1) The document discusses Albert Einstein's theory of special relativity, which was published in 1905 and built upon previous work by Michelson, Lorentz, Poincaré, and others. It describes Einstein's two postulates of relativity and the constant speed of light. 2) It summarizes the Michelson-Morley experiment, which found no evidence for the hypothesized luminiferous ether, and how this led to Lorentz developing the Lorentz transformations. 3) The Lorentz transformations show that time and length are relative between reference frames in motion, resulting in time dilation and length contraction as predicted by special relativity.

1. Engineering Physics I Unit I
Theory of Relativity
Presentation By
Dr.A.K.Mishra
Professor
Jahangirabad Institute of Technology, Barabanki
Email: akmishra.phy@gmail.com
Arun.Kumar@jit.edu.in
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
1

2. Theory of relativity
• Albert Einstein published the theory of special relativity in
1905, building on many theoretical results and empirical
findings obtained by Albert A. Michelson, Hendrik Lorentz,
Henri Poincaré and others. Max Planck, Hermann Minkowski
and others did subsequent work.
• In Albert Einstein's original pedagogical treatment, it is based
on two postulates:
• The laws of physics are invariant (i.e. identical) in all inertial
systems (non-accelerating frames of reference).
• The speed of light in a vacuum is the same for all observers,
regardless of the motion of the light source.
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
2

3. Frame of reference
• To locate/Measure an event in the space we need a coordinate
system i.e. known as the frame of reference.
Like as (x,y,z,t) and (x’,y’,z’,t’)
where x,y,z are called spacial part and t is
temporal part.
• Basically two types of frames,
Inertial frame (un accelerated frame):
Which obey the Newtonian mechanics or
all the law of physics holds good.
Non Inertial frame (accelerated frame):
Which does not obey the Newtonian mechanics.
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
3

4. Galilean Transformation
• -
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
4
O’
y’
X’X
Y
O
vt X’
x
Frame S’Frame S Event
Einstein.bygivenpostulateper theas
nexplanatiorysatisfactogiven thehasLorentzonLater
denied.stheory wahissoacceptablenotist'but t
ion.TranformatGalileanasknownareeqet thest'
zz'
yy'
vt-xx'
thencity v.with veloStorelativedirection
xinmovingisS'whereframestwothebes'ands
n





 veLet

5. Concept of Ether
• In nineteenth century physicist assume that electromagnetic waves
also requires medium for propagation.
• They assume a hypothetical medium ether is filled in whole
universe, because ether is mass less and rigid. By which the EM
wave propagate.
• Due to which prediction the whole Maxwell eqn must be modified
because all the eqn is strictly based on without medium.
• To prove the existence of ether as a medium, A. A. Michelson and
E.W. Morley performed an experiment throughout the year
in different season at different place but they failed to prove the
existence and the concept is denied.
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
5

6. Michelson–Morley experiment
• -
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
6
v.isearthofvelocitytheorbit withsearth'
theofdirectionthealongmovetoarrangeisopratusThe
elescope.through tobservedbecan
fringesceinterferenandAatinterferewavestwothese
back.reflect
andM2towardstravellsbeamdtransmittesimilarly
backreflectandM1towardstravellbeamreflected
thepart,twointosplitA whichplateinclined
anndLlensonfallsssourceticmonochroma
fromlightexperimentMorley-Michelson•
A

7. Michelson–Morley experiment
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
7
)1(....................
v-
Dc2DD
TTT
asgivenistimefroandtototalThe
soA'toM'fromis
TandMA tofromtravellight tobytakntimethebeTlet
vcearhofmotiontheofdirectionoppsiteinand
v-cearhofmotiontheofdirectionin thelightofvelocity
DAM2AMdistancethe
2221
2
221
1
cvcvc
Let









8. Michelson–Morley experiment
The total distance travelled by light
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
8
.(3)..........).........
2
1
2D(1x
ctxtravelleddistanceTotal
)
2
1
(1
c
2D
2T'T
A'.back toand
'MA tofromgoinginlightby thetakentimeTotal
)
2
1
(1
c
D
'
1
DD
'
T'VDT'c
vT'ARdistanceThe
R.toshiftedisAand'MtoshiftedisMtimethisduring
T'.be'MA tofromtravellight tobytakentimeLet the
.(2)…………………)
c
v
(12D
2Dc
=cxT=x
2
2
2
2
2
2
1
2
2
2
222
22222
11
1
2
2
22
2
1
c
v
c
v
c
v
T
c
v
c
vc
T
vc













