tinframeSandx’,y’,z’andt’inframeS’isdonebyviathefollowingLorentzcoordinatetransformations
x’=𝛾 (x-ut)Lorentzcoordinatetransformations
t’=𝛾 (t-ux/c2)
y’=yand z’=zsincetheyareperpendiculartox
128
![Page 129: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/129.jpg)
Withoutperformingadetailedderivation,thetransformationofaneventwithspacetimecoordinatesx,y,zand tinframeSandx’,y’,z’and t’inframeS’isdonebyviathefollowingLorentzcoordinatetransformations
x’=𝛾 (x-ut)Lorentzcoordinatetransformations
t’=𝛾 (t-ux/c2)
y’=yand z’=zsincetheyareperpendiculartox
129
![Page 130: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/130.jpg)
Spaceandtimehaveclearlybecomeintertwinedandwecannolongersaythatlengthandtimehaveabsolutemeaningsindependentoftheframeofreference
Timeandthethreedimensionsofspacecollectivelyforafour-dimensionalentitycalledspacetime andwecallxandttogetherthespacetimecoordinatesofanevent
130
![Page 131: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/131.jpg)
Spaceandtimehavebecomeintertwinedandwecannolongersaythatlengthandtimehaveabsolutemeaningsindependentoftheframeofreference
Timeandthethreedimensionsofspacecollectivelyformafour-dimensionalentitycalledspacetime andwecallx,y,zandt togetherthespacetimecoordinatesofanevent
UsingtheLorentzcoordinatetransformationswecanderiveasetofLorentzvelocitytransformations
Theresult(withoutderivation)isshowninthenextslide131
![Page 132: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/132.jpg)
Aswesawyesterday,spaceandtimehavebecomeintertwinedandwecannolongersaythatlengthandtimehaveabsolutemeaningsindependentoftheframeofreferenceTimeandthethreedimensionsofspacecollectivelyforafour-dimensionalentitycalledspacetime andwecallx,y,zandt togetherthespacetimecoordinatesofanevent
UsingtheLorentzcoordinatetransformationswecanderiveasetofLorentzvelocitytransformations
Theresult(withoutderivation)isshowninthenextslide132
![Page 133: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/133.jpg)
Aswesawyesterday,spaceandtimehavebecomeintertwinedandwecannolongersaythatlengthandtimehaveabsolutemeaningsindependentoftheframeofreferenceTimeandthethreedimensionsofspacecollectivelyforafour-dimensionalentitycalledspacetime andwecallx,y,zandt togetherthespacetimecoordinatesofanevent
UsingtheLorentzcoordinatetransformationswecanderiveasetofLorentzvelocitytransformations
Theresult(withoutderivation)isshowninthenextslide133
![Page 134: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/134.jpg)
In the extreme case where vx = cwe get
vx’ = (c-u)/(1-uc/c2) = c(1-u/c)/(1-u/c) = c
This means that anything moving at c measured in S isalso travelling at c when measured in S’ despite therelative motion of the two frames
134
vx’=(vx – u)/(1- uvx/c2)Lorentzonedimensionalvelocitytransformation
![Page 135: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/135.jpg)
In the extreme case where vx = cwe get
vx’ = (c-u)/(1-uc/c2) = c(1-u/c)/(1-u/c) = c
This means that anything moving at c measured in S isalso travelling at c when measured in S’ despite therelative motion of the two frames
135
vx’=(vx – u)/(1- uvx/c2)Lorentzonedimensionalvelocitytransformation
![Page 136: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/136.jpg)
In the extreme case where vx = cwe get
vx’ = (c-u)/(1-uc/c2) = c(1-u/c)/(1-u/c) = c
This means that anything moving at c measured in S isalso travelling at c when measured in S’ despite therelative motion of the two frames
136
vx’=(vx – u)/(1- uvx/c2)Lorentzvelocitytransformation
![Page 137: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/137.jpg)
TheLorentzvelocitytransformationshowsthatabodywithaspeedlessthanc inoneframeofreferencealwayshasaspeedlessthanc ineveryotherframeofreference
Thisisonereasonforconcludingthatnomaterialbodymaytravelwithaspeedgreaterthanorequaltothespeedoflightinavacuum,relativetoanyinertialreferenceframe
137
![Page 138: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/138.jpg)
TheLorentzvelocitytransformationshowsthatabodywithaspeedlessthanc inoneframeofreferencealwayshasaspeedlessthanc ineveryotherframeofreference
Thisisonereasonforconcludingthatnomaterialbodymaytravelwithaspeedgreaterthanorequaltothespeedoflightinavacuum,relativetoanyinertialreferenceframe
138
![Page 139: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/139.jpg)
Let'sconsideranexampleofthevelocitylimitwhichanyobservercanreachrelativetosomeotherobserver
IfwehadasetoffivespaceshipsstackedlikeRussiandollswhereeachshipcouldlaunchtheremainingshipsatavelocityequaltotherelativevelocityofthelaunchingshipasobservedfromearthwhatrelativevelocitiescouldthevariousshipsachieverelativetotheearthobserver?
