Lorentz o'zgarishi

Fizikada Lorents o'zgarishlari fazoda koordinatali ramkadan birinchisiga nisbatan doimiy tezlikda harakatlanadigan boshqa ramkaga chiziqli o'zgarishlarning olti parametrli oilasidir. O'zgarishlar golland fizigi tomonidan aniqlangan va Hendrik Lorentz sharafiga nomlangan.

Haqiqiy doimiy bilan parametrlashtirilgan transformatsiyaning eng keng tarqalgan shakli $v,$ x - yo'nalishi bilan chegaralangan tezlikni ifodalovchi^[1]^[2] kabi ifodalanadi. ${\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c^{2}}}\right)\\x'&=\gamma \left(x-vt\right)\\y'&=y\\z'&=z\end{aligned}}$ bu yerda $(t, x, y, z)$ va $(t', x', y', z')$ koordinatalari kelib chiqishi $t$ = $t'$ =0 ga toʻgʻri keladi. Koordinatalar o'qi bo'ylab $v$ tezlik bilan harakatlanayotgani ko'rinadi va bu yerda $c$ - yorug'lik tezligi va ${\textstyle \gamma =\left({\sqrt {1-{\frac {v^{2}}{c^{2}}}}}\right)^{-1}}$ Lorents omilidir . Tezlik $v$ $c$ dan ancha kichik bo'lsa, Lorentz omili 1 dan deyarli farq qiladi, lekin $v$ $c$ ga yaqinlashganda, $\gamma$ cheksiz o'sadi. Transformatsiya mantiqiy bo'lishi uchun $v$ qiymati $c$ dan kichik bo'lishi kerak.

Tezlikni quyidagicha ifodalash ${\textstyle \beta ={\frac {v}{c}},}$ transformatsiyaning ekvivalent shakli^[3] va u quyidagicha: ${\begin{aligned}ct'&=\gamma \left(ct-\beta x\right)\\x'&=\gamma \left(x-\beta ct\right)\\y'&=y\\z'&=z.\end{aligned}}$ Malumot ramkalarini ikki guruhga bo'lish mumkin: inertial (doimiy tezlik bilan nisbiy harakat) va inertial bo'lmagan (tezlanuvchi, egri yo'llarda harakatlanuvchi, doimiy burchak tezligi bilan aylanish harakati va boshqalar.). "Lorentz o'zgarishlari" atamasi odatda maxsus nisbiylik kontekstida inertial tizimlar orasidagi o'zgarishlarni anglatadi.

Har bir mos yozuvlar tizimida kuzatuvchi uzunliklarni o'lchash uchun mahalliy koordinatalar tizimidan (odatda bu kontekstda Dekart koordinatalari) va vaqt oralig'ini o'lchash uchun soatdan foydalanishi mumkin. Hodisa - bu kosmosning bir nuqtasida vaqtning bir lahzasida yoki rasmiy ravishda fazoda sodir bo'ladigan narsa. O'zgartirishlar har bir kadrda kuzatuvchi tomonidan o'lchangan hodisaning makon va vaqt koordinatalarini bog'laydi.^{[nb 1]}

Ular Nyuton fizikasining mutlaq fazo va vaqtni o'z ichiga olgan Galiley o'zgarishining o'rnini bosadi (qarang: Galiley nisbiyligi). Galiley o'zgarishi yorug'lik tezligidan ancha past nisbiy tezliklarda yaxshi taxminiy hisoblanadi. Lorentz o'zgarishlari Galiley o'zgarishlarida uchramaydigan bir qator intuitiv xususiyatlarga ega. Misol uchun, ular turli tezliklarda harakat qilayotgan kuzatuvchilar turli masofalarni, o'tgan vaqtlarni va hatto hodisalarning turli tartiblarini o'lchashlari mumkinligini aks ettiradi, lekin har doim yorug'lik tezligi barcha inertial sanoq sistemalarida bir xil bo'ladi. Yorug'lik tezligining o'zgarmasligi maxsus nisbiylik postulatlaridan biridir .

]=[Tarixiy jihatdan, o'zgarishlar Lorentz va boshqalarning yorug'lik tezligi qanday qilib mos yozuvlar tizimidan mustaqil ekanligini tushuntirishga va elektromagnetizm qonunlarining simmetriyalarini tushunishga urinishlari natijasidir. Lorents o'zgarishi Albert Eynshteynning maxsus nisbiylik nazariyasiga mos keladi, lekin birinchi bo'lib olingan.

Elektromagnit maydonning o'zgarishi

Lorentz o'zgarishlari magnit maydoni $B$ va elektr maydoni $E$ bir xil kuchning oddiygina turli tomonlari ekanligini ko'rsatish uchun ishlatilishi mumkin - elektromagnit kuch, elektr zaryadlari va kuzatuvchilar o'rtasidagi nisbiy harakat natijasida.^[4] Elektromagnit maydonning relyativistik ta'sir ko'rsatishi oddiy fikrlash tajribasini o'tkazish orqali aniq bo'ladi.^[5]