9. • From eqn (2) and (3) the path difference can be given as
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
9
fringes.0.2
m/s)10x(3m)10x5(
m/s)(3x10(10m)
c
Dvx
n
Therefore,90byrotatedisapparatustheand
nm.500isusedlightofhwavelengttheandm10=DIf
c
Dvx
nor
nx
havethen wefringesnofshiftingthe
toscorrespond(4)eqnindifferencepaththeIf
)4....(....................
2Dv
x
)
2
1
(12D-)
2
1
(1
c
2D
x
287-
24
2
2
0
2
2
2
2
2
2
2
2
21












c
c
v
c
v
x

10. Negative result of the Michelson – Morley experiment
• -
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
10
.
v
-1factorabymotionofdirectionthe
incontractedisetherthroughmovingbodymaterialthe
hypothesisncontractioFitzgerald–LorentztoAccording•
observer.and
sourceofmotionanyofregardlesseverywheresame
theisspacefreeinlightofspeedthat thesuggestsIt•
ether.theofhypothesistheuntenablerenderedIt•
2
2
c

11. Lorentz transformation
• -
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
11
ct'r'andctr
bygiveniso'andofromPpointthetodistanceThe
o'.fromr'andofromr
distanceaatPathappendiseventanlater timesomeAt
t'.at tcoincideframestwooforigineinstant thAt the
t).z,y,(x,coordinatesusesframeinobseverstationary
while)t',z',y',(x'scoordinatewithframes'inaxisxx'
alongvspeedawithmovingflashbulbaConsider
Einstein.byrecognisedandeqn
tiontransfomathedevelopedwasLorentzAH1890in.cv0
speedallateqnonansformaticorrect trthedetermineto
light.ofspeedhighatnot validistionTransformaGalilean



The
O O’
YY’
X’X
r
O
v
X X’
Z Z’
Frame S’Frame S
Event
O’
y’
P
r’
t = t’ = 0

12. 9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
12
O’
y’
X’X
Y
O
vt X’
x
Frame S’Frame S Event

13. Lorentz transformation
• If we accept Einstein second postulate then t and t’ must be different. it is contrast to Galeliean.
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
13
c).(vspeedlowfor
equationGalelieantoreducebecanthisconstant,iskwhere
..(4)..........vt)......-(xkx'
aswrittenbecanx'andxtorelatingequationationtransform
)3(....................'-x'tc-x
getwe(1),from(2)gsubtractin
z'z&y'y)unaffectedare(theyequal,alwaysare
scoordinatezandymeansxx'alongiss'ofmotionthesin
)2...(..........'z'y'x':s'inobserver
...(1)..........tczyx:sinobserver
expressionfollowingobtain thewehence
s'.inobserverbymeasuredz'y'x'r'
likewiseandsinobserverbymeasuredzyxr
isspheretheofradiusofequationtheknowwe
222222
22222
22222
2222
2222








the
tc
ce
tc

14. Lorentz transformation
similarly
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
14
)11.......(..........
c
v
b
)10.........(..........
c
v
-1
1
ak
getwebandak,forequationthesesolving
..(9)....................1
c
vk
-a
)8.........(..........0bac-vk
..(7)..........1.........bac-k
havewe(6)intermingcorrespondoftscoefficien
)6...(t)c
c
vk
-(a-xt)bac-v(k2-)xbac-(ktc-x
bx)-(tac-vt)-(xktc-x
getwe(3)equationin
t'andfor x'valuestheseputtingconstant,areb&awhere
......(5)..........bx).......-(ta'
2
2
2
2
22
2
2222
2222
22
2
22
2222222222222
22222222








