Physics Primer

物理入门


The LIght Cone

光锥             

The light cone can help us understand howcausality depends on a reference frame. Special relativity affects causalitybecause it reverses the order in which events can happen. If in one referencesystem event A takes place before event B, in a different reference systemevent B could take place before event A. If we thought that A caused B, it isclear that in the second reference frame this cannot hold anymore because now Btakes place before A, and no effect can take place before its cause.

 光锥可以帮助我们理解因果关系是如何依赖于参照系的。狭义相对论影响因果关系,因为它颠倒了事件发生的顺序。如果在一个参考系统事件A发生在事件B之前,在一个不同的参考系统中,事件B可以发生在A事件之前,如果我们认为A导致了B,很明显在第二个参考帧中,这个不能再持有了,因为现在B发生在A之前,并且在它的原因之前不能发生任何影响。

The light cone illustrates that eventspositioned in the absolute past or absolute future will always preserve thesame order regardless of our reference system. However, one can always find areference frame for which the order of two events in the absolute away isreversed.

光锥表明,不管我们的参照系如何,处于绝对过去或绝对未来的事件总是保持相同的顺序。然而,人们总能找到一个参考帧,其中两个事件的先后顺序颠倒过来。

The Order of Events

时间顺序


For an observer at rest, event A takesplace before event B. We know that because for the observer at rest the line ofsimultaneity for A is below the line of simultaneity of B, or . Now, imaginethat the observer starts moving. Then, the lines of simultaneity will starttilting. For small velocities, the line of simultaneity for A will still beunder the line of simultaneity of B. For v=0.5 c, the two lines of simultaneitycoincide, meaning that the two events are simultaneous. If we go beyoned that velocity,the line of simultaneity of A will be above the line of simultaneity of B,meaning that , or thatevent A takes place after event B in this reference frame.

对于静止的观察者来说,事件A发生在事件B之前,我们知道,因为对于静止的观察者来说,A的同时线低于B,或。现在,假设观察者开始移动。然后,同步线将开始倾斜。对于小的速度,A的同时线仍然在B的同时线下,v0.5 C,两行同时重合,表示两个事件同时发生。如果我们要高于这个速度,同时一个线将同时B线以上,这意味着,或事件发生的事件在这个参考系后。


Causality

因果关系

The things we have covered above migth seemvery unsettling. If the order of events depends on the reference frame, thenwouldn't observers disagree about causation? Because in one frame A can be thecause of B, while in a different frame, B could be the cause of A.

我们已经涵盖了以上的事情可能非常不安。如果事件的顺序取决于参考帧,那么观测者不会对因果关系不同意吗?因为在一个帧A可以是B的原因,而在另一帧中,B可能是A的原因。

However, this cannot actually happen. Let'sset the origin of our reference system at A. Any event in the future that A cancause should be inside the space determined by the ±45° light-lines. Anything inside this cone can be reached by a signaltraveling with a speed v<c. Anything outside the cone is too far for event Ato reach it. Thus, event C could have been caused by event A, but not event B.

然而,这实际上是不可能发生的。让我们把我们的参考系原点在任何事件以后,会造成内部应该由±45°光线确定的空间。这个圆锥内的任何东西都可以通过速度为v的信号到达。锥外的任何东西都太远了,无法到达A。因此,事件C可能是由事件A引起的,而不是事件B