时间、距离、速度、 红移时间、距离、速度、 红移 基本物理概念的演变简史基本物理概念的演变简史江 涛 gA |tz江 涛 gA |tzDunsink observatory, Dublin Institute for Advanced Studies, Dublin 15, IrelandV = 0 牛顿x = x，y = y, z = z, t = t， 狭义同上V 0 牛顿 x = x+ vt, y=y, z=z t = t狭义 x = x +t，y=y,z=z t =x + t ， ( = v / c，= (1-2)-1/2) 不变量 狭义(s)2= (t)2-(x)2+ (y)2+ (z)2牛顿t?不变量狭义(s)2= (t)2-(x)2+ (y)2+ (z) 2广义(d s)2= g(d) ( d)狭义 (d s)2= (d t)2(d x)2+ (d y)2+ (d z)2 = (d t )2(d r)2+ r2(d)2+ sin2(d)2 宇宙 (d s)2= (d t)2 R 2(t) (d r)2+ r2d)2+ sin2(d)2 11111111For N （牛顿）, time and space are separate, and t is the same for all observers in arbitrary relative motion For SR （狭义), each observer conceives time and space the same way as Newton did. But what is the same for all inertial observers now is the quantity (t)2-(x)2+ (y)2+ (z)2 For GR (广义), finite time intervals and space intervals are not defined.For K (宇宙), time and space are again separate; time is now “super-newtonian”, t itself is now the same for all equivalent observers; space is now expanding: we now have D = R(t) r, a formula unique to K.: Time-2.pptD = R(t) rt = t ds2 = dt2 - R2(t) d2宇宙ds2 = gdd广义s2 =t2- 2狭义x =x + vt t =t 牛顿距离时间间隔Jet源有限距离处无定义z = v cos 无限制红移速度（c=1）121cos11 vvz +=+)(1 tRrph=&)(11 emstrz=+rRrR&+=0emttsR(t)dtr) t (R 1(t)rH&=(t)rr(t)Hs s=1rRvp&2pv-1cosv1z1D+=+)z)(1z(1z1Dsjet+=+D.ds2 = dt2 - R2(t) dr2 + d2 + d2distance = scale facotr x coord. dist. D = R(t) x r General Relativity Cosmological Principle jet r const. Vjet = Vs +Vp rhorizon = 00) ( ttRdthorizon 1+z = 1/R(tem) cosmol.redshift rPLC(t)= 0) (/ tttRdt past light cone source r = const. Vs(t)=rs/rH(t) rH(t)=1/R(t) ( ) V = R r + R r = Vs + Vp inbound photon )(1 tRdtdr= outbound photon )(1 tRdtdr+= Time-3-can-we.pptT.Kiang, Chinese Astronomy and Astrophysics (1997) 21: 1-18. = 江涛：天体物理学报 （1997）17：225-238 在我们现在看到的源（类星体）中，有没有这样的 源，它们在发射此刻到达我们的光的时候，它们相 对（那时候的）我们的退行速度，vs(tem)， 是大于 光速的 ?既然 vs(tem) = rs/ rH(tem)，而分子分母都依赖于尺度因子 R(t)，所以答案依赖于所采取的宇宙学模型。对于标准大爆炸模型：R(t) = (t / t0)2/3, 答案是 有对于弯曲空间大爆炸模型，答案也是 有。对于稳态模型：R(t) = exp (Ht), 答案则是 没有。考虑了 0 的模型。 发现，不管是否等于0， 如果宇宙的膨胀以一个奇点方式开始，答案则是有。如 果是从零或某个非零值，从无穷远的过去，无限缓慢地开 始， 答案则是没有 （T. Kiang, Chinese Astronomy and Astrophysics, (2003) 27:247-251)Time-4-redshift.pptT. Kiang, Chinese and Astrophysics, (2001), 25: 141-146 A unified definition of redshift经典多普勒红移：zclassical= vcos 相对论多普勒红移： 1 + zDoppler= (1+ v cos )/(1- v2)1/2宇宙学红移：1+ zcosmological= 1 / R(tem)三个表达式的形式和意义都很不相同，但都可以从下列的定义 推导出来：1 + z = (tobs)obs/ (tem)em