# Events occuring acording to Relativity of simultaneity

I have seen a picture on wikipedia, which states that Events A,B and C can occur - depending on motion - in the order A,B,C; C,B,A or at the same time.

Let Event A be the birth Odilo, Event B is Odilo impregnating Maria and Event C is Maria giving birth to Odilos child Corentin.

Depending on Motion, there should be an observer for whom Corentin is born before his father Odilo. There exists also a perspective where these Events happen at the same time.

What is wrong with my assumption and how can you "trick" causality to reverse?

best regards :)

• Causal connected events (in jargon timelike) are always in the same order, regardless of the observer motion. Causally disconnected events (spacelike) can be in any order – FrodCube Jul 25 '18 at 16:11
• Imagine two trees, a maple and an oak. Is the maple tree to the left of the oak or to the right of the oak? The answer is neither: Trees don't have a left or a right. How it appears to you depends on where you stand relative to the trees. It's the same deal when you talk about the "order" of spacelike-separated events. They don't have an order. How it looks to you depends on the path of your worldline in spacetime relative to the events in question. – Solomon Slow Jul 25 '18 at 17:27
• Does this mean Events are casual connected iff they have the same order to any observer. – Markus Krumpl Jul 29 '18 at 9:45

I think FrodCube answered you question exactly. The word "event" is sort of complicated in relativity theory.

In relativity, events are separated by three kinds of intervals: space-like, time-like, and light-like (or null). Light travels along null intervals/geodesics.

When a space-like interval separates two events, an observer viewing those events can view them in any order (with respect to time) because the events are not causally connected, i.e. you can observe both events if you have speed $v>c$. Therefore, any massive particle does not observe space-like events. When a time-like interval separates two events, these occur always in the same order (with respect to time) because the events are causally connected. And due to this, now the two events can influence each other.

So, there is no trick needed - it's built into the causal structure of spacetime - since the case where the child is born before its father is not causally connected.

You might find this previous entry helpful.

According to SR, relativity of simultaneity is a concept that distant simultaneity is not absolute, but depends on the observer's reference frame.

Now it is impossible to say that two distant events accur at the same time if those events are separated in space.

However, if the events are casually connected, precedence order is reserved in all frames of reference.

Now to say that they are not casually connected, we must assume that the time between A, B, and the time between B, C (and the time between A,C) is less then the distance between them divided by c. Why do we need that?

We need to assume that because in this case according to SR, there is no way that information can reach from A to B inbetween the two happenings. If you send a photon from A at the time when A happens, this photon will only reach B after B already happened. A cannot influence B.

Events A,B,C will occur in different order depending on the relative motion of the observer.

The white line represents a plane of simultaneity. In the first picture, the events happen at the same time from the observer's frame. The white line moves upwards.

If the observer starts moving with o.3c, the events from his frame will not seem to be simultaneous, C will happen first.

If the same observer is moving in the opposite direction, with -0.5c, then A will seem to happen first.

This is only true, if the events are not casually connected.