课堂讲义（林志方，徐建军）.pdf

²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ E ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï E ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) E âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ E ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ ϦÎ܃é؇¦åƐ§§‡¦ E ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ ϦÎ܃é؇¦åƐ§§‡¦ (1) E ÷vâÔ[C5§Lo‘ n Üþ§ ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ ϦÎ܃é؇¦åƐ§§‡¦ (1) ÷vâÔ[C5§Lo‘ n Üþ§ (2) 3 v  c ž§#åƐ§òzÚ E ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ ϦÎ܃é؇¦åƐ§§‡¦ (1) ÷vâÔ[C5§Lo‘ n Üþ§ (2) 3 v  c ž§#åƐ§òzÚ d§AòåƐ§¥ˆ«Ônþ¤o‘Cþ" E ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ ϦÎ܃é؇¦åƐ§§‡¦ (1) ÷vâÔ[C5§Lo‘ n Üþ§ (2) 3 v  c ž§#åƐ§òzÚ d§AòåƐ§¥ˆ«Ônþ¤o‘Cþ" ˜!o‘ E ŒÆ ÔnX ˜¥þ§o‘„Ý¥þ§o‘\„Ý¥þ “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ ϦÎ܃é؇¦åƐ§§‡¦ (1) ÷vâÔ[C5§Lo‘ n Üþ§ (2) 3 v  c ž§#åƐ§òzÚ d§AòåƐ§¥ˆ«Ônþ¤o‘Cþ" ˜!o‘ ˜¥þ§o‘„Ý¥þ§o‘\„Ý¥þ o‘ ˜¥þµxµ = (~ r , ict) E ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ ϦÎ܃é؇¦åƐ§§‡¦ (1) ÷vâÔ[C5§Lo‘ n Üþ§ (2) 3 v  c ž§#åƐ§òzÚ d§AòåƐ§¥ˆ«Ônþ¤o‘Cþ" ˜!o‘ ˜¥þ§o‘„Ý¥þ§o‘\„Ý¥þ o‘ ˜¥þµxµ = (~ r , ict) dxµ dxµ o‘„Ý¥þµUµ = = γu = γu(~ u, ic) dτ dt E ŒÆ ÔnX “ Mï
1 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light § 8.6 ƒ é Ø å Æ ÚîåƐ§3³|ÑC†e´C§ØÎ܃é؇¦§Ï (1) âÚîåƧ3ðåŠ^e§ÔN„݌ÁOŒ (2) ÚîåÆØ÷vâÔ[C5§Ø´o‘¥þ½Üþ§ ϦÎ܃é؇¦åƐ§§‡¦ (1) ÷vâÔ[C5§Lo‘ n Üþ§ (2) 3 v  c ž§#åƐ§òzÚ d§AòåƐ§¥ˆ«Ônþ¤o‘Cþ" ˜!o‘ ˜¥þ§o‘„Ý¥þ§o‘\„Ý¥þ o‘ ˜¥þµxµ = (~ r , ict) dxµ dxµ o‘„Ý¥þµUµ = = γu = γu(~ u, ic) dτ dt   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c E ŒÆ ÔnX “ Mï
1 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c E ŒÆ ÔnX “ Mï
2 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c dU1 dτ E = γu ŒÆ dU1 d = γu (γuu1) dt dt ÔnX |^ µU 1 = γ u u 1 “ Mï
2 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c dU1 dτ E dU1 d = γu (γuu1) dt dt   du1 dγu = γ u γu + u1 dt dt = γu ŒÆ ÔnX |^ µU 1 = γ u u 1 du1 |^µ = a1, dt dγu γu3 = 2 (~ u·~ a) dt c “ Mï
2 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c dU1 dτ E dU1 d = γu (γuu1) dt dt   du1 dγu = γ u γu + u1 dt dt i h γu2 2 u·~ a)u1 = γu a1 + 2 (~ c |^ = γu ŒÆ ÔnX µU 1 = γ u u 1 du1 |^µ = a1, dt =⇒ a1 = γu2 dγu γu3 = 2 (~ u·~ a) dt c i h γu2 u·~ a)u1 a1 + 2 (~ c “ Mï
2 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c dU1 dτ dU4 dτ E dU1 d = γu (γuu1) dt dt   du1 dγu = γ u γu + u1 dt dt i h γu2 2 u·~ a)u1 = γu a1 + 2 (~ c |^ = γu = γu ŒÆ dU4 d = iγu (γuc) dt dt ÔnX µU 1 = γ u u 1 du1 |^µ = a1, dt =⇒ a1 = γu2 dγu γu3 = 2 (~ u·~ a) dt c i h γu2 u·~ a)u1 a1 + 2 (~ c |^ µU4 = γu ic “ Mï
2 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c dU1 dτ dU4 dτ dU1 d = γu (γuu1) dt dt   du1 dγu = γ u γu + u1 dt dt i h γu2 2 u·~ a)u1 = γu a1 + 2 (~ c = γu dU4 d = iγu (γuc) dt dt dγu = γu ic dt E |^ = γu ŒÆ ÔnX µU 1 = γ u u 1 du1 |^µ = a1, dt =⇒ a1 = γu2 dγu γu3 = 2 (~ u·~ a) dt c i h γu2 u·~ a)u1 a1 + 2 (~ c |^ µU4 = γu ic dγu γu3 |^µ = 2 (~ u·~ a) dt c “ Mï
2 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c dU1 dτ dU4 dτ dU1 d = γu (γuu1) dt dt   du1 dγu = γ u γu + u1 dt dt i h γu2 2 u·~ a)u1 = γu a1 + 2 (~ c |^ = γu = γu du1 |^µ = a1, dt =⇒ dU4 d = iγu (γuc) dt dt E ŒÆ ÔnX a1 = γu2 dγu γu3 = 2 (~ u·~ a) dt c i h γu2 u·~ a)u1 a1 + 2 (~ c |^ µU4 = γu ic dγu γu3 |^µ = 2 (~ u·~ a) dt c dγu = γu ic dt γu4 = i (~ u·~ a) c µU 1 = γ u u 1 =⇒ γu4 a4 = i (~ u·~ a) c “ Mï
2 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c dU1 dτ dU4 dτ dU1 d = γu (γuu1) dt dt   du1 dγu = γ u γu + u1 dt dt i h γu2 2 u·~ a)u1 = γu a1 + 2 (~ c |^ = γu = γu du1 |^µ = a1, dt =⇒ dU4 d = iγu (γuc) dt dt a1 = γu2 dγu γu3 = 2 (~ u·~ a) dt c i h γu2 u·~ a)u1 a1 + 2 (~ c |^ µU4 = γu ic dγu γu3 |^µ = 2 (~ u·~ a) dt c dγu = γu ic dt γu4 = i (~ u·~ a) c µU 1 = γ u u 1 =⇒ γu4 a4 = i (~ u·~ a) c o‘\„ÝéE,§‡òÚî1½Æ¤C/ª§„´lÄþÑu E ŒÆ ÔnX “ Mï
2 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light   2 2 dUµ γ γ ~ (~ ~ · ~a o‘\„Ý¥þµaµ = = γu2 ~a + 2u u u · ~a), i u u dτ c c dU1 dτ dU4 dτ dU1 d = γu (γuu1) dt dt   du1 dγu = γ u γu + u1 dt dt i h γu2 2 u·~ a)u1 = γu a1 + 2 (~ c |^ = γu = γu du1 |^µ = a1, dt =⇒ a1 = γu2 dU4 d = iγu (γuc) dt dt dγu γu3 = 2 (~ u·~ a) dt c i h γu2 u·~ a)u1 a1 + 2 (~ c |^ µU4 = γu ic dγu γu3 |^µ = 2 (~ u·~ a) dt c dγu = γu ic dt γu4 = i (~ u·~ a) c µU 1 = γ u u 1 =⇒ γu4 a4 = i (~ u·~ a) c o‘\„ÝéE,§‡òÚî1½Æ¤C/ª§„´lÄþÑu ~ ~ dv dp ~ f = m~ a=m = dt dt E ŒÆ ÔnX “ Mï
2 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 !o‘Äþ¥þ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c E ŒÆ ÔnX i = 1, 2, 3 “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ =⇒ E ŒÆ m0 A²;åÆ¥·ŽŸþ£$„$ĞŸþ¤ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ m0 A²;åÆ¥·ŽŸþ£$„$ĞŸþ¤ i m0c2 Pµ 1o‡©þµ P4 = γum0 ic = p c 1 − u2/c2 =⇒ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ m0 A²;åÆ¥·ŽŸþ£$„$ĞŸþ¤ i m0c2 Pµ 1o‡©þµ P4 = γum0 ic = p c 1 − u2/c2  i 1 2 2 $„ÐmµP4 = m0c + 2 m0u + · · · c =⇒ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ m0 A²;åÆ¥·ŽŸþ£$„$ĞŸþ¤ i m0c2 Pµ 1o‡©þµ P4 = γum0 ic = p c 1 − u2/c2  i 1 2 2 $„ÐmµP4 = m0c + 2 m0u + · · · c 1‘²;åÆ¥ÄU§ m0c2 AUþ =⇒ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ m0 A²;åÆ¥·ŽŸþ£$„$ĞŸþ¤ i m0c2 Pµ 1o‡©þµ P4 = γum0 ic = p c 1 − u2/c2  i 1 2 2 $„ÐmµP4 = m0c + 2 m0u + · · · c 1‘²;åÆ¥ÄU§ m0c2 AUþ ·ŽÔN·UµW0 =⇒ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ m0 A²;åÆ¥·ŽŸþ£$„$ĞŸþ¤ i m0c2 Pµ 1o‡©þµ P4 = γum0 ic = p c 1 − u2/c2  i 1 2 2 $„ÐmµP4 = m0c + 2 m0u + · · · c 1‘²;åÆ¥ÄU§ m0c2 AUþ ·ŽÔN·UµW0 ~ m0u p ~= p ¡ÔNƒéØÄþ 2 2 1 − u /c =⇒ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ m0 A²;åÆ¥·ŽŸþ£$„$ĞŸþ¤ i m0c2 Pµ 1o‡©þµ P4 = γum0 ic = p c 1 − u2/c2  i 1 2 2 $„ÐmµP4 = m0c + 2 m0u + · · · c 1‘²;åÆ¥ÄU§ m0c2 AUþ ·ŽÔN·UµW0 ~ m0u p ~= p ¡ÔNƒéØÄþ 2 2 1 − u /c m0c2 W =p ¡ÔNƒéØUþ£oUþ¤ 2 2 1 − u /c =⇒ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light !o‘Äþ¥þ ½Âo‘Äþ¥þµPµ = m0Uµ Uµ o‘„Ý¥þ§m0 äkŸþþjo‘Iþ" m0ui , Pµ cn‡©þµ Pi = γum0ui = p 2 2 1 − u /c i = 1, 2, 3 3$„ž§γu ≈ 1§µPi = pi = m0ui§Aòzn‘Äþ m0 A²;åÆ¥·ŽŸþ£$„$ĞŸþ¤ i m0c2 Pµ 1o‡©þµ P4 = γum0 ic = p c 1 − u2/c2  i 1 2 2 $„ÐmµP4 = m0c + 2 m0u + · · · c 1‘²;åÆ¥ÄU§ m0c2 AUþ ·ŽÔN·UµW0 ~ m0u p ~= p ¡ÔNƒéØÄþ 2 2 1 − u /c ƒéØÄþUþ¤o‘Äþ¥þµ 2   m0c i W =p ¡ÔNƒéØUþ£oUþ¤ ~, W Pµ = p 1 − u2/c2 c =⇒ E ŒÆ ÔnX “ Mï
