# Difficulty in understanding the three classes of events of light-cone

Recently I'm reading Chapter 2: Space and Time of A Brief History of Time. The paragraph that follows the light cone says:

Given an event P, one can divide the other events in the universe into three classes. Those events that can be reached from the event P by a particle or wave traveling at or below the speed of light are said to be in the future of P. ... Only events in the future of P can be affected by what happens at P because nothing can travel faster than light.

Let me explain my understanding and how that confuses me using the "events in the future of P".

First of all, I think the "event" here means the occurrence of something. For example: a plane lands in the airport; an apple falls off the tree; a volcano erupts.

Second, the "future" means the occurrence of another event, say, Q, is after the occurrence of event P. In other words, all the observers should agree that the order of occurrences of P and Q is "P first, Q next". (Note: Does this understanding imply an absolute order of event occurrences which may further imply the notion of absolute time? If so, I think I'm already wrong here because it's agreed that there is no absolute time.)

Third, when we say an event is "in the future", we mean the occurrence, not the observation, of this event is in the future. For example, when I say "See you 9 am tomorrow", I mean the occurrence of "me seeing you" happens in a future moment (9 am tomorrow). I am not saying that I have already seen you today but somebody else observes "me seeing you" at 9 am tomorrow.

Next, let me use the example in the book to explain my confusion:

For example, if the sun were to cease to shine at this very moment, it would not affect things on earth at the present time because they would be in the elsewhere of the event when the sun went out. We would know about it only after eight minutes, the time it takes light to reach us from the sun. Only then would events on earth lie in the future light cone of the event at which the sun went out.

Here, let's say:

• Time T0: Event P is the sun ceases to shine.
• Time T1 (one minute after T0): Event E1 is It starts to rain.
• Time T2 (two minutes after T0): Event E2 is A car crashes into a tree.
• Time T8 (eight minutes after T0): Event E8 is John Doe observes the sun goes out.
• Time T10 (ten minutes after T0): Event E10 is Jane Doe's laptop battery dies.

The last sentence of the example says:

Only then would events on earth lie in the future light cone of the event at which the sun went out.

Therefore, only E8 and E10 lie in the future light cone of P, which suggests that, according to my understanding, only E8 and E10 are in the future of P. I can see that because E8 and E10 do occur after P.

But what about E1 and E2? Don't they also occur after P? Shouldn't they be counted as "in the future" of P as well?

In addition, even if E8 and E10 lie in the future light cone of P, their occurrences can't be observed by the observers on the sun. Then what is the point of saying "...can be reached from the event P"? In my example, the light that P emits has reached the events E8 and E10, then what?

If I shift my understanding of "event" from "occurrence" to "observation", it seems to make more sense. For example, if I redefine my example above as follows:

• Time T0: Event P is the sun ceases to shine. At the same time, a car crashes into a tree on the Earth.
• Time T8 (eight minutes after T0): Event E8 is An observer on the sun observes the car crash.

This makes some sense because if an observer on the sun wants to observe an event, this event must happen within the boundary of P's light cone. However, the term event would have two meanings in the same context: it refers to the "occurrence" for P but the "observation" for E8. This seems to violate the need for consistency in logic.

Thanks for any help! It's a nice weekend but I'm struggling with this issue for quite a while. Maybe I should just close up the book and go to bed...

• "I think the "event" here means the occurrence of something" Correct, but in relativity "event" has a more precise meaning than it does in non-technical language. An event is localised in time and in space. Commented Apr 7, 2019 at 8:05

## 1 Answer

Events E1 and E2 are not in the future of event E0 because no signal from E0 could have reached them. (The fastest signal takes eight minutes, not one or two, to travel from Sun to Earth.) They are not in the forward lightcone of EO. They are in what Hawking calls the “elsewhere” of E0, neither in its forward lightcone or its backward lightcone.

You may observe them as occurring one and two minutes after E0, but, if observed by another inertial observer moving relative to you, they could be two and three minutes before E0. Or one of them could be before, and the other after, E0. Thus they cannot be described as being in either the future or the past of E0!

There is an absolute temporal order for events inside the lightcone, but not for events outside the light cone.

The absolute temporal order of events inside the lightcone does not imply absolute time. It happens because Lorentz transformations preserve the temporal ordering within the lightcone, even though they do not preserve the numerical temporal separation of the events.

• I think you need to clarify that "event" in relativity means a point in spacetime. Commented Apr 7, 2019 at 7:57
• I think what you mean is: when we talk about whether an event Q is in the future or past of event P, first of all, we must observe Q. Then we will have information to measure if Q is before or after P because the time is relative to the observer. In other words, the book is assuming an observer who is in the same inertial reference frame as the event P and who observes and measures the temporal order of those events. Am I correct? Commented Apr 7, 2019 at 14:09
• The phrase “an observer who is in the same inertial frame as the event” is meaningless. All observers and all events are in all inertial frames. Commented Apr 7, 2019 at 16:34
• The phrase “an observer at event P” indicates confusion. You don’t have to be “at” an event to observe it. Commented Apr 7, 2019 at 16:38
• All observers and all events are in the same shared spacetime, but the various inertial frames for various observers have different coordinate systems for assigning $(t,x,y,z)$ coordinates to each event. There is no absolute time. There is a “time axis” for each frame. This is why there can be time dilation. Commented Apr 7, 2019 at 16:41