Re: Time question

You have already received several incorrect and misleading replies.

Howard wrote:
I just got the book Spacetime Physics, and am working through the first chapter. Already, I have a question I need answered, before I can reasonably continue. Sorry if this is really basic, but I'm just starting out with this... 

OK. Good choice of textbook.


In the first chapter of the book, the author describes certain events occuring at specific times and locations in the observer's frame. Specifically, a rocket shoots by, just a millimeter away from the observer, into a room (which the observer is standing at the door of). The events described, from the viewpoint of that observer, are 1) a spark which leaps from the rocket to the observer as the rocket passes, and 2) another spark which leaps from the rocket to some object in the room beyond as it passes that object. (There are other spakrs/objects, but let's deal with just this one.)

Time and distance values are given for these events, expressed in the observer's frame. My question is this: for the second spark, which occurs at some distance from the observer, what does the "time" of the event mean?

Because the transmission of signals is plagued by time delays, the best way to observe an event is to have an assistant pre-positioned where it will happen, and for the co-located assistant to observe the event. For some situations it is easy to predict where to pre-position the assistant, but in general one can imagine a host of assistants nestled together quite densely so they cover the entire region of interest, and whichever one is closest to the second spark observes and records it.

This introduces a problem: how do you and these assustants communicate, and reconcile observations so you end up with a single, consistent record of all that happened? The way to do that is to issue each assistant a clock, and to ensure that before anything happens all the assistants' clocks are synchronized to yours. You also need to lay out rulers appropriately and have every assistant include his position on the rulers in his report to you.

The reason we go to all this trouble to lay out a coordinate system is that is ultimately makes things simpler. If you tried to formulate the laws of physics using a single observation point and the propagation of light signals from the world to your eyeball, you would find there are serious ambiguities and problems (e.g. how good is your depth perception? how do you observe events behind that wall?).

I'll bet that Taylor and Wheeler will discuss this quite soon in the book....


Is that the time when the observer "sees" the spark, or is it the actual time in his frame when the spark occured, which can be computed by knowing the distance and the speed of light and calculating backwards from the observation to its "actual" time in his frame?

The latter. That is equivalent to having a co-located assistant (with clock synchronized to yours) observe it, record its time on his clock, and report back to you. But your method requires knowing c over that specific light path, while the assistants don't need to know that (their reports come at leisure after the fact).


Tom Roberts	tjroberts@xxxxxxxxxx
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Relevant Pages

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