3 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 E ŒÆ ÔnX 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p “ i W c  Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø E ŒÆ ÔnX “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX E ŒÆ ÔnX “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) E ƒéØUþ¹ ŒÆ ÔnX ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 E ŒÆ ÔnX “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 (3) E W0 ·ŽUþ§oUþ W = T + W0"3šƒé؜/§Uþ¥\˜~êâS¿Â§ ŒÆ ÔnX “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 (3) W0 ·ŽUþ§oUþ W = T + W0"3šƒé؜/§Uþ¥\˜~êâS¿Â§ 3šƒé؜/ÄUþÅðžÃLÄ W0 ‘" E ŒÆ ÔnX “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 (3) W0 ·ŽUþ§oUþ W = T + W0"3šƒé؜/§Uþ¥\˜~êâS¿Â§ 3šƒé؜/ÄUþÅðžÃLÄ W0 ‘" 3ƒé؜/§W0 ‘Ñy´Ôn5ÆC5‡¦ E ŒÆ ÔnX “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 (3) W0 ·ŽUþ§oUþ W = T + W0"3šƒé؜/§Uþ¥\˜~êâS¿Â§ 3šƒé؜/ÄUþÅðžÃLÄ W0 ‘" 3ƒé؜/§W0 ‘Ñy´Ôn5ÆC5‡¦ ,˜¡§= W0 ‘U=z¤Ù§/ªUþž§W0 ÑyâkÔn¿Â ÏdQ,ƒéØ¥Ôn5ÆC5‡¦ W0 Ñy3UþLˆª¥ XJC5´(§@o W0 ‘˜½Œ=z¤Ù§/ªUþ E ŒÆ ÔnX “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 (3) W0 ·ŽUþ§oUþ W = T + W0"3šƒé؜/§Uþ¥\˜~êâS¿Â§ 3šƒé؜/ÄUþÅðžÃLÄ W0 ‘" 3ƒé؜/§W0 ‘Ñy´Ôn5ÆC5‡¦ ,˜¡§= W0 ‘U=z¤Ù§/ªUþž§W0 ÑyâkÔn¿Â ÏdQ,ƒéØ¥Ôn5ÆC5‡¦ W0 Ñy3UþLˆª¥ E XJC5´(§@o W0 ‘˜½Œ=z¤Ù§/ªUþ fU|^ ŒÆ “ ÔnX Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 (3) W0 ·ŽUþ§oUþ W = T + W0"3šƒé؜/§Uþ¥\˜~êâS¿Â§ 3šƒé؜/ÄUþÅðžÃLÄ W0 ‘" 3ƒé؜/§W0 ‘Ñy´Ôn5ÆC5‡¦ ,˜¡§= W0 ‘U=z¤Ù§/ªUþž§W0 ÑyâkÔn¿Â ÏdQ,ƒéØ¥Ôn5ÆC5‡¦ W0 Ñy3UþLˆª¥ XJC5´(§@o W0 ‘˜½Œ=z¤Ù§/ªUþ (4) E Pµ o‘¥þ§PµPµ 7,o‘Iþ§l ŒÆ ÔnX ~2 − Pµ Pµ = p fU|^ 1 2 W ´ØCþ 2 c “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 (3) W0 ·ŽUþ§oUþ W = T + W0"3šƒé؜/§Uþ¥\˜~êâS¿Â§ 3šƒé؜/ÄUþÅðžÃLÄ W0 ‘" 3ƒé؜/§W0 ‘Ñy´Ôn5ÆC5‡¦ ,˜¡§= W0 ‘U=z¤Ù§/ªUþž§W0 ÑyâkÔn¿Â ÏdQ,ƒéØ¥Ôn5ÆC5‡¦ W0 Ñy3UþLˆª¥ XJC5´(§@o W0 ‘˜½Œ=z¤Ù§/ªUþ (4) Pµ o‘¥þ§PµPµ 7,o‘Iþ§l 3ƒéuÔN·Ž.5X§PµPµ = −m20c2 E ŒÆ ÔnX fU|^ 1 2 W ´ØCþ 2 c 1 2 2 ~ − 2 W = −m20c2 p c ~2 − Pµ Pµ = p =⇒ “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ~=p p ~ m0u 1 − u2/c2 2 , W =p m0c 1 − u2/c2  o‘Äþ¥þµPµ = ~, p i W c  ?Ø (1) ²;åÆ¥§ÄþÚUþþÝԟ$Äü‡þ§3ƒéØ¥¤˜‡Ú˜o‘¥þ L²ÄþUþmS3éX (2) ƒéØUþ¹ ~ = 0 ž§ƒéØUþòzÔN·UµW0 = m0c2 ÔNÄU§3 u ƒéØ¥ÔNÄU T = W − W0§$„eòz²;/ªµT = 12 m0u2 (3) W0 ·ŽUþ§oUþ W = T + W0"3šƒé؜/§Uþ¥\˜~êâS¿Â§ 3šƒé؜/ÄUþÅðžÃLÄ W0 ‘" 3ƒé؜/§W0 ‘Ñy´Ôn5ÆC5‡¦ ,˜¡§= W0 ‘U=z¤Ù§/ªUþž§W0 ÑyâkÔn¿Â ÏdQ,ƒéØ¥Ôn5ÆC5‡¦ W0 Ñy3UþLˆª¥ XJC5´(§@o W0 ‘˜½Œ=z¤Ù§/ªUþ (4) Pµ o‘¥þ§PµPµ 7,o‘Iþ§l 3ƒéuÔN·Ž.5X§PµPµ = −m20c2 E ŒÆ ÔnX fU|^ 1 2 W ´ØCþ 2 c 1 2 2 ~ − 2 W = −m20c2 p c ~2 − Pµ Pµ = p =⇒ “ Mï
4 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) E 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 ŒÆ ÔnX =⇒ W = q p2c2 + m20c4 “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X E ŒÆ ÔnX “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X (5) E o‘Äþ¥þC†'X ŒÆ ÔnX “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X (5) o‘Äþ¥þC†'X
v 0 P x = γv P x − 2 W c Py0 = Py , Pz0 = Pz W 0 = γv (W − vPx) E ŒÆ ÔnX “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X (5) o‘Äþ¥þC†'X
v 0 P x = γv P x − 2 W c Py0 = Py , Pz0 = Pz W 0 = γv (W − vPx) n!Uþ!ÄþÅð½Æ E ŒÆ ÔnX “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X (5) o‘Äþ¥þC†'X
v 0 P x = γv P x − 2 W c Py0 = Py , Pz0 = Pz W 0 = γv (W − vPx) n!Uþ!ÄþÅð½Æ ¢L²§3ƒéØ¥§oUþÚoÄþÅð½Æ,¤á" E ŒÆ ÔnX “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X (5) o‘Äþ¥þC†'X
v 0 P x = γv P x − 2 W c Py0 = Py , Pz0 = Pz W 0 = γv (W − vPx) n!Uþ!ÄþÅð½Æ ¢L²§3ƒéØ¥§oUþÚoÄþÅð½Æ,¤á" eâfmƒpŠ^´]mu)3˜m,:§Kkµ oUþÅðµ N X n=1 E ŒÆ ÔnX 0 W a(n) = N X W b(n0) n0 =1 “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X (5) o‘Äþ¥þC†'X
v 0 P x = γv P x − 2 W c Py0 = Py , Pz0 = Pz W 0 = γv (W − vPx) n!Uþ!ÄþÅð½Æ ¢L²§3ƒéØ¥§oUþÚoÄþÅð½Æ,¤á" eâfmƒpŠ^´]mu)3˜m,:§Kkµ oUþÅðµ N X n=1 E ŒÆ ÔnX 0 W a(n) = N X n0 =1 W b(n0) oÄþÅðµ N X 0 ~ a(n) = p N X ~ b(n0) p n0 =1 n=1 “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X (5) o‘Äþ¥þC†'X
v 0 P x = γv P x − 2 W c Py0 = Py , Pz0 = Pz W 0 = γv (W − vPx) n!Uþ!ÄþÅð½Æ ¢L²§3ƒéØ¥§oUþÚoÄþÅð½Æ,¤á" eâfmƒpŠ^´]mu)3˜m,:§Kkµ oUþÅðµ N X n=1 0 W a(n) = N X n0 =1 W b(n0) oÄþÅðµ N X 0 ~ a(n) = p N X ~ b(n0) p n0 =1 n=1 a, b L«ÐÚª"N , N 0 ƒpŠ^£-E¤c âfê" E ŒÆ ÔnX “ Mï
5 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (4) 1 2 ~ PµPµ = p − 2 W = −m20c2 c 2 =⇒ W = q p2c2 + m20c4 ƒé؟þ!Uþ!Äþƒm˜‡­‡'X (5) o‘Äþ¥þC†'X
v 0 P x = γv P x − 2 W c Py0 = Py , Pz0 = Pz W 0 = γv (W − vPx) n!Uþ!ÄþÅð½Æ ¢L²§3ƒéØ¥§oUþÚoÄþÅð½Æ,¤á" eâfmƒpŠ^´]mu)3˜m,:§Kkµ oUþÅðµ N X n=1 0 W a(n) = N X W b(n0) n0 =1 oÄþÅðµ N X 0 ~ a(n) = p N X ~ b(n0) p n0 =1 n=1 a, b L«ÐÚª"N , N 0 ƒpŠ^£-E¤c âfê" 3ƒéØ¥§ŒÚ˜¤o‘ÄþÅð" E ŒÆ ÔnX “ Mï
