( 1)

Maxwell ether ether Michelson-Morley half-silver A B l1 A C l2 A D - (fringe) ether l1 = l2 D l1 l2 U X A B

t2 A C A C C ether d = Ut2/2 X A d X

ether c

l1=l2=l

t (fringe shift) 90 Michelson-Morley 6 U2/c2 Michelson Morley sensitive Lorentz Lorentz 2 1. 2. Lorentz ether potential () R = q/R ( q ) v ether ether electrical potential potential equipotentials ( ) potential ( ) equipotential l0 l = l0 v Michelson-Morley interferometer ( ) l2 = l0 ( v = U)

l1 = l0

Lorentz Michelson Morley Lorentz contraction

( 2) Lorentz Lenz (electromotive force) a (back force) F1 = -a ( q r0 = q2/r0) mma = -a + F mm (mechanical mass) F (mm + )a = F ma = F m = mm + (effective mass) m (observed mass) (electromagnetic mass) mm effective mass hydrodynamics Lorentz ether

0 ether

mm v m e/m m v mm ( )

m0 ether Lorentz (harmonic oscillator) MX = -KX m K (force constant)

Lorentz ether oscillate K

T0 ether T ether ether =

lab

physical-chemical l0 ether T0 ether Lorentz Fizeau Fizeau A L B T C = 2L/T

Fizeau ether V 36 Fizeau V ether C ether C-V C+V

V/C Lorentz ether c t = 0 ( ether) Lab v ether t1 A B L + vt1 = ct1 t1 = L/(c-v) t2 = L/(c+v) T = t1 + t2 = 2L/[c(1-v2/c2)] ... (*)

Lorentz L = L0( T = T0( ) (*)

)

T0 = 2L0/c Lab 2L0/T0 Fizeau Lorentz contraction Lorentz Fizeau ether v

Faraday

(emf)

Lenz (emf) + -

H.A. Lorentz

( 1)Lecture Notes on Special Relativity Dr.Tatsu Takeuchi, Department of Physics, Virginia Tech lecture notes . Tatsu Takeuchi 1. (Frames of Reference) ? (reference point) (origin) x y z t

(frame)

2. (Inertial Frames) (Law of Inertia) 1. 2. ! (?) (inertial frame) (non-inertial frame)

3. (Laws of Physics in Inertial Frames) ? A (x,t) B (x',t') v x A (x,t) A (x',t') B (x,t) (x',t') x' = x - vt, t' = t t' = t = 0 A B (Galilei transformation)

" " 4. (Newton's Second Law) F m F m 1. 2. F = ma A B x' = x - vt, t' = t A B u' = u - v a' = a

20 /. 20 /. 100 120 40 60 -

5. (Laws of Physics in Non-Inertial Frames) ( "" )

F = ma " " (fake force) ( -inertial force)

( 2)

Lecture Notes on Special Relativity Dr.Tatsu Takeuchi, Department of Physics, Virginia Tech lecture notes . Tatsu Takeuchi 6. (The Special and General Theories of Relativity) c = 3x108 m/s ( 1905 10 ) c = 3x108 m/s + c = 3x108 m/s ( "" ) ( ) 7. (Some History) 17 18 19 19 c = 3x108 m/s ! (ether) Michelson-Morley

Michelson-Morley : ? 1905

(simultaneity)

8. Lorentz (The Lorentz Transformation)

Lorentz

v c v/c v Lorentz (x,t) (x',t') x'=x=0 t'=t=0 c t=T x = cT (x,t)

(x',t')

Lorentz

( 3)Lecture Notes on Special Relativity Dr.Tatsu Takeuchi, Department of Physics, Virginia Tech lecture notes . Tatsu Takeuchi

9. (The Concept of Simultaneity) Lorentz t=t' (simultaneity) c = 3x108 m/s c

2 A B 2 A B (chronological order) - (x,t) A B - (x',t') A B - (x'',t'') A B (experimental fact)

10. (Faster than Light Travel) (causality)

(cause) (effect) A B A B A B B A ? 1. A 2. A B 3. B (x,t) (x',t') (x'',t'') ! ? A B

7 "The Einstein Paradox and other Science Mysteries Solved by Sherlock Holmes" Colin Bruce (Perseus Books, ISBN 0738200239) A D B C 1. 2. 3. 4. A B B B C C D D A

A D !

A B A B

( ) ( ) ( ) c !

( 4)Lecture Notes on Special Relativity Dr.Tatsu Takeuchi, Department of Physics, Virginia Tech lecture notes . Tatsu Takeuchi 11. (Synchronization of Clocks) (simultaneity) ()

12. (Time Dilation) : 1. 2. " " " " " " (origin) 1 2 (: )

" " " " " " " " !

" " T " " T' T T'

v (time dilation) 13. Lorentz (Lorentz Contraction) "" " " ? ? ( ) ! " " L' " " L L'! Lorentz

Lorentz Lorentz

L' L v ( ' L' ) () Lecture Notes on Special Relativity Dr.Tatsu Takeuchi, Department of Physics, Virginia Tech lecture notes . Tatsu Takeuchi 14. (The Equivalence of All Inertial Frames) Lorentz Lorentz

15. (The Twin Paradox)

? ? ? ? (twin paradox)

()

(non-inertial frame) C C A C B A B () 16. (Conclusion) : 1. 2. 3. ( ,causality) 4. Lorentz 5. (Physics is fun!)