Thefollowingslideshowsthevelocityprofilesofthefivespaceshipsrelativetoanearthobserver
139
![Page 140: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/140.jpg)
Let'sconsideranexampleofthevelocitylimitwhichanyobservercanreachrelativetosomeotherobserver
IfwehadasetoffivespaceshipsstackedlikeRussiandollswhereeachshipcouldlaunchtheremainingshipsatavelocityequaltotherelativevelocityofthelaunchingshipasobservedfromearthwhatrelativevelocitiescouldthevariousshipsachieverelativetotheearthobserver?
Thefollowingslideshowsthevelocityprofilesofthefivespaceshipsrelativetoanearthobserver
140
![Page 141: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/141.jpg)
Let'sconsideranexampleofthevelocitylimitwhichanyobservercanreachrelativetosomeotherobserver
IfwehadasetoffivespaceshipsstackedlikeRussiandollswhereeachshipcouldlaunchtheremainingshipsatavelocityequaltotherelativevelocityofthelaunchingshipasobservedfromearthwhatrelativevelocitiescouldthevariousshipsachieverelativetotheearthobserver?
Thefollowingslideshowsthevelocityprofilesofthefivespaceshipsrelativetoanearthobserver
141
![Page 142: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/142.jpg)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rocketspeedsrelativetospeedof
lightcasasobservedonearth
Rocketspeedsrelativetospeedoflightcobservedbysuccessiveshipobserverswhenu=v
Relative rocket ship speeds
Mothership Rocket 1 Rocket 2 Rocket 3 Rocket 4 Rocket 5
142
![Page 143: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/143.jpg)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rocketspeedsrelativetospeedof
lightcasasobservedonearth
Rocketspeedsrelativetospeedoflightcobservedbysuccessiveshipobserverswhenu=v
Relative rocket ship speeds
Mothership Rocket 1 Rocket 2 Rocket 3 Rocket 4 Rocket 5
143
![Page 144: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/144.jpg)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rocketspeedsrelativetospeedof
lightcasasobservedonearth
Rocketspeedsrelativetospeedoflightcobservedbysuccessiveshipobserverswhenu=v
Relative rocket ship speeds
Mothership Rocket 1 Rocket 2 Rocket 3 Rocket 4 Rocket 5
144
![Page 145: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/145.jpg)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rocketspeedsrelativetospeedof
lightcasasobservedonearth
Rocketspeedsrelativetospeedoflightcobservedbysuccessiveshipobserverswhenu=v
Relative rocket ship speeds
Mothership Rocket 1 Rocket 2 Rocket 3 Rocket 4 Rocket 5
145
![Page 146: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/146.jpg)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rocketspeedsrelativetospeedof
lightcasasobservedonearth
Rocketspeedsrelativetospeedoflightcobservedbysuccessiveshipobserverswhenu=v
Relative rocket ship speeds
Mothership Rocket 1 Rocket 2 Rocket 3 Rocket 4 Rocket 5
146
![Page 147: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/147.jpg)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rocketspeedsrelativetospeedof
lightcasasobservedonearth
Rocketspeedsrelativetospeedoflightcobservedbysuccessiveshipobserverswhenu=v
Relative rocket ship speeds
Mothership Rocket 1 Rocket 2 Rocket 3 Rocket 4 Rocket 5
147
![Page 148: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/148.jpg)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rocketspeedsrelativetospeedof
lightcasasobservedonearth
Rocketspeedsrelativetospeedoflightcobservedbysuccessiveshipobserverswhenu=v
Relative rocket ship speeds
Mothership Rocket 1 Rocket 2 Rocket 3 Rocket 4 Rocket 5
Nomatterhowmanysuccessiverocketsarelaunchedtheirvelocitywillneverexceedc!
148
![Page 149: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/149.jpg)
Test your understanding of time dilationPeter,whoisstandingontheground,startshisstopwatchthemomentthatSarahfliesoverheadinaspaceshipataspeedof0.6cAtthesameinstantSarahstartsherstopwatchAsmeasuredinPeter’sframeofreference,whatisthereadingonSarah’sstopwatchattheinstantpeter’sstopwatchreads10s?a)10s,b)lessthan10sorc)morethan10s?AsmeasuredinSarah’sframeofreference,whatisthereadingonPeter’sstopwatchattheinstantthatSarah’sstopwatchreads10s?a)10s,b)lessthan10sorc)morethan10s?Whosestopwatchisreadingpropertimeintheabovetwoexamples?
![Page 150: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/150.jpg)
Test your understanding of length contraction
Aminiaturespaceshipfliespastyouhorizontallyat0.99cAtacertaininstantyouobservethatthatthenoseandtailofthespaceshipalignexactlywiththetwoendsofameterstickthatyouholdinyourhandRankthefollowingdistancesinorderfromlongesttoshortest:a)theproperlengthofthemeterstick;b)theproperlengthofthespaceship;c)thelengthofthespaceshipmeasuredinyourreferenceframe;d)thelengthofthemeterstickmeasuredinthespaceship’sframeofreference?
![Page 151: Special Relativity · 2020-01-09 · Special Relativity Presentation to UCT Summer School Jan 2020 (Part 2 of 3) By Rob Louw roblouw47@gmail.com 1. Test your understanding of simultaneity](https://reader034.vdocuments.site/reader034/viewer/2022050100/5f3f93efcfb3e46890683a3d/html5/thumbnails/151.jpg)