5 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 o!ƒéØåƐ§ E ŒÆ ÔnX “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ E ŒÆ ÔnX ~ dp ~ F = dt “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ E ŒÆ ÔnX ~ dp ~ F = dt d Pµ Kµ = dτ (1) “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ ~ dp ~ F = dt d Pµ Kµ = dτ (1) du dPµ ´o‘¥þ§dτ Iþ =⇒ Kµ ´o‘¥þ§(1) ´ƒéØC E ŒÆ ÔnX “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ ~ dp ~ F = dt d Pµ Kµ = dτ (1) du dPµ ´o‘¥þ§dτ Iþ =⇒ Kµ ´o‘¥þ§(1) ´ƒéØC o‘¥þ Kµ ¿Âµ E ŒÆ ÔnX “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ ~ dp ~ F = dt d Pµ Kµ = dτ (1) du dPµ ´o‘¥þ§dτ Iþ =⇒ Kµ ´o‘¥þ§(1) ´ƒéØC o‘¥þ Kµ ¿Âµ Kµ cn‡©þµ E ŒÆ ÔnX dPi dPi d Ki = = γu = γu (γum0ui) dτ dt dt “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ ~ dp ~ F = dt d Pµ Kµ = dτ (1) du dPµ ´o‘¥þ§dτ Iþ =⇒ Kµ ´o‘¥þ§(1) ´ƒéØC o‘¥þ Kµ ¿Âµ Kµ cn‡©þµ $„ž γu ≈ 1µ E ŒÆ ÔnX dPi dPi d Ki = = γu = γu (γum0ui) dτ dt dt d ~ ~ ) = F~ K = (m0u òzÚ dt “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ ~ dp ~ F = dt d Pµ Kµ = dτ (1) du dPµ ´o‘¥þ§dτ Iþ =⇒ Kµ ´o‘¥þ§(1) ´ƒéØC o‘¥þ Kµ ¿Âµ dPi dPi d Kµ cn‡©þµ Ki = = γu = γu (γum0ui) dτ dt dt d ~ ~ ) = F~ $„ž γu ≈ 1µ K = (m0u òzÚ dt Ïdé$„šƒé؜/o‘¥þ Kµ cn‡©þòz²;n‘å¥þ E ŒÆ ÔnX “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ ~ dp ~ F = dt d Pµ Kµ = dτ (1) du dPµ ´o‘¥þ§dτ Iþ =⇒ Kµ ´o‘¥þ§(1) ´ƒéØC o‘¥þ Kµ ¿Âµ dPi dPi d Kµ cn‡©þµ Ki = = γu = γu (γum0ui) dτ dt dt d ~ ~ ) = F~ $„ž γu ≈ 1µ K = (m0u òzÚ dt Ïdé$„šƒé؜/o‘¥þ Kµ cn‡©þòz²;n‘å¥þ ép„ƒé؜¹µ E ŒÆ ÔnX d d Ki = γu (γum0ui) = γu (Pi) dt dt “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ ~ dp ~ F = dt d Pµ Kµ = dτ (1) du dPµ ´o‘¥þ§dτ Iþ =⇒ Kµ ´o‘¥þ§(1) ´ƒéØC o‘¥þ Kµ ¿Âµ dPi dPi d Kµ cn‡©þµ Ki = = γu = γu (γum0ui) dτ dt dt d ~ ~ ) = F~ $„ž γu ≈ 1µ K = (m0u òzÚ dt Ïdé$„šƒé؜/o‘¥þ Kµ cn‡©þòz²;n‘å¥þ ép„ƒé؜¹µ ~ = γuF~ µK E ŒÆ ÔnX d d Ki = γu (γum0ui) = γu (Pi) dt dt ! ~ d d m0u ~ p F = (~ p) = β = u/c 2 dt dt 1−β “ Mï
6 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!ƒéØåƐ§ šƒéØÄåƐ§µ í2ƒé؜/µ ~ dp ~ F = dt d Pµ Kµ = dτ (1) du dPµ ´o‘¥þ§dτ Iþ =⇒ Kµ ´o‘¥þ§(1) ´ƒéØC o‘¥þ Kµ ¿Âµ dPi dPi d Kµ cn‡©þµ Ki = = γu = γu (γum0ui) dτ dt dt d ~ ~ ) = F~ $„ž γu ≈ 1µ K = (m0u òzÚ dt Ïdé$„šƒé؜/o‘¥þ Kµ cn‡©þòz²;n‘å¥þ ép„ƒé؜¹µ ~ = γuF~ µK E ŒÆ ÔnX d d Ki = γu (γum0ui) = γu (Pi) dt dt ! ~ d d m0u ~ p F = (~ p) = β = u/c 2 dt dt 1−β ƒéØen‘ÄåƐ§" “ Mï
6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ E ŒÆ ÔnX ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 i
~, W , Pµ = p c ~ m0u p ~= , p 2 1−β “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ E ŒÆ ÔnX ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = E ŒÆ ÔnX “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = Kµ 1o‡©þµ E ŒÆ ÔnX 2 i d~ p dP4 i dW id p 2 2 c 2 4 ~· p K4 = = = p c + m0c = dτ c dτ c dτ cW dτ “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = Kµ 1o‡©þµ 2 i d~ p dP4 i dW id p 2 2 c 2 4 ~· p K4 = = = p c + m0c = dτ c dτ c dτ cW dτ d~ p ic γu ic γu ~ ~ · F~ p· p = = W dt W E ŒÆ ÔnX “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = Kµ 1o‡©þµ 2 i d~ p dP4 i dW id p 2 2 c 2 4 ~· p K4 = = = p c + m0c = dτ c dτ c dτ cW dτ d~ p ic γu ic γu ~ ~ · F~ p· p = = W dt W E ŒÆ ÔnX |^µ ~ = γum0u ~, p W = γum0c2 “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = Kµ 1o‡©þµ 2 i d~ p dP4 i dW id p 2 2 c 2 4 ~· p K4 = = = p c + m0c = dτ c dτ c dτ cW dτ d~ p ic γu ic γu ~ ~ · F~ p· p = = W dt W |^µ ~ = γum0u ~, p W = γum0c2 i i ~ ~ ~ ·F = u ~ ·K K4 = γuu c c E ŒÆ ÔnX “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = Kµ 1o‡©þµ 2 i d~ p dP4 i dW id p 2 2 c 2 4 ~· p K4 = = = p c + m0c = dτ c dτ c dτ cW dτ d~ p ic γu ic γu ~ = γum0u ~, p ~ ~ ~ p· p · F |^µ = = W = γum0c2 W dt W i i dW dW ~ ~ ~ ~ ~ = ~ = ~ ·F = u ~ ·K K4 = γuu 1o‡§µK · u ½ F ·u c c dτ dt E ŒÆ ÔnX “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = Kµ 1o‡©þµ 2 i d~ p dP4 i dW id p 2 2 c 2 4 ~· p K4 = = = p c + m0c = dτ c dτ c dτ cW dτ d~ p ic γu ic γu ~ = γum0u ~, p ~ ~ ~ p· p · F |^µ = = W = γum0c2 W dt W i i dW dW ~ ~ ~ ~ ~ = ~ = ~ ·F = u ~ ·K K4 = γuu 1o‡§µK · u ½ F ·u c c dτ dt

i i ~ ~ ~ ~ ~ · K = γu F , u ~ ·F o‘å¥þµ Kµ = K, u c c E ŒÆ ÔnX “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = Kµ 1o‡©þµ 2 i d~ p dP4 i dW id p 2 2 c 2 4 ~· p K4 = = = p c + m0c = dτ c dτ c dτ cW dτ d~ p ic γu ic γu ~ = γum0u ~, p ~ ~ ~ p· p · F |^µ = = W = γum0c2 W dt W i i dW dW ~ ~ ~ ~ ~ = ~ = ~ ·F = u ~ ·K K4 = γuu 1o‡§µK · u ½ F ·u c c dτ dt

i i ~ ~ ~ ~ ~ · K = γu F , u ~ ·F o‘å¥þµ Kµ = K, u c c dPµ ƒéØÄåƐ§µ Kµ = dτ E ŒÆ ÔnX “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light d Pµ , ƒéØÄåƐ§µ Kµ = dτ Kµ cn‡©þµ ~ = γuF~ , K ~ m0u p ~= , p 2 ! 1−β ~ m0u p (1) 2 1−β i
~, W , Pµ = p c ~ d dp ~ F = = dt dt d Pµ cn©þƒéØåƐ§ dτ ~ Ø´o‘¥þ Kµ cn©þ§ γuF ~ â´ Kµ cn©þ" 5¿n‘å¥þ F Kµ ¡o‘å¥þ§Kµ = Kµ 1o‡©þµ 2 i d~ p dP4 i dW id p 2 2 c 2 4 ~· p K4 = = = p c + m0c = dτ c dτ c dτ cW dτ d~ p ic γu ic γu ~ = γum0u ~, p ~ ~ ~ p· p · F |^µ = = W = γum0c2 W dt W i i dW dW ~ ~ ~ ~ ~ = ~ = ~ ·F = u ~ ·K K4 = γuu 1o‡§µK · u ½ F ·u c c dτ dt

i i ~ ~ ~ ~ ~ · K = γu F , u ~ ·F o‘å¥þµ Kµ = K, u c c  d~ p d~ p  ~ ~  K= ½ F = dPµ dτ dt =⇒ ƒéØÄåƐ§µ Kµ = dW dW  dτ ~ ·u ~ ·u  K ~ = ~ = ½ F dτ dt E ŒÆ ÔnX “ Mï
7 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ƒéØÄåƐ§µ E ŒÆ ÔnX Kµ = dPµ dτ “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ƒéØÄåƐ§µ E ŒÆ ÔnX dPµ Kµ = dτ =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c E ŒÆ ÔnX =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv E ŒÆ ÔnX =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† E ŒÆ ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† Fy0 = E dp0y d t0 ŒÆ ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† Fy0 = E dp0y = 0 dt ŒÆ dpy γβ γ dt − dx c ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† Fy0 = E dp0y = 0 dt ŒÆ dpy dpy /dt  =  γβ β dx γ dt − dx γ 1− c c dt ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† Fy0 = E dp0y = 0 dt ŒÆ dpy dpy /dt Fy = =  γβ β dx γ(1 − βux/c) γ dt − dx γ 1− c c dt ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† Fy0 = E dp0y = 0 dt ŒÆ dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† dp0y dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt Fz 0 aq/µFz = γ(1 − βux/c) Fy0 = E = 0 dt ŒÆ ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† dp0y dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt Fz 0 aq/µFz = γ(1 − βux/c) Fy0 = = 0 dt 0 d p Fx0 = x0 dt E ŒÆ ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† dp0y dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt Fz 0 aq/µFz = γ(1 − βux/c) Fy0 = = 0 dt 0 d p γ(dpx + iβ dP4) x 0 Fx = = d t0 γ[dt − (β/c) dx] E ŒÆ ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† dp0y dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt Fz 0 aq/µFz = γ(1 − βux/c) Fy0 = = 0 dt 0 d p γ(dpx + iβ dP4) dpx/dt − (β/c)(dW/dt) x 0 Fx = = = d t0 γ[dt − (β/c) dx] 1 − (β/c) dx/dt E ŒÆ ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† dp0y dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt Fz 0 aq/µFz = γ(1 − βux/c) Fy0 = = 0 dt 0 ~) d p γ(dpx + iβ dP4) dpx/dt − (β/c)(dW/dt) Fx − (β/c)(~ u·F x 0 Fx = = = = d t0 γ[dt − (β/c) dx] 1 − (β/c) dx/dt 1 − βux/c E ŒÆ ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† dp0y dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt Fz 0 aq/µFz = γ(1 − βux/c) Fy0 = = 0 dt 0 ~) d p γ(dpx + iβ dP4) dpx/dt − (β/c)(dW/dt) Fx − (β/c)(~ u·F x 0 Fx = = = = d t0 γ[dt − (β/c) dx] 1 − (β/c) dx/dt 1 − βux/c ~ =⇒ E ŒÆ Fx − (β/c)(~ u · F) 0 Fx = 1 − βux/c ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† dp0y dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt Fz 0 aq/µFz = γ(1 − βux/c) Fy0 = = 0 dt 0 ~) d p γ(dpx + iβ dP4) dpx/dt − (β/c)(dW/dt) Fx − (β/c)(~ u·F x 0 Fx = = = = d t0 γ[dt − (β/c) dx] 1 − (β/c) dx/dt 1 − βux/c ~ =⇒ Fx − (β/c)(~ u · F) 0 Fx = 1 − βux/c e3 S .5X¥âf´·Ž§Kkµ E ŒÆ ÔnX ~0 = 1 F ~⊥, F ⊥ γ F||0 = F|| “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light dPµ ƒéØÄåƐ§µ Kµ = dτ   i ~, W o‘Äþ¥þµPµ = p c o‘Äþ¥þC†'XµPx0 = γv =⇒  ~  ~ = dp  K dτ dW  ~ ·u  K ~ = dτ ½ ½ ~ dp ~ F = dt dW ~ ·u ~ = F dt
v Px − 2 W , Py0 = Py , Pz0 = Pz , W 0 = γv (W − vPx) c ØÓ.5X¥åC† dp0y dpy dpy /dt Fy Fy = =  =⇒ Fy0 = γβ β dx γ(1 − βux/c) γ(1 − βux/c) γ dt − dx γ 1− c c dt Fz 0 aq/µFz = γ(1 − βux/c) Fy0 = = 0 dt 0 ~) d p γ(dpx + iβ dP4) dpx/dt − (β/c)(dW/dt) Fx − (β/c)(~ u·F x 0 Fx = = = = d t0 γ[dt − (β/c) dx] 1 − (β/c) dx/dt 1 − βux/c ~ =⇒ Fx − (β/c)(~ u · F) 0 Fx = 1 − βux/c e3 S .5X¥âf´·Ž§Kkµ ~0 = 1 F ~⊥, F ⊥ γ F||0 = F|| § 8.5 p15, ~ 1 ^ù‡úª E ŒÆ ÔnX “ Mï
8 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X E ŒÆ ÔnX ÄUúª ŸU'X “ Mï
9 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X ÄUúª ŸU'X Ÿ„'X ~ = γum0u ~ ƒéØÄþµ p ƒéØUþµ W = γum0c2 -µm = γu m0§m ¡ÔN$ğþ§Kµ~ p = m~ u, E ŒÆ ÔnX W = mc2 “ †$„ƒq Mï
9 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X ÄUúª ŸU'X Ÿ„'X ~ = γum0u ~ ƒéØÄþµ p ƒéØUþµ W = γum0c2 -µm = γu m0§m ¡ÔN$ğþ§Kµ~ p = m~ u, p m = m0/ 1 − u2/c2, E ŒÆ ÔnX W = mc2 †$„ƒq Ÿþ„Ý'Xª “ Mï
9 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X ÄUúª ŸU'X Ÿ„'X ~ = γum0u ~ ƒéØÄþµ p ƒéØUþµ W = γum0c2 -µm = γu m0§m ¡ÔN$ğþ§Kµ~ p = m~ u, p m = m0/ 1 − u2/c2, W = mc2 †$„ƒq Ÿþ„Ý'Xª ?Ø E ŒÆ ÔnX “ Mï
9 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X ÄUúª ŸU'X Ÿ„'X ~ = γum0u ~ ƒéØÄþµ p ƒéØUþµ W = γum0c2 -µm = γu m0§m ¡ÔN$ğþ§Kµ~ p = m~ u, p m = m0/ 1 − u2/c2, W = mc2 †$„ƒq Ÿþ„Ý'Xª ?Ø (1) E lŸþ„Ý'XŒ§ÔNŸþØ´~ê§ ´‘„ÝO\ ŒÆ ÔnX “ Mï
9 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X ÄUúª ŸU'X Ÿ„'X ~ = γum0u ~ ƒéØÄþµ p ƒéØUþµ W = γum0c2 -µm = γu m0§m ¡ÔN$ğþ§Kµ~ p = m~ u, p m = m0/ 1 − u2/c2, W = mc2 †$„ƒq Ÿþ„Ý'Xª ?Ø (1) (2) E lŸþ„Ý'XŒ§ÔNŸþØ´~ê§ ´‘„ÝO\ ~ ~ dp du ~ ~ Ï 3²;åÆ¥§§ F = ÚF = m d dt dt ~ ~ dp du ~ ~ 3ƒéØ¥§duŸþ†„Ýk'§Ek F = § F = m ؤá dt dt ŒÆ ÔnX “ Mï
9 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X ÄUúª ŸU'X Ÿ„'X ~ = γum0u ~ ƒéØÄþµ p ƒéØUþµ W = γum0c2 -µm = γu m0§m ¡ÔN$ğþ§Kµ~ p = m~ u, p m = m0/ 1 − u2/c2, W = mc2 †$„ƒq Ÿþ„Ý'Xª ?Ø (1) (2) (3) E lŸþ„Ý'XŒ§ÔNŸþØ´~ê§ ´‘„ÝO\ ~ ~ dp du ~ ~ Ï 3²;åÆ¥§§ F = ÚF = m d dt dt ~ ~ dp du ~ ~ 3ƒéØ¥§duŸþ†„Ýk'§Ek F = § F = m ؤá dt dt ˜‡Ÿ„'X{üÔn¯~ ŒÆ ÔnX “ Mï
9 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X ÄUúª ŸU'X Ÿ„'X ~ = γum0u ~ ƒéØÄþµ p ƒéØUþµ W = γum0c2 -µm = γu m0§m ¡ÔN$ğþ§Kµ~ p = m~ u, p m = m0/ 1 − u2/c2, W = mc2 †$„ƒq Ÿþ„Ý'Xª ?Ø (1) (2) (3) lŸþ„Ý'XŒ§ÔNŸþØ´~ê§ ´‘„ÝO\ ~ ~ dp du ~ ~ Ï 3²;åÆ¥§§ F = ÚF = m d dt dt ~ ~ dp du ~ ~ 3ƒéØ¥§duŸþ†„Ýk'§Ek F = § F = m ؤá dt dt ˜‡Ÿ„'X{üÔn¯~ kü‡.5Xµ¢¿.5X S Úƒé† S ±„Ý v ÷ +x •$Ä.5X S 0 E ŒÆ ÔnX “ Mï
9 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light o!Ÿ„'X ÄUúª ŸU'X Ÿ„'X ~ = γum0u ~ ƒéØÄþµ p ƒéØUþµ W = γum0c2 -µm = γu m0§m ¡ÔN$ğþ§Kµ~ p = m~ u, p m = m0/ 1 − u2/c2, W = mc2 †$„ƒq Ÿþ„Ý'Xª ?Ø (1) (2) (3) lŸþ„Ý'XŒ§ÔNŸþØ´~ê§ ´‘„ÝO\ ~ ~ dp du ~ ~ Ï 3²;åÆ¥§§ F = ÚF = m d dt dt ~ ~ dp du ~ ~ 3ƒéØ¥§duŸþ†„Ýk'§Ek F = § F = m ؤá dt dt ˜‡Ÿ„'X{üÔn¯~ kü‡.5Xµ¢¿.5X S Úƒé† S ±„Ý v ÷ +x •$Ä.5X S 0 A, B ü‡·ŽŸþя m0 âf§3 S 0 X¥„Ý©O ±v êx§Šš5-E E ŒÆ ÔnX “ Mï
9 Let there be light (3) E ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 ˜‡Ÿ„'X{üÔn¯~£Y¤ ŒÆ ÔnX “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E E ŒÆ ÔnX üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) E ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v ŒÆ ÔnX “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 E ŒÆ ÔnX “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 v+v d„ÝC†úªµu = 1 − v 2/c2 E ŒÆ ÔnX “ (1) Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 v+v d„ÝC†úªµu = (1) 2 2 1 − v /c 3 S X§-EcÄþµPa = mu + m0 0§-E üâf܏˜§„ݏ v " E ŒÆ ÔnX “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 v+v d„ÝC†úªµu = (1) 2 2 1 − v /c 3 S X§-EcÄþµPa = mu + m0 0§-E üâf܏˜§„ݏ v " 3 S X§-E E ŒÆ ÔnX ÄþµPb = (m + m0)v § “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 v+v d„ÝC†úªµu = (1) 2 2 1 − v /c 3 S X§-EcÄþµPa = mu + m0 0§-E üâf܏˜§„ݏ v " 3 S X§-E ÄþµPb = (m + m0)v § ÄþÅðµPa = Pb E ŒÆ ÔnX =⇒ mu = (m + m0)v (2) “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 v+v d„ÝC†úªµu = (1) 2 2 1 − v /c 3 S X§-EcÄþµPa = mu + m0 0§-E üâf܏˜§„ݏ v " 3 S X§-E ÄþµPb = (m + m0)v § ÄþÅðµPa = Pb =⇒ mu = (m + m0)v p d (1 - 2) µm = m0/ 1 − u2/c2 ƒé؟„'X E ŒÆ ÔnX (2) “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 v+v d„ÝC†úªµu = (1) 2 2 1 − v /c 3 S X§-EcÄþµPa = mu + m0 0§-E üâf܏˜§„ݏ v " 3 S X§-E ÄþµPb = (m + m0)v § ÄþÅðµPa = Pb =⇒ mu = (m + m0)v p d (1 - 2) µm = m0/ 1 − u2/c2 ƒé؟„'X ÄU½nµ E ŒÆ ÔnX (2) ƒéØÄUµT = W − W0 = (m − m0)c2 “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 v+v d„ÝC†úªµu = (1) 2 2 1 − v /c 3 S X§-EcÄþµPa = mu + m0 0§-E üâf܏˜§„ݏ v " 3 S X§-E ÄþµPb = (m + m0)v § ÄþÅðµPa = Pb =⇒ mu = (m + m0)v p d (1 - 2) µm = m0/ 1 − u2/c2 ƒé؟„'X ÄU½nµ (2) ƒéØÄUµT = W − W0 = (m − m0)c2 dm 2 dW dT ~ = c = = F~ · u dt dt dt E ŒÆ ÔnX “ Mï
