Lecture physics a2 special relativity

SPECIAL RELATIVITY Albert Einstein (1879 1955) Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 OUTLINES • Einstein’s Postulates • Lorentz Transformation • The Lorentz Velocity Transforma[.]

SPECIAL RELATIVITY

Albert Einstein (1879-1955)

Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016

OUTLINES

• Einstein’s Postulates

• Lorentz Transformation

• The Lorentz Velocity Transformation

• Relativity of Simultaneity

• Relativity of Length –Contraction of length

• Relativity of Time interval –Time dilatation

• Invariance of Space –Time interval

• Relativistic Dynamics

• Relativistic Energy, Relativistic Kinetic energy

Einstein’s Postulates

of relativity,states:The laws of physics are the same in all inertial frames of reference

speed of light in vacuum is the same in all

inertial frames of reference and is

independent of the motion of the source

dt dW

The Ultimate Speed Limit

 Einstein’s second postulate immediately implies the

following result: It is impossible for an inertial observer to travel at c, the speed of light in vacuum

 We can prove this by showing that travel at c implies a logical contradiction Suppose that the spacecraft is moving at the speed of light c relative to an observer on the earth, so that If the spacecraft turns on a headlight, the

second postulate now asserts that the earth observer measures the

headlight beam to be also moving at c Thus this observer measures that the headlight beam and the spacecraft move together and are always at the

same point in space But Einstein’s second postulate also asserts that the headlight beam moves at a speed relative to the spacecraft, so they cannot

be at the same point in space This contradictory result can be avoided only

if it is impossible for an inertial observer, such as a passenger on the

spacecraft, to move at c As we go through our discussion of relativity, you may find yourself asking the question Einstein asked himself as a 16-year-old student, “What would I see if I were traveling at the speed of light?”

Einstein realized only years later that his question’s basic flaw was that he could nottravel at c

go by them with the same speed

c

v

Both guys see the light flash

travel with velocity = c

No matter how fast the

guy on the rocket

is moving!!

Even when the light flash is

traveling in an opposite direction

c

v

Both guys see the light flash

travel past with velocity = c

The Lorentz Coordinate

Transformation

2 2 2

2 2

2 2 2

2 2

c

v 1

'

x c

v ' t t

; ' z z

; ' y y

; c

v 1

' vt ' x x

c

v 1

x c

v t

' t

; z ' z

; y ' y

; c

v 1

vt x

'

x

































Event A observed in reference frame O at

(x,y,z,t) , is observed at in ereference frame

O’(x’,y’,z’,t’)

The relationships between (x,y,z,t) and

(x’,y’,z’,t’) are given by the Lorentz

Coordinate Transformation

t=t’=0 , O  O’

x’

y’

y

z

O O’

x z’

V=const

t

t’

Derivation of The Lorentz

Coordinate Transformation

)

x c

v t

(

'

t

)

x c

v ct

(

'

ct

c

v 1

1

' tt ) v c

( '

tt

c

) ' vt ' ct

(

ct

) vt ct

(

'

ct

) ' vt '

x

(

x

) vt x

(

'

x

2

2 2

2 2

2 2































   





   

t=t’=0 , O  O’

x’

y’

y

z

O O’

x z’

V=const

t

t’

2 2 2

2

2

c

v 1

'

x c

v ' t t

; ' z z

; ' y y

; c

v 1

' vt ' x x

















The Lorentz Velocity

Transformation

 The relationships between The velocity of a point mass in the RF O and RF O’ u  ( ux, uy, uz ), u  ' ( u 'x , u 'y , u 'z )

x 2

2

2 '

z z

x 2

2

2 '

y y

x 2

' x x

x 2

2

2 z

' z x

2

2

2 y

' y x

2

x

'

x

'

u c

v 1

c

v 1 u

u

; '

u c

v 1

c

v 1 u

u

; '

u c

v 1

v u

u

u c

v 1

c

v 1 u

u

; u

c

v 1

c

v 1 u

u

; u

c

v 1

v u

u





































) ' u , ' u , ' u ( ' u ), u , u , u (

x 2

2

2 z

z 2

2 2

2

2 2

x 2

2

2 y

y 2

2 2

2

2 2

x 2

x x

2

2 2 2

2 2

2 2 2

2 2

u c

v 1

c

v 1 u '

u dt

dx c

v 1

c

v 1 dt dz

dx c

v dt

c

v 1 dz

'

dt

'

dz

u c

v 1

c

v 1 u '

u dt

dx c

v 1

c

v 1 dt dy

dx c

v dt

c

v 1 dy

'

dt

'

dy

u c

v 1

v u

' u dt

dx c

v 1

v dt dx

c

v 1

dx c

v dt

c

v 1

vdt dx

'

dt

'

dx

c

v 1

dx c

v dt

' dt ,

dz '

dz ,

dy '

dy

;

c

v 1

vdt dx

'

dx

















































































DERIVATION: