“视界”与退行速度大于光速的星系可否被观测到的问题

Horizon and the Question Whether Galaxies that Recede Faster Than Light are Observable

对于“我们能否观测到退行速度大于光速的星系”这个问题，目前大多数宇宙学家将回答：“不能，因为这些星系处在我们的视界之外”．这里的思想是，相对论宇宙学中的速度必须由相对论多普勒红移公式来定义．然而在宇宙学中，红移是“宇宙学”的而非“多普勒”的，并且有一个速度的独立定义可以应用．由于宇宙学原理，使我们有了一个与距离无关的普适时间ｔ，以及一个与时间有关的瞬时距离ｌ，于是速度可以自然地定义为ｄｌ／ｄｔ．利用这一定义以及红移的宇宙学解释，可以表明：（１）既然“视界”是指由于红移无限大而造成的观测限制，而宇宙学中红移和速度并没有直接关系，因此“视界”与上述问题并没有关系．（２）上述问题的答案必须依赖于特定的宇宙学模型．例如，对于稳恒态模型其答案是“不能”，而对于大爆炸模型（宇宙曲率ｋ＝０，－１，＋１三种情况）的答案都是“能”．对于具体的ｋ＝０情况，所有红移大于１．２５的天体在发射我们今日收到的辐射那一时刻的退行速度都大于光速．把宇宙学中和黑洞物理学中的时间、距离的特性加以对比，将有助于我们对这一问题的理解．本文对时间、距离、速度和红移的历史给予简要回顾，结果表明，多普勒公式不能应用于退行速度．基于这一理解而建立的“宇宙?

To the question, “Can we observe galaxies that recede faster than light￣?”, the great majority of cosmologists at present would answer, “No, such galaxies are outside our horizon”. Underlying this answer is the idea that velocity in relativistic cosmology has to be defined by the relativistic Doppler shift formula. But in cosmology, redshift is“cosmological” and not “Doppler”. And there  is available an independent definition of velocity. Thanks to the Cosmological Principle, there is a distance- independent,universal time t and a time dependent, instantaneous distance l, and velocity can naturally be defined as dl/dt.With this definition and the cosmological interpretation of redshift, it is shown: (1) That “horizon”, which owes its role as the limit of observation to its association with infinite redshift, is irrelevant to the question. (2) That the answer must depend on the particular cosmological model. Specifically. the answer is NO for the steady state model, and YES for all three types (k=0,-1,+1) of the big bang model;in the k=0 model, all sources with redshifts greater than 1.25 would have had their recession velocities at the time of emission greater than 1 light velocity. It has been found useful to contrast the character of time and distance in cosmology and black hole physics. A brief history of time, distance, velocity and redshift is given to show that the Doppler formula is inapplicable to recession velocities. Based on the present approach, a “World Atlas of the Universe” is constructed, which shows,  inter alia, that recession and photon velocities at distant points obey the old, pre-relativity law of addition, while the  local speed of light is kept constant.