10 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) ˜‡Ÿ„'X{üÔn¯~£Y¤ 3 S 0 X§š5-E üâf܏˜§„ݏ 0§ƒéu S 0 X·Ž 3 S X§š5-E üâf܏˜§„ݏ v 3 S X§-Ec A, B üâf„Ý©O u Ú 0§Ÿþ©Oµm Ú m0 v+v d„ÝC†úªµu = (1) 2 2 1 − v /c 3 S X§-EcÄþµPa = mu + m0 0§-E üâf܏˜§„ݏ v " 3 S X§-E ÄþµPb = (m + m0)v § ÄþÅðµPa = Pb =⇒ mu = (m + m0)v p d (1 - 2) µm = m0/ 1 − u2/c2 ƒé؟„'X ÄU½nµ (2) ƒéØÄUµT = W − W0 = (m − m0)c2 dm 2 dW dT ~ = c = = F~ · u dt dt dt dT ~ ~ = ƒéØ¥§ÄU½nE,¤áµF · u dt E ŒÆ ÔnX “ Mï
10 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 ŸU'Xµ $ÄÔNUþµW = mc2 E ŒÆ ÔnX ·ŽÔNUþµW0 = m0c2 “ Mï
11 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 ŸU'Xµ $ÄÔNUþµW = mc2 ·ŽÔNUþµW0 = m0c2 ?Ø E ŒÆ ÔnX “ Mï
11 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ŸU'Xµ $ÄÔNUþµW = mc2 ·ŽÔNUþµW0 = m0c2 ?Ø (1) ŸU'X‡N ˜½Ÿþâfäk˜½SÜ$ÄUþ ‘k˜½SÜ$ÄUþâfKLyÑk˜½.5Ÿþ E ŒÆ ÔnX “ Mï
11 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ŸU'Xµ $ÄÔNUþµW = mc2 ·ŽÔNUþµW0 = m0c2 ?Ø (1) ŸU'X‡N ˜½Ÿþâfäk˜½SÜ$ÄUþ ‘k˜½SÜ$ÄUþâfKLyÑk˜½.5Ÿþ (2) ŸU'XÓ·ÜuEÜâf"éEÜâf§W0 ´ÔNŸ%·ŽžoSÜUþ 3Ÿ%.5X§EÜâfUþ W0 = M0c2§M0 ÔNoŸþ" W0 = M0c2 E ŒÆ ÔnX “ Mï
11 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ŸU'Xµ $ÄÔNUþµW = mc2 ·ŽÔNUþµW0 = m0c2 ?Ø (1) ŸU'X‡N ˜½Ÿþâfäk˜½SÜ$ÄUþ ‘k˜½SÜ$ÄUþâfKLyÑk˜½.5Ÿþ (2) ŸU'XÓ·ÜuEÜâf"éEÜâf§W0 ´ÔNŸ%·ŽžoSÜUþ 3Ÿ%.5X§EÜâfUþ W0 = M0c2§M0 ÔNoŸþ" X X X 2 2 2 W0 = M0 c = mi0c + Ti + U 6= mi0c i i i )ˆâf·ŽUþ§ƒéuŸ%$ÄÄU§ÚâfmƒpŠ^U E ŒÆ ÔnX “ Mï
11 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ŸU'Xµ $ÄÔNUþµW = mc2 ·ŽÔNUþµW0 = m0c2 ?Ø (1) ŸU'X‡N ˜½Ÿþâfäk˜½SÜ$ÄUþ ‘k˜½SÜ$ÄUþâfKLyÑk˜½.5Ÿþ (2) ŸU'XÓ·ÜuEÜâf"éEÜâf§W0 ´ÔNŸ%·ŽžoSÜUþ 3Ÿ%.5X§EÜâfUþ W0 = M0c2§M0 ÔNoŸþ" X X X 2 2 2 W0 = M0 c = mi0c + Ti + U 6= mi0c i i i )ˆâf·ŽUþ§ƒéuŸ%$ÄÄU§ÚâfmƒpŠ^U X 2 ∆W = W0 − mi0c ¡ÔN(ÜU i ∆W < 0 L«EÜâf´­½§|∆W | ŒL«EÜâf­½ E ŒÆ ÔnX “ Mï
11 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ŸU'Xµ $ÄÔNUþµW = mc2 ·ŽÔNUþµW0 = m0c2 ?Ø (1) ŸU'X‡N ˜½Ÿþâfäk˜½SÜ$ÄUþ ‘k˜½SÜ$ÄUþâfKLyÑk˜½.5Ÿþ (2) ŸU'XÓ·ÜuEÜâf"éEÜâf§W0 ´ÔNŸ%·ŽžoSÜUþ 3Ÿ%.5X§EÜâfUþ W0 = M0c2§M0 ÔNoŸþ" X X X 2 2 2 W0 = M0 c = mi0c + Ti + U 6= mi0c i i i )ˆâf·ŽUþ§ƒéuŸ%$ÄÄU§ÚâfmƒpŠ^U X 2 ∆W = W0 − mi0c ¡ÔN(ÜU i ∆W < 0 L«EÜâf´­½§|∆W | ŒL«EÜâf­½ l |∆W | âf |∆W | Œâf=C E ŒÆ ÔnX º˜Uþ=ØU “ Mï
11 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ŸU'Xµ $ÄÔNUþµW = mc2 ·ŽÔNUþµW0 = m0c2 ?Ø (1) ŸU'X‡N ˜½Ÿþâfäk˜½SÜ$ÄUþ ‘k˜½SÜ$ÄUþâfKLyÑk˜½.5Ÿþ (2) ŸU'XÓ·ÜuEÜâf"éEÜâf§W0 ´ÔNŸ%·ŽžoSÜUþ 3Ÿ%.5X§EÜâfUþ W0 = M0c2§M0 ÔNoŸþ" X X X 2 2 2 W0 = M0 c = mi0c + Ti + U 6= mi0c i i i )ˆâf·ŽUþ§ƒéuŸ%$ÄÄU§ÚâfmƒpŠ^U X 2 ∆W = W0 − mi0c ¡ÔN(ÜU i ∆W < 0 L«EÜâf´­½§|∆W | ŒL«EÜâf­½ l |∆W | âf |∆W | Œâf=C X 2 EÜâfŸþµM0 = W0/c 6= mi0 º˜Uþ=ØU i E ŒÆ ÔnX “ Mï
11 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light ŸU'Xµ $ÄÔNUþµW = mc2 ·ŽÔNUþµW0 = m0c2 ?Ø (1) ŸU'X‡N ˜½Ÿþâfäk˜½SÜ$ÄUþ ‘k˜½SÜ$ÄUþâfKLyÑk˜½.5Ÿþ (2) ŸU'XÓ·ÜuEÜâf"éEÜâf§W0 ´ÔNŸ%·ŽžoSÜUþ 3Ÿ%.5X§EÜâfUþ W0 = M0c2§M0 ÔNoŸþ" X X X 2 2 2 W0 = M0 c = mi0c + Ti + U 6= mi0c i i i )ˆâf·ŽUþ§ƒéuŸ%$ÄÄU§ÚâfmƒpŠ^U X 2 ∆W = W0 − mi0c ¡ÔN(ÜU i ∆W < 0 L«EÜâf´­½§|∆W | ŒL«EÜâf­½ l |∆W | âf |∆W | Œâf=C º˜Uþ=ØU X 2 EÜâfŸþµM0 = W0/c 6= mi0 i X 2 ∆M = M0 − mi0 = ∆W/c ¡Ÿþº›"∆M > 0 âfòu)guPC" i E ŒÆ ÔnX “ Mï
11 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ E ŒÆ ÔnX Doppler A “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ E ŒÆ ÔnX “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§ E ŒÆ ÔnX “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" E ŒÆ ÔnX “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c E ŒÆ ÔnX “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) E lþfåÆÝw ŒÆ ÔnX “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw ~ = ~~ 1fÄþ p k§1fUþµW = ~ω E ŒÆ ÔnX “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw ~ = ~~ 1fÄþ p k§1fUþµW = ~ω
i i
~, W = ~ ~ üö¤o‘Äþ¥þµPµ = p k, ω c c E ŒÆ ÔnX “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw ~ = ~~ 1fÄþ p k§1fUþµW = ~ω
i i
~, W = ~ ~ üö¤o‘Äþ¥þµPµ = p k, ω c c E ŒÆ ÔnX l µ ~ k, i
ω ´o‘¥þ c “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw (2) ~ = ~~ 1fÄþ p k§1fUþµW = ~ω
i i
~, W = ~ ~ üö¤o‘Äþ¥þµPµ = p k, ω c c l²¡>^Å>^|Üþw E ŒÆ ÔnX l µ ~ k, i
ω ´o‘¥þ c “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw (2) ~ = ~~ 1fÄþ p k§1fUþµW = ~ω
i i
~, W = ~ ~ üö¤o‘Äþ¥þµPµ = p k, ω c c l²¡>^Å>^|Üþw ~ =E ~ 0ei~k·~r−iωt, 鲡>^ŵE E ŒÆ ÔnX l µ ~ k, i
ω ´o‘¥þ c ~ =B ~ 0ei~k·~r−iωt, B “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw l (2) ~ = ~~ 1fÄþ p k§1fUþµW = ~ω
i i
~, W = ~ ~ üö¤o‘Äþ¥þµPµ = p k, ω c c l²¡>^Å>^|Üþw ~ =E ~ 0ei~k·~r−iωt, 鲡>^ŵE =⇒ E ŒÆ ÔnX ~ =B ~ 0ei~k·~r−iωt, B µ ~ k, i
ω ´o‘¥þ c ~ 0 ik·~ Fµν = Fµν e r−iωt “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw l (2) ~ = ~~ 1fÄþ p k§1fUþµW = ~ω
i i
~, W = ~ ~ üö¤o‘Äþ¥þµPµ = p k, ω c c l²¡>^Å>^|Üþw ~ =E ~ 0ei~k·~r−iωt, 鲡>^ŵE =⇒ ~ =B ~ 0ei~k·~r−iωt, B µ ~ k, i
