Believers in Einstein’s theory must accept a fundamental principle: the speed of light is the fastest speed in the universe. No object’s speed can exceed the speed of light (even for two beams of light emitted in opposite directions, their relative speed remains c, not 2c).
However, there is an undeniable fact: astronomers have indeed observed celestial bodies moving at speeds greater than the speed of light. How can this be? Was Einstein wrong? Is relativity incorrect? Or are there other secrets unknown to us?
But if one hopes to overturn relativity with this fact, it is quite unlikely, because followers of Einstein have explained this phenomenon using simple geometric theorems.
First, we must ask ourselves: can we actually observe speed? Clearly not. What we can measure are distance and time; we cannot observe speed directly. We only obtain speed indirectly using the formula v = s/t. Consequently, the problem lies with s and t. What exactly is the problem? Please refer to the diagram below:
Let P be the observer and O be the moving celestial body. The object moves in the direction OQ with velocity v. OP is the line-of-sight direction, and RQ is the transverse direction. Let OQ = r, then the actual travel time is t = r/v. However, the time interval we perceive for the celestial body to move from R to Q is r/v - \frac{r \cos\theta}{c}. Thus, the transverse velocity we observe is: v' = \frac{r \sin\theta}{r/v - \frac{r \cos\theta}{c}} = \frac{cv \cdot \sin\theta}{c - v \cos\theta} By calculating \frac{dv'}{d\theta} = 0, it is not difficult to find that the maximum value is reached when c \cdot \cos\theta = v. At this point: v' = \frac{v}{\sqrt{1 - \frac{v^2}{c^2}}}
As v \to c, then v' \to \infty. Therefore, it is possible for us to observe celestial bodies moving at arbitrarily high apparent speeds!
When reposting, please include the original article address: https://kexue.fm/archives/671
For more detailed reposting matters, please refer to: Scientific Space FAQ