대상의빠르기

양자장 이론

- Pauli Adrien Maurice Dirac (1902. 8. 8-1984. 10. 20), - Wolfgang Pauli

(1900. 4. 25-1958. 12. 15), - Julian Seymour Schwinger (1918. 2. 12 - ),

- Richard Phillips Feynman (1918. 5. 11-1988. 2. 15),

상대론적 역학

- Albert Einstein

(1879. 3. 14-1955. 4. 18), - Hermann Minkowski (1864. 6. 22-1909. 1. 12),

. . .

양자역학

- Niels Hendrik David Bohr (1885. 10. 7-1962. 11. 18), - Erwin Schrödinger

(1887. 8. 12-1961. 1. 4), - Werner Heisenberg (1901. 12. 5-1976. 2. 1), .

.

고전역학

- Galileo Galilei

(1564. 2. 15-1642. 1. 8), - Isaac Newton

(1642. 12. 25-1727. 3. 20), - Joseph Louis Lagrange (1736. 1. 25-1813. 4. 10), - Pierre Simon de Laplace (1749. 3. 23-1827. 3. 5),

계의 크기

대상의 빠르기

운동: : 상대적 r v a F    , , , 

기준틀 (관측자) 명시

p. 1257

정지 pion에서 잰 값과 같음을 확인함

C=299 792 458[m/s] : ultimate speed

C=299 792 458[m/s] : ultimate speed

Space-Time Coordinates

1. Space coordinates: three dimensional array of measuring rods 2. Time coordinate: Synchronized clocks at each measuring rod intersection

How do we synchronize the clocks?

3D array of synchronized clocks and rods

• 공간좌표

• 시간좌표

Event A: x=3.6 rod lengths, y=1.3 rod lengths, z=0, time=reading on nearest clock; A(3.6,1.3,0,t)

사건의 측정

“All clocks read exactly the same time if you were able to look at them all a once!”

1) 같은 종류의 시계를 한 곳에 모아서 동기화 한 다음

2) 각자의 곳으로 옮기는 경우: 시계의 진행률이 변할 수 있다.

3) 시계를 각자의 자리에 놓은 다음에 동기화 해야 한다.

4) t_i = r_i / c 3D array of synchronized clocks and rods

동시성 : 상대적인 개념

3D array of synchronized clocks and rods

사건의 동시성, simultaneity

Time interval measurement:

1 1

' '

1 2 2

2 2 1

1 2

( ', ), ( ', ) t ( , ), ( , )

'=t ' t t t t

'

= A

A r t

r t B r t

t

B r  

 



  

 

' ' '

1 2

r   r   r 

고유시간 간격

(proper time interval)

0 :

 t

시간의 상대성 p. 1263

 

0

2 D Sally

t c

 

 

2 Sam

  L

t c

 

0

2 0

1

>

  

 t 

t

v c

t

 

   

2 2

1 2

2 2

1 1

2 2 0

  

   

L v t D

L v t c t

The Relativity of Time, cont'd

37-

 When two events occur at the same location in an inertial

reference frame, the time interval between them, measured in that frame, is called the proper time (interval).

 Measurements of the same time interval from any other inertial reference frame are always greater.

 

2 2

1 1

(37-8)

1 1 v c

 ^   ^ 

In previous example, who measures the proper time?

Lorentz factor:

0 ( time dila tio n ) (37-9) t  t

  

  v c

Speed Parameter:

• Lorentz factor  as a function of the speed parameter 

The Relativity of Time, cont'd

두 끝의 좌표를 동시에 측정!

platform의 길이

고유길이

0 0 :

x L

 

The Relativity of Length

Moving object shrinks!

length of train station

Train

Sam

Sally v

A B

p. 1268

고유길이 or 정지길이

(x, y, z, t) (x’,y’,z’,t’)

p. 1272

(x, y, z, t) (x’,y’,z’,t’)

What about S coordinates in terms of S' coordinates?

 ^' ' and   ' ' ² 

x   x  v t t   t  v x c

( Switch from one frame to the other by letting v→ -v )

(x, y, z, t) (x’,y’,z’,t’)

2 1

2 1 2

' ' ' ( )

' ' ' (

, )

x x x x v t

t t t t v x

c





      

      

2 1

2 1 2

, ( ' ') ( ' ')

x x x x v t

t t t t v x

c





      

      

( ' v

')

t t x

 c

    

( ' ')

x  x v t

    

2

'

t v x

 c

  

I f  t '  0 ,

시간팽창

시간팽창

( ' ') x  x v t

    

Need   t 0,

2 2

0 2

0 2

(1 ) '

( ' ) =

'

'

v x

c

L

x x

x L

c

x  v 











 













' v 2 '

t x

 c

   

: 고유길이, L

: S’

( ' v 2 ')

t t x

 c

    

(classical velocity transformation) (37-30) '

u   u v

p. 1277

•

GPS satellites have atomic clocks accurate to 1 nanosecond (one billionth of a second)

•

computed by comparing time and location of the signals from several satellites.

Satellites moving at 14,000 km/hr

• Using 4 satellites one can obtain the 4 variables: x, y, z, t.

 Special Relativity

 “ Clocks run slow by 7000 ns per day ^!”

• Knowing the distance from one satellite  places you somewhere on a spherical

that's centered around the satellite.

• Knowing distances from two satellites  places you somewhere along a circle Distance from each satellite

=

c = 1자/1nano초

It works because of special relativity!

“c does not depend on satellite motion.”

C=299 792 458[m/s] : ultimate speed

Relativistic Momentum and Energy

0 0

x x x t x

p m p m m m

t t t t t

p mv





    

    

    

 

Momentum

 

0 0 0

v v v

dr dr dp ds vdp vp pdv

dt K F dp

dt

Kinetic Energy

  ^  ^   ^  ^       

‘정지’ 질량 Rest mass

p. 1280

A New Look at Energy

2

0 (37-43) E  mc

Mass energy or rest energy :

Object Mass (kg) Energy Equivalent

Electron ≈ 9.11x10

≈ 8.19x10

J (≈ 511 keV) Proton ≈ 1.67x10

≈ 1.50x10

J (≈ 938 MeV) Uranium atom ≈ 3.95x10

≈ 3.55x10

J (≈ 225 GeV) Dust particle ≈ 1x10

≈ 1x10

J (≈ 2 kcal.)

Table 37-3 The Energy Equivalents of a Few Objects

2 2 0

2

E E K mc K mc E mc

Total Energy Mass Energy



    



2 2

0

2

2

( ) ( )

E  pc  mc  p c  E

양자장 이론

- Pauli Adrien Maurice Dirac (1902. 8. 8-1984. 10. 20), - Wolfgang Pauli

(1900. 4. 25-1958. 12. 15), - Julian Seymour Schwinger (1918. 2. 12 - ),

- Richard Phillips Feynman (1918. 5. 11-1988. 2. 15),

상대론적 역학

- Albert Einstein

(1879. 3. 14-1955. 4. 18), - Hermann Minkowski (1864. 6. 22-1909. 1. 12),

. . .

양자역학

- Niels Hendrik David Bohr (1885. 10. 7-1962. 11. 18), - Erwin Schrödinger

(1887. 8. 12-1961. 1. 4), - Werner Heisenberg (1901. 12. 5-1976. 2. 1), .

.

고전역학

- Galileo Galilei

(1564. 2. 15-1642. 1. 8), - Isaac Newton

(1642. 12. 25-1727. 3. 20), - Joseph Louis Lagrange (1736. 1. 25-1813. 4. 10), - Pierre Simon de Laplace (1749. 3. 23-1827. 3. 5),

계의 크기

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