ω ´o‘¥þ c ~ 0 ik·~ Fµν = Fµν e r−iωt 0 ~ 0 du Fµν ´o‘Üþ§3,˜.5XµFµν = aµλaντ Fλτ = aµλaντ Fλτ eik·~r−iωt | {z } 00 Fµν E ŒÆ ÔnX “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw l (2) ~ = ~~ 1fÄþ p k§1fUþµW = ~ω
i i
~, W = ~ ~ üö¤o‘Äþ¥þµPµ = p k, ω c c l²¡>^Å>^|Üþw ~ =E ~ 0ei~k·~r−iωt, 鲡>^ŵE =⇒ ~ =B ~ 0ei~k·~r−iωt, B µ ~ k, i
ω ´o‘¥þ c ~ 0 ik·~ Fµν = Fµν e r−iωt 0 ~ 0 du Fµν ´o‘Üþ§3,˜.5XµFµν = aµλaντ Fλτ = aµλaντ Fλτ eik·~r−iωt | {z } 00 0 0 0 i~ k·~ r −iωt F µν =µF = F e µν E ŒÆ ÔnX µν “ Mï
12 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ê!o‘Å¥þ Doppler A l²;åÆ¥µ Å ‚C* öž§* öÿªÇo´puÅ ƒéu* ö·ŽžÿªÇ Å l* öž§* öÿªÇo´$uÅ ƒéu* ö·ŽžÿªÇ 3ƒéØ¥9ØÓ.5XƒmªÇC†'X§o‘Å¥þ¯K" i
~ kµ = k, ω ´o‘¥þ c (1) lþfåÆÝw l (2) ~ = ~~ 1fÄþ p k§1fUþµW = ~ω
i i
~, W = ~ ~ üö¤o‘Äþ¥þµPµ = p k, ω c c l²¡>^Å>^|Üþw ~ =E ~ 0ei~k·~r−iωt, 鲡>^ŵE =⇒ ~ =B ~ 0ei~k·~r−iωt, B µ ~ k, i
ω ´o‘¥þ c ~ 0 ik·~ Fµν = Fµν e r−iωt 0 ~ 0 du Fµν ´o‘Üþ§3,˜.5XµFµν = aµλaντ Fλτ = aµλaντ Fλτ eik·~r−iωt | {z } 00 0 0 0 i~ k·~ r −iωt −1 0 0 F µν =µF = F e |^µx = [a ] x = a x µν E ŒÆ ÔnX µν µ µν nu νµ ν “ Mï
12 Let there be light (2) E ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 l²¡>^Å>^|Üþw (Y) ŒÆ ÔnX “ Mï
13 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt E ŒÆ ÔnX “ Mï
13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt E ŒÆ ÔnX ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c “ Mï
13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t E ŒÆ ÔnX “ Mï
13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t E ŒÆ ÔnX ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c “ Mï
13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t E ŒÆ ÔnX ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c “ Mï

13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t (3) E ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c
l˜‡{üÔn¯~w ŒÆ ÔnX “ Mï
13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t (3) E ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c
l˜‡{üÔn¯~w ŒÆ ÔnX “ Mï
13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t (3) ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c
l˜‡{üÔn¯~w S 0 ƒéu S X±„Ý v ÷ +x •$ħt = t0 = 0 ž:­Ü ²¡>^ŵϕ = ϕ0 cos(kx − ωt) E ŒÆ ÔnX “ Mï
13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t (3) ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c
l˜‡{üÔn¯~w S 0 ƒéu S X±„Ý v ÷ +x •$ħt = t0 = 0 ž:­Ü ²¡>^ŵϕ = ϕ0 cos(kx − ωt) Ÿ A ˆ S X:¯‡ A§Å¸ B ˆ S X:¯‡ B E ŒÆ ÔnX “ Mï
13 Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t (3) ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c
l˜‡{üÔn¯~w S 0 ƒéu S X±„Ý v ÷ +x •$ħt = t0 = 0 ž:­Ü ²¡>^ŵϕ = ϕ0 cos(kx − ωt) Ÿ A ˆ S X:¯‡ A§Å¸ B ˆ S X:¯‡ B ¯‡ A ž˜‹Iµ(x = x0 = 0, t = t0 = 0) ¯‡ B ž˜‹Iµ(x = 0, t = T )§(x0, t0) E ŒÆ ÔnX “ Mï
13 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t (3) |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c
l˜‡{üÔn¯~w S 0 ƒéu S X±„Ý v ÷ +x •$ħt = t0 = 0 ž:­Ü ²¡>^ŵϕ = ϕ0 cos(kx − ωt) Ÿ A ˆ S X:¯‡ A§Å¸ B ˆ S X:¯‡ B ¯‡ A ž˜‹Iµ(x = x0 = 0, t = t0 = 0) ¯‡ B ž˜‹Iµ(x = 0, t = T )§(x0, t0) 3 S X§¯‡ B éA>^Ń E ŒÆ ÔnX µkx − ωt = −ωT = −2𠓐 Mï
13 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t (3) |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c
l˜‡{üÔn¯~w S 0 ƒéu S X±„Ý v ÷ +x •$ħt = t0 = 0 ž:­Ü ²¡>^ŵϕ = ϕ0 cos(kx − ωt) Ÿ A ˆ S X:¯‡ A§Å¸ B ˆ S X:¯‡ B ¯‡ A ž˜‹Iµ(x = x0 = 0, t = t0 = 0) ¯‡ B ž˜‹Iµ(x = 0, t = T )§(x0, t0) 3 S X§¯‡ B éA>^Ń µkx − ωt = −ωT = −2π 3 S 0 X§¯‡ B éA>^Ń µk0x0 − ω 0t0 E ŒÆ ÔnX “ Mï
13 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6  Let there be light (2) l²¡>^Å>^|Üþw (Y) ~ 0 0 0 ik·~ =µFµν = Fµν e r−iωt ~0 0 0 0 0 0 0 ik ·~ Fµν = Fµν e r −iω t (3) |^µxµ = [a−1]µν x0nu = aνµx0ν  ω
0   kx = γ kx − β ,   c   0 ky = ky , Ù¥µ   kz0 = kz ,     ω 0 = γ(ω − vk ) x  x = γ(x0 + vt0)     0   y=y 0 = z = z     βx0
   t=γ t+ c =⇒ kµ0 = aµν kν i ku = ~ k, ω c
l˜‡{üÔn¯~w S 0 ƒéu S X±„Ý v ÷ +x •$ħt = t0 = 0 ž:­Ü ²¡>^ŵϕ = ϕ0 cos(kx − ωt) Ÿ A ˆ S X:¯‡ A§Å¸ B ˆ S X:¯‡ B ¯‡ A ž˜‹Iµ(x = x0 = 0, t = t0 = 0) ¯‡ B ž˜‹Iµ(x = 0, t = T )§(x0, t0) 3 S X§¯‡ B éA>^Ń µkx − ωt = −ωT = −2π 3 S 0 X§¯‡ B éA>^Ń µk0x0 − ω 0t0 3 S 0 X* E ŒÆ ÔnX §¯‡ B u)ž§Å¸ A ®ˆ A0 : “ Mï
13 Let there be light (3) E ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 l˜‡{üÔn¯~w (Y) ŒÆ ÔnX “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ E ŒÆ ÔnX kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* E ŒÆ ÔnX kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå E ŒÆ ÔnX “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå E 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 ŒÆ ÔnX “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 λ0 = 2πc/ω 0 E ŒÆ ÔnX =⇒ 0 0 2πc/ω λ = t0 = v+c v+c “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c E ŒÆ ÔnX “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c x0, t0 “\ k0x0 − ω 0t0 ¿|^ k0 = ω 0/c =⇒ E ŒÆ ÔnX k0x0 − ω 0t0 = −2𠓐 Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c x0, t0 “\ k0x0 − ω 0t0 ¿|^ k0 = ω 0/c =⇒ =µ¯‡ B éA>^Ń E ŒÆ ÔnX k0x0 − ω 0t0 = −2π é S Ú S 0 XÑ´ −2𠧃 kx − ωt ´ØCþ “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c x0, t0 “\ k0x0 − ω 0t0 ¿|^ k0 = ω 0/c =⇒ =µ¯‡ B éA>^Ń µkx − ωt = kµxµ, E ŒÆ ÔnX k0x0 − ω 0t0 = −2π é S Ú S 0 XÑ´ −2𠧃 kx − ωt ´ØCþ xµ ´o‘¥þ§kµxµ ´o‘Iþ =⇒ kµ 7o‘¥þ" “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c x0, t0 “\ k0x0 − ω 0t0 ¿|^ k0 = ω 0/c =⇒ =µ¯‡ B éA>^Ń µkx − ωt = kµxµ, lþ©Û§ƒ E ŒÆ ÔnX k0x0 − ω 0t0 = −2π é S Ú S 0 XÑ´ −2𠧃 kx − ωt ´ØCþ xµ ´o‘¥þ§kµxµ ´o‘Iþ =⇒ kµ 7o‘¥þ" ØC55g1„ØC" “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c x0, t0 “\ k0x0 − ω 0t0 ¿|^ k0 = ω 0/c =⇒ =µ¯‡ B éA>^Ń µkx − ωt = kµxµ, lþ©Û§ƒ , E ŒÆ é S Ú S 0 XÑ´ −2𠧃 kx − ωt ´ØCþ xµ ´o‘¥þ§kµxµ ´o‘Iþ =⇒ kµ 7o‘¥þ" ØC55g1„ØC" §3 S X§¯‡ A, B u)uÓ/§Ùžmm ÔnX k0x0 − ω 0t0 = −2𠧏=>^Å±Ï T 7,´kž “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c x0, t0 “\ k0x0 − ω 0t0 ¿|^ k0 = ω 0/c =⇒ =µ¯‡ B éA>^Ń µkx − ωt = kµxµ, lþ©Û§ƒ , é S Ú S 0 XÑ´ −2𠧃 ŒÆ kµ 7o‘¥þ" ØC55g1„ØC" §3 S X§¯‡ A, B u)uÓ/§Ùžmm ÔnX kx − ωt ´ØCþ xµ ´o‘¥þ§kµxµ ´o‘Iþ =⇒ 3 S 0 X§¯‡ A, B u)uÉ/§Ùžmm E k0x0 − ω 0t0 = −2𠧏=>^Å±Ï T 7,´kž t0 7,´$Ğmµ “ Mï