equating
t

15. Lorentz transformation
• -
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
15
equations.tionTransforma
Galelieanisht whict',zz',yy',vt-xx'
(11)equationfromthen1
c
v
-1
1
0
c
v
,cvvelocitylowFor
ZZ',YY',
c
v
-1
c
vx'
t'
t,
c
v
-1
vt'x'
x
equation,above
inv-byvreplacingandscoordinatetheinginterchangby
obtainedbecanequationationtransformLorentzinversethe
Z'Z,Y'Y,
c
v
-1
c
vx
-t
t',
c
v
-1
vt-x
x'
equation.tionTransforma
Lorentzget thewe(5)&(4)invaluethese
2
2
2
2
2
2
2
2
2
2
2
2









gsubtitutin

16. Length Contraction
• -
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
16
O’
y’
X’
X
Y
O
S’
S
rod.theofend
theofcoordinatethebex'2andLet x'1.
S'.inrestatABlengthofrodaconsider.
Storelativecity vwith velomovingisS'.
0t'at tcoincides'andsconsider.
n.ContractioLorentzasknownis
motiontheofdirectionin the
c
v
-1amount
anhimrest w.r.tatisitan whenshorter thbeto
observerthetoappearsobserver.tmotion w.r
inrodtheoflenghthat theobservedis
2
2

It

17. Length Contraction
• The
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
17
)3.........(..........
c
v
-1l
c
v
-1
1
ll
c
v
-1
1
l
c
v
-1
x-x
c
v
-1
vt-x
-
c
v
-1
vt-x
x'-x'
)2.....(
c
v
-1
vt-x
x'&......(1)
c
v
-1
vt-x
x'x-xl
S.ininstantsame
at therodtheofendtheofcoordinatethebexandlet x-
rest.atobserverbymeasuredx'-x'llength
2
2
0
2
20
2
2
2
2
12
2
2
1
2
2
2
12
2
2
1
1
2
2
2
212
21
120






l
proper

18. Length Contraction
• Reference frame at rest
• Reference frame in motion
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
18
ly.respectiveellipseanandrectanglebetoreferenceofframeotherthe
inobserverthetoappearsframeoneincircleaandsquareA
:examplesthearefollowing
motion.of
directionthelar toperpendicuinncontractionoisThere
.
c
v
-1
1
factorabycontractediss'inrodtheoflengththat the
findssinobservethe.thusllclear that(3)equationtheFrom
2
2
0

19. Time Dilation
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
19
...(4)....................
c
v
-1
t
t
tt-tandtt'-Let t'
.(3)....................
c
v
-1
t-t
t'-t'
getw e(2),from(1)equation
)2.....(..........
c
v
-1
c
vx
-t
t',.....(1)..........
c
v
-1
c
vx
-t
t'
equations,tiontransforma
Lorentzfromthen,t'-t'isclockmovingthew hereas
t-tisclockstationarybymeasuredintervaltimeThe
ship.rocketinsay,framemoving
inisoneotherandframestationaryinoneputand
initiallyedsynchronizexactlyclockstw osupposeusLet•
observer.theandeventsebetw een thmotion
relativeon thedependitbutabsolutenotisintervalTime•
2
2
0
01212
2
2
12
12
2
2
22
2
2
2
21
1
12
12





gsubtractin

20. Time Dilation
-From (4) it is clear
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
20
an this.greater thtime10thanmorealtitudeatcreated
meson-m.while600)10x(2)10x(2.994distanceaat
can travelandm/s10x2.994ofspeedahavemesonssuch
sec.10x2istimelifeitsmeans
sec.10x2timeaverageaninelectronanin todecayits
level.seaatreachandparticlesrayscosmicfastby
atmosphereinhighcreatedmesons-:EXAMPLE
delation.Timecallediseffect
icrelativistdown.thisslowedisclockmovingmean the
clock.itstationarybymeasuredtinervaltimethan the
moreisclockmovingbymeasuredast,intervaltime
6-8
8
6-
6-
0




the

21. Time Dilation
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
21
effect.realisdilationtimeHence,relativityoftheoryspecial
usingbyresolvedisioncontradictmeson-theNow
m9500
)10x(2.994x10x31.7
ismeson-by thetravelleddistancethe
10x31.7
063.0
10x2
)
c
0.998
(-1
10x2
c
v
-1
t
t
ascalculatedbecanreferenceofframeourin
meson-oflifetimethe,dilationtimeofexpressionthe
86-
6-
6-
2
6-
2
2
0








