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
: EventP
isthe sun ceases to shine
. - Time
T1
(one minute afterT0
): EventE1
isIt starts to rain
. - Time
T2
(two minutes afterT0
): EventE2
isA car crashes into a tree
. - Time
T8
(eight minutes afterT0
): EventE8
isJohn Doe observes the sun goes out
. - Time
T10
(ten minutes afterT0
): EventE10
isJane 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
: EventP
isthe sun ceases to shine
. At the same time, a car crashes into a tree on the Earth. - Time
T8
(eight minutes afterT0
): EventE8
isAn 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...