Mapping Space with Clocks: Deduce Distances/Observers w/ Constant Light Speed

[I_ponder]

Suppose that we do not have any way to measure distance, but do have clocks. There are N observers, who can all see the distant events, say spaceships taking off and landing on far away planets. The question is: assuming the speed of light is constant, can we deduce the distance to the events and other observers based on differing delays? What is the minimum number of observers/observations required?

I know this is a general question, but I would be interested in a general solution, and any necessary preconditions.

 

[Dale]

If you have clocks and light signals then you can measure distance.

 

[I_ponder]

I think you missed the point.

If I have 1 observer, he cannot measure distance just using a clock. All he can do is time events. That's not measuring distance.

If the there are 2 observers, and they both see the same events, then they can time events, and one observer can tell the other one what they saw as the delay in between them. But using that information how do they know how far apart they are? Or how far the event was? Perhaps one is accelerating? Perhaps they are both are? Perhaps they are tracking a single object that is accelerating?

How many observations do we need? How many observers?

Can anyone produce an algorithm?

 

[A.T.]

... light signals ...

...what they saw as the delay...

Seems like you are saying the same thing as DaleSpam.

 

[Dale]

If I have 1 observer, he cannot measure distance just using a clock

If he can use light signals in conjunction with his clock then he certainly can use his clock to measure distance. This is called RADAR

 

[Dale]

If you have one unknown event and four known events which are null separated (meaning that a light signal can go between the known events and the unknown event) then you can write four equations in four unknowns and solve for the time and position of the unknown event. The four events have to be known, otherwise you have more unknowns than equations.

So you would need more than just the clocks, they would need to be synchronized and you would need to know their positions in some reference frame. This is how GPS works. One of the very important parts of the GPS system is the radars which are used to make sure that we accurately know the positions of the GPS satellites. It is all just clocks and light signals. You cannot do it without the light signals, but with them it is possible to determine the time and location of an unknown event using four "observer clocks".