14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c x0, t0 “\ k0x0 − ω 0t0 ¿|^ k0 = ω 0/c =⇒ =µ¯‡ B éA>^Ń µkx − ωt = kµxµ, lþ©Û§ƒ , é S Ú S 0 XÑ´ −2𠧃 ŒÆ kµ 7o‘¥þ" ØC55g1„ØC" §3 S X§¯‡ A, B u)uÓ/§Ùžmm ÔnX kx − ωt ´ØCþ xµ ´o‘¥þ§kµxµ ´o‘Iþ =⇒ 3 S 0 X§¯‡ A, B u)uÉ/§Ùžmm E k0x0 − ω 0t0 = −2𠧏=>^Å±Ï T 7,´kž t0 7,´$Ğmµt0 = γT = γ “ Mï
2π ω 14 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) l˜‡{üÔn¯~w (Y) S X§¯‡ B éAƒ 3 S 0 X* kx − ωt = −2π S 0 X§¯‡ B éAƒ k0x0 − ω 0t0 §¯‡ B u)ž§Å¸ A ®ˆ A0 : >^Åŏü‡Å¸ƒmmå 3 S 0 X* §Å λ0 = OO 0 + O 0A0 = vt0 + ct0 d?|^ >^Å3?Û.5X„Ýя c§ O 0A0 = ct0 0 0 2πc/ω λ = λ0 = 2πc/ω 0 =⇒ t0 = v+c v+c 0 2πvc/ω x0 = −OO 0 = −vt0 = − v+c x0, t0 “\ k0x0 − ω 0t0 ¿|^ k0 = ω 0/c =⇒ =µ¯‡ B éA>^Ń µkx − ωt = kµxµ, lþ©Û§ƒ , k0x0 − ω 0t0 = −2π é S Ú S 0 XÑ´ −2𠧃 kx − ωt ´ØCþ xµ ´o‘¥þ§kµxµ ´o‘Iþ =⇒ kµ 7o‘¥þ" ØC55g1„ØC" §3 S X§¯‡ A, B u)uÓ/§Ùžmm 3 S 0 X§¯‡ A, B u)uÉ/§Ùžmm §=>^Å±Ï T 7,´kž t0 7,´$Ğmµt0 = γT = γ 0 0 λ 2πc/ω éá t0 = = µω 0 = γω(1 − v/c) = γ(ω − vk) v+c v+c E ŒÆ ÔnX “ Mï
2π ω 14 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c E ŒÆ ÔnX “ Mï
15 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c  S Ú S 0 Aσ'.5X 3 S 0 X¥§~k0 † x0 ¶¤ θ0 §3 S X¥§~k † x ¶¤ θ §K kx = k cos θ ky = k sin θ kx0 = k 0 cos θ0 ky0 = k 0 sin θ E ŒÆ ÔnX “\ kµ0 = aµν kν µ “ Mï
15 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c  S Ú S 0 Aσ'.5X 3 S 0 X¥§~k0 † x0 ¶¤ θ0 §3 S X¥§~k † x ¶¤ θ §K kx = k cos θ ky = k sin θ kx0 = k 0 cos θ0 ky0 = k 0 sin θ “\ kµ0 = aµν kν µ
i 0 i ω =γ ω − iβkx c c E ŒÆ ÔnX “ Mï
15 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c  S Ú S 0 Aσ'.5X 3 S 0 X¥§~k0 † x0 ¶¤ θ0 §3 S X¥§~k † x ¶¤ θ §K kx = k cos θ ky = k sin θ kx0 = k 0 cos θ0 ky0 = k 0 sin θ “\ kµ0 = aµν kν µ
i 0 i ω =γ ω − iβkx =⇒ ω 0 = γ ω(1 − β cos θ) c c E ŒÆ ÔnX “ Mï
15 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c  S Ú S 0 Aσ'.5X 3 S 0 X¥§~k0 † x0 ¶¤ θ0 §3 S X¥§~k † x ¶¤ θ §K kx = k cos θ ky = k sin θ kx0 = k 0 cos θ0 ky0 = k 0 sin θ “\ kµ0 = aµν kν µ
i 0 i ω =γ ω − iβkx =⇒ ω 0 = γ ω(1 − β cos θ) =⇒ c c E ŒÆ ÔnX ω0 ω= γ(1 − β cos θ) “ Mï
15 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c  S Ú S 0 Aσ'.5X 3 S 0 X¥§~k0 † x0 ¶¤ θ0 §3 S X¥§~k † x ¶¤ θ §K kx = k cos θ ky = k sin θ kx0 = k 0 cos θ0 ky0 = k 0 sin θ “\ kµ0 = aµν kν µ
i 0 i ω =γ ω − iβkx =⇒ ω 0 = γ ω(1 − β cos θ) =⇒ c c ω0 ω= γ(1 − β cos θ) 0 ω e3 S 0 X¥1 ·Ž§K f 0 = = f0 ¡ kªÇ§þªL² 2π ω 3ƒéu1 $Ä S X¥§f = 6= f0 ƒéØ Doppler A 2π E ŒÆ ÔnX “ Mï
15 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c  S Ú S 0 Aσ'.5X 3 S 0 X¥§~k0 † x0 ¶¤ θ0 §3 S X¥§~k † x ¶¤ θ §K kx = k cos θ ky = k sin θ kx0 = k 0 cos θ0 ky0 = k 0 sin θ “\ kµ0 = aµν kν µ
i 0 i ω =γ ω − iβkx =⇒ ω 0 = γ ω(1 − β cos θ) =⇒ c c ω0 ω= γ(1 − β cos θ) 0 ω e3 S 0 X¥1 ·Ž§K f 0 = = f0 ¡ kªÇ§þªL² 2π ω 3ƒéu1 $Ä S X¥§f = 6= f0 ƒéØ Doppler A 2π ?Ø E ŒÆ ÔnX “ Mï
15 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c  S Ú S 0 Aσ'.5X 3 S 0 X¥§~k0 † x0 ¶¤ θ0 §3 S X¥§~k † x ¶¤ θ §K kx = k cos θ ky = k sin θ kx0 = k 0 cos θ0 ky0 = k 0 sin θ “\ kµ0 = aµν kν µ
i 0 i ω =γ ω − iβkx =⇒ ω 0 = γ ω(1 − β cos θ) =⇒ c c ω0 ω= γ(1 − β cos θ) 0 ω e3 S 0 X¥1 ·Ž§K f 0 = = f0 ¡ kªÇ§þªL² 2π ω 3ƒéu1 $Ä S X¥§f = 6= f0 ƒéØ Doppler A 2π ?Ø s (1) E ŒÆ f0 1+β e3 S X θ = 0§K f = = f0 > f0 γ(1 − β) 1−β ¡b£§=1 •* ö‚CžªÇu)b£ ÔnX “ Mï
15 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light i
~ Q, kµ = k, ω ´o‘¥þ§Kkµkµ0 = aµν kν c  S Ú S 0 Aσ'.5X 3 S 0 X¥§~k0 † x0 ¶¤ θ0 §3 S X¥§~k † x ¶¤ θ §K kx = k cos θ ky = k sin θ kx0 = k 0 cos θ0 ky0 = k 0 sin θ “\ kµ0 = aµν kν µ
i 0 i ω =γ ω − iβkx =⇒ ω 0 = γ ω(1 − β cos θ) =⇒ c c ω0 ω= γ(1 − β cos θ) 0 ω e3 S 0 X¥1 ·Ž§K f 0 = = f0 ¡ kªÇ§þªL² 2π ω 3ƒéu1 $Ä S X¥§f = 6= f0 ƒéØ Doppler A 2π ?Ø s (1) (2) E ŒÆ f0 1+β e3 S X θ = 0§K f = = f0 > f0 γ(1 − β) 1−β ¡b£§=1 •* ö‚CžªÇu)b£ s 1−β e θ = π §K f = f0 < f0"1 l* öžªÇu)ù£ 1+β ÔnX “ Mï
15 Let there be light (3) E e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ŒÆ ÔnX ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 ù£ î• Doppler A “ Mï
16 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò E ŒÆ ÔnX î• Doppler A Ay⃘" “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò (4) E Û θ = 0 éAu1 ŒÆ ÔnX ‚C* ö§θ = π 7,éAu1 î• Doppler A Ay⃘" l* öíº “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò ‚C* (4) Û θ = 0 éAu1 (5) 3ØÓ.5X§Œ±* E ŒÆ ÔnX ö§θ = π 7,éAu1 î• Doppler A Ay⃘" l* öíº ØÓD• “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò ‚C* Ay⃘" (4) Û θ = 0 éAu1 (5) 3ØÓ.5X§Œ±* ØÓD•  β
0 0 0    kx = k cos θ = γ k cos θ − ω c 0 0 0 0 d kµ0 = aµν kν k sin θ = k sin θ, k = ω /c, k = ω/c    0 ω = γ(ω − βk cos θ) = γ(ω − ωβ cos θ) E ŒÆ ÔnX ö§θ = π 7,éAu1 î• Doppler A l* öíº ) “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò ‚C* î• Doppler A Ay⃘" (4) Û θ = 0 éAu1 (5) 3ØÓ.5X§Œ±* ØÓD•  β
0 0 0    kx = k cos θ = γ k cos θ − ω c 0 0 0 0 d kµ0 = aµν kν ) k sin θ = k sin θ, k = ω /c, k = ω/c    0 ω = γ(ω − βk cos θ) = γ(ω − ωβ cos θ) ω ω ω
−β + cos θ 0 0 cos θ = γ cos θ − β =⇒ cos θ = c c c 1 − β cos θ ω ω sin θ ω0 sin θ 0 = sin θ =⇒ sin θ 0 = 0 sin θ = c c ω γ(1 − β cos θ) E ŒÆ ÔnX ö§θ = π 7,éAu1 l* öíº “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò ‚C* î• Doppler A Ay⃘" (4) Û θ = 0 éAu1 (5) 3ØÓ.5X§Œ±* ØÓD•  β
0 0 0    kx = k cos θ = γ k cos θ − ω c 0 0 0 0 d kµ0 = aµν kν ) k sin θ = k sin θ, k = ω /c, k = ω/c    0 ω = γ(ω − βk cos θ) = γ(ω − ωβ cos θ) ω ω ω
