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.
Introduction to Classical Mechanics:
UNIT-I : Elementary survey of Classical Mechanics: Newtonian mechanics for single particle and system of particles, Types of the forces and the single particle system examples, Limitation of Newton’s program, conservation laws viz Linear momentum, Angular Momentum & Total Energy, work-energy theorem; open systems (with variable mass). Principle of Virtual work, D’Alembert’s principle’ applications.
UNIT-II : Constraints; Definition, Types, cause & effects, Need, Justification for realizing constraints on the system
Study on Transmission Probabilities for Some Rectangular Potential Barriersijtsrd
In this research, we apply the time independent Schroedinger equation for a particle moving in one dimensional potential barrier of finite width and height. We study the two cases which corresponds to the particle energies being respectively larger and smaller than the potential barrier. Then, we calculate transmission coefficient T as a function of particle energy E for a potential barrier by changing the barrier height V0 and width L using Propagation Matrix Method. If we keep the barrier width constant and varying the height, we see that the passing limit is shifting towards the higher energies when barrier height is increased. If we keep the barrier height constant and change the barrier width, we see significance change in oscillations. Aye Than Kyae | Htay Yee | Thida Win | Aye Aye Myint | Kyaw Kyaw Naing "Study on Transmission Probabilities for Some Rectangular Potential Barriers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26813.pdfPaper URL: https://www.ijtsrd.com/physics/other/26813/study-on-transmission-probabilities-for-some-rectangular-potential-barriers/aye-than-kyae
Introduction to Classical Mechanics:
UNIT-I : Elementary survey of Classical Mechanics: Newtonian mechanics for single particle and system of particles, Types of the forces and the single particle system examples, Limitation of Newton’s program, conservation laws viz Linear momentum, Angular Momentum & Total Energy, work-energy theorem; open systems (with variable mass). Principle of Virtual work, D’Alembert’s principle’ applications.
UNIT-II : Constraints; Definition, Types, cause & effects, Need, Justification for realizing constraints on the system
Study on Transmission Probabilities for Some Rectangular Potential Barriersijtsrd
In this research, we apply the time independent Schroedinger equation for a particle moving in one dimensional potential barrier of finite width and height. We study the two cases which corresponds to the particle energies being respectively larger and smaller than the potential barrier. Then, we calculate transmission coefficient T as a function of particle energy E for a potential barrier by changing the barrier height V0 and width L using Propagation Matrix Method. If we keep the barrier width constant and varying the height, we see that the passing limit is shifting towards the higher energies when barrier height is increased. If we keep the barrier height constant and change the barrier width, we see significance change in oscillations. Aye Than Kyae | Htay Yee | Thida Win | Aye Aye Myint | Kyaw Kyaw Naing "Study on Transmission Probabilities for Some Rectangular Potential Barriers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26813.pdfPaper URL: https://www.ijtsrd.com/physics/other/26813/study-on-transmission-probabilities-for-some-rectangular-potential-barriers/aye-than-kyae
De Alembert’s Principle and Generalized Force, a technical discourse on Class...Manmohan Dash
A technical discourse on formal classical mechanics. This is a 12 slide introduction to the basics of how Newton's Laws are generalized into a Lagrangian Dynamics apt at the level of an advance student of Physics.
It covers all the Maxwell's Equation for Point form(differential form) and integral form. It also covers Gauss Law for Electric Field, Gauss law for magnetic field, Faraday's Law and Ampere Maxwell law. It also covers the reason why Gauss Laws are also known as Maxwell's Equation.
De Alembert’s Principle and Generalized Force, a technical discourse on Class...Manmohan Dash
A technical discourse on formal classical mechanics. This is a 12 slide introduction to the basics of how Newton's Laws are generalized into a Lagrangian Dynamics apt at the level of an advance student of Physics.
It covers all the Maxwell's Equation for Point form(differential form) and integral form. It also covers Gauss Law for Electric Field, Gauss law for magnetic field, Faraday's Law and Ampere Maxwell law. It also covers the reason why Gauss Laws are also known as Maxwell's Equation.
X-ray Crystallography is a scientific method used to determine the arrangement of atoms of a crystalline solid in three dimension. It is based on x ray diffraction. Reveals structure of a crystal at atomic level.
The paper proposes a model of a unitary quantum field theory where the particle is represented as a wave packet. The frequency dispersion equation is chosen so that the packet periodically appears and disappears without changing its form. The envelope of the process is identified with a conventional wave function. Equation of such a field is nonlinear and relativistically invariant. With proper adjustments, they are reduced to Dirac, Schroedinger and Hamilton-Jacobi equations. A number of new experimental effects are predicted both for high and low energies.
Reply to the Note of Jeremy Dunning-Davies Shafiq Khan
The open challenge was put forward by me and one professor of physics namely Jeremy Dunning-Davies accepted the challenge and wrote a note and that note was kept on General Science Journal & viXra. This is the published version of the reply to the note of Jeremy Dunning-Davies.
Superconductors and NANOTECHNOLOGY,Properties of nanomaterial's,Production of Buckyballs,Uses of Buckyballs,Carbon Nano tubes (CNTs) ,Applications of Superconductivity,BCS THEORY,London Penetration depth,TYPE OF SUPERCONDUCTORS,Meissner Effect (Effect of magnetic field)
Dielectric and Magnetic Properties of materials,Polarizability,Dielectic loss...A K Mishra
In this PPT contains ,Dia,Para,Ferromagnetism,Clausius-Mossoti equation,Dielectric Loss ,Hysteresis,Hysteresis loss and its Applications,Determination of susceptibility,types of polarisation in mateials,relative permability
SEMICONDUCTORS,BAND THEORY OF SOLIDS,FERMI-DIRAC PROBABILITY,DISTRIBUTION FUN...A K Mishra
This PPT contains valence band,conduction band& forbidden energy gap,Free carrier charge density,intrinsic and extrinsic semiconductors,Conductivity in semiconductors
Maxwells equation and Electromagnetic WavesA K Mishra
These slide contains Scalar,Vector fields ,gradients,Divergence,and Curl,Gauss divergence theorem,Stoks theorem,Maxwell electromagnetic equations ,Pointing theorem,Depth of penetration (Skin depth) for graduate and Engineering students and teachers.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
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
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
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)
2
1
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c
D
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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
)
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1
(12D-)
2
1
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c
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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’
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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