thus
s
From

22. Velocity Addition Theorem
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
22
c
v
-1
c
dx'v
dt'
dt,dz'dz,dy'dysimilarly
c
v
-1
dt'dx'
c
v
-1dt
dt'dx'
c
v
-1
dt
dt'
v
dt
dx'
dt
c
v
-1
vt'x'
x
obtainedt w e,t w .r.tandzy,for x,equations
ationtransformLorentzinversetheatingdifferenti
dt'
dz'
u',
dt'
dy'
u',
dt'
dx'
u'
measures'in
observeranw hile
dt
dz
u,
dt
dy
u,
dt
dx
u
component,velocitythemeasuressinobserverAn
s'.andstorelativemovingisparticleaconsiderus
2
2
2
2
2
2
2
2
2
2
2
zyx
zyx












dx
dx
By
Let

23. Velocity Addition Theorem
-Therefore
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
23
2
x
2
2
z
z
2
x
2
2
y
y
2
x
x
2
x
2
x
u'v
1
c
v
-1u'
u,
u'v
1
c
v
-1u'
u
c
u'v
1
vu'
'
dx'
c
v
1
v
dt'
dx'
u
r.denominatoandnumeratorindt'byR.H.S
c
dx'v
dt'
dt'vdx'
dt
dx
u
cc
dt
dividing














24. Velocity Addition Theorem
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
24
constant.absoluteislightofvelocityThe
light.of
velocitythereproducesmerelylightofvelocitythelight toof
velocityofadditionthat theshowsThisc
c
cc
1
cc
u
thenvcu'whenother,
ofvelocitythewhatevercalwayisvelocityrelativetheir
other thenw.r.tccitywith velomovesobjectanifthus,
c
c
vc
1
vc
c
u'v
1
cu'
u
velocitythemeasure
willsinobserverthes,torelativemotionofdirection
in thes'framemovinginemittedislightifi.ecu'
2
x
x
22
x
x
x
x












if

25. Variation of mass with velocity
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
25
y’ v
O’ X’
X
Y
O
S’S
A B
u -u
momentumofonconservatioflawgconsiderin
body.oneinto
coalesceandothereachwithcollidethey
u).-andu(i.espeedequalatother
eachapprochmmassofeachBandA
ballselesticsimilarexactelyLet two
direction.xvein
elocity vconstant vwithmoving
iss',s'andsframewoConsider t


26. Variation of mass with velocity
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
26
3).........(..........v)m(mumum
momentum
ofonconservatioflawfromthens.frameinm&uis
Bballandm&ubeAballofvelocity&masslet the
s.relativevismasscoalescedofvelocitycollision
)2.........(..........
c
uv
1
vu
u
)........(1..........
c
uv
1
vu
u
s.thentorelativeballsofvelocity
thebeuandus.letfrmaew.r.tcollisionheconsider tNow
frame.s'inrestatmasscoalescedThus
mass).coalescedof
(Momentumo(-mu)mui.e.masscoalescedof
MomentumBballofAballof
212211
22
11
2
2
2
1
21









after
MomentumMomentum

27. Variation of mass with velocity
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
27
)
c
uv
(1
)
c
v
-(1u
m
)
c
uv
(1
)
c
v
-(1u
m
)
c
uv
1
vu-
(-vmv-)
c
uv
1
vu
(m
v)m(m)
c
uv
1
vu-
(m)
c
uv
1
vu
(m
(2)&(1)equationfromu&ufor
2
2
2
2
2
2
2
1
2
2
2
1
21
2
2
2
1
21


























































gsubtitutin

28. Variation of mass with velocity
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
28
2
2
2
2
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
2
1
)1(
)1(
c
-1
c
-1
(5)eqsby(6)eqs
)6....(....................
)1(
)
c
v
-)(1
c
u
-(1
c
-1
)5.(..........
)1(
)
c
v
-)(1
c
u
-(1
)1(
)
c
vu
(
-1
c
-1
termtheofvalueheconsider tus
)4.......(....................
c
uv
1
c
uv
1
m
m
u
u
u
u
c
uv
c
uv
Dividing
c
uv
c
uv
c
uv
Let
or