−β + cos θ 0 0 cos θ = γ cos θ − β =⇒ cos θ = c c c 1 − β cos θ ω ω sin θ ω0 sin θ 0 = sin θ =⇒ sin θ 0 = 0 sin θ = c c ω γ(1 − β cos θ) =⇒ E ŒÆ ö§θ = π 7,éAu1 sin θ tan θ = γ(cos θ − β) ÔnX 0 11 l* öíº úª “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò ‚C* î• Doppler A Ay⃘" (4) Û θ = 0 éAu1 (5) 3ØÓ.5X§Œ±* ØÓD•  β
0 0 0    kx = k cos θ = γ k cos θ − ω c 0 0 0 0 d kµ0 = aµν kν ) k sin θ = k sin θ, k = ω /c, k = ω/c    0 ω = γ(ω − βk cos θ) = γ(ω − ωβ cos θ) ω ω ω
−β + cos θ 0 0 cos θ = γ cos θ − β =⇒ cos θ = c c c 1 − β cos θ ω ω sin θ ω0 sin θ 0 = sin θ =⇒ sin θ 0 = 0 sin θ = c c ω γ(1 − β cos θ) =⇒ E ŒÆ ö§θ = π 7,éAu1 sin θ tan θ = γ(cos θ − β) ÔnX 0 11 l* öíº úª “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò ‚C* î• Doppler A Ay⃘" (4) Û θ = 0 éAu1 (5) 3ØÓ.5X§Œ±* ØÓD•  β
0 0 0    kx = k cos θ = γ k cos θ − ω c 0 0 0 0 d kµ0 = aµν kν ) k sin θ = k sin θ, k = ω /c, k = ω/c    0 ω = γ(ω − βk cos θ) = γ(ω − ωβ cos θ) ω ω ω
−β + cos θ 0 0 cos θ = γ cos θ − β =⇒ cos θ = c c c 1 − β cos θ ω ω sin θ ω0 sin θ 0 = sin θ =⇒ sin θ 0 = 0 sin θ = c c ω γ(1 − β cos θ) =⇒ ö§θ = π 7,éAu1 sin θ tan θ = γ(cos θ − β) 0 11 l* öíº úª X S ¥,ð(u1§/¥ƒéu S „ݏ v 3X.5X* E ŒÆ ÔnX – α = π − θ “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò ‚C* î• Doppler A Ay⃘" (4) Û θ = 0 éAu1 (5) 3ØÓ.5X§Œ±* ØÓD•  β
0 0 0    kx = k cos θ = γ k cos θ − ω c 0 0 0 0 d kµ0 = aµν kν ) k sin θ = k sin θ, k = ω /c, k = ω/c    0 ω = γ(ω − βk cos θ) = γ(ω − ωβ cos θ) ω ω ω
−β + cos θ 0 0 cos θ = γ cos θ − β =⇒ cos θ = c c c 1 − β cos θ ω ω sin θ ω0 sin θ 0 = sin θ =⇒ sin θ 0 = 0 sin θ = c c ω γ(1 − β cos θ) =⇒ ö§θ = π 7,éAu1 sin θ tan θ = γ(cos θ − β) 0 11 l* öíº úª X S ¥,ð(u1§/¥ƒéu S „ݏ v 3X.5X* 3/¥.5X* E ŒÆ ÔnX – α = π − θ – α0 = π − θ 0 “ Mï
16 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light (3) e θ = π/2§K f = f0/γ µR†u1 $ЕŒ* ù£ î• Doppler A3²;Ôn¥Ø3§Ïd´ƒé؞mò ‚C* î• Doppler A Ay⃘" (4) Û θ = 0 éAu1 (5) 3ØÓ.5X§Œ±* ØÓD•  β
0 0 0    kx = k cos θ = γ k cos θ − ω c 0 0 0 0 d kµ0 = aµν kν ) k sin θ = k sin θ, k = ω /c, k = ω/c    0 ω = γ(ω − βk cos θ) = γ(ω − ωβ cos θ) ω ω ω
−β + cos θ 0 0 cos θ = γ cos θ − β =⇒ cos θ = c c c 1 − β cos θ ω ω sin θ ω0 sin θ 0 = sin θ =⇒ sin θ 0 = 0 sin θ = c c ω γ(1 − β cos θ) =⇒ ö§θ = π 7,éAu1 sin θ tan θ = γ(cos θ − β) 0 11 l* öíº úª X S ¥,ð(u1§/¥ƒéu S „ݏ v 3X.5X* 3/¥.5X* – α = π − θ – α0 = π − θ 0 sin α sin α tan α = ≈ , γ(cos α + β) cos α + β 0 E ŒÆ ÔnX /¥ú=§Œ* 5g Әð(1‚•Š±ÏCz" “ Mï
16 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Ainsi, toujours poussées vers de nouveaux rivages, Dans la nuit éternelle emportés sans retour, Ne pourrons-nous jamais sur l’ocean des ages§ Jeter l’ancre un seul jour? E ŒÆ ÔnX “ Mï
17 Let there be light ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Ainsi, toujours poussées vers de nouveaux rivages, Dans la nuit éternelle emportés sans retour, Ne pourrons-nous jamais sur l’ocean des ages§ Jeter l’ancre un seul jour? As we are pushed toward new shores, Swept along to the eternal night without return, Can we ever on the ocean of the ages Let the anchor down for one day? E ŒÆ ÔnX “ Mï
17 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ainsi, toujours poussées vers de nouveaux rivages, Dans la nuit éternelle emportés sans retour, Ne pourrons-nous jamais sur l’ocean des ages§ Jeter l’ancre un seul jour? As we are pushed toward new shores, o´ùí•))*W§ Swept along to the eternal night without return, Can we ever on the ocean of the ages Let the anchor down for one day? E ŒÆ ÔnX “ Mï
17 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ainsi, toujours poussées vers de nouveaux rivages, Dans la nuit éternelle emportés sans retour, Ne pourrons-nous jamais sur l’ocean des ages§ Jeter l’ancre un seul jour? As we are pushed toward new shores, o´ùí•))*W§ Swept along to the eternal night without return, ÐL[𖧘ØEˆ¶ Can we ever on the ocean of the ages Let the anchor down for one day? E ŒÆ ÔnX “ Mï
17 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ainsi, toujours poussées vers de nouveaux rivages, Dans la nuit éternelle emportés sans retour, Ne pourrons-nous jamais sur l’ocean des ages§ Jeter l’ancre un seul jour? As we are pushed toward new shores, o´ùí•))*W§ Swept along to the eternal night without return, ÐL[𖧘ØEˆ¶ Can we ever on the ocean of the ages 3•°¥§·‚UĊ§ Let the anchor down for one day? E ŒÆ ÔnX “ Mï
17 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ainsi, toujours poussées vers de nouveaux rivages, Dans la nuit éternelle emportés sans retour, Ne pourrons-nous jamais sur l’ocean des ages§ Jeter l’ancre un seul jour? As we are pushed toward new shores, o´ùí•))*W§ Swept along to the eternal night without return, ÐL[𖧘ØEˆ¶ Can we ever on the ocean of the ages 3•°¥§·‚UĊ§ Let the anchor down for one day? =ùҘUÊѺ E ŒÆ ÔnX “ Mï
17 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ainsi, toujours poussées vers de nouveaux rivages, Dans la nuit éternelle emportés sans retour, Ne pourrons-nous jamais sur l’ocean des ages§ Jeter l’ancre un seul jour? As we are pushed toward new shores, o´ùí•))*W§ Swept along to the eternal night without return, ÐL[𖧘ØEˆ¶ Can we ever on the ocean of the ages 3•°¥§·‚UĊ§ Let the anchor down for one day? =ùҘUÊѺ From “Le Lac” by A. De Lamartine (1790-1869)µ{I›Ê­V1˜ E ŒÆ ÔnX Lû “ ˜< Mï
17 ²;>ÄåÆØ 1ÔÙµdƒéØ § 8.6 Let there be light Ainsi, toujours poussées vers de nouveaux rivages, Dans la nuit éternelle emportés sans retour, Ne pourrons-nous jamais sur l’ocean des ages§ Jeter l’ancre un seul jour? As we are pushed toward new shores, o´ùí•))*W§ Swept along to the eternal night without return, ÐL[𖧘ØEˆ¶ Can we ever on the ocean of the ages 3•°¥§·‚UĊ§ Let the anchor down for one day? =ùҘUÊѺ From “Le Lac” by A. De Lamartine (1790-1869)µ{I›Ê­V1˜ Lû ˜< †ÆLdƒéØ!=òÚ\ŒoÔnXÓÆ
ž E ŒÆ ÔnX “ Mï
17