Manbalar

Veb-saytlar

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Dennery, Philippe; Krzywicki, André. Mathematics for Physicists. Courier Corporation, 2012. ISBN 978-0-486-15712-2.
Cottingham, W. N.; Greenwood, D. A.. An Introduction to the Standard Model of Particle Physics, 2nd, Cambridge University Press, 2007. ISBN 978-1-139-46221-1.
Young, H. D.; Freedman, R. A.. University Physics – With Modern Physics, 12th, 2008. ISBN 978-0-321-50130-1.
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Forshaw, J. R.; Smith, A. G.. Dynamics and Relativity, Manchester Physics Series. John Wiley & Sons Ltd, 2009 — 124–126-bet. ISBN 978-0-470-01460-8.
Wheeler, J. A.; Taylor, E. F. Spacetime Physics. Freeman, 1971. ISBN 978-0-7167-0336-5.
Wheeler, J. A.; Thorne, K. S.; Misner, C. W.. Gravitation. Freeman, 1973. ISBN 978-0-7167-0344-0.
Carroll, S. M.. Spacetime and Geometry: An Introduction to General Relativity, illustrated, Addison Wesley, 2004 — 22-bet. ISBN 978-0-8053-8732-2.
Grant, I. S.; Phillips, W. R. „14“, . Electromagnetism, 2nd, Manchester Physics, John Wiley & Sons, 2008. ISBN 978-0-471-92712-9.
Griffiths, D. J.. Introduction to Electrodynamics, 3rd, Pearson Education, Dorling Kindersley, 2007. ISBN 978-81-7758-293-2.
Hall, Brian C.. Lie Groups, Lie Algebras, and Representations An Elementary Introduction. Springer, 2003. ISBN 978-0-387-40122-5.
Weinberg, S. (2008), Cosmology, Wiley, ISBN 978-0-19-852682-7
Weinberg, S. (2005), The quantum theory of fields (3 vol.), 1-jild, Cambridge University Press, ISBN 978-0-521-67053-1
Ohlsson, T. (2011), Relativistic Quantum Physics, Cambridge University Press, ISBN 978-0-521-76726-2
Goldstein, H.. Classical Mechanics, 2nd, Reading MA: Addison-Wesley, 1980. ISBN 978-0-201-02918-5.
Jackson, J. D. „Chapter 11“, . Classical Electrodynamics, 2nd, John Wiley & Sons, 1975 — 542–545-bet. ISBN 978-0-471-43132-9.
Landau, L. D.; Lifshitz, E. M.. The Classical Theory of Fields, 4th, Course of Theoretical Physics, Butterworth–Heinemann, 2002 — 9–12-bet. ISBN 0-7506-2768-9.
Feynman, R. P.; Leighton, R. B.; Sands, M. „15“, . The Feynman Lectures on Physics. Addison Wesley, 1977. ISBN 978-0-201-02117-2.
Feynman, R. P.; Leighton, R. B.; Sands, M. „13“, . The Feynman Lectures on Physics. Addison Wesley, 1977. ISBN 978-0-201-02117-2.
Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald. Gravitation. San Francisco: W. H. Freeman, 1973. ISBN 978-0-7167-0344-0.
Rindler, W. „Chapter 9“, . Relativity Special, General and Cosmological, 2nd, Dallas: Oxford University Press, 2006. ISBN 978-0-19-856732-5.
Ryder, L. H.. Quantum Field Theory, 2nd, Cambridge: Cambridge University Press, 1996. ISBN 978-0521478144.
Sard, R. D.. Relativistic Mechanics - Special Relativity and Classical Particle Dynamics. New York: W. A. Benjamin, 1970. ISBN 978-0805384918.
Sexl, R. U.; Urbantke, H. K.. Relativity, Groups Particles. Special Relativity and Relativistic Symmetry in Field and Particle Physics. Springer, 2001. ISBN 978-3211834435.
Gourgoulhon, Eric. Special Relativity in General Frames: From Particles to Astrophysics. Springer, 2013 — 213-bet. ISBN 978-3-642-37276-6.
Chaichian, Masud; Hagedorn, Rolf. Symmetry in quantum mechanics:From angular momentum to supersymmetry. IoP, 1997 — 239-bet. ISBN 978-0-7503-0408-5.
Landau, L.D.; Lifshitz, E.M.. The Classical Theory of Fields, 4th, Course of Theoretical Physics, Butterworth–Heinemann, 2002. ISBN 0-7506-2768-9.

↑ Rao, K. N. Srinivasa. The Rotation and Lorentz Groups and Their Representations for Physicists, illustrated, John Wiley & Sons, 1988 — 213-bet. ISBN 978-0-470-21044-4. Equation 6-3.24, page 210
↑ Forshaw & Smith 2009
↑ Cottingham & Greenwood 2007, s. 21
↑ Grant & Phillips 2008
↑ Griffiths 2007

↑ One can imagine that in each inertial frame there are observers positioned throughout space, each with a synchronized clock and at rest in the particular inertial frame. These observers then report to a central office, where all reports are collected. When one speaks of a particular observer, one refers to someone having, at least in principle, a copy of this report. See, e.g., Sard (1970).

[1] Rao, K. N. Srinivasa. The Rotation and Lorentz Groups and Their Representations for Physicists, illustrated, John Wiley & Sons, 1988 — 213-bet. ISBN 978-0-470-21044-4. Equation 6-3.24, page 210

[2] Forshaw & Smith 2009

[3] Cottingham & Greenwood 2007, s. 21

[5] Grant & Phillips 2008

[6] Griffiths 2007

[4] One can imagine that in each inertial frame there are observers positioned throughout space, each with a synchronized clock and at rest in the particular inertial frame. These observers then report to a central office, where all reports are collected. When one speaks of a particular observer, one refers to someone having, at least in principle, a copy of this report. See, e.g., Sard (1970).

[1]

[2]

[3]

[nb 1]

[4]

[5]