29. Variation of mass with velocity
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
29
body thus,theof
massresttheism0w herem
c
-1m
c
-1m
constant,aiseachonly w hen
truebemayresultthisandanotheroneoftindependen
areRHSandLHSclear thatisiteqsabovethe
)8......(..........
c
-1m
c
-1m
c
-1
c
-1
m
m
(7)and(4)equationfrom,
)7...(....................
)1(
)1(
c
-1
c
-1
02
2
2
22
2
1
1
2
2
2
22
2
1
1
2
2
1
2
2
2
2
1
2
2
2
2
1
2
2
2
uu
uu
u
u
u
u






From
Thus
c
uv
c
uv

30. Variation of mass with velocity
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
30
.mmThus
neglected,
bemay
c
thenc,when vi.e,elocityordinary vat
mass.infinitehavedlight woulofspeed
withvellingobject traani.e,m,cwhen v
city.with velomassof
variationfor theformulaicrelativisttheiseqsabove
)9.........(..........
c
-1
m
mthenvvelocity
awithmovingisitbody whentheofmassthebemif
c
-1
m
m
0
2
2
2
2
0
2
2
1
0
1
u





v
v

31. MASS-ENERGY EQUIVALENCE
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
31
)3.....(....................
c
v
-1
m
m
citywith velomassofvariationtoAccording
)v).....(2
dt
dx
(dm.vdvmv
dx
dt
dm
vdx
dt
dv
mdxFdEnow
variableare
velocityandmassbothrelativityoftheoryfrom
)1..(..........
dt
dm
v
dt
dv
m(mv)
dt
d
FThus,
momentumofchangeofrateasdefinedisForce
(Fdx).doneworktoequalisbodythe
of)(dEKEin theincreasethen thedx.distanceaghbody throu
thedisplacsforcetheandity vwith velocdirectionsamein theF
forceabyuponactedmmassofparticleaconsiderus
2
2
0
2
k
k





because
Let

32. MASS-ENERGY EQUIVALENCE
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
32
m.becomesmassitsvisvelocity
itswhenandmmandzeroisenergykineticzero,isvelocityits
restatisbodywhenbecause)m-m(cdmcdEE
(5)eqsgintegratinredm.therefomassinchangeao
alproportiondirectelyisdEkenergykineticinchangeaThus
..(5)....................dmcdE
(4)and(2)eqsFrom
.(4)..........dm........vdvmvdmc
dm2mv2vdvmdm2mc
getwemw.r.tatingdifferenti
vmccm
c
v
-1
m
getwe(3)eqssideboth
0
0
2
m
m o
2
E
0
kk
2
k
22
222
2222
0
22
2
2
2
02
k
m
m














Squaring

33. MASS-ENERGY EQUIVALENCE
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
33
process.reversibletheisthisparticles.
ngdisappeariofEtoequalisenergyradientwhoseradiationcalledradiation
energyhighfindwedisappear,andcombinepositronandelectronWhen-
fusion.andfissionassuchreactionnuclearexplainmcE
statement'thefollowsrelationThisrelation.energy-massEinsteinsis
)7...(..........mccmcm-mccmEE
isbodytheofEenergytotaltheThus
energy.massrestcallediswhichcmisbodyin thestoredenergy
restatisbodytheenrgy.whenkineicforformulaicrelativisttheis
)6......(..........cm-mcE
2
22
0
2
0
22
0k
2
0
2
0
2
k




This
this

34. MASS-ENERGY EQUIVALENCE
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
34













































2
2
22
0
2
2
1
2
2
2
o2
2
0
2
02
2
2
1
2
2
2
o
2
o
2
k
c
v
-1
c
c
E
(1)equationfrom
...(2)....................mvp
)1.........(..........
c
v
-1
cm
mcEenergyTotal
momentumandenergyrestenergy,talbetween toRe
vm
2
1
cm1-
2c
v
1
1-
c
v
-1cmcm-mcE
c.for v
formulaclassicaltoreducesenergykineticforformula
m
momentum
lation
The

35. MASS-ENERGY EQUIVALENCE
-
9/13/2017
Dr A K Mishra, Academic Coordinator,
JIT Jahangirabad
35
)3..(....................cpc
P-
c
E
c
c
v
c
mc
-
c
E
c
c
v
c
E
-
c
E
c
v
-1
c
E
c
4242
0
2
2
2
22
0
2
2222
22
0
2
222
2
22
22
0
m